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An aperture synthesis radiotelescope and a deep sky survey at 22 MHz Dewdney, Peter Edward Forbes 1978

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i AN APERTURE SYNTHESIS RADIOTELESCOPE AND A DEEP SKY SURVEY AT 22 MHz. by Peter E. Dewdney A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF J DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES Department of E l e c t r i c a l Engineering We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA August, 1978 (c) Peter E. Dewdney, 1978 In presenting th i s thes is in pa r t i a l fu l f i lment of the requirements for an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make it f ree ly ava i lab le for reference and study. I further agree that permission for extensive copying of th is thesis for scho lar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or pub l i ca t ion of th is thes is for f inanc ia l gain sha l l not be allowed without my writ ten permission. Department of E l e c t r i c a l Engineering The Univers i ty of B r i t i s h Columbia 2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5 Date Sept. 28, 1978 A b s t r a c t A l o w - f r e q u e n c y r a d i o a s t r o n o m y t e l e s c o p e h a s b e e n c o n s t r u c t e d a t t h e D o m i n i o n R a d i o A s t r o p h y s i c a l O b s e r v a t o r y f o r o p e r a t i o n a t 22.25 MHz. I t o p e r a t e s on t h e p r i n c i p l e o f a p e r t u r e s y n t h e s i s , and h a s b e e n u s e d t o map a r e g i o n o f s k y n o r t h o f d e c l i n a t i o n 70 d e g r e e s . The r e s o l u t i o n and s e n s i t i v i t y o f t h e t e l e s c o p e f o r d i s c r e t e s o u r c e s a r e 15 a r c m i n u t e s and 2 J a n s k y r e s p e c t i v e l y . T he d e s i g n o f t h e t e l e s c o p e and some o f t h e o b s e r v a t i o n s a r e d e s c r i b e d h e r e i n . The o b s e r v a t i o n s were t a k e n d u r i n g t h e s u n s p o t minimum, m o s t l y d u r i n g t h e w i n t e r o f 19 76. The t h e s i s i n c l u d e s a p r e l i m i -n a r y map w i t h h a l f t h e u l t i m a t e r e s o l u t i o n (30 a r c m i n . ) . F u r t h e r d a t a p r o c e s s i n g i s p l a n n e d . A b o u t 300 r a d i o s o u r c e s h a v e b e e n c a t a l o g u e d and l o w - f r e q u e n c y s p e c t r a d e f i n e d . Some t e c h n i q u e s f o r w i d e - f i e l d a p e r t u r e s y n t h e s i s a r e d e s c r i b e d . Key Words: A s t r o n o m y , r a d i o a s t r o n o m y , t e l e s c o p e , , l o w - f r e q u e n c y a s t r o n o m y , a p e r t u r e s y n t h e s i s , r a d i o t e l e s c o p e , r a d i o s o u r c e s . i i i Table of Contents T i t l e Page. i Abstract. i i Table of Contents. i i i L i s t of Figures and I l l u s t r a t i o n s . v Acknowledgement. x i Chapter One. Introduction and Summary of Previous Work 1.1 Introduction 1 1.2 Astrophysical J u s t i f i c a t i o n 2 1.3 Instrumental Consideration 7 1.4 Establishing Terminology for the Thesis 11 Chapter Two. Overall Design of the New Telescope 2.1 Telescope Configuration 16 2.2 Basic Performance Specifications 24 Chapter Three. Detailed Design of the Components of the Telescope 3.1 Design of Antennas 31 3.2 Site Selection for the West Outer Element 43 3.3 Construction of New Arrays 54 3.4 Array Feed System 60 3.5 Receivers 69 3.6 D i s t r i b u t i o n of Local O s c i l l a t o r and Clock Signals 72 3.7 Signal D i g i t i z i n g , Sampling and Delay 79 3.8 Electro n i c s i n the East Outer Element and the West Outer Element 88 3.9 Correlator Design 104 3.10 Developing the Prototype Interferometer and Testing Assembled Correlators 120 i v 3.11 Design of the Cal i b r a t i o n System 3.12 System Control and Data Logging 123 136 Chapter Four. Data Reduction and Computation of Results 4.1 Data Reduction: Pre-Map Stage 4.2 Applying C a l i b r a t i o n Signals to Interferometer Data 4.3 The S e n s i t i v i t y of Fringe Phase to Baseline Errors 4.4 Forming an Image from the Interferometer Data 4.4.1 Computation of Fan Beams 4.4.2 Computation of Maps 140 148 154 161 173 Chapter Five. The Observations Chapter Six. Conclusions. References. 180 210 214 Appendices. A l A2 A3 A4 A5 A6 A7 A8 Derivation of the C e l e s t i a l Orientation of the Telescope Properties of a One B i t by Analog Correlator Design, Construction, and Testing of the Receivers Measuring Positions on Aperture Synthesis Maps The E f f e c t s of R.F. Bandwidth on Resolution The Eff e c t on S e n s i t i v i t y of the Sampling D i s t r i b u t i o n and Apodizing i n the U-V Plane The Prototype System Contour Maps of the F i e l d of View 218 225 230 251 258 264 269 289 L i s t of Figures and I l l u s t r a t i o n s 2.1.1 Surveying several f i e l d s around the North Polar Cap. 2.1.2 Two conceivable configurations f o r the new telescope. 2i.l.3 A schematic diagram of the layout with the positions of correl a t o r units shown. 2.2.1 22 MHz map of the area around the North C e l e s t i a l Pole (Costain and Roger - unpublished data). 3.1.1 East array of eight dipoles. 3.1.2 Undetermined West array. 3.1.3 A flow diagram of the computer c a l c u l a t i o n of antenna responses. 3.1.4 An E plane diagram of the elemental arrays. 3.1.5 Array factor for two antennas. 3.1.6 Array geometry for an odd number of dipoles. 3.1.7 Array geometry for an even number of dipoles. 3.1.8 E-plane f i e l d pattern of the elemental arrays. 3.1.9 Best mean square approximation to above using 4 rows of dipoles. 3.1.10 Residual H-plane response. 3.1.11 Best mean square approximation using 7 rows of dipoles. 3.1.12 F i n a l E-plane power pattern. 3.1.13 F i n a l H-plane power pattern. 3.2.1 An a e r i a l photograph of the o r i g i n a l 22 MHz antenna and i t s surrounding t e r r a i n . 3.2.2 The basic geometry of an interferometer. 3.2.3 A cut through the t e r r a i n near the point where the new outer element was to be placed. 3.2.4 F i n a l layout of West Outer Element. ;Vi 3.3.1 An i l l u s t r a t i o n of the antenna switching scheme used to f i l l interleaved spacings. 3.3.2 Some views of the W.O.E. and the E.O.E. 3.3.3 The dipoles and feeds for the Outer Elements. 3.4.1 The antenna combining network used on the East arrays. 3.4.2 A photograph'of the network shown in Figure 3.4.1. 3.4.3 A setup f o r measuring antenna amplitudes and phases. 3.4.4 The dipoles and feeds for the East arrays. 3.4.5 Typical amplitude and phase measurements on the E.O.E. 3.4.6 Fringe amplitudes of CASS A. 3.5.1 A block diagram of the basic receiver and correlator system. 3.6.1 Local o s c i l l a t o r and clock d i s t r i b u t i o n systems. 3.6.2 Source c i r c u i t r y used to generate and combine l o c a l o s c i l l a t o r (27.25 MHz) and clock signals (1.175 MHz). 3.6.3 C i r c u i t r y used to separate the l o c a l o s c i l l a t o r and clock signals at the inputs to the Binary Branching Systems. 3.6.4 The binary branching systems f o r the L.O. and clock signals. 3.7.1 Sampling diagram for a baseband signal. 3.7.2 Sampling diagram for a bandpass signal. 3.7.3 A wide band spectrum of d i g i t i z e d receiver noise. 3.7.4 A narrow band spectrum of d i g i t i z e d receiver noise. 3.7.5 "Variable delay*' connections used i n the d i g i t a l delay l i n e . 3.7.6 Delay ranges covered by each of the connections of the delay l i n e . 3.8.1 A block diagram of equipment needed i n the E.O.E. 3.8 .2 A photograph o f the ^ /2 switch used i n the ou t e r elements 3.8.3 The photograph of the d i s t r i b u t i o n system f o r the f i r s t l o c a l o s c i l l a t o r . 3.8.4 A phase lock system f o r producing second l o c a l o s c i l l a t o r 3.8.5 A photograph of the second mixer stages and the q u a s i -baseband output a m p l i f i e r s . 3.8.6 The c a l i b r a t i o n s w i t c h i n g system. 3.8.7 A photograph o f the d i p l e x f i l t e r s f o r the W.O.E. cable c o n n e c t i o n . 3.8.8 A photograph o f the c a l i b r a t i o n system f o r the W.O.E. 3.8.9 A photograph of the switch c o n t r o l l e r f o r the V 2 switche and the antenna switches. 3.8.10 A t e m p e r a t u r e - c o n t r o l l e d phase s h i f t e r . 3.9.1 E a r l y c o r r e l a t o r d e s i g n . 3.9 .2 B a s i c s i g n a l m u l t i p l i e r c i r c u i t . 3.9.3 Output s i g n a l c u r r e n t versus input s i g n a l v o l t a g e f o r R = 0. e 3.9.4 E x c l u s i v e OR phase switch f o r the d i g i t a l s i d e o f the c o r r e l a t o r . 3.9.5 A d i f f e r e n t i a l i n t e g r a t o r and phase switch demodulator. 3.9.6 High impedance video a m p l i f i e r f o r the analog s i d e o f the c o r r e l a t o r s . 3.9.7 A t a b l e showing s i g n a l s to be c o r r e l a t e d . 3.9.8 An assembled c o r r e l a t o r u n i t . 3 . 1 0 . 1 A bench t e s t o f a c o r r e l a t o r u n i t . 3 . 11 .1 A blo c k diagram of the c a l i b r a t i o n system. 3 . 11 .2 A simple dual d i r e c t i o n a l c o u p l e r . 3.11.3 The "extended probe" method o f measuring phases. v i i i 3.11.4 The "chaining" method of measuring phases. 3.12.1 The system c o n t r o l l e r . 4.1.1 Plots of the c a l i b r a t i o n s for eight correlators. 4.1.2 Plots of v i s i b i l i t i e s f or four spacings. 4.2.1 A schematic diagram of a co r r e l a t i o n interferometer showing the aspects pertinent to c a l i b r a t i o n . 4.3.1 Phase error as a resu l t of an error i n d plotted as a function of spacing. 4.3.2 Phase error as a resu l t of an error i n X plotted as a function of spacing. 4.3.3 Phase error r e s u l t i n g from an error i n h plotted as a function of spacing. 4.3.4 Phase error r e s u l t i n g from an error i n D plotted as a function of polar distance. 4.4.1 A c i r c u l a r f i e l d showing the sinusoidal corrugations (fringes) which rotate with respect to the m axes. 4.4.2 Geometry of an interferometer with respect to the C e l e s t i a l Sphere. 4.4.3 The u-v plane showing a projection of the baseline, Dcos0. 4.4.4 Fringe patterns as cut by the plane containing the baseline and the North C e l e s t i a l Pole. 4.4.5 Geometry of a fan beam reconstruction process. 4.4.6 "Grading" function used to multiply data on " r a d i a l s " i n the u-v plane before transforming to fan beams. 4.4.7 The geometry of summing fan beams to output gr i d points i n the -£-m plane. 5.1.2 A grid showing how the map was divided so that fluxes could be read. I X 5.1.3 An overlay of the positions of sources measured by Branson at 81.5 MHz on one of the maps made with present instrument. 5.1.4 The plot of fl u x densities of the c a l i b r a t i o n sources as measured with the o r i g i n a l 22 MHz T system i n Jansky versus those measured with the present system i n arbit r a r y units. 5.1.5 The polar diagram of the elemental antennas as estimated from theory. 5.1.6 A plot of the flux densities of two surveys near 80 MHz used to determine the flux scale of the Branson polar cap survey. 5.1.7 Well determined spectra of strong sources using the 4C, branson, WKB, and 22 MHz fluxes from the present survey. 5.1.8 A histogram of spectral i n d i c i e s as determined from Table 5.1.1. A l . l D e f i n i t i o n s of angles NX and ZZ' i n the l o c a l a l t i t u d e -azimuth coordinate system. A1.2 The C e l e s t i a l Sphere. A2.1 A 1 b i t by analog correlator. A3.1 Pole-zero position f o r a maximally f l a t f i l t e r . A3.2 Model of a doubly tuned c i r c u i t . A3.3 The input c i r c u i t of a cascode amplifier. A3.4 An impedance transforming c i r c u i t to go between the secondary tuned c i r c u i t of one stage to the input of the following stage. A3.5 Receiver band shapes. A3.6 Geometry of pole positions near the resonance of the doubly tuned c i r c u i t stage. A3.7 C o i l form cross-section. X A3.8 The input c i r c u i t to the receivers. A3.9 Aeross-the-band phase measurements of f i v e receivers. A4.1 C e l e s t i a l Sphere. A6.1 The signal-to-noise reduction factors for various apodizing functions i n the u-v plane. A7.1 A laboratory system for developing the prototype and for testing the correlator units. A7.2 The autocorrelation function of the input noise measured by adjusting the length of the d i g i t a l delay l i n e . A7.3 A set of a r t i f i c i a l "fringes" produced i n quadrature by two c o r r e l a t o r outputs. A7.4 Correlator outputs for a 10 db range of input power. A7.5 Testing the "back end" of the c o r r e l a t o r system. A7.6 System signal-to-noise r a t i o measurement. A7.7 Large signal test of correlator. A7.8 A spectrum of the receiver output. A7.9 A spectrum of the output of one of the analog input amplifiers. A7.10 A wide frequency range spectrum of one of the analog input amplifiers. A 7 . l l A histogram of correlator output noise i n a 9 hour test on uncorrelated inputs. Appendix 8: a) Repeat of Figure 5.1.2 b) The Maps used to produce the source l i s t . Acknowledgement s x i The work described i n t h i s thesis was performed at the Dominion Radio Astrophysical Observatory i n Penticton, B r i t i s h Columbia. My appreciation i s expressed here f o r the continuous support given me by i t s Director, Dr. John Gait; also for his personal encouragement. Gratitude i s due also to my supervisor, Professor F r i t z Bowers, for encouraging me to carry out the project, and for enduring me for so long. I n i t i a l encouragement from Drs. Carman Costain and Rob Roger and t h e i r whole-hearted support throughout i s also appreciated, e s p e c i a l l y i n providing a share of the Observatory's only computer for the c o l l e c t i o n of data. Thanks i s due to Dr. Costain for help in programming the computer and for amalgama-ting my observing programs with those for the 1420 MHz telescope. Drs. Roger and Costain have also made available unpublished data from the observations taken with the 22 MHz Tee instrument. Advice and encouragement from Dr. Tom Landecker was of great benefit to me and to the project. Thanks i s due for his time taken to help with such tasks as measuring phases outdoors i n b i t t e r l y cold weather. Acknowledgement i s also owing to other members of the Observatory s t a f f for services rendered and f o r unstinting help when required: Messrs. David Lacey, Walter Gully, Roy Hamilton, Jack Dawson, Rod Stuart, Bud Orge, and Mrs. Dorothy Stewart. I am also grateful to Mr. Ray Stewart for keeping the arrays clear of snow, for helping unstick vehicles, and for help i n constructing a bridge. I am also indebted to Mrs. E. Rohner for typing the thesis so quickly and accurately. I also acknowledge the l i v i n g allowances and f i n a n c i a l assistance to the project given to me by the University of B r i t i s h Columbia (NRC Grant No. 3295) and by the National Research Council. 1 Chapter One  O u t l i n e of the 22 MHz P o l a r Cap Survey .1.1 I n t r o d u c t i o n The astronomer's quest i s always f o r a more accurate measure-ment o f the r a d i a t i o n emanating from a wide v a r i e t y o f sources o u t s i d e the e a r t h ' s sphere. T h i s quest attempts to f u l f i l l the need f o r new and more p r e c i s e experimental data on which t h e o r i e s of astronomy, cosmology, and a s t r o p h y s i c s stand o r f a l l . P a r t o f the i n v e s t i g a t o r ' s job i s to b u i l d t e l e s c o p e s u s i n g r a d i a t i o n measurement techniques both i n v e n t e d by themselves and adapted from o t h e r f i e l d s . In i t s broadest sense, the word t e l e s -cope d e s c r i b e s instruments designed to measure r a d i a t i o n from a f a r . In t h i s sense these instruments range from the machines used to attempt to d e t e c t g r a v i t a t i o n a l waves through the v a r i e t y of r a d i o , i n f r a r e d , o p t i c a l , x-ray, and cosmic ray d e t e c t o r s . T h i s concept a p p l i e s s p e c i f i c a l l y to low frequency r a d i o astronomy, and i t was i n t h i s v e i n t h a t the p r o j e c t at hand, a 22 MHz deep sky survey, was conceived. A low-frequency r a d i o astronomy p r o j e c t has been undertaken at the Dominion Radio A s t r o p h y s i c a l Observatory u s i n g aperture s y n t h e s i s techniques to map a 40 degree f i e l d o f view c e n t r e d on the North C e l e s t i a l Pole with h i g h r e s o l u t i o n and s e n s i t i v i t y . The expected r e s o l u t i o n of 15 minutes of arc i s the h i g h e s t so f a r i n t h i s frequency range. T h i s instrument i s s e n s i t i v e to f l u x d e n s i t y as low as 2. Jansky ( l Jy a,,-10~ watts m Hz~ ). The t e l e s c o p e u t i l i z e s the d i p o l e antennas o r i g i n a l l y p a r t o f the 2 East-West arm of the 22 MHz, T-shaped array at the Dominion Radio Astrophysical Observatory (1) for most of i t s c o l l e c t i n g area. Two smaller dipole arrays have been constructed to double the line a r extent of the telescope. So f a r , reduction of the obser-vations i s not complete. Lower resolution maps (30 arc minutes). have been produced, however, and the low-frequency spectra of about 300 radio sources have been measured. More res u l t s are expected from continuing analysis of the data. 1.2 Astrophysical J u s t i f i c a t i o n Cosmic radio radiation can be divided empirically into a smooth, resolved component and "point sources" - bright regions of angular extent much smaller than the resolving power of the telescope. This d e f i n i t i o n i s of p r a c t i c a l significance even though i t depends upon the instrument used to make measurements. Measurements of point sources (and also sources which have been p a r t i a l l y resolved) are commonly expressed as the t o t a l observed flux density, S ( f ) . The smooth component of radiation i s expressed i n terms of brightness, B ( f ) , or i n terms of equivalent black-body temperature, T ( f ) . The unit of fl u x density — 26 — 2 used i n radio astronomy i s the Jansky, equal to 10" watts-m~ --1 -1 Hz . The unit of brightness i s Jy-steradian . The unit of temperature i s the Kelvin. D e f i n i t i o n of fl u x density, brightness, and. brightness temperature are fundamental to a l l radio astronomy, and can be found i n the l i t e r a t u r e (25). The spectra of radio sources are perhaps t h e i r most important 3 o b s e r v a b l e f e a t u r e s . So f a r no s p e c t r a l l i n e s have been d i s c o v e -r e d a t low f r e q u e n c i e s . T h i s means t h a t low f r e q u e n c y r a d i o astronomy i s based on the s t u d y o f continuum r a d i a t i o n . That i s , t h e spectrum o f t h e r a d i a t i o n does not show sharp d i s c o n t i n u i t i e s . The v a r i a t i o n o f i n t e n s i t y i n b o t h th e smooth and d i s c r e t e compo-n e n t s o f t h e continuum has e m p i r i c a l l y been found t o be an expo-n e n t i a l f u n c t i o n o f f r e q u e n c y . A c c o r d i n g l y , t h i s f r e q u e n c y dependence can be w r i t t e n as T ( f ) B k f " p ( f ) o r , f o r f l u x d e n s i t i e s S ( f ) * )cf-0fif) where 6 ( f ) and or(f) are c a l l e d t h e t e m p e r a t u r e s p e c t r a l i n d e x and t h e f l u x d e n s i t y s p e c t r a l i n d e x r e s p e c t i v e l y . S i n c e t h e i n t e n s i t y u s u a l l y v a r i e s i n v e r s e l y w i t h f r e q u e n c y , ty and 8 are p o s i t i v e . I f ry and B are not f u n c t i o n s o f f o v e r a c e r t a i n f r e q u e n c y r a n g e , t h e n the term "power-law spectrum" i s used. Sources o f cosmic r a d i a t i o n can g e n e r a l l y be d i v i d e d i n t o two c l a s s e s : a) G a l a c t i c S o u r c e s : These s o u r c e s u s u a l l y l i e c l o s e t o t h e G a l a c t i c p l a n e . They c o n s i s t o f a smooth component o f r a d i a t i o n as w e l l as many d i s c r e -t e s o u r c e s . A l t h o u g h th e t e l e s c o p e under c o n s i d e r a t i o n i s s e n s i t i -ve t o b r oad s t r u c t u r e , t h e N o r t h C e l e s t i a l P o l a r Region i s not i n t h e G a l a c t i c P l a n e , and emphasis has not been g i v e n t o t h i s compo-nent i n t h i s t h e s i s . The d i s c r e t e s o u r c e s c o n s i s t f o r t h e most p a r t o f H I I r e g i o n s and supernova remnants. The HIT r e g i o n s a r e 4 clouds of ionized hydrogen and produce "thermal" radio emission. Supernova remnants are "non-thermal" sources associated with an expanding cloud of matter ejected by supernova explosions. The synchrotron mechanism (see below) i s responsible for the radio emission from these sources. There are several other types of Galactic sources but they are weak at low frequencies. Also, time-varying sources of radiation such as pulsars and f l a r e stars are not good subjects for investigation with aperture synthesis techniques. b) Extra-Galactic Sources: A l l galaxies seem to be emitters of radio waves i n some degree, but some emit staggering amounts of radiation. Extra-Galactic radio sources are sometimes c l a s s i f i e d on the basis of source strength. The "normal" galaxies, such as our own, are f a i r l y weak radiators at low frequencies - hence they are d i f f i c u l t to detect at large distances. The strong radio sources are the most enigmatic, however, and much study has been devoted to understand-ing t h e i r nature. Because these sources are so powerful, they can be studied at great distances. Some of them have o p t i c a l counterparts which show them to be related to such objects as giant e l l i p t i c a l galaxies, N-type galaxies, and q u a s i - s t e l l a r objects. These l a t t e r objects are i n t e r e s t i n g because of t h e i r small angular si z e , sometimes less than .01 arc second. It i s well known that the "non-thermal" radio emission from most of these sources i s caused by the synchrotron mechanism i n 12 which r e l a t i v i s t i c electrons with energies,of about 10 eV i n t e r -act with magnetic f i e l d s . The spectrum of the radio radiation i s 5 dependent upon the energy spectrum of the r e l a t i v i s t i c e l e c t r o n s . I f the energy spectrum o f the e l e c t r o n s f o l l o w s a power law, N(E)dEcrE~ vdE where N(E) i s the number o f e l e c t r o n s i n an energy i n t e r v a l dE. The r a d i o r a d i a t i o n w i l l then have a s t r a i g h t spectrum i n which 01, the s p e c t r a l index, i s given by Q- = ( y - D / 2 Since such a spectrum i n c r e a s e s without bound at low f r e -quencies, a " t u r n - o v e r " o f the spectrum i s r e q u i r e d at some low frequency. The nature o f the " t u r n - o v e r " i s a s u b j e c t f o r study with low-frequency r a d i o t e l e s c o p e s . A summary o f the r e s u l t s o f t h e o r e t i c a l i n v e s t i g a t i o n s o f s p e c t r a l shapes at low f r e q u e n c i e s has been given by B r i d l e (24). The low frequency s p e c t r a o f the b r i g h t r a d i o sources have been s t u d i e d and c l a s s i f i e d by Roger, B r i d l e , and C o s t a i n (26). Some of the p h y s i c a l mechanisms which cause d e v i a t i o n o f source s p e c t r a from power law w i l l be given here. a) A low-energy c u t - o f f i n the e l e c t r o n spectrum o r m u l t i p l e p o p u l a t i o n s o f e l e c t r o n s . The source o f r e l a t i v i s t i c e l e c t r o n s may o n l y produce them above a c e r t a i n energy l i m i t . The r e s u l t i n g r a d i o spectrum would e x h i b i t a t u r n - o v e r at some frequency below which i t would have a s p e c t r a l index o f about - 1/3. There may a l s o be m u l t i p l e sources o f e l e c t r o n s with d i f f e r e n t energy s p e c t r a . Since they may be s p a t i a l l y separated but s t i l l w i t h i n the beam of a low-frequency 6 telescope, the radio spectrum may be complex. b) Thermal absorption by ionized gas. Ionized gas either within the source or between the earth and the source can lead to low-frequency absorption of the radio radiation. These two cases can be d i s t i n -guished by the sharpness of the cut-off. The cut-off i s sharper when the cloud i s between the source and the telescope. This l a t t e r case i s more l i k e l y i f the Extra-Galactic source i s near the Gal a c t i c plane. c) Synchrotron Self-absorption: This mechanism i s important i n sources with high r e l a t i -v i s t i c p a r t i c l e density and small angular diameter. The source i t s e l f becomes o p t i c a l l y thick. This re s u l t s i n a radiation spectrum which cuts o f f very sharply, producing a spectral index of about - 2.5 below the cut-off frequency. There are other, less important, e f f e c t s which w i l l not be discussed here. The study of the evolution of bright radio sources i s an important one for astronomy and cosmology. An aspect of t h i s study connected with low frequency radioastronomy i s the discovery of steep spectrum sources. The source of r e l a t i v i s t i c electrons which has been i n j e c t i n g p a r t i c l e s into a p a r t i c u l a r source may at some point have turned o f f . The rad i a t i v e loss due to the synch-rotron process i s proportional to the square of the energy of the electrons. In. other- words, the higher energy electrons lose 7 energy f a s t e r than the lower energy ones. T h i s causes the energy spectrum o f e l e c t r o n s to s e l f - s t e e p e n . The degree o f steepening may gi v e a c l u e to the age o f the source. In any case t h e r e i s evidence from p r e v i o u s o b s e r v a t i o n s at 22 MHz and 10 MHz t h a t there i s a d i s t i n c t c l a s s o f extended o b j e c t s with steep s p e c t r a . I t has been suggested t h a t these are a s s o c i a t e d with X-ray sources and c l u s t e r s o f g a l a x i e s ( 2 ) . I t i s p o s s i b l e that such sources w i l l be r e s o l v e d with the new s y n t h e s i s t e l e s c o p e . Using two p r e v i o u s surveys o f t h i s a rea, the R y l e - N e v i l l e survey (3) at 178 MHz and the Branson survey (4) at 81.5 MHz, i t w i l l be p o s s i b l e t o analyze the low-frequency s p e c t r a o f many r a d i o sources f o r the f i r s t time. A t o t a l o f more than 300 new f l u x d e n s i t y measurements have so f a r appeared from t h i s survey. Some of them are l i k e l y to have o p t i c a l c o u n t e r p a r t s . L a s t l y , although the c o s m o l o g i c a l i n t e r p r e t a t i o n o f number-f l u x d e n s i t y r e l a t i o n s has proved more d i f f i c u l t than p r e v i o u s l y thought ( 5 ) , t h i s survey w i l l extend the frequency range over which these r e l a t i o n s have measured. P a r t o f the survey should be complete down to a f l u x d e n s i t y o f a few Jansky. 1.3 Instrumental C o n s i d e r a t i o n s Although the e a r l i e s t measurements i n r a d i o astronomy were made a t f r e q u e n c i e s below 40 MHz, the r a p i d development o f new r e c e i v e r s encouraged o b s e r v e r s to take advantage o f the g r e a t e r r e s o l v i n g power a c h i e v a b l e with antennas o f any given s i z e o p e r a t i n g at s h o r t e r wavelengths. Other d i f f i c u l t i e s a l s o a f f l i c t low frequency o b s e r v a t i o n s . The presence o f the e a r t h ' s ionosphere can cause not o n l y severe d i s t o r t i o n o f the incoming cosmic r a d i o waves, but can a l s o d e f l e c t i n t e r f e r i n g t e r r e s t r i a l s i g n a l s i n t o the antenna. These l a t t e r d i f f i c u l t i e s l i m i t the amount o f time a v a i l a b l e f o r u n i n t e r r u p t e d o b s e r v i n g . These l i m i t a t i o n s on low frequency radioastronomy have been summarized by Roger (32). R e c e i v i n g equipment i s e a s i e r to b u i l d at low f r e q u e n c i e s and antenna t o l e r a n c e s are not so s t r i n g e n t . N e v e r t h e l e s s , f o r a given r e s o l u t i o n low frequency t e l e s c o p e s are d i f f i c u l t and expen-s i v e to b u i l d , and comparatively few have c o n s t r u c t e d at frequen-c i e s below 100 MHz. Many o f the e a r l y works were s t u d i e s o f Galac t i c r a d i o emission r e q u i r i n g r e l a t i v e l y low r e s o l u t i o n . The angular r e s o l u t i o n s o f r a d i o t e l e s c o p e s which have been used or are i n use are summarized i n F i g u r e 1.3.1. (32). Part o f the nature o f t h i s experiment i s to e s t a b l i s h the u s e f u l n e s s o f ape r t u r e s y n t h e s i s techniques to low frequency r a d i o astronomy. Aperture s y n t h e s i s techniques allow the d e s i g n e r to b u i l d t e l e s c o p e s with high r e s o l u t i o n but small c o l l e c t i n g areas. Low frequency t e l e s c o p e s are u s u a l l y r e s o l u t i o n l i m i t e d . A l s o , the c o s t o f a low-frequency t e l e s c o p e i s p r o p o r t i o n a l to i t s c o l l e c t i n g area. The a p p l i c a t i o n of ape r t u r e s y n t h e s i s techniques to low frequency instruments allows a freedom of de s i g n not enjoyed by the d e s i g n e r o f f i l l e d a p e r t u r e systems. S e v e r a l f e a t u r e s o f t h i s p a r t i c u l a r d e s i g n are i n c l u d e d to overcome some problems unique t o low frequency aperture s y n t h e s i s . One important d i f f i c u l t y i s the i m p o s i t i o n o f i o n o s p h e r i c d i s t o r -Frequency (MHz) Figure 1 . 3 . 1 : Angular resolution versus frequency of operation of low frequency telescopes. Broad-band telescopes are denoted by l i n e s . The lower resolution telescopes have been used c h i e f l y f o r Galactic astronomy. 10 t i o n on the r e c e i v e d s i g n a l s , p a r t i c u l a r l y i o n o s p h e r i c r e f r a c t i o n and s c i n t i l l a t i o n . Because of these problems, i t i s necessary to be able to measure a l l the s p a t i a l components i n 12 hours. T h i s i s done by c o n s t r u c t i n g a l i n e a r a r r a y o f i n t e r f e r o m e t e r s a l l o p e r a t i n g s i m u l t a n e o u s l y . These i n t e r f e r o m e t e r s f i l l i n a l l the r e q u i r e d spacings, and are swept through a l l the r e q u i r e d p o s i t i o n angles as the e a r t h r o t a t e s . T h i s technique allows the observer to s e l e c t a n i g h t when there i s l i t t l e i o n o s p h e r i c s c i n t i l l a t i o n . A l s o , n i g h t - t o - n i g h t v a r i a t i o n s i n r e f r a c t i o n need not be c o n s i -dered. Another problem i s the enormous range o f source s t r e n g t h s i n the sky at these f r e q u e n c i e s . In t h i s p a r t i c u l a r case C a s s i o p e i a A tends to dominate the f i e l d of view with a f l u x d e n s i t y o f about 50,000 Jy (as compared with about 2 Jy, the weakest source being measured). S l i g h t v a r i a t i o n s owing to i o n o s p h e r i c e f f e c t s i n the apparent p o s i t i o n o r s t r e n g t h o f t h i s source cause a r t e f a c t s on the map. T h e r e f o r e , the antennas used i n the survey have been s p e c i a l l y designed to m i t i g a t e t h i s e f f e c t by suppressing Cass A. The p h y s i c a l s i z e of t h i s instrument (approximately 2.6 km long) causes another problem - a g e o m e t r i c a l one. There i s not enough f l a t ground i n the v a l l e y at D.R.A.O. to b u i l d the system i n the o p t i m a l p o s i t i o n . T h i s causes a d i s t o r t i o n of the f i e l d o f view which cannot be r e c t i f i e d by a simple t r a n s f o r m a t i o n o f c o o r d i n a t e s . The r e s u l t i s t h a t the data cannot be F o u r i e r t r a n s -formed i n t o a map i n the u s u a l way. A method has been developed which overcomes t h i s problem. I t i s d e s c r i b e d i n chapter 4.4. 11 1.4 E s t a b l i s h i n g Terminology f o r the T h e s i s A b r i e f o u t l i n e of the terminology used i n connec t i o n with aperture s y n t h e s i s techniques w i l l be given here. Aperture s y n t h e s i s i s b a s i c a l l y e q u i v a l e n t to measuring and combining par-t i a l coherence f u n c t i o n s . The gen e r a l theory o f p a r t i a l l y coherent l i g h t has long been known, as the Van C i t t e r t - Z e r n i k e theorem (23), but was f i r s t a p p l i e d to r a d i o astronomy by Ryle (18). There are many d i f f e r e n t k i n d s o f aperture s y n t h e s i s t e l e s c o p e s . A more thorough d i s c u s s i o n o f the way i n which these p a r t i c u l a r i n t e r f e r o -meter measurements are combined to produce maps of the sky occurs i n chapter 4.4. A d i s c u s s i o n o f elementary aperture s y n t h e s i s can a l s o be found i n chapter 7 o f Radio T e l e s c o p e s " (19). F i g u r e 1.4.1 i l l u s t r a t e s i n one dimension the b a s i c F o u r i e r t r a n s f o r m r e l a t i o n s h i p between the s p a t i a l frequency domain ( i n 2 dimensions c a l l e d the u-v plane) and the angular spectrum domain (Z-m plane or b r i g h t n e s s d i s t r i b u t i o n ) . In two dimensions the i n t e r f e r e n c e p a t t e r n on the sky i s a set o f s i n u s o i d a l c o r r u g a t i o n s c a l l e d " f r i n g e s " . As the i n t e r f e -rometer i s f i x e d to a r o t a t i n g e a r t h , the f r i n g e s r o t a t e with r e s p e c t to the sky. The angle between the f r i n g e s and l i n e s o f constant r i g h t ascension i s c a l l e d the " p o s i t i o n angle". The incr e m e n t a l s e p a r a t i o n between the antennas o f the i n t e r f e r o m e t e r (shown as d i n F i g u r e 1.4.1) i s c a l l e d a " s p a c i n g " . T h i s c o r r e s -ponds to the sampling i n t e r v a l i n the u-v plane. A given spacing and p o s i t i o n angle d e f i n e a p o i n t i n the u-v plane i n the u s u a l r a d i a l c o o r d i n a t e sense. The u-v plane i s s a i d to be " f i l l e d " i f a l l p o i n t s out a 12 S p a t i a l Frequency Domain S p a t i a l Spectrum of Sky (Hermitian) S(u) 4 4 Aperture D i s t r i b u t i o n (Complex i n general, u s u a l l y r e a l and even Auto-correlation of Elemental u Aperture D i s t r i b u t i o n (Hermitian i n general, u s u a l l y r e a l and even) -Hd 4 4 Sampling Function ( r e a l ) u L(u) • w- 4 0 S p a t i a l Frequency L i m i t Function - Grading shown dotted ( r e a l ) Equivalent Synthesized Aperture D i s t r i b u t i o n = A * S ' L Fourier Transform Relations A(u) S(u) L(u) P(u) F(x) G(x) P(x) T(x) Widths shown are equivalent widths -co Figure 1.4.1 a) A one-dimension synopsis of the Fourier transform relationships between the measurements made with interferometers and the sky brightness d i s t r i b u t i o n . 13 Angular Spectrum Domain T(x) Brightness D i s t r i b u t i o n ( r e a l p o s i t i v e ) i 1 " \ D F(x) X Elemental Beam P a t t e r n o r F i e l d of View ( u s u a l l y r e a l and even) G(x) B(x) > w d XJL G r a t i n g F u n c t i o n ( r e a l ) Synthesized Beam ( r e a l ) E q u ivalent Synthesized Beam = F*G*B Figure 1.4.1 b) 14 given radius (maximum sp a t i a l frequency) have been measured, and i f the spacing between the points does not v i o l a t e sampling theory. The points near the centre of the u-v plane are c a l l e d "low-order spacings", and the central point i s the "zero-spacing component". In many p r a c t i c a l systems the u-v plane i s f i l l e d except f o r the low-order spacings and the zero spacing component. The instrument function of an aperture synthesis telescope i s often c a l l e d the "synthesized beam". As with any f i e l d involving Fourier transforms, there i s a trade-off between a narrow beam and large sidelobes. The "grading" or apodizing (shown i n Figure 1.4.1 as L(u) of the u-v plane)governs the degree of trade-off. The grading function m u l t i p l i e s the u-v plane. One which decreases the weight of the high s p a t i a l frequencies produces a wider beam with lower sidelobes. This technique i s c a l l e d "windowing" i n many f i e l d s . The shape of the window function used depends upon the nature of the data, and upon the signal-to-noise r a t i o of the measurements. In radioastronomy, i n which signal-to-noise r a t i o s are quite low, a Gaussian function truncated at the 20 percent l e v e l i s most commonly used. Of course, i f the u-v plane i s not f i l l e d , much worse sidelobes can r e s u l t . Various techniques have been developed for improving them, but these w i l l not be dealt with here. The size of the beam of the elemental antennas of the i n t e r -ferometer govern the area of sky which can be mapped with a single set of observations. It i s often c a l l e d the " f i e l d of view". The ra t i o of the size of the f i e l d of view to the synthesized beam-size governs the number of points i n the u-v plane (or the number o f p i x e l s i n the i-m p l a n e ) . The sky i s assumed to be completely dark o u t s i d e the f i e l d o f view. I f , however, strong sources are not completely suppressed by the elemental beam p a t t e r n , they w i l l be a l i a s e d i n t o the map. The exact s i z e o f the f i e l d o f view i s governed by the s i g n a l -t o - n o i s e r a t i o near the edge of the map. I t i s q u i t e common to sy n t h e s i z e a map out to the o n e - t h i r d p o i n t on the elemental beam. In low frequency r a d i o astronomy the map w i l l o f t e n be c o n f u s i o n l i m i t e d . T h i s i s a r e s u l t o f having many un r e s o l v e d sources i n the s y n t h e s i z e d beam at one time so t h a t a d d i t i v e n o i s e i s not the l i m i t i n g f a c t o r . In t h i s case i t may be p o s s i b l e to make maps which go to a lower p o i n t on the elemental beam. 16 Chapter Two  O v e r a l l Design o f the New Telescope 2.1 Telescope C o n f i g u r a t i o n As o u t l i n e d i n the i n t r o d u c t i o n , i t was decided to t r y to use p a r t o f the e x i s t i n g 22 MHz antenna a r r a y to b u i l d a t e l e s c o p e with high s e n s i t i v i t y and r e s o l u t i o n . V a r i o u s means o f doing t h i s were c o n s i d e r e d . Two methods were ex p l o r e d at length and one o f these was f i n a l l y adopted. a) One method would use the East-West arm o f the o r i g i n a l 22 MHz a r r a y with a l l i t s feed s t r u c t u r e as p a r t o f a compound i n t e r f e r o m e t e r . The o t h e r p a r t would be a small antenna at a d i s t a n c e away equal to the le n g t h o f the arm. Such a system c o u l d not i n i t s e l f form an image o f the p o l a r cap. I f , however, a phase r o t a t i o n system were i n s e r t e d i n the b i n a r y branching system (1) o f the e x i s t i n g antenna, a f a n beam c o u l d sweep across the p o l a r cap at a l l necessary p o s i t i o n angles i n a 12 hour p e r i o d . b) Another method would s p l i t the o r i g i n a l antenna i n t o small p a r t s . Each p a r t would form one h a l f o f an i n t e r f e r o m e t e r . The o t h e r would be e i t h e r one or two new antennas. T h i s a l t e r n a t i v e i s c o n c e p t u a l l y s i m i l a r to the method of aperture s y n t h e s i s u s i n g a s i n g l e i n t e r f e r o m e t e r except t h a t h a l f the r e q u i r e d i n t e r f e r o m e t e r spacings are present simultaneously. A simple t i m e - s h a r i n g technique would supply the o t h e r h a l f o f the spacings. Both methods a) and b) are r e s t r i c t e d i n the f o l l o w i n g way: 17 Unlike most synthetic aperture systems which use steerable elements, i t i s not possible to track an a r b i t r a r y piece of sky long enough to record a l l p o s i t i o n angles using the antennas at hand. Moreover, the system would require automatically adjustable delay l i n e s f o r each interferometer. However, i t i s possible to gather almost a l l position angles for a certain declination range by s a c r i f i c i n g the advantage of being able to produce a map i n one 12 hour period. Depending upon the decl i n a t i o n , a small number of observations are required. Figure 2.1.1 shows three f i e l d s of view i n a s i m p l i f i e d polar projection. F i e l d A i s the polar cap. F i e l d s B and C are at adjacent declinations. A l l sources within the f i e l d go through a range of position angles while the f i e l d remains fixed at a certain hour angle. I f contiguous f i e l d s are observed i n t h i s way, a f u l l 180 degree range of po s i t i o n angles can be co l l e c t e d . Of course, the delay would have to be adjusted for each new hour angle. Although the technical d i f f i c u l t i e s involved i n surveying more than just the polar cap may not be insurmountable, i t was f e l t that at t h i s frequency, the p r i n c i p l e of synthetic apertures for t h i s resolution had to be proved to be workable. Instrumentation could be added l a t e r i f warranted. The two methods presented above each had o f f s e t t i n g advantages and disadvantages. The amount of instrumentation which would have had to be constructed was about the same for both. In the f i r s t case phase rotators would have had to have been i n s t a l l e d i n each 2X antenna segment. This would l i k e l y have been done at high signal l e v e l so that receivers would have been required on each segment. Because of the complex geometry of the telescope, these phase rotators would have had to be programmed i n d i v i d u a l l y . On 18 F i g u r e 2.1.1: A method of surveying'the p o l a r cap f i e l d as w e l l as s e v e r a l adjacent ones. Each source goes through a small range o f p o s i t i o n angles i n each o f the o u t s i d e f i e l d s b e f o r e p a s s i n g out of t h a t f i e l d i n t o the next one. 19 the other hand, only a small number of correlators would have been needed (perhaps two or four). The second case required many correlators instead of phase rotators. It also required delay l i n e s to equalize signal delays before c o r r e l a t i o n . I t has the minor advantage of being s t a t i c (requiring no control signals) while observing was i n progress. But i t had one over-riding advantage. The s p a t i a l Fourier compo-nents were to be collected i n d i v i d u a l l y . Corrections for geometry could be done in the computer. Furthermore, corrections for ionos-pheric e f f e c t s could be on a "per s p a t i a l component" basis. For t h i s reason the second alternative was selected. To proceed further with the design, i t was now necessary to compare possible physical layouts of the system. It should be pointed out here that the d i s t r i b u t i o n of signal processing i n s t r u -mentation i s inherently d i f f u s e rather than central. That i s to say that i t i s f a r more p r a c t i c a l to b u i l d the correlators i n the f i e l d near the antennas than to t r y to bring together hundreds of R.F. signals to one location. I f t h i s were done i n the most di r e c t way using one signal per cable, over 50 km of cable would have been required to d e l i v e r the signals to the observatory building. The c o r r e l a t o r units were therefore constructed to operate outside. Many of the design d e t a i l s of the ensuing layout were based upon minimizing the number and length of signal cables. Depending upon the s e n s i t i v i t y required and the number of correlators to be constructed, some alternative time-sharing techniques were available. Because samples are taken at discrete i n t e r v a l s , adequate sampling rates must be b u i l t into any time-sharing scheme. Referring to figure 1.4.1 note that i n order for no more than one grating, G(x), to appear inside the f i r s t zeros of the f i e l d of view, B(x) , that d<§ For a more r e a l i s t i c pattern of ex c i t a t i o n of the elements of the interferometer, adequate sampling can be attained with However, i n the situ a t i o n at hand an overlap of 50 percent was both adequate and p r a c t i c a l . Since the elements of one side of each interferometer are p h y s i c a l l y contiguous, the overlap must be provided by the shared elements. Figure 2.1.2 shows two configurations of interferometer elements which provide the necessary overlap, and also feature various degrees of time-sharing with concomitant s e n s i t i v i t y . The f i r s t configuration i s impossible to r e a l i z e because of the topography of the antenna s i t e . The East end of the o r i g i n a l a e r i a l array butts up against the base of a steep h i l l . The second configuration with 200 correlators was adopted. The t e l e s -cope s e n s i t i v i t y quoted i n the introduction has taken into account the time-sharing factor shown above. I f only 100 correlators were used, the telescope would have been resolution limited. The considerations dealt with so f a r more or less determine the layout of the system. A number of p r a c t i c a l d e t a i l s were taken into account. F i r s t l y , because two antenna elements were shared Outer Elements Outer Elements Original Array Relative S e n s i t i v i t y 1 Original Array I i T-rr • i j i _ 2/i Outer Elements 200 100 1/JT ill Figure 2.1^2: Two conceivable configurations f o r the telescope. The top one with 400 correlators would have the maximum s e n s i t i v i t y but i s impossible to r e a l i z e because of the topology of the s i t e . Note that the second configuration with 200 correlators has the same r e l a t i v e s e n s i t i v i t y as the f i r s t one with 200 correlators. 22 among approximately 100 interferometers, i t was d i f f i c u l t to arrange t h e i r location so that signal delays from the two sides of each interferometer would be equalized. Secondly, i t was desira-ble to have receivers as close as possible to the antenna elements to which they were connected. Thir d l y , i t was economic to house as much instrumentation i n one weatherproof enclosure as possible. With these ideas i n mind, i t was decided to put the correlators right under the East half of each interferometer. The structure of the feed system f o r the antenna elements made i t convenient to house two receivers in a single box. The signal on the output of each receiver could be correlated with each of the shared antenna elements. This was done i n quadrature p a i r s , of course, making eight correlators per unit. Such a group of eight correlators (with associated other signal processing instrumentation), housed i n one enclosure, w i l l henceforth be referred to as a "correlator unit". Each cor r e l a t o r unit services two antenna elements which are 8-dipole segments of the o r i g i n a l array. So f a r , the main d i f f i c u l t y with t h i s layout has not been emphasized, that of equalizing signal delays. Figure 2.1.3 shows a s i m p l i f i e d schematic representation of the system with the appropriate delays. Each quadrature pair of correlators required a delay which was dependent upon i t s p o s i t i o n i n the system. The maximum delay required was about 15 iisec. Since 100 delay lines were required, the type of l i n e had to be simple and r e l i a b l e . The only type of analog delay which had these properties was coaxial cable. But the amount required was enormous, amounting to about a hundred kilometers altogether. Various other types of analog delay l i n e s e x i s t . H e l i c a l f e r r i t e delay l i n e s have much more Antenna Element (X) C o r r e l a t o r Phase S h i f t Y C o r r e l a t o r Unit East Outer Element West Outer Element Figure 2.1.3: A schematic of the layout of the system with the correlator units placed under each of the East antenna elements. Delays (6t's) are needed to equalize the signal path required to go from the outer elements to the correlator units. IV) CO delay per unit length than coaxial cable. They suffer, however, from poor s t a b i l i t y , high dispersion, high loss, and small band-width. They are also d i f f i c u l t to adjust accurately (6). U l t r a -sonic wire, glass, and mercury delays have similar d i f f i c u l t i e s . It appeared then that d i g i t a l delay l i n e s would be more appropriate to t h i s s i t u a t i o n . Their chief disadvantage i s that the quantization of the signal reduces the s e n s i t i v i t y of the instrument. The degree of reduction depends upon the number of quantization l e v e l s used, and to a lesser extent upon the sampling rate ( 7 ) . The decrease i n s e n s i t i v i t y w i l l be derived i n the discussion on correlators. The bandwidth of the d i g i t a l delay l i n e s i s not as great as that for coaxial cable, but i s adequate for the s i t u a t i o n at hand. Their cost i s r e l a t i v e l y low; they are stable and can be made rea d i l y adjustable. Because of t h e i r s i m p l i c i t y , one b i t d i g i t a l s h i f t r e g i s t e r s were employed. 2.2 Basic Performance Specifications of the Telescope At the outset t h e o r e t i c a l estimates were made of the at t a i n -able resolution, s e n s i t i v i t y , range of sky coverage, and the number of sources expected to be observed. Ionospheric e f f e c t s w i l l be ignored here. It should be borne i n mind, however, that the ionospheric e f f e c t s were the main reason for the p a r t i c u l a r design of t h i s telescope. The f i n a l r e a l i z e d values of the above parameters w i l l depend c r i t i c a l l y upon ionospheric e f f e c t s . However, accurate a p r i o r i estimates of these e f f e c t s are d i f f i c u l t 25 to make. The c a l c u l a t i o n of the above performance sp e c i f i c a t i o n s requires that c e r t a i n parameters be selected. For many, such as the frequency of operation, the selection was pre-determined. Others required an estimate of what could be achieved i n the construction of instrumentation. The most important of these w i l l be dealt with here. Because the telescope i s an array of tuned dipoles, i t i s b a s i c a l l y a single frequency device. Astronomically, the exact frequency of operation i s obviously not important, since i n t h i s frequency range no l i n e spectra have been observed. The frequency 22.250 MHz, the band centre, was chosen by Costain et a l (1) on the basis of a survey of frequencies near 20 MHz f o r a r e l a t i v e l y interference-free band. This frequency i s i n a marine band used c h i e f l y by f i s h i n g boats. Since the telescope i s located about 200 miles inland, ground-wave interference i s u n l i k e l y . The range of sky coverage, or f i e l d of view, i s also pre-determined by the size and construction of the East-West portion of the 22 MHz array. Fortunately, t h i s i s quite apt, and the array was s p l i t into square arrays 2\ by 2\. This r e s u l t s i n a f i e l d width of about 30 degrees to half power. The resolution of the instrument can be worked out from the following formula: 0 ~ f(MHz)?D(km) a r C m i n u t e s where f i s the R.F. centre frequency D i s t h e maximum e x t e n t o f t h e s y s t e m . T h i s f o r m u l a t a k e s i n t o a c c o u n t a G a u s s i a n g r a d i n g f u n c t i o n i n t h e u - v p l a n e . T h i s f u n c t i o n r e d u c e s t h e v a l u e o f t h e o u t e r - m o s t s p a c i n g by a f a c t o r o f 5. The r e s u l t i s a s y n t h e s i z e d beam w i t h a s i d e l o b e l e v e l o f 5 p e r c e n t . F o r t h i s c a s e D i s 2.586 km g i v i n g a beam w i d t h o f 15 a r c m i n u t e s . No m a t t e r how s e n s i t i v e a t e l e s c o p e i s a s f a r as d e t e c t i n g weak s o u r c e s i s c o n c e r n e d , t h e r e i s a l o w e r l i m i t t o t h e s t r e n g t h o f s o u r c e s t h a t t h e t e l e s c o p e w i l l be a b l e t o d e t e c t . A v e r y s e n s i t i v e t e l e s c o p e w i t h low r e s o l u t i o n w i l l have f l u c t u a t i o n s on t h e r e c o r d f r o m s e v e r a l s o u r c e s s i m u l t a n e o u s l y i n t h e beam w h i c h c a n n o t be r e d u c e d by r e p e a t e d a v e r a g i n g o f o b s e r v a t i o n s . I t h a s been shown by e x p e r i e n c e w i t h r e s o l u t i o n - l i m i t e d t e l e s c o p e s (8) t h a t i t i s p o s s i b l e t o d e t e c t a p p r o x i m a t e l y one s o u r c e i n 20 beam a r e a s ( u n d e r s u r v e y c o n d i t i o n s ) . I t i s a l s o p o s s i b l e t o i n f e r c o u n t s o f r a d i o s o u r c e s b y a n a l y z i n g t h e " n o i s e " on t h e r e c o r d s o f a r e s o l u t i o n - l i m i t e d t e l e s c o p e ( 9 ) . However, u n d e r t h e more d i f f i -c u l t o b s e r v i n g c o n d i t i o n s a t low f r e q u e n c i e s w i t h h o t G a l a c t i c f o r e g r o u n d , p o s s i b l e s i d e l o b e r e s p o n s e s , i o n o s p h e r i c s c i n t i l l a t i o n s and r e f r a c t i o n , and t e r r e s t r i a l i n t e r f e r e n c e i t may o n l y be p o s s i b l e t o d e t e c t one s o u r c e i n 40 beam a r e a s . T h e s e e f f e c t s may a l s o p r o d u c e o t h e r k i n d s o f " n o i s e " on t h e r e c o r d w h i c h c a n n o t e a s i l y be a v e r a g e d o u t . F o r t h e s e r e a s o n s i t i s n o t p o s s i b l e t o p r e d i c t ( p r o b a b l y n o t b e t t e r t h a n t o w i t h i n a f a c t o r o f 2 o r 3) how many s o u r c e s w i l l be o b s e r v e d . N e v e r t h e l e s s , u s i n g a s o u r c e d e n s i t y o f 1 i n 40 beam a r e a s and L o g N - L o g S c u r v e s c a l e d f r o m 81.5 MHz (4) by a mean s p e c t r a l 27 index of .7, one gets S = 3.5 Jy res J The r e s u l t i n g number of sources i n a f i e l d 30 degrees wide would be about 360. The choice of R.F. bandwidth for the telescope a f f e c t s c h i e f l y the s e n s i t i v i t y . It i s normally chosen to be as large as possible subject to li m i t a t i o n s imposed by interference. However, there are also other considerations for image-forming telescopes which provide a r e s t r i c t i o n on the maximum bandwidth. These res-t r i c t i o n s are dealt with i n Appendix A5. The bandwidth chosen was 300 kHz. This was found to be acceptable from an interference point of view. An estimate of the th e o r e t i c a l s e n s i t i v i t y can be made once the bandwidth, observing time, and the size of the antennas have been selected. However, an estimate of the aperture e f f i c i e n c y of the antennas i s also required. The aperture e f f i c i e n c y does not turn out to have a major e f f e c t on the s e n s i t i v i t y because the chief source of system noise i s from the sky i t s e l f . Losses encountered i n the antenna elements attenuate the signal from point sources and the noise from bright foreground sky equally. Receiver noise, however, does add to the system temperature after antenna losses have taken place. Because the arrays used i n t h i s system are not steerable, and in any case do not have enough gain, d i r e c t measurement of the antenna temperature produced by a point source cannot be made. An estimate can be made, however, from the equivalent temperature a v a i l a b l e at the input to the r e c e i v e r . These have been measured to be 8700 K and 8000 K ± 300 K r e s p e c t i v e l y f o r the East and West pa r t s of each i n t e r f e r o m e t e r . Figure 2.2.1 shows a contour map made at 22.25 MHz by Costai n et a l ( 1 0 ) . Although the a c t u a l p o l a r cap i s omitted, the average brightness temperature i n t h i s area i s approximately 35,000 K. Since a l o s s l e s s antenna would produce an antenna temperature equal to the average brightness temperature, the r a t i o of these two q u a n t i t i e s i s the l o s s f a c t o r . The e f f e c t -i v e area can then be estimated as a product of the l o s s f a c t o r and the p h y s i c a l area. A . = 194 m2 A , = 309 m2 east west The minimum d e t e c t a b l e f l u x d e n s i t y f o r a source i s given by the f o l l o w i n g r e l a t i o n : AS . m m _ 2.5./?-V2 ,-k. TsysE TsysW East west where the f a c t o r s i n the numerator are 2 i f o n l y one p o l a r i z a t i o n i s measured 5 i f the det e c t a b l e l i m i t i s taken to be 5 times rms noise JfT i s a f a c t o r r e s u l t i n g from q u a n t i z a t i o n of the s i g n a l (see Appendix A2.) f? i s a s t a t i s t i c a l constant f o r m u l t i p l y i n g two random v a r i a b l e s k i s Boltzmann's constant T s y s E ' TsysW a r e t h e s V s t e m temperatures f o r the two pa r t s of the int e r f e r o m e t e r 29 Figure 2.2.1: The 22 MHz map of the North C e l e s t i a l Polar region made by Costain and Roger. The edge of the map i s at a declination of approximately 65 degrees. The Galactic plane i s i n the d i r e c t i o n of the bottom edge, and the brightness temperature slopes away from the Galactic plane. (Contour marked i n units of K i l o Kelvin.) 30 and the factors i n the denominator are Av i s the R.F. bandwidth t i s the observing time or averaging time f o r the sample 2yA^ J T A,. , i s the t o t a l e f f e c t i v e c o l l e c t i n g area for the East west ^ interferometer With an R.F. bandwidth of 300 kHz, system temperatures of 8700 K and 8000 K respectively (including receiver noise of 700 K), and the c o l l e c t i n g areas derived above, the l i m i t i n g s e n s i t i v i t y i s given by A C 760 T AS . = -==• Jy min /tT 7 1 Since a l l the samples i n the u-v plane are e f f e c t i v e l y added together to make a single point i n the r e s u l t i n g image, t can be taken to be N-12 hours where N i s the number of spacings. For N a 96 AS . =. .4 Jy min 2 This i s the the o r e t i c a l s e n s i t i v i t y l i m i t for the instrument at the centre of the f i e l d of view. I f the telescope turns out to be resolution limited, or limited by ionospheric e f f e c t s , then the weakest detectable source on the map would be larger than .4 Jy. 31 Chapter Three Detailed Design of the Components of the Telescope This chapter describes the d e t a i l s of the system sta r t i n g at the antennas and proceeding as much as possible along the signal path to the f i n a l data c o l l e c t i o n point. 3.1 Design of Antennas This section describes the design and implementation of the antenna patterns of the i n d i v i d u a l elements of the interferometer p a i r s . A more quantitative summary follows. The chief r e s t r i c t i o n on the design was that one element of each pair existed already, i . e . an 8-dipole, 2X x 2X segment of the e x i s t i n g array. This was, fortunately, a reasonably appro-priate size. However, th i s array, when phased to have a maximum at a zenith angle of 41 degrees, has very large sidelobes. Freedom of design could be had only i n the other element i n the pai r . There were two main design goals for the antenna patterns. It was the suppression of Cass A at a declination of 58.5 degrees (polar distance 31.5 degrees). Therefore, the pattern should have as nearly as possible a c i r c u l a r n u l l at t h i s point. Even at the zenith, however, i t i s impossible to get a p e r f e c t l y c i r c u l a r n u l l with square arrays of only a few dipoles. The second goal was to achieve o v e r a l l symmetry to the main lobe of the antenna pattern. Because t h i s antenna pattern deter-mines the f i e l d of view of the synthesis telescope, a non-symme-32 t r i e p a t t e r n w i l l cause s p a t i a l F o u r i e r components at d i f f e r e n t p o s i t i o n angles to be weighted d i f f e r e n t l y . The f o l l o w i n g technique was used to produce an optimum antenna response. F i g u r e 3.1.1 shows a schematic o f the East h a l f o f each i n t e r f e r o m e t e r p a i r ( h e n c e f o r t h r e f e r r e d to as the East a r r a y ) . The E-plane response of t h i s a r r a y has a n u l l v ery c l o s e to the p o i n t r e q u i r e d to suppress Cass A. T h i s response, t h e r e f o r e , serves as a good s t a r t i n g p o i n t . The i d e a l o v e r a l l p a t t e r n would have the same main lobe response i n the H plane, but s h i f t e d approximately 41 degrees no r t h from the z e n i t h . The combined antenna p a t t e r n s o f both the East and West h a l v e s o f the i n t e r f e -rometer was needed to achieve a reasonable approximation to the i d e a l response. The o v e r a l l antenna p a t t e r n o f an i n t e r f e r o m e t e r i s p r o p o r t i o n a l to the geometric mean o f the i n d i v i d u a l antenna p a t t e r n s . F i g u r e 3.1.2 shows the West a r r a y with an undetermined number o f rows. I t s E-plane response i s , o f course, the same as t h a t f o r the East a r r a y . A l t o g e t h e r , to be determined are the number o f rows to be c o n s t r u c t e d f o r the West a r r a y s , and the amplitudes and phases to be imposed upon the rows o f both the East and West a r r a y s . I t i s widely known t h a t an a r r a y o f t h i s type forms an antenna p a t t e r n which can be decomposed i n t o a F o u r i e r s e r i e s (11). I t i s a l s o a w e l l known p r o p e r t y o f t r u n c a t e d F o u r i e r s e r i e s , t h a t a g i v e n number o f terms i n the s e r i e s produces the best mean square approximation to a g i v e n shape (12). The obvious approach to the problem at hand i s t h e r e f o r e to r e p r e s e n t the 33 -2 A F i g u r e 3.1.1: East A r r a y o f E i g h t D i p o l e s i f * - i r F i g u r e 3.1.2: Undetermined West A r r a y 34 d e s i r e d response as a F o u r i e r s e r i e s (each term determining the amplitude and r e l a t i v e phase o f a p a i r o f d i p o l e rows), and then to s e l e c t the number o f rows i n the West a r r a y on the b a s i s o f a compromise between the c o s t o f c o n s t r u c t i o n and the t o l e r a b l e s i d e lobe l e v e l . A s o r t o f i n t e r a c t i v e computer programme was developed a c c o r d i n g to the flow c h a r t i n F i g u r e 3.1.3. T h i s was thought necessary because, although the s e r i e s approximation i s the best i n the mean square sense, the d e t a i l e d e r r o r d i s t r i b u t i o n i s not determined p r e c i s e l y . The manual m a n i p u l a t i o n o f amplitudes and phases produced a s l i g h t l y more symmetrical r e s u l t . The above approach w i l l now be developed q u a n t i t i v e l y . The p r i n c i p a l t o o l i s known i n antenna terminology as the A r r a y o f A r r a y s Theorem, o r , i n F o u r i e r t r a n s f o r m terminology, as the C o n v o l u t i o n Theorem. The E Plane response o f the a r r a y s i s separable i n t o three f a c t o r s : the element f a c t o r , the a r r a y f a c t o r , and the screen f a c t o r . A diagram o f the a r r a y s i n the E plane i s shown i n F i g u r e 3.1.4. The elements are f e d in-phase with equal a m p l i t u -des. The element f a c t o r f o r a f u l l wave d i p o l e i s (13) _ , . v cos ( 2 s i n 8) E (9) <* 1 cos 9 The a r r a y f a c t o r f o r two p o i n t antennas separated by one wave-le n g t h i s as i l l u s t r a t e d i n F i g u r e 3.1.5, E_(9) a E e j * / 2 + E e ~ ^ / 2 & cos (2rr s i n 9) 2 o o Start n » 4 Determine desired H-plane response from E-plane response 1 » Obtain the best 2-terra approximation to the desired response (representing the c o n t r i b u t i o n from the East array) Divide r e s u l t i n t o desired response I Obtain the best n-term approximation to the desired response (representing the c o n t r i b u t i o n from the West array) I M u l t i p l y the two responses and d i s p l a y r e s u l t . Examine symmetry, p o s i t i o n of n u l l s , sidelobes, e t c . manually. Manually manipulate amplitudes and phases to attempt to improve response and d i s p l a y r e s u l t . Increment n No Yes Stop F i g u r e 3.1.3: A Flow Diagram o f the Computer C a l c u l a t i o n o f Antenna Responses. F i g u r e 3.1.4: An E Plane Diagram of the Elemental A r r a y s F i g u r e 3.1.5: A Diagram Leading to the E v a l u a t i o n o f the A r r a y F a c t o r f o r Two Antennas. 37 A3 A2 A, A 0 A, A2 A3 F i g u r e 3.1.6: The A r r a y Geometry f o r an Odd Number o f D i p o l e s . '-0* -0-A^ . Ao A2 A, A, M l 4 F i g u r e 3.1.7: The A r r a y Geometry f o r an Even Number o f D i p o l e s . 38 where $ - ~ y ~ s i n e and b The screen f a c t o r can be c a l c u l a t e d i n the same way as the a r r a y f a c t o r . The r e f l e c t i n g screen, Vs below the d i p o l e s , produces an antiphase image V 4 below the d i p o l e . T h e r e f o r e , t h i s can be t r e a t e d as a v e r t i c a l a r r a y o f p o i n t antennas f e d out o f phase and separated by ^ 4 . U s i n g the same approach as f o r the a r r a y f a c t o r , the r e s u l t i s (6) tv s i n (~ cos 9). Each o f the above f a c t o r s r e p r e s e n t s e l e c t r i c f i e l d , not power p a t t e r n s . T h e i r product i s the o v e r a l l E plane response. F i g u r e 3.1.8 shows the d e s i r e d H plane response. As e x p l a i n e d above, t h i s i s simply the E plane response t r u n c a t e d at the f i r s t z e r o s , and s h i f t e d t o a z e n i t h angle o f 41 degrees. The F o u r i e r s e r i e s r e p r e s e n t a t i o n o f a r r a y s appears i n many p l a c e s i n the l i t e r a t u r e (14) and w i l l not be repeated here. I t i s necessary, however, to r e s t a t e the r e s u l t s i n a form a p p l i c a b l e to the s i t u a t i o n at hand. F i g u r e 3.1.6 shows the a r r a y geometry f o r an odd number o f antennas; F i g u r e 3.1.7, f o r an even number. T „ , , 2nd „. _ 2nd _ L e t ijr = — ^ — s i n * —-— ? Then f o r an odd number of antennas the d e s i r e d p a t t e r n E (§) i s p r o p o r t i o n a l to A + t, (a. cos Ic iff + b, s i n k^f) 0 k=l K K where ^ , / a r 2 + b k 2 39 an d , . - tan"* & ) k The a^'s, t>k* s and A q can be calculated from the desired response E (§) by the following Fourier transform relationships (for the case d = -|-). ak = i i c o s ( n k ? ) d ? bk = i l E ( § ) s i n ( t t 1 c ? ) d 5 A Q - J a E(f) d ? The r e s u l t i n g amplitudes ( A ^ ' s ) and phases ( 0 k's) are applied as shown i n Figure 3.1.6. S i m i l a r l y , for an even number of antennas E ( 0 a S (a. cos ((2k-l)-|) + b, sin ((2k-l)A) k - 1 K ^ where a£ = J a E(5> cos (4f (2k-l) ?) d S b k = | a E(?) sin (2k-l) ?) d § The A^ .' s and $ k's are calculated i n the above way, and are applied as shown i n Figure 3.1.7. The above equations formed the basis f o r the set of computer programmes outlined i n Figure 3.1.3. Figure 3.1.9 shows one of the four-dipole approximations (representing the East array) to the desired response. It i s the response produced by the Fourier series but with an extra "progressive" phase s h i f t of 6 degrees. This appeared to be the best possible with four dipoles. The sidelobe l e v e l of t h i s array by i t s e l f i s obviously i n t o l e r a b l y 40 large. Figure 3.1.10 shows the desired response divided by the f i r s t approximation. Figure 3.1.11 shows the seven-dipole approximation to the response of Figure 3.1.10. Figures 3.1.12 and 3.1.13 show the o v e r a l l power pattern with a 4 dipole x 7 dipole interferome-ter . Both the six and seven dipole arrays would l i k e l y have been adequate. Both have less than one percent response at zenith angles 9.5 and -9.0 degrees (corresponding to the declinations of Cass A and Cyg A). The peak-to-peak sidelobe structure f o r the seven dipole array i s less than f o r the six dipole array. Also, the main lobe of the seven dipole array i s s l i g h t l y more symme-t r i c a l . "Seven dipoles"was chosen on t h i s basis and on the basis that phase errors i n the feed structure might have less e f f e c t for a larger array. Both combinations of arrays have the d i f f i c u l t y that there i s not a n u l l at a zenith angle of 72.5 degrees corresponding to the lower culmination of Cass A. A l l Fourier series represent periodic functions. In the case of these antenna arrays, the pattern i s designed to repeat on the horizons. Also, the conju-gate variable i n the Fourier series i s sin 9, not 9. Near the zenith a small increment i n 9 i s an almost equal increment in sin 9. However, near the horizon an equal increment i n 9 i s a much smaller increment i n sin 9. Therefore, steep sides on the antenna pattern near the horizon, or even at 72.5 degrees requires more Fourier terms (and consequently more dipoles) than at the zenith. Fortunately, the r e f l e c t i n g screen i s e s s e n t i a l l y a 41 Figure 3.1.8: E-plane f i e l d pattern shifted to the zenith angle of the North C e l e s t i a l Pole - desired pattern i n the H-plane. Figure 3.1.9: Best mean square approximation to above using 4 rows of dipoles. Figure 3.1.10: Residual H-plane response. Figure 3.1.11: Best mean square approximation using 7 rows of dipoles. 42 F i g u r e 3 .1 .12 : F i n a l E-plane power pattern. 40 bo 80 F i g u r e 3 .1 .13 : F i n a l H-plane power pattern. ! 1 .1" 1 1 ' 1 ^0 60 eo 43 v e r t i c a l , two element array with "end-fire" phasing. I t , there-fore, has a n u l l on the horizon which reduces the l e v e l of the response at 72.5 degrees by a factor of 4.28. Therefore, mostly because of the screen factor, the o v e r a l l response of the i n t e r -ferometer i s about 5 percent for Cass A i n lower culmination. Since the flux of t h i s source i s about 50,000 Jy, a dynamic range of 2500:1 i s required of the system as a whole if'observations are made with Cass A i n lower culmination. Therefore, optimum observing conditions occur when Cass A i s i n the southern part of the sky at night. This occurs during September. March, therefore, i s a poor time to observe with t h i s instrument. 3.2 Site Selection for the West Outer Element After the general layout of the antenna system had been decided upon, a suitable location had to be found f o r the small antenna array that would double the resolving power of the telescope. An a e r i a l photograph of part of the White Lake v a l l e y , relevant to the telescope, i s shown i n Figure 3.2.1. For reasons that have been discussed, i t was decided to b u i l d a small array on the end of the East-West arm of the T-telescope as well as one to the West at a distance from the west end approximately equal to i t s own length. Hereafter, the East-West arm w i l l be denoted by EWA, the array attached to the end of the EWA by EOE (East Outer Element), and the array to the west by WOE (West Outer Element). 44 The l i n e (A-B) on the a e r i a l photograph d e f i n e s the locus of p o i n t s i n the plane of the EWA which would be at approximately the r i g h t d i s t a n c e from i t . Given the topology i n that area, the problem remained to f i n d the l o c a t i o n f o r the antenna which would provide the best coverage o f the s p a t i a l frequency plane. F i g u r e 3.2.2 shows the geometry o f an i n t e r f e r o m e t e r i n any plane c o n t a i n i n g i t s b a s e l i n e . The f r i n g e system of the i n t e r f e r o m e t e r i s on l i n e s o f constant $ where i> = 2TT? s i n 9 ( f o r the case i n which a l l i n s t r u -mental phase and d e l a y paths are e q u a l i z e d ) . In three-dimension-a l space the f r i n g e s are r o t a t i o n a l l y symmetric about the base-l i n e . T h i s e x p r e s s i o n f o r <b i s d e r i v e d i n Chapter 4.4 i n terms o f c e l e s t i a l c o o r d i n a t e s : and <fi = 2rr^ ( s i n d s i n 6 + cos d cos 6 cos (H-h)) ' H = hour angle of S 6 = d e c l i n a t i o n o f S h = e q u i v a l e n t hour angle o f the b a s e l i n e d « e q u i v a l e n t d e c l i n a t i o n of the b a s e l i n e The r e l a t i o n i s c o n s i d e r a b l y s i m p l i f i e d i f d = 0. I f d ss 0, then the b a s e l i n e i s contained i n the e q u a t o r i a l plane. Most s y n t h e t i c aperture systems b u i l t f o r r a d i o astronomy are so arranged. Under c e r t a i n c o n d i t i o n s encountered i n t h i s t e l e s c o p e , severe d i s t o r t i o n s i n the beamshape can r e s u l t i f d / 0. A f u l l d i s c u s s i o n o f t h i s t o p i c i s presented i n chapter 4. 4. The i n i t i a l p l a n was to arrange t h a t the e n t i r e system be Figure 3.2.1: An a e r i a l photograph of the o r i g i n a l 22 MHz antenna and i t s surrounding t e r r a i n . The l i n e on the extreme l e f t i s the l i n e AB referred to i n the text. The c i r c l e s mark the eventual location of the Outer Elements. The arrow i s directed North. 0 1 Incoming R a d i a t i o n F i g u r e 3 . 2 . 2 : The b a s i c geometry an i n t e r f e r o m e t e r . contained i n the equatorial plane. Since the EWA was already-contained therein, i t remained only to f i n d the inter s e c t i o n of the equatorial plane with the surface of the ground at a distance equal the length of the EWA from i t s West end. Figure 3.2.3 shows a cross-section corresponding to the l i n e A-B i n Figure 3.2.1. The intersection of the equatorial plane with the ground surface i s at point S. Unfortunately, t h i s i s very steep ground. Moreover, i t i s a Southerly slope so that an array b u i l t p a r a l l e l to the ground would have required a large phasing angle to point at the North C e l e s t i a l Pole. An array b u i l t h o r i z o n t a l l y would also have required t a l l poles to compen-sate for a v e r t i c a l drop of about 40 feet on one side. Access to t h i s area would have been d i f f i c u l t . With these d i f f i c u l t i e s i n mind, i t was decided to locate the array farther down the h i l l on a more l e v e l section of ground. The f i n a l location was approximately at the point S', 750 feet south of the point where the projection of the EWA intersects the plane of Figure 3.2.3. As mentioned above, with more computational e f f o r t , the deleterious e f f e c t on beamshape mentioned above can be removed. Many aperture synthesis instruments determine t h e i r position by means c a l i b r a t i o n observations of strong point sources. This instrument has not been designed to observe ar b i t r a r y pieces of .sky. It was also anticipated that problems with signal phases might arise because of ionospheric or instrumental e f f e c t s . Rather than having the geometrical errors as unknowns to be corrected by observation, extra care was taken with the surveying E l e v a t i o n F i g u r e 3.2.3: H o r i z o n t a l Distance from P o i n t A 49 of the antennas so that other important quantities could be derived. There being no accurate map of the area required that much time had to be spent doing rough measuring and general reconoite-ring of the area. The f i n a l accuracy required i s not d i f f i c u l t to achieve, but pains-taking care i s needed to assure that blunders do not occur. Including the laying out of the position of each pole i n the new arrays, t h i s surveying took about four months work. Preliminary surveying began with projecting the l i n e of the EWA 4224 feet i n order to get into the plane of Figure 3.2.3. This was done using a 300 f t . tape. The array i t s e l f served as a good guide for keeping successive measurements i n a straight l i n e . Point S' was found approximately 750 feet south of t h i s l i n e near the road to Twin Lakes from the Observatory. A survey marker (Station 61) was placed at t h i s point. The plan was to accurately' f i n d the p o s i t i o n of Station 61, and from i t the f i n a l p o s i t i o n of the array could be established with a r e l a t i v e l y short survey l i n k . A more accurate position of Station 61 was obtained by stadia measurements, a triangulation method involving a base tri a n g l e i n t e r n a l to the optics of the t r a n s i t . By t h i s method, i t i s possible, with moderate accuracy, to obtain a l l three coordinates of a point i n a single survey. This was done for Station 61 r e l a t i v e to the end of the EWA. Two loop traverses were used. Table 3.2.1. shows the positions obtained f o r Station 61. The s t a d i a measurements confirmed t h a t S t a t i o n 61 was not f a r from the new a r r a y c e n t r e . An accurate measurement o f i t s p o s i t i o n was then warranted. In the h o r i z o n t a l p l a n e, a s e r i e s o f accurate t r i a n g u l a t i o n measurements were taken u s i n g s t a t i o n s as o u t l i n e d i n F i g u r e 3.2.4. Usi n g standard averaging techniques ( 3 9 ) , angles were measured with an average e r r o r o f 16 sec. o f a r c . U s i n g p a r t o f the EWA as a base, the p o s i t i o n o f S t a t i o n 61 p r o j e c t e d on the h o r i z o n t a l plane was e s t a b l i s h e d to w i t h i n about .5 f t . with r e s p e c t to the EWA. Included w i t h i n the network o f t r i a n g l e s was a p a i r o f azimuth markers e r e c t e d by the Geodetic Survey o f Canada. Us i n g these as an azimuth the v a r i o u s b a s e l i n e s could be found. A l s o , a d i s t a n c e between the markers at mean sea l e v e l was a l s o known (17). Our value f o r t h i s d i s t a n c e was 1564.72 m., 32 cm d i f f e r e n t from the value quoted, c o r r e c t e d f o r mean e l e v a -t i o n . T h i s e s t a b l i s h e d confidence t h a t the h o r i z o n t a l p o s i t i o n o f S t a t i o n 61 was known to at l e a s t t h i s accuracy. There remained to f i n d an accurate a l t i t u d e f o r S t a t i o n 61. T h i s was not a c t u a l l y o b t a i n e d u n t i l a f t e r the a r r a y was b u i l t . I t was o b t a i n e d by running a s e r i e s o f l e v e l t r a v e r s e s from the end o f the EWA. The r e s u l t i n g measurement i s shown i n Tab l e 3.2.1. In due course, a f t e r the p o s i t i o n o f S t a t i o n 61 was a c c u r a t e -l y e s t a b l i s h e d , the exact l o c a t i o n o f the WOE was s e l e c t e d . S t a d i a measurements were made to determine a topographic map o f the r e g i o n surrounding S t a t i o n 61. A b a s e l i n e of 145X was chosen F i g u r e 3.2.4: F i n a l layout o f West Outer•Element. 52 Table 3.2.1: Summary of pos i t i o n measurements using various methods of surveying f o r Station 61. X Y Z a x CTy CTz Stadia 758.93 4181.10 1195.27 1.6 3.3 1.7 feet Triangulation 758.78 4179.14 - .2 .9 '» Level - - 1195.86 - - .06 " T a b l e 3.2.2: B a s e l i n e g e o m e t r i c a l parameters f o r r e p r e s e n t a t i v e i n t e r f e r o m e t e r b a s e l i n e s i n the t e l e s c o p e . B a s e l i n e No. D d h 46 45.79X .005° 89.52° 98 98.00X 4.52° 80.6° 145 144.31X 3.07° 83. 5° 193 191.84X 2.31° 85.0° 54 from the c e n t r e o f the EWA to the e a s t e r l y phase c e n t r e o f the WOE. (As e x p l a i n e d e a r l i e r , the WOE and the EOE c o n s i s t o f two o v e r l a p p i n g elements). F i g u r e 3.2.4 shows the l a y o u t . Using the b a s e l i n e c o n s t r a i n t , the a r r a y was p l a c e d i n the best p o s i t i o n from the standpoint o f ease o f c o n s t r u c t i o n . The v a l u e s o f d, h, and D are d e r i v e d i n Appendix A l i n terms o f angles and d i s t a n c e s i n the h o r i z o n t a l plane. T a b l e 3.2.2 shows the v a l u e s f o r some r e p r e s e n t a t i v e b a s e l i n e s i n the o u t e r h a l f of the u-v plane. 3.3 C o n s t r u c t i o n of New A r r a y s Two a r r a y s , each o f seven rows o f d i p o l e s , were r e q u i r e d to form a common element f o r each i n t e r f e r o m e t e r p a i r i n the system. I t was a l s o p o i n t e d out i n chapter 2.1 t h a t p r o v i s i o n would have to be made f o r samples o f the u-v plane along a r a d i u s to be c l o s e enough to avoi d g r a t i n g responses. In a system i n which the elements o f an i n t e r f e r o m e t e r can be moved, s u c c e s s i v e measurements are made at spacing i n t e r v a l s o f l e s s than one elemental width. In t h i s t e l e s c o p e c o n f i g u r a t i o n , however, because the elements are p h y s i c a l l y contiguous, they cannot be overlapped. I t i s a l s o shown i n chapter 2.1 t h a t the same e f f e c t as o v e r l a p p i n g can be o b t a i n e d by t i m e - s h a r i n g . F i g u r e 3.3.1 shows how t h i s i s done. Each a r r a y c o n t a i n s twenty-one d i p o l e s ( t h r e e rows o f seven). The EOE i s attached to the o r i g i n a l a r r a y . The WOE i s l o c a t e d West o f the o r i g i n a l a r r a y approximately 1.3 km away. The a c t u a l l\ «H 1 One Row ^ \ of 7 D i p o l e s T Out ; A schematic o f the antenna s w i t c h i n g system d e v i s e d to f i l l i n the i n t e r -leaved spacings. The d i p o l e s are shown i n the E plane, and a row o f seven would be p e r p e n d i c u l a r t o the page. The c e n t r a l row i s always connected while the o u t e r two rows are a l t e r n a t e l y connected to the summing network. The r e s u l t i s that the phase c e n t r e o f the a r r a y i s s h i f t e d back and f o r t h by IX. Figure 3.3.2 a): A view of the W.O.E. showing the end row of poles, the East row of dipoles i n the upper r i g h t , and various st r u c t u r a l parts of the W.O.E. The transmission l i n e from the E.O.E. had not been i n s t a l l e d when t h i s photograph was taken. Figure 3.3.2 b): One of the dipoles and the feed l i n e s i n the W.O.E. i s shown silouetted against the sky. The r e f l e c t i n g screen can be seen as a band of dark l i n e s against the mountain. Springs used to keep the dipoles stretched can also be seen. 57 Figure 3.3.2 c): A photograph of the point where the E.O.E. joins the o r i g i n a l 22 MHz array. Because there are an odd number of dipoles i n the E.O.E., the dipoles had to be suspended from both adjoining poles i n the o r i g i n a l array. 5 8 position of these elements and the concomitant geometrical e f f e c t s on the system are discussed i n chapters 3.2 and 4.4. Some of the design of the arrays was patterned after that of the o r i g i n a l 22 MHz array. The dipoles themselves, of course, were r e p l i c a s . The feed and support structureswere d i f f e r e n t . Only half as many wooden poles per dipole were used. Figure 3.3.2 shows some photographs of the arrays. A construction contract was drawn up to b u i l d the structural part of the arrays and the dipoles. The feeds were added after the dipoles and r e f l e c t i n g screen were i n place so that exact impedance measurements could be made in s i t u . The part of the feed system connecting the dipoles them-selves to the combining network i s shown in Figure 3.3.3. The combining networks are described i n chapter 3.4. The v e r t i c a l twin wire transmission l i n e i s a | impedance transformer from 2000.A. to 200.a. At t h i s point there i s a 4:1 balun, balanced to unbalanced, to transform impedance to 50A. A length of RG58 cable, an i n t e g r a l number of half wavelengths long, connects the balun to the combining network. 59 - F u l l Wave "Broad Band" Dipole \ • .84 )i ± .045 T . o n ^ —10:1 Transmission Line Transformer C* -50 £1 RG 58 Cable Figure 3 .3 .3 a): The dipoles and the feeds f o r the Outer Elements. Figure 3 .3 .3 b): A photograph of the lower end of the transmission l i n e feed and of the balun shown above. 60 3*4 A r r a y Feed System In o r d e r t o achieve the designed p a t t e r n the a p p r o p r i a t e amplitudes and phases o f the incoming r a d i a t i o n have to be present at each d i p o l e antenna. The f o r e g o i n g c a l c u l a t i o n s were done without regard to p o s s i b l e mutual c o u p l i n g between the d i p o l e elements o f each a r r a y . For t h i s reason, a feed system f o r the a r r a y s which p r o v i d e s i s o l a t i o n between the v a r i o u s d i p o l e rows i s d e s i r a b l e . Apart from the p r o p e r t y o f i s o l a t i o n , t h e r e are o t h e r requirements f o r the feed system. I t must not be too l o s s y . A l i m i t f o r the l o s s can be estimated from the r a t i o o f the b r i g h t -ness temperature o f the c e l e s t i a l p o l a r r e g i o n to the r e c e i v e r n o i s e temperature. In t h i s case the r a t i o i s about 17 db. I f one takes 10 db as a design goal f o r the s i g n a l - t o - n o i s e r a t i o at the r e c e i v e r i n p u t s , then 7 db l o s s i n the antenna system i s al l o w a b l e . Since p a r t o f the feed system a l r e a d y e x i s t e d f o r the East a r r a y s , the phasing system to be added t o i t had to be compatible. The outputs from each row o f d i p o l e s i s a v a i l a b l e i n RG 8 c o a x i a l c a b l e (50 ohms unbalanced). T h e r e f o r e , the phasing system f o r these a r r a y s had to be a f i v e - p o r t d e v i c e matched to 50 ohms at a l l p o r t s . The f i n a l c r i t e r i o n i s t h a t the d e v i c e be as inexpensive as p o s s i b l e . F i f t y such networks are r e q u i r e d f o r the East h a l v e s o f each i n t e r f e r o m e t e r . S i x of the e i g h t - p o r t v a r i e t y are r e q u i r e d f o r the West h a l v e s . One of the most common feed systems, the binary branching system or corporate feed structure does not provide good enough i s o l a t i o n between input ports unless each junction i s a hybrid. Also, i t can be proved that los s l e s s matching of a l l three ports of each junction i n the same impedance i s impossible (15). Furthermore, only 2 n inputs are possible with t h i s system. A signal combiner adapted from a microwave device was found to have almost a l l of the desirable properties (16). A schematic diagram i s shown in Figure 3.4.1. Each of the four L-C sections serves as a 90 degree phase i n s e r t i o n . Signal entering one of the input ports t r a v e l s to each of the other input ports v i a two routes. One i s d i r e c t l y through the r e s i s t o r network; the other, v i a two ^ sections, thereby cancelling the d i r e c t signal. Although the design i s b a s i c a l l y a narrow band one, the p r a c t i c a l bandwidth i s about 20 percent. The i n s e r t i o n loss i s 10 log (n-l) db (where n i s the number of ports). Each dipole i n the array i s exposed to an average sky bright-ness temperature of 35000 K. In the i d e a l case there would be equivalent power available at each input to the combining network. The power available at the output i s , taking into account the above loss, also 35000 K. However, the signal from each dipole i n t h i s case i s attenuated according to the r e l a t i v e amplitudes worked out i n chapter 3.1. The equivalent output attenuation f o r the 7-dipole array i s 2.9 db; f o r the 4-dipole array, 1.7 db. A photograph of one of the combining networks constructed i s shown in Figure 3.4.2. Any p r a c t i c a l system has losses over and above th e o r e t i c a l Output Load Figure 3.4.1: A schematic diagram of the 4-element combining network used on the East arrays. The generators shown represent the dipole rows. The 50 ohm r e s i s t o r s represent a d i r e c t path f o r the signal which i s cancelled by an antiphase signal from any of the other inputs. Input i s o l a t i o n i s achieved by means of t h i s d i s t r u c t i v e interference. ro Figure 3.4.2: The combining network f o r the East arrays (4 dipole rows). The amplitudes are determined by attenuators inside the box; the phases, by the RG58 cables seen attached to the four inputs. The phase reference input i s , of course, the short one on the r i g h t . l o s s e s . Measurements of the a c t u a l power a v a i l a b l e at the output p o r t s of the antennas y i e l d 8700 K and 8000 K ± 150 K r e s p e c t i v e -l y f o r the 4 - d i p o l e and 7-dipole a r r a y s . T h i s means t h a t i n c i d e n -t a l l o s s e s are 3.7 db and 3.1 db f o r the two a r r a y s r e s p e c t i v e l y . The feed system d e s c r i b e d above reduces the e f f e c t of mutual impedances but does not, o f course, e l i m i n a t e them a l t o g e t h e r . The amplitudes and phases o f v o l t a g e s on the d i p o l e s i s the v e c t o -r i a l sum of the impressed v o l t a g e s and the induced v o l t a g e s . I f , however, the v o l t a g e s can be shown to be equal to the c a l c u l a t e d ones, and at the same time the d i p o l e s are matched, then the beamshape w i l l be as expected. A setup f o r measuring the v o l t a g e amplitudes and phases at a s u i t a b l e p l a c e on each d i p o l e i s shown i n F i g u r e 3.4.3. The probe was p l a c e d at a 200 ohm p o i n t o f each row o f the East a r r a y s as shown i n F i g u r e 3.4.4. The West a r r a y s were t r e a t e d s i m i l a r l y . With t h i s system the v o l t a g e induced by a neighbouring d i p o l e can be measured d i r e c t l y . An attempt was made at p r e d i c t i n g the d r i v i n g v o l t a g e s r e q u i r e d to achieve a g i v e n r e s u l t as measured on the d i p o l e s themselves. A matrix, M, of the measured induced v o l t a g e s can be formed t h a t , when m u l t i p l i e d by a column v e c t o r o f d r i v i n g v o l t a g e s , V^, should y i e l d a column v e c t o r o f r e s u l t a n t v o l t a g e s , V , on the d i p o l e s . MV , = V d r T h i s i s t r u e , of course, o n l y when impedances are h e l d constant on the d i p o l e s . A measurement was done on the seven d i p o l e a r r a y to determine to what extent t h i s e quation i s t r u e . 65 RG 58 Cable Vector Voltmeter 50:tZOO_ IL S/OJ2. - v w — ° •AAAA o SI on. ± ~4- Balanced Probe Power S p l i t t e r RG 58 Cable -4>- To Feed System Figure 3.4.3: A measurement setup f o r measuring the r e l a t i v e amplitudes and phases on the in d i v i d u a l dipoles of one of the elemental arrays. F u l l Wave Dipoles ^ / R e f l e c t i n g Screen Transformers-Probe JL Matching Stub Balun To Antenna Combining Network Figure 3.4.4: A schematic diagram of the dipoles and feed structure f o r the East array, part of the o r i g i n a l system. The point at which the probe of Figure 3.4.3 i s attached i s also shown. The r e s u l t i s d i s p l a y e d i n F i g u r e 3.4.5. The method does not g i v e a very good q u a n t i t a t i v e r e s u l t , but some q u a l i t a t i v e trends can be p r e d i c t e d . F i r s t l y , i t appears that mutual e f f e c t s r e s u l t i n changes i n phase more than amplitude. Secondly, i n most o f the cases f o r l a r g e amplitudes the c a l c u l a t e d phase d e v i a t i o n s were o f the c o r r e c t s i g n but not as l a r g e i n magnitude as the measured d e v i a -t i o n s . In the p r e s e n t cases an i t e r a t i v e method was used to get the a p p r o p r i a t e amplitudes and phases on the d i p o l e s . The above method was used to p r e d i c t the next i t e r a t i o n . A l s o , i n view o f the t r e n d s mentioned above, amplitude e r r o r s and phase e r r o r s were t r e a t e d s e p a r a t e l y . A l t o g e t h e r , f o u r i t e r a t i o n s on the 4-dipole a r r a y and s i x i t e r a t i o n s on 7-dipole a r r a y were r e q u i r e d . Because t h i s a r r a y has f i x e d phasing, i t can p o i n t to o n l y one p a r t o f the sky. Cass A i s overwhelmingly powerful i n t h i s p a r t o f the sky, even though i t has been attenuated as much as p o s s i b l e . F i g u r e 3.4.6 i s a p l o t of the v i s i b i l i t y amplitude o f Cass A as measured with an i n t e r f e r o m e t e r 97X long. The sharp i n c r e a s e at an hour angle o f about 11 hours i s the " n o r t h e r n toe" o f the antenna beam d i s c u s s e d i n chapter 3.1. I f t h i s " t o e " i s taken to be at the 20 percent l e v e l as p r e d i c t e d , then Cass A i s suppressed to about 2 percent elsewhere i n the hour angle range. i g u r e 3.4.5: R e l a t i v e amplitudes and phases o f v o l t a g e s f o r the E.O.E. The v e c t o r s with c i r c l e s are the d r i v i n g v o l t a g e s ; those with b a r s , the measured v o l t a g e s . The c a l c u l a t e d v o l t a g e s are shown without e i t h e r c i r c l e s o r bars. Percent of Polar Diagramme Maximum 304 10} Upper Cass. A I .0' I I I I I I I I I II Lower Cass. A I I 18H • i i i OH 6 H 12H S.T. F i g u r e 3.4.6: F r i n g e amplitudes of the r a d i o source CASS A as i t s k i r t s the beam o f a prototype i n t e r f e r o m e t e r . The t r a n s i t s o f CASS A are shown i n the South near 0 Hours and i n the North near 12 Hours. 69 3.5 R e c e i v e r s T h i s p r o j e c t r e q u i r e s about 55 s p e c i a l i z e d r e c e i v e r s which are to be rugged, designed f o r medium s c a l e p r o d u c t i o n , and which must meet unusual s p e c i f i c a t i o n s o f phase and gain matching. B r i e f l y , they are as f o l l o w s : Average S p e c i f i c a t i o n s Performance Centre Frequency 22.250 MHz 22.250 MHz Bandwidth 300 kHz 300 kHz Intermediate Frequency l e s s than 7 MHz 5.0 MHz L o c a l O s c i l l a t o r " h i g h s i d e " yes Receiver n o i s e l e s s than 1000 K 700 K Gain at l e a s t 122 db 130 db ( a d j u s t a b l e ) Gain matching w i t h i n ± .2 db ± .2 db Phase matching w i t h i n ± 5 degrees between 3 db p o i n t s ± 2 degrees Image r e j e c t i o n more than 30 db 60 db Suppression at 22 MHz more than 30 db 27 db The c e n t r e frequency and bandwidth are d e a l t with i n chapter 3. The Intermediate Frequency was r e q u i r e d to be l e s s than 7 MHz because i t was to be d i g i t i z e d . R e a d i l y a v a i l a b l e i n t e g r a t e d c i r c u i t s would operate b e s t below 7 MHz (see chapter 3.7). A "high s i d e " l o c a l o s c i l l a t o r was chosen because o f the spectrum o f i n t e r f e r i n g s i g n a l s . The image frequency i s 32.25 MHz. Propaga-t i o n o f man-made s i g n a l s i s much b e t t e r at 12 MHz than at 30 MHz; consequently, t h e r e are many more t r a n s m i t t e r s at 12 MHz. Because the frequency band i s next t o an A e r o n a u t i c a l Mobile band (ending at 22.0 MHz), i t was c o n s i d e r e d wise to have about 30 db o f s u p p r e s s i o n at t h i s frequency. A s i x p o l e f i l t e r would produce 27 db suppression at 22.0 MHz. A l s o , a s i x p o l e I.F. s t r i p would r e q u i r e 3 stages o f a m p l i f i c a t i o n , which c o u l d produce the r e q u i r e d I.F. g a i n . The o v e r a l l g a i n should be at l e a s t 122 db, h i g h enough to produce more than 5 mw o f output power from i t s own f r o n t end n o i s e . To achieve the r e q u i r e d phase matching, the gains are a l s o c l o s e l y matched (± .2 db). Phase matching i s as important here as i n any o t h e r p a r t of the i n t e r f e r o m e t e r . I t was f e l t wise to have as much f i l t e r i n g b efore the f i r s t t r a n s i s t o r as p o s s i b l e ( c o n s i s t a n t with n o i s e f i g u r e c o n s t r a i n t s ) . The f i l t e r i n g would reduce the p o s s i b i l i t y t h a t a strong o u t - o f -band s i g n a l would s a t u r a t e the f r o n t end. L i k e many oth e r p a r t s o f t h i s t e l e s c o p e , the design, c o n s t r u c -t i o n , and t e s t i n g of the r e c e i v e r s was an important but t e d i o u s p a r t of the c o n s t r u c t i o n . I t i s d e s c r i b e d i n d e t a i l i n Appendix A3 as an example o f the method o f a t t a c k on s i m i l a r problems germane to t h i s t e l e s c o p e . A block diagram o f the b a s i c r e c e i v e r and c o r r e l a t o r system i s i n c l u d e d here i n F i g u r e 3.5.1 as a guide to the r e s t o f t h i s c hapter. The b l o c k s correspond to the major components o f the system. I t must be noted, however, t h a t some of them, such as the l o c a l o s c i l l a t o r system, are i n h e r e n t l y d i f f u s e - encompassing a l a r g e d i s t r i b u t i o n network. 71 Antenna D i r e c t i o n a l Coupler 22.250 MHz Receiver Sampler 5.0 MHz D i g i t a l Delay L i n e 1.175 MHz C a l . S i g n a l Generator 22.250 MHz 27.250 MHz 1 L.O. s t 4.70 MHz Antenna D i r e c t i o n a l Coupler 22.250 MHz Receiver 5.0 MHz X 300 KHz Mixer Switch Decoder, Read Command from C o n t r o l l e r Output to C o n t r o l l e r F i g u r e 3 . 5 . 1 : A b lock diagram of the b a s i c r e c e i v e r and c o r r e l a t o r system. 72 3*6 D i s t r i b u t i o n o f L o c a l O s c i l l a t o r and Clock S i g n a l s Besides the c a l i b r a t i o n s i g n a l , t h e r e are two o t h e r s i g n a l s which have to be d i s t r i b u t e d throughout the system, the l o c a l o s c i l l a t o r s i g n a l at 27.25 MHz, and the c l o c k f o r the d e l a y l i n e s at 1.175 MHz. The c l o c k a l s o serves as a second l o c a l o s c i l l a t o r i n a way t h a t i s e x p l a i n e d i n chapter 3.7. F o r t u n a t e l y , most o f the cab l e f o r d i s t r i b u t i o n o f these s i g n a l s came from the b i n a r y branching system o f the 22 MHz T arr a y . The d i s t r i b u t i o n system a c t u a l l y c o n s i s t s o f three b i n a r y branching networks, one f o r each t h i r d o f the system. I t i s necessary f o r the l o c a l o s c i l l a t o r s i g n a l and the c l o c k s i g n a l to share a s i n g l e c a b l e from the c e n t r e to the oute r t h i r d s . ( F i g u r e 3.6.1). Otherwise, the networks, themselves, are separate. At the West end of the d i s t r i b u t i o n system, a small amount o f each s i g n a l i s " s n i f f e d o f f " the l a s t i n p u t to a c o r r e l a t o r u n i t f o r use i n the E.O.E. The l o c a l o s c i l l a t o r i s used f o r r e c e i v e r s i n the E.O.E. and W.O.E. The c l o c k i s m u l t i p l i e d i n frequency from 1.175 MHz to 4.7 MHz f o r use i n the E.O.E. and W.O.E. as a second l o c a l o s c i l l a t o r . The second I.F. frequency, 300 kHz, i s the frequency at which the c o r r e l a t o r s operate. Great care must be taken i n both the l o c a l o s c i l l a t o r and cl o c k systems to avoid c r o s s - t a l k , the leakage o f s i g n a l from the East h a l f o f an i n t e r f e r o m e t e r i n t o the West, o r v i c e v e r s a . The s i g n a l - t o - n o i s e r a t i o f o r the output o f a giv e n i n t e r f e r o m e t e r a f t e r an i n t e g r a t i o n p e r i o d o f T i s (see Appendix A2) £ - £ r F W »/S7 a TT EW 73 8 Outputs 8 Outputs 8 Outputs East Binary Branching System Centre Binary Branching System West Binary Branching System to E.O.E, Clock & L.O. F i g u r e 3.6.1: A schematic diagram o f the f i r s t l o c a l o s c i l l a t o r and c l o c k d i s t r i b u t i o n systems. The b l o c k l a b e l l e d "Clock and L.O." i s l o c a t e d at the centre o f the E.W.A. They share c a b l e s going to each o f the B i n a r y Branching Systems. where B i s the bandwidth r„,, i s the c o r r e l a t i o n c o e f f i c i e n t Ew p, i s the mean output a i s the standard d e v i a t i o n o f the output In t h i s case T = N (43 , 2 0 0 ) sec where N i s the number o f spacings and ^ r e p r e s e n t s the s i g n a l - t o - n o i s e r a t i o at a given p o i n t on the map. For y, = a i I r„,, = VJT = 8 . 0 x 1 0 " 7 m -61 db. E W 2 / 2 B V T h i s i s the c o r r e l a t i o n c o e f f i c i e n t r e q u i r e d to produce a d e f l e c -t i o n o f one standard d e v i a t i o n . Leakage at t h i s l e v e l would produce a s i m i l a r o f f s e t on the map. Of course, t h i s i s the upper l i m i t o f t o l e r a b l e leakage. One would p r e f e r -70 db. More-over, i f leakage from an a m p l i f i e d s i g n a l were to f i n d i t s way i n t o the antenna o r the input o f the p r e a m p l i f i e r , t h a t leakage path would have to be f u r t h e r attenuated. The l o c a l o s c i l l a t o r system i s p a r t i c u l a r l y s u s c e p t i b l e to t h i s e f f e c t . S i g n a l l e v e l a t the mixer i s h i g h e r than the input s i g n a l l e v e l by the g a i n o f the p r e a m p l i f i e r , about 30 db. Any path l e a d i n g to the o p p o s i t e p r e a m p l i f i e r i n p u t must have at l e a s t 100 db o f i s o l a t i o n . C o n s i d e r a b l e d i f f i c u l t y with t h i s c r o s s - t a l k problem was experienced d u r i n g e a r l y c o r r e l a t o r experiments. The advantages o f frequency changing are perhaps obvious, but i f t h i s system had been designed to c o r r e l a t e at 22.25 MHz, these c r o s s -t a l k problems might have been insurmountable. In the case of the l o c a l o s c i l l a t o r system, the defence a g a i n s t c r o s s - t a l k has mainly been the use of h y b r i d s p l i t t i n g and f i l t e r i n g . Because of the hybrids, signals can only t r a v e l either towards or away from the source of the binary branching system. The hybrids used in s p l i t t i n g the l o c a l o s c i l l a t o r signal were made from cables and are inherently narrow band. Their e f f e c t i v e bandwidth i s about 10 percent of the centre frequency. They were designed, therefore, at approximately 25 MHz so that they would be e f f e c t -ive at both the signal and l o c a l o s c i l l a t o r frequencies. The res u l t i n g i s o l a t i o n i s s t i l l about 10 db at both these frequencies. Power requirements for the l o c a l o s c i l l a t o r can be calculated from losses and the t o t a l power requirement of the receivers. With 48 receivers, approximately 11 db cable loss, and about 10 db of loss i n f i l t e r s , combiners, etc. the t o t a l requirement i s 38 db more power than i s needed for a single receiver. Each receiver needs about .4 mw to drive the mixers adequately, thereby requiring a source of about 2.5 watts. The clock signal requires a similar power. A block diagram of the system i s shown i n Figures 3.6.2, 3.6.3, and 3.6.4. F i l t e r i n g the L.O. system at strategic points with narrow band f i l t e r s i s the most e f f e c t i v e way of l i m i t i n g cross-talk. There are f i l t e r s at the L.O. port of each correlator u n i t , and there are f i l t e r s at each of the three most s i g n i f i c a n t branches of the binary branching system. (See Figures 3.6.3 and 3.6.4.) Chapter 3.8 discusses the link between the rest of the system and the E.O.E. This link i s also f i l t e r e d . 4.7 Mhz Crystal Osc. T .4 1.175 MHz Filter Clock Output For Centre Section 30 V D.C. 27.25 MHz Crystal Osc. Diplex Combiner 3 - Way Hybrid Splitter East Combined Outputs West L-°» + Clock + D.C. Note: D.C. used for remote amplfiers and F.E.T. switches. All Amplifiers Tuned High Pass Filter L.O. Output For Centre Section 1.175 MHz Termination F i g u r e 3.6.2: Source c i r c u i t r y used to generate and combine l o c a l o s c i l l a t o r (27.25 MHz) and c l o c k s i g n a l s (1.175 MHz). cn 27.25 27.25 MHz MHz Filter From L.O. and Clock Source Circuitry To L.O. Distribution System To Clock Distribution System D.C. F i g u r e 3 . 6 . 3 : C i r c u i t r y used to separate the l o c a l o s c i l l a t o r and c l o c k s i g n a l s at the i n p u t s to the B i n a r y Branching Systems. To Receivers To Delay Line Two Way Filter To F.E.T. Integrate Switch Circuitry From Separator Circuitry From Separator Circuitry Correlator Chassis Figure 3.6.4: The binary branching systems for the L.O. and clock signals. 79 3.7 S i g n a l D i g i t i z i n g , Sampling, and Delay The s i g n a l from the East h a l f o f each i n t e r f e r o m e t e r must be delayed to e q u a l i z e the d e l a y o f the s i g n a l a r r i v i n g from the E.O.E. and the W.O.E. Because the c o r r e l a t o r u n i t s are very c l o s e to the East h a l f o f the i n t e r f e r o m e t e r s , the d e l a y r e q u i r e d i s approximately equal to the s i g n a l t r a v e l time o f the e n t i r e l e n g t h o f a p a r t i c u l a r i n t e r f e r o m e t e r . The type o f d e l a y s e l e c t e d was a d i g i t a l s h i f t r e g i s t e r , the advantages of which are d i s c u s s e d i n chapter 2.1. The simplest system uses o n e - b i t d i g i t i z a t i o n . The s i g n a l - t o - n o i s e degrada-t i o n r e s u l t i n g from o n e - b i t sampling i s d i s c u s s e d i n Appendix A2. The band to be sampled i s the I.F. band o f the r e c e i v e r s , 300 kHz wide and centred at 5 MHz. The sampling theorem i n d i c a t e s t h a t i f the samples are taken at e q u a l l y spaced i n t e r v a l s , at l e a s t ~2Q- a p a r t , t h a t a l l the i n f o r m a t i o n contained i n the s i g n a l i s a l s o c o n t a i n e d i n the samples. In t h i s case, because the band i s not baseband, a p r o v i s o must be added to the above statement o f the sampling theorem. The theorem can be proved h e u r i s t i c a l l y i n a few steps u s i n g F o u r i e r t r a n s f o r m theory. F i g u r e 3.7.1 i l l u s t r a t e s the s i t u a t i o n . Samp-l i n g i n the time domain i s the e q u i v a l e n t o f m u l t i p l y i n g the ^ t s i g n a l to be sampled by a " b e d - o f - n a i l s " f u n c t i o n denoted I I I ( - ) where T i s the sample i n t e r v a l . The F o u r i e r t r a n s f o r m o f I I I ( ^ ) i s I l K f r ) . The e q u i v a l e n t o f m u l t i p l y i n g the s i g n a l by III(£) i n the time domain i s c o n v o l v i n g i t s F o u r i e r t r a n s f o r m i n the frequency domain. The averaged F o u r i e r t r a n s f o r m o f a random process i s i t s power spectrum, S ( f ) . 80 S(f) 1 1 I III(f-T) s(f)*ni(f •?*) h — £ — H Figure 3.7.1: Sampling diagram for a baseband signal. Figure 3.7.2: Sampling diagram for a bandpass signal. I f T = "2g—, then the above c o n v o l u t i o n , I I I ( f T) »S(f) , w i l l be as d e p i c t e d i n F i g u r e 3.7.1. The power spectrum, S ( f ) , can be recovered by low-pass f i l t e r i n g . I f T < , the convolved func-t i o n w i l l o v e r l a p , making a simple r e c o v e r y o f S ( f ) i m p o s s i b l e . B / I f , as d e p i c t e d i n F i g u r e 3.7.2, S.Cf) i s not c e n t r e d at '2, an added r e s t r i c t i o n upon the sampling waveform r e s u l t s . F i g u r e 3.7.2 shows a l i m i t i n g case. Even though T = i f a harmonic o f the sampling frequency i s w i t h i n the range o f f r e q u e n c i e s occupied by S ( f ) , " f o l d i n g " about t h a t frequency w i l l o c cur, and informa-t i o n w i l l be l o s t . By examining a few more cases, the sampling theorem can be r e s t a t e d f o r the more g e n e r a l case. No m u l t i p l e o f the sampling r a t e may l i e between 2f^ and 2 f 2 where f ^ i s the lower frequency c u t o f f , and i s the upper frequency c u t o f f o f the spectrum o f the sampled s i g n a l . The sampling theorem assumes t h a t an accurate r e p r e s e n t a t i o n o f each sample i s r e t a i n e d a f t e r each sampling i n s t a n t . In t h i s case, o n l y the s i g n o f the sampled s i g n a l i s r e t a i n e d . F o r t u n a t e -l y , because the s i g n a l - t o - n o i s e r a t i o i s so low i n the f i r s t p l a c e , not much i n f o r m a t i o n i s l o s t . Furthermore, i t has been shown (7) t h a t some o f the i n f o r m a t i o n can be recovered by sampling at a f a s t e r r a t e than 2B. Based upon the above d i s c u s s i o n , the sample r a t e f o r the 4.8 - 5.2 MHz band was s e l e c t e d to be 1.175 MHz, approximately double the minimum r a t e . The f o u r t h harmonic a c t s e f f e c t i v e l y as a l o c a l o s c i l l a t o r at 4.7 MHz. The r e s u l t i n g band at 300 kHz i s used tp c o r r e l a t e with the analog band at 300 kHz. Measured s p e c t r a o f the sampled output from the r e c e i v e r s i s shown i n 82 F i g u r e s 3.7.3 and 3.7.4. As with any o t h e r l o c a l o s c i l l a t o r , phase c o i n c i d e n c e must be preserved between the two s i d e s o f the i n t e r f e r o m e t e r . A d i s c u s s i o n o f how t h i s i s achieved o c c u r s i n chapter 3.8. Q u a n t i z a t i o n i n t h i s case i s performed by a comparator opera-t i n g as a z e r o - c r o s s i n g d e t e c t o r . The output o f the comparator i s sampled wi t h a D-type o r l a t c h i n g f l i p - f l o p , c a l l e d the sampling f l i p - f l o p . These two o p e r a t i o n s need not be performed i n t h i s o r d e r , but the a l t e r n a t i v e i s to "sample and h o l d " the analog s i g n a l u n t i l i t can be quantized. Once the s i g n a l has been sampled, i t i s s h i f t e d through a s h i f t r e g i s t e r u s i n g the sample p u l s e s as a c l o c k . A d i f f i c u l t y e x i s t s i f a continuous range o f d e l a y s are r e q u i r e d , as they are here. Two c o n t i n u o u s l y a d j u s t a b l e d e l a y taps f o r each d e l a y l i n e are needed. A monostable i s used to p r o v i d e an a d j u s t a b l e phase f o r the c l o c k p u l s e t r i g g e r i n g the l a s t element of the d e l a y l i n e . Two b a s i c connection arrangements are needed to cover the complete range o f d e l a y s . They are shown i n F i g u r e 3.7.5. F i g u r e 3.7.6 shows the d e l a y ranges covered by each connection. A c t u a l l y , the connections used were r a t h e r more complicated, because the f l i p - f l o p used i n the d e l a y l i n e were o l d RTL f l i p -f l o p s which happened to be a v a i l a b l e . The sampling f l i p - f l o p s were D type 7474. A photograph o f the f o u r d e l a y l i n e s needed f o r each c o r r e l a t o r u n i t i s shown i n the photograph o f the e n t i r e c o r r e l a t o r u n i t i n chapter 3.9. The s e t t i n g accuracy and s t a b i l i t y o f the d e l a y l i n e s must F i g u r e 3.7.3: A spectrum o f r e c e i v e r n o i s e a f t e r having been d i g i t i z e d at the one b i t l e v e l and sampled at 1.175 MHz by a sampling f l i p - f l o p . The o r i g i n a l band being sampled i s marked " I . F . Band", and the a c t u a l band used f o r c o r r e l a t i n g i s l a b e l l e d "Quasi Baseband". The sharp " s p i k e s " are harmonics o f the sampling waveform. of •+• MHz 0 .2 .8 1.0 1.2 1.4 1.6 1.8 2.0 F i g u r e 3.7.4: A l a r g e r s c a l e p l o t o f the spectrum shown i n f i g u r e 3.7.3. The band used f o r c o r r e l a t i n g s t a r t s at 150 kHz and ends at 450 kHz. 85 (n-l)*"* 1 element th , n element from th (n-2) element Clock D Q T D Q to correlator from th (n-2)1 element Clock D Q T r> r\ to correlator Figure 3.7.5: Connections used at the ends of a d i g i t a l s h i f t r e g i s t e r l i n e i n order to produce continuously variable, overlapping delay ranges. The blocks marked "At" are monostables with adjustable RC time constants. The elements are D type f l i p - f l o p s . 86 Clock Cycles |* .8510JISQC 0 1 h*— .6838 ^usec I B Figure 3.7.6: The delay ranges covered by each of the connections of the delay l i n e . The minimum delay,is about .15 u.sec. The maximum delay depends upon the length of the s h i f t r e g i s t e r . In t h i s case i t was about 14 |j,sec. be considered i n r e l a t i o n to the bandwidth and phase of the signal respectively. The interferometer i s measuring the autocorrelation function of a signal ( i n the presence of many other signals and noise) from a p a r t i c u l a r point i n the f i e l d of view. Ideally, the delay should be set to the peak of the autocorrelation function for best signal to noise r a t i o . The autocorrelation function i s the Fourier transform of the power spectrum of the signal. For t h i s purpose the power spectrum can be taken as the "rectangular" band pass of the receivers. The autocorrelation function i s then „ / . , s sin TT BAt  C ( A t ) - TtBAt If a l i m i t of 5 percent loss of signal due to delay misalign-ment i s put upon delay errors, C(At) > .95. Solving for At y i e l d s At a .6 y,sec. This i s obviously not a d i f f i c u l t s p e c i f i c a t i o n to meet. The s t a b i l i t y of the delay l i n e determines i n part the phase s t a b i l i t y of the system. At a centre frequency of 300 kHz, one degree of phase corresponds to 9.3 nsec of delay, or approximately 1 percent of a clock cycle. The monostable used to determine the timing of the l a s t stage i n the delay l i n e must, therefore, be stable to within 1 percent. Changes i n the position or phase of the pulses used to clock the s h i f t r e g i s t e r and to sample the analog input signal also af f e c t s the output correspondingly. The temperature dependence of the clock-to-output delay i n the f l i p - f l o p s of the delay l i n e produce the same r e s u l t . Short term " j i t t e r " occurs on a time scale shorter than one integration period. I t could contribute noise to the map i n d i r e c t r e l a t i o n to the amplitude of the " j i t t e r " . In the laboratory tests and i n subsequent tests of prototype delay l i n e s , " j i t t e r " was not found to be a s i g n i f i c a n t problem. Slow changes are less of a problem because the periodic c a l i b r a t i o n removes t h e i r e f f e c t s . 3.8 Elect r o n i c s i n the E.O.E. and the W.O.E. A general outline of the various functions performed i n the E.O.E. and the W.O.E. has been given i n chapter 2.1. These two elements are shared as the West h a l f of each of the interferome-ters of the telescope. They provide the signal for the "analog" part of the 1 b i t by analog correlators. Figure 3.8.1 i s a diagram of the basic layout of the system. Each of the antennas i n Figure 3.8.1 i s a row of seven dipoles amalgamated by the combining networks discussed i n chapter 3.4. Alternate samples are taken with the East-West switch i n alternate positions. The unused antenna at any given time i s kept terminated. Every second pair of samples i s taken with the ^/2 Switch i n alternate positions. The re s u l t i n g cycle of four i s demodulated i n the computer by subtracting, the t h i r d sample from the f i r s t ; the fourth from the second... A photograph of one of the antenna switches i s shown i n Figure 3.8.2. Upon command from the c o n t r o l l e r i n the observatory building the c a l i b r a t i o n switch changes over to the c a l i b r a t i o n signal. 89 Noise Generator Mixer i Calibration Signal First | Local | Oscillator! Phase Lock Frequency i Multiplier ! L.O. Interchange Switch 3oo KHz. F i g u r e 3.8.1: A block diagram o f the equipment i n the E.O.E. A s i m i l a r arrangement e x i s t s f o r the W.O.E. except t h a t o n l y the equipment down to the f i r s t R.F. preamp i s needed on the a c t u a l s i t e . The r e s t i s with the E.O.E. equipment. The East-West Switch i s used to f i l l i n i n t e r l e a v e d spacings. The \/2 switch i s designed to e l i m i n a t e slow b a s e l i n e changes i n the output data. The L.O. interchange switch i s a c t i v a t e d d u r i n g c a l i b r a t i o n s so t h a t f o u r phase quadrants are measured. The output a m p l i f i e r s feed the c a b l e s which d e l i v e r the analog s i g n a l t o a l l the c o r r e l a t o r s i n the system. Both In-phase (I.P.) and Quadrature (QU) s i g n a l s are r e q u i r e d . Figure 3 . 8 . 2 : The V 2 switch. The r o l l of cable i s approximately * /2 long. The phase difference between the two paths i s exactly 180 degrees at 22.250 MHz. U n c o r r e l a t e d n o i s e i s added t o the c a l i b r a t i o n s i g n a l to simulate a c t u a l c o n d i t i o n s and to keep l e v e l s c o n s t a n t . The c o n t r o l l e r a l s o a c t u a t e s the second l o c a l o s c i l l a t o r changeover switch, i n t e r c h a n g i n g in-phase and quadrature o s c i l l a t o r s i g n a l s . A c y c l e o f f o u r i s again used f o r the c a l i b r a t i o n , one at each o f fo u r phases, 0 ° , 180°, 90°, and 270°. They are demodulated i n the computer i n the same way as normal samples to produce a p a i r o f quadrature c a l i b r a t i o n s . T h i s procedure i s d i s c u s s e d more f u l l y i n chapter 4.1. The a p p l i c a t i o n o f the c a l i b r a t i o n s to the raw data i s d i s c u s s e d i n chapter 4.2. • The E.O.E. and the W.O.E. e l e c t r o n i c s perform the same func-t i o n s f o r t h e i r r e s p e c t i v e antennas, but the W.O.E. s e c t i o n i s implemented r a t h e r d i f f e r e n t l y . Most o f the e l e c t r o n i c equipment f o r both p a r t s o f the system i s housed i n a t r a i l e r s i t u a t e d under the E.O.E. The East p a r t w i l l be d e s c r i b e d f i r s t . The three input s i g n a l s are r e q u i r e d , the f i r s t l o c a l o s c i l l a t o r , the c a l i b r a t i o n s i g n a l , and the c l o c k s i g n a l . They are brought i n by cab l e from the b i n a r y branching system i n the a d j o i n i n g a r r a y . The cl o c k and the l o c a l o s c i l l a t o r s i g n a l s are p i c k e d up by a r e s i s t i v e " s n i f f e r " . As a b a r r i e r to c r o s s - t a l k , the s n i f f e r s have about 26 db l o s s . A 10 db d i r e c t i o n a l c o u p l e r i s used to feed c a l i b r a -t i o n s i g n a l to the E.O.E. The l o c a l o s c i l l a t o r at 27.25 MHz must be shared between the E.O.E. and the W.O.E. I t s use f o r the E.O.E. i s s t r a i g h t f o r w a r d . A photograph o f the equipment used to produce t h i s l o c a l o s c i l l a -t o r s i g n a l i s shown i n F i g u r e 3.8.3. F i l t e r i n g and c a r e f u l l a y o u t Figure 3.8.3: The d i s t r i b u t i o n system f o r the f i r s t l o c a l o s c i l l a t o r . Tuned amplifiers and hybrid s p l i t t e r s were used to avoid cross-leakage between inputs of cor r e l a t o r s . The temperature controlled phase s h i f t e r i s i n the upper right corner. 93 techniques were used to avoid introduction of any signals i n the L.O. system which might introduce f a l s e c o r r e l a t i o n . As previously noted, the second l o c a l o s c i l l a t o r at 4.7 MHz must be derived from the d i g i t a l delay l i n e clock signal at 1.175 MHz to preserve phase coherence. A d i g i t a l phase-lock loop i s used to perform t h i s task. The c i r c u i t i s straightforward, and i s shown i n Figure 3.8.4. The receiver used i s one of the standard receivers. A photograph of the second mixers and following quasi baseband amplifiers i s shown i n Figure 3.8.5. The signals from both outer elements are treated the same way at t h i s point. Figure 3.8.6 shows the part of the c a l i b r a t i o n system r e l e -vant to the E.O.E. The system i s controlled by 500 kHz tone bursts sent through the network of cables carrying the signal i t s e l f . The c a l i b r a t i o n system i s e n t i r e l y passive and there are no amplifiers i n the R.F. c i r c u i t . When the c a l i b r a t i o n i s on, the switching signal normally used f o r the East-West switch i s routed to the second l o c a l o s c i l l a t o r interchange switch. The noise source i s a s o l i d state device, a s p e c i a l l y fabricated diode which produces broad-band noise dependent upon the current passing through i t . I t i s surrounded by ins u l a t i o n and kept at a control-led temperature. The s i t u a t i o n for the W.O.E. i s more d i f f i c u l t because i t i s rather remote. It has no mains power, and there was at f i r s t only one, l a t e r two, cables available to run from the E.O.E. to the W.O.E. Consequently, the R.F. signal i s simply preamplified at the s i t e of the W.O.E., and returned at 22.25 MHz to the E.O.E. t.nr MHz * 4 4.7 MHz Tuned Amp Voltage C o n t r o l l e d O s c i l l a t o r Figure 3.8.4: A phase-lock loop used to t r a n s l a t e the 1.175 MHz clock s i g n a l to the required 4.7 MHz second l o c a l o s c i l l a t o r s i g n a l . Quadrature Outputs are r e q u i r e d to produce quadrature p a i r s of s i g n a l s to be c o r r e l a t e d . 95 F i g u r e 3.8.5: The second m i x e r s and o u t p u t a m p l i f i e r s (see f i g u r e 3.8.1). Four o u t p u t s are r e q u i r e d . Each o f the E.O.E. and W.O.E. must produce an i n - p h a s e and q u a d r a t u r e s i g n a l . RF from Antenna Switch C a l i b r a t i o n S i g n a l from C e n t r a l D i s t r i b u t i o n System 4' East-West Antenna Switch S i g n a l F i g u r e .3.8.6: The c a l i b r a t i o n s w i t c h i n g system. The c a l i b r a t i o n s i g n a l along with a 500 kHz tone b u r s t are sent out by the c e n t r a l c o n t r o l l e r each time a c a l i b r a t i o n i s needed. The Pulse Length D i s c r i m i n a t o r accepts " l o n g " and"short" tone b u r s t s f o r "on" and " o f f " r e s p e c t i v e l y . The output of the D i s c r i m i n a t o r switches the r e c e i v e r input to the c a l i b r a t i o n s i g n a l , and d i r e c t s the E a s t -West switching s i g n a l to a c t i v a t e the Second L.O. Interchange Switch shown i n F i g u r e 3.8.1. 97 where i t i s down-converted to 5 MHz, the standard I.F. Neverthe-l e s s , i t i s necessary to r e t a i n a l l switches and c o n t r o l c i r c u i t r y o c c u r i n g b e f o r e the p r e a m p l i f i e r . Switching s i g n a l s , power, and r e t u r n i n g R.F. s i g n a l are a l l on the same c a b l e . F i g u r e 3.8.7 i s a photograph o f the c i r c u i t r y used t o separate the s i g n a l s . Because the c a b l e s c a r r y i n g the r e t u r n i n g R.F. s i g n a l and the c a l i b r a t i o n s i g n a l are strung on the same messenger wire, p r e c a u t i o n s to av o i d leakage o f one s i g n a l i n t o the o t h e r c a b l e must be taken. As noted elsewhere, the c a l i b r a t i o n s i g n a l i s sent down t h i s c a b l e at 11.125 MHz. At the W.O.E. i t i s doubled to 22.250 MHz i n a frequency doubler. The r e s u l t i n g s i g n a l i s attenuated, and added to the u n c o r r e l a t e d component i n the same way as i n the E.O.E. The c o n t r o l c i r c u i t r y f o r the c a l i b r a t i o n i s i d e n t i c a l w i t h t h a t i n the E.O.E. A photograph o f the c a l i b r a -t i o n system f o r the W.O.E. i s shown i n F i g u r e 3.8.8. So f a r , t h e r e has not been any mention o f how the c e n t r a l c o n t r o l l e r s i g n a l s the v a r i o u s switches. As o u t l i n e d i n chapter 3.12, a l l p o s s i b l e c o n t r o l f u n c t i o n s are performed by b i n a r y codes m u l t i p l e x e d onto a few c o n t r o l w ires. F i g u r e 3.8.9 i s a photo-graph o f the switch c o n t r o l l e r . A f t e r each read-out c y c l e and bef o r e the s t a r t o f the next one, the c o n t r o l l e r sends out the antenna switch command which i s r e c o g n i z e d by a decoder. The decoder advances the modulo 4 counter by one, a c t i v a t i n g the ap p r o p r i a t e switches. Normally, the decoder a l s o causes one b u r s t o f 1 kHz tone to be sent to the W.O.E. In o r d e r to synchronize the counter with a s i m i l a r one i n the c o n t r o l l e r , a "synch" code i s sent out i n s t e a d o f the normal switch 9 8 Figure 3.8.7: Separator f i l t e r s f or the W.O.E. cable connection. Switching signals (tone bursts), 22.250 MHz returning R.F., and power for the W.O.E. ele c t r o n i c s are present. Figure 3.8.8: The c a l i b r a t i o n system for the W.O.E. The input signal i s at 11.125 MHz. It i s doubled to 22.250 MHz as explained i n Chapter 3.11. A noise source i n an insulated, temperature controlled box i s also shown. This noise source substitutes uncorrelated noise for the "sky noise" normally received. 3 . 8 . 9 : The switch c o n t r o l l e r . T h i s system i n c o r p o r a t e s a m o d i f i e d v e r s i o n o f one of the standard decoders to a c t i v a t e antenna switches f o r both the E.O.E. and W.O.E. I t a l s o houses the e l e c t r o n i c s f o r producing the tone b u r s t s which c o n t r o l the W.O.E. antenna switches. 101 code to set the counter to the (1, 1) s t a t e . When the counter i s i n the (1, 1) s t a t e , i t causes continuous tone b u r s t s o f 1 kHz to be sent to the W.O.E. u n t i l a 20 kHz r e p l y s i g n a l i s r e t u r n e d to stop the b u r s t s . At the W.O.E. each 1 kHz tone b u r s t advances a s i m i l a r modulo f o u r counter. When t h i s counter reaches the (1, 1) s t a t e a 20 kHz tone b u r s t i s sent to the E.O.E. T h e r e f o r e , when the counter i n the E.O.E. reaches the (1, 1) s t a t e , i t advances the counter i n the W.O.E. to the (1, 1) s t a t e as w e l l , thereby synch-r o n i z i n g i t . The s w i t c h i n g system i n the E.O.E. a l s o sends a r e t u r n p u l s e to the c e n t r a l c o n t r o l l e r each time the (1, 1) s t a t e i s reached. I f t h i s does not correspond to the same s t a t e i n the c o n t r o l l e r , an e r r o r f l a g i s s e t , and logged with the data on computer tape. Before the c a l i b r a t i o n c a b l e was i n s t a l l e d , an attempt was made to compensate f o r the change i n le n g t h o f the c a b l e c a r r y i n g the 22 MHz s i g n a l from the W.O.E. The temperature o f the ca b l e was measured at one p l a c e and used to s h i f t the phase o f the l o c a l o s c i l l a t o r s i g n a l . The phase s h i f t was estimated to be about 3 degrees o f phase per degree C e l c i u s . F i g u r e 3.8.10 i l l u s t r a t e s the method used. A v a r a c t o r diode was used as the c a p a c i t o r i n an RC, 90°, phase s h i f t network. With RC = - ^ f i t n e r a t e of change o f phase with C i s g r e a t e s t . Even a f t e r the c a l i b r a t i o n c a b l e was i n s t a l l e d , t h i s d e v i c e was l e f t i n s e r v i c e because i t tended to make c a l i b r a t i o n outputs e a s i e r to i n t e r p r e t f o r the out e r elements. The c a b l e l o s s encountered by the 22 MHz s i g n a l r e t u r n i n g Temperature Sensor 27. 25 MHz L.O. — Phase * S h i f t e d L.O. F i g u r e 3 .8 .10 : A temperature c o n t r o l l e d phase s h i f t e r f o r the f i r s t l o c a l o s c i l l a t o r . I t u t i l i z e s the v o l t a g e - v a r i a b l e capac i tance of a v a r a c t o r diode i n an RC phase s h i f t e r connected between the emi t t e r and the c o l l e c t o r o f a t r a n s i s t o r . from the W.O.E. i s about 40 db. Rather than a m p l i f y i n g the s i g n a l enough to overcome the l o s s at the W.O.E., s e v e r a l l i n e a m p l i f i e r s were b u i l t and i n s t a l l e d i n the c a b l e . These were designed to amplify the R.F. s i g n a l without a f f e c t i n g any o f the o t h e r s i g n a l s on the l i n e . Since t h i s c a b l e c a r r i e s the s i g n a l at the same frequency as r e c e i v e d by the antennas, care had to be taken to ensure t h a t no s i g n i f i c a n t s i g n a l was being r e c e i v e d from c a b l e leakage. The cabl e was run w e l l below the antenna r e f l e c t i n g screens ( p a r a l l e l w ith the r e f l e c t i n g w i r e s ) . The s i g n a l l e v e l was kept to a minimum c o n s i s t e n t with the s i g n a l - t o - n o i s e r a t i o o f the l i n e a m p l i f i e r s . An experiment was done at the W.O.E. i n which a 22 MHz o s c i l l a t o r s i g n a l was sent down the c a b l e . At the same time the output o f the r e c e i v e r was monitored with a spectrum a n a l y z e r . No d e t e c t a b l e s i g n a l was present while u s i n g o s c i l l a t o r power e q u i v a l e n t to t h a t normally produced at the r e c e i v e r output. T h i s c a b l e i s long enough t h a t a d i f f e r e n t i a l l o s s o c c u r s a c r o s s the frequency band. T h i s was compensated f o r by an o f f -s e t t i n g slope i n t r o d u c e d i n t o one of the f r o n t end tuned stages . 104 3.9 Correlator Design For each interferometer i n the system there are two corre-l a t o r s . The correlators multiply the signals from the two halves of the interferometer, and integrate the r e s u l t for a specified time. Discussion elsewhere has led to the conclusion that the correlator be of the 1 b i t by analog variety: that i s that one of the signals be quantized into a series of 1's and O's correspond-i n g to the sign of the input voltage. Such a signal can be sampled and stored i n d i g i t a l s h i f t r e g i s t e r . The t h e o r e t i c a l properties of t h i s form of correlator are discussed i n Appendix A2. The m u l t i p l i e r i s reduced to a device which e f f e c t i v e l y a l t e r s the sign of the analog signal at each sample i n t e r v a l according to the usual rule f o r the m u l t i p l i c a t i o n of signs. The r e s u l t i n g signal w i l l have a constant or dc component proportional to the cross-correlation c o e f f i c i e n t of the two signals. Specifications for the correlator are not very stringent, which i s fortunate since approximately 200 units were required. Centre Frequency 300 kHz minimum ^ Bandwidth 300 kHz minimum denoted "quasi-baseband" Output Fluctuation Level 1 a = 150 mv Output D r i f t « 1 o i n 20 sec. Output Noise « 1 a Spurious Correlation < -100 db referred to the input Dynamic Range > 115 CT Integration Time 1 - 40 sec. Gain - automatic gain control - adjustable set point Analog input Impedance » 50A D i g i t a l Input TTL l o g i c l e v e l s , 0 - 5 V o l t s A d i s c u s s i o n o f the s p e c i f i c a t i o n s f o l l o w s : The c e n t r e frequency was chosen to be an easy one f o r which to b u i l d a c o r r e l a t o r . The bandwidth i s an o v e r a l l system para-meter and has been d i s c u s s e d elsewhere. Note that near-zero f r e q u e n c i e s are to be avoided because o f the d i f f i c u l t y o f f i l t e r i n g the s i g n a l from D.C. power l i n e s t o the e l e c t r o n i c s . S i g n a l s at zero frequency, i t s e l f , are d i f f i c u l t to manage because o f d r i f t problems. The output f l u c t u a t i o n l e v e l (as determined by system tempe-r a t u r e , not c o r r e l a t o r n o ise) was set at approximately 150 mv so t h a t output d r i f t and n o i s e do not c o n t r i b u t e s i g n i f i c a n t l y to th s i g n a l q u a n t i z a t i o n n o i s e : The output s i g n a l i s quantized with l e v e l s spaced 40 mv apart. The a l l o w a b l e l e v e l o f spurious c o r r e l a t i o n has been d i s c u s -sed i n chapter 3.6. S i m i l a r arguments apply here. The dynamic range has been c a l c u l a t e d on the b a s i s o f a c e r t a i n percentage o f the f l u x o f CASS A. I t has been shown t h a t the minimum d e t e c t a b l e f l u x at the 5 a l e v e l i s g i v e n approximately by A O 1475 . . c AS = -j^-— j an sky = 5 a I f 15% o f the f l u x o f CASS A i s allowed f o r , t h a t i s , i f the c o r r e l a t o r must cope with 7500 jansky, then g i v e n T = 20 sec, AS = 33- jansky and 106 S -vf*- m 23 at the 5 a l e v e l . AS The r e q u i r e d dynamic range i s , t h e r e f o r e , 115 a f o r T = 20 sec. For T — 10 sec. , the requirement i s 80 cr. The dynamic range and the i n t e g r a t i o n time must be co n s i d e r e d t o g e t h e r along with the d i g i t i z i n g l e v e l o f the a n a l o g - t o - d i g i t a l c o n v e r t e r . S i n c e the l a t t e r i s f i x e d f o r o t h e r reasons, T can always be made s h o r t e r to i n c r e a s e dynamic range w i t h i n the a v a i l a b l e range o f c o r r e l a t o r g a i n . This i s , however, done at the expense o f r e c o r d i n g more data. The o v e r a l l p r e - c o r r e l a t i o n g a i n i s set by the s i z e o f the quasi-baseband s i g n a l emanating from the E.O.E. T h i s s i g n a l t r a v e l s down a 5 0 A c o a x i a l c a b l e and i s " s n i f f e d o f f " at each c o r r e l a t o r u n i t by a hig h input-impedance a m p l i f i e r . Because o f cab l e l o s s , the ga i n o f t h i s a m p l i f i e r must be a d j u s t a b l e . I t was made a u t o m a t i c a l l y a d j u s t a b l e to account f o r p o s s i b l e changes i n i n p u t s i g n a l l e v e l with temperature. T h i s c o r r e l a t o r c o u l d have been r e a l i z e d a number o f ways. Two techniques were t r i e d . The f i r s t one was a very simple d e s i g n . I t i s i l l u s t r a t e d i n F i g u r e 3 .9 .1 i n b l o c k diagram form. D i f f i c u l t y with t h i s c o r r e l a t o r was encountered i n s e v e r a l areas. The s w i t c h i n g response o f the F.E.T.'s was not q u i t e f a s t enough to operate at the upper end o f the band. Large s w i t c h i n g t r a n s i e n t s were c o n t r i b u t i n g to a " n o i s y " output. Because of the l a r g e s w i t c h i n g v o l t a g e s needed to d r i v e the F.E.T.'s, there was d i f f i c u l t y e l i m i n a t i n g c r o s s - l e a k a g e o f the d i g i t a l s i g n a l i n t o 10 7 F i g u r e 3.9.1: I n i t i a l C o r r e l a t o r Design 108 the analog one. Also, t h i s c i r c u i t i s not balanced. Changes i n the F.E.T.'s r e s u l t i n an output o f f s e t or possibly d i f f e r e n t gains for p o s i t i v e and negative c o r r e l a t i o n c o e f f i c i e n t s . The m u l t i p l i e r part of the second correlator design uses a well known c i r c u i t , a combination of emitter-coupled t r a n s i s t o r stages. I t i s now used i n many forms i n integrated c i r c u i t s as signal m u l t i p l i e r s , modulators, etc. The basic c i r c u i t i s shown in Figure 3.9.2. The 1 b i t input i s v ; the analog one, v. . The c i r c u i t sw' i n i s doubly balanced i n the sense that not only does the output, vC2"" v ci» n o t d e P e n d upon the t o t a l bias current, I, but also i t does not depend upon the bias difference, ^ - I ^ . This i s true f o r the c i r c u i t only i f v" has an average duty cycle of 50%. Let I, 1^, 1^, ^ci? I C 2 ' b e bias currents as shown i n Figure 3.9.2. Then, X l + X2 I = —= = i c l 2 c2. and I - I , + I 2 Therefore I „ - I . ss 0 regardless of the dc values of I, I„ , and cc c l 1 Note that i f the top t r a n s i s t o r s were used i n a l i n e a r mode, that the above i s s t i l l true. The c i r c u i t , however, would s t i l l be sensitive to changes i n the bias of the upper bases. P o s i t i v e Supply Negative Supply; F i g u r e 3.9.2: B a s i c m u l t i p l i e r c i r c u i t . The c r o s s -l i n k e d , e m i t t e r coupled p a i r s p r o v i d e c a n c e l l a t i o n o f even harmonics. I t i s a l s o doubly balanced. The bottom d i f f e r e n t i a l p a i r has the d i f f e r e n t i a l a m p l i f i e r ' well-known p r o p e r t i e s o f c a n c e l l a t i o n o f even harmonics. The r e s i s t o r s , R g, g i v e the l i n e a r p a r t a wide dynamic range. Using the n o t a t i o n t h a t majescules correspond to b i a s , and minuscules, to s i g n a l s , the f o l l o w i n g t h r e e equations apply to F i g u r e 3.9.2. 1 " ^ 1 + ^ 1 + Xe2 + ^ 2 v i n = ( W - ( V 2 + V 2 ) + V W W " R e ( I e 2 + i e 2 ) I + i * I ( e m ( V l + v l ) + l ) where m . kT/q. e e o ^ Since the c i r c u i t i s balanced, I „ = I and V„ » V_ e l e2 1 2 and v i n - v l " v 2 + R ( i e l - i e 2 ) Combining the above equations r e s u l t s i n £mAv I ^ + i = I ( — r — ) where Av = v,, - v„ e l e l „ mAv 1 2 1+e I „ + i _ = I ( — 1 . ) e2 e2 ^ mAv 1+e i i s i - i = i t a n h ( m A v ) where i i a i - i e l e2 2 e l e2 a l s o , from above v. = Av + R A i xn e For the case where R g = 0, the above two equations can be solved e x p l i c i t l y . A i = I t a n M ^ ^ ) F i g u r e 3.9.3 shows t h i s r e l a t i o n s h i p . For v ^ n very l a r g e , the d i f f e r e n t i a l p a i r switches c u r r e n t from one sid e to the. o t h e r . T h i s i s what happens f o r the two d i f f e r e n F i g u r e 3.9.3: Output s i g n a l c u r r e n t versus input s i g n a l v o l t a g e f o r R = 0. . 112 t i a l p a i r s i n the top p a r t of the c i r c u i t . I f i s s m a l l , s e r i e s expansion f o r tanh can be t r u n c a t e d . v. 3 V- 3 5,,. 5 A* T (m i n m v m m v i n * a i s M 2 " 24 + 240 " * " ; As mentioned above, A i c o n t a i n s no even terms. The slope o f the l i n e a r p a r t can be decreased ( c o r r e s p o n d i n g l y i n c r e a s i n g i t s extension) by i n c l u d i n g R^. Using o n l y the l i n e a r term, Ai = I ( m ( v . -R A i ) ) 2. i n e S o l v i n g f o r A i Ai = i n 2 - + R ml e I f R g » , the slope i s c o n t r o l l e d by R g, and decreased by the r a t i o 2/ml. For R = 100A, t h i s r a t i o i s approximately R e .03. e T h i s d esign o f s i g n a l m u l t i p l i e r was the one adopted. Because o f the d i f f i c u l t i e s o f b u i l d i n g s t a b l e d.c. ampli-f i e r s , i t i s d e s i r a b l e t h a t the output o f the s i g n a l m u l t i p l i e r not be d.c. Phase s w i t c h i n g i s used to t h i s end i n many d e v i c e s and systems. In t h i s case, phase s w i t c h i n g i s very easy to implement. The 1 b i t s i g n a l a r r i v i n g from the d i g i t a l d e l a y system i s " e x c l u s i v e or'ed" with the switch frequency as i n F i g u r e 3.9.4. The r e s u l t i n g phase modulation causes c o r r e l a t e d s i g n a l s to appear as a square wave at the switch frequency, u s u a l l y from Square Wave • \ 1 D i g i t a l To C o r r e l a t o r Input F i g u r e 3.9.4: E x c l u s i v e OR phase switch f o r the d i g i t a l s i d e o f the c o r r e l a t o r . F i g u r e 3.9.5: A d i f f e r e n t i a l i n t e g r a t o r and phase switch demodulator. The switches are d r i v e n by the same s i g n a l t h a t d r i v e s the modulator o f f i g u r e 3.9.4. 114 200 to 2000 Hz. In t h i s case about 200 Hz i s used so that several harmonics can e a s i l y be saved i n the subsequent f i l t e r i n g . An operational amplifier i s used at the output c o l l e c t o r s of the m u l t i p l i e r . I t has the dual function of re j e c t i n g the common mode voltage at the c o l l e c t o r s as well as amplifying the correlated component. Its limited bandwidth also rejects high frequency noise components present at the c o l l e c t o r s . This i s followed by a f i l t e r and a phase demodulator. The phase demodulator i s an integrated c i r c u i t containing four MOS FET switches. The two outputs of the demodulator must be subtracted. A f u l l d i f f e r e n t i a l integrator i s shown i n Figure 3.9.5. In order to keep the c i r c u i t as small as possible, the capacitor on the non-inverting input has been dropped. The inputs are a l t e r n a t e l y switched between input signal and ground. When the signal i s on the inverting input the output of an id e a l operational amplifier would be When the signal i s on the non-inverting input, no input current i s drawn. The feedback works to minimize Av, causing v i to appear on the inverting input as well. Therefore, T where T i s the integrating period. o T v. dt + v. i n I i n . o The r e s u l t i n g output has some high frequency input signal added to i t during h a l f of the phase switch cycle. This i s not 115 a problem because i t has been arranged to read ( i . e . d i g i t i z e ) the output o n l y d u r i n g the p a r t of the phase switch c y c l e d u r i n g which the i n t e g r a t o r i n p u t s i g n a l i s not p r e s e n t . The i n t e g r a t o r c i r c u i t i s the o n l y one s u b j e c t to d.c. d r i f t . The i n p u t o f f s e t v o l t a g e s and c u r r e n t s f o r the o p e r a t i o n a l ampli-f i e r used, a 741, are a f u n c t i o n of temperature. T y p i c a l l y , they are 3. ^ V / / C and 50 pA/°C r e s p e c t i v e l y . Output d r i f t , as a r e s u l t , i s AS v S - i - Av At + 1 Ai At. o In t h i s case C « 6.8 u,f, and R = 100 KA, g i v i n g AE v m .235 mv/o c o One would expect a temperature change of not more than 20°C d u r i n g an o b s e r v a t i o n , sending E to 4.7 mv. T h e r e f o r e , the g a i n o must be ad j u s t e d so t h a t a , » 4.7 mv. out At the end o f each i n t e g r a t i o n p e r i o d , the output of the i n t e g r a t o r i s d i g i t i z e d , and the c a p a c i t o r i s d i s c h a r g e d u s i n g an FET as a switch. A s e l f - b i a s i n g FET c i r c u i t i s used as a m u l t i -p l e x switch f o r the outputs o f the i n t e g r a t o r s . The " i n t e g r a t e and dump" scheme i s used because i n t e r f e r e n c e and o t h e r t r a n s i e n t s a f f e c t no more than one output sample. A smoothing c i r c u i t with a time constant comparable to the i n t e g r a -t i o n p e r i o d would take s e v e r a l time c o n s t a n t s to s e t t l e down a f t e r a l a r g e t r a n s i e n t . 1 1 6 A more complete d i s c u s s i o n o f the read-out c y c l e can be found i n the s e c t i o n on c o n t r o l o f the t e l e s c o p e . The analog input s i g n a l i s pr o v i d e d by an a m p l i f i e r which has a d i f f e r e n t i a l output, shown i n o u t l i n e i n F i g u r e 3.9.6. I t has approximately a 20 db AGC range, much more than i s needed f o r the task. Each c o r r e l a t o r u n i t r e q u i r e s e i g h t c o r r e l a t o r s . The E.O.E. and W.O.E. each produce an in-phase and quadrature s i g n a l . A l s o , because each u n i t s e r v i c e s two halve s o f an i n t e r f e r o m e t e r , there are two one b i t s i g n a l s . The one b i t s i g n a l s are each delayed to match the de l a y o f the s i g n a l s a r r i v i n g from the E.O.E. and the W.O.E. The s i t u a t i o n i s i l l u s t r a t e d i n F i g u r e 3.9.7. A photograph o f an e n t i r e assembled c o r r e l a t o r u n i t i s shown i n F i g u r e 3.9.8. I t s e r v i c e s two i n t e r f e r o m e t e r p a i r s . T h e r e f o r e , t h e r e are two r e c e i v e r s , f o u r d e l a y l i n e s , f o u r analog a m p l i f i e r s , e i g h t c o r r e l a t o r s i n t h i s u n i t . There i s a l s o one o f the standard decoder boards f o r use d u r i n g readout. 117 Input Amplifier F i g u r e 3 . 9 . 6 : A hig h input-impedance video a m p l i f i e r c i r c u i t used f o r " s n i f f i n g " the analog s i g n a l from the E.O.E. and the W.O.E. t> 1 1 8 Analog E.O.E, W.O.E. D i g i t a l •Long East<C_, fc Short / L o ng West<" ^ S h o r t IP QU - IP QU X X X X X X X X Figure 3.9.7: A t a b l e showing which s i g n a l s are to be c o r r e l a t e d . (X - c o r r e l a t e d , blank -not c o r r e l a t e d ) . 1 1 9 F i g u r e 3.9 .8 : An assembled c o r r e l a t o r u n i t . Lower l e f t : D i r e c t i o n a l c o u p l e r s Middle l e f t : R eceivers Top middle: Delay l i n e s Bottom middle: Analog Input A m p l i f i e r Top r i g h t : C o r r e l a t o r s Bottom R i g h t : Decoder Board 120 3.10 Developing the Prototype I n t e r f e r o m e t e r and T e s t i n g  Assembled C o r r e l a t o r s C o n s i d e r a b l e e f f o r t was expended to make sure t h a t as many design i m p e r f e c t i o n s as p o s s i b l e were c o r r e c t e d i n the p rototype stage. A s o p h i s t i c a t e d l a b o r a t o r y bench system was e s t a b l i s h e d to t r y to simulate a c t u a l c o n d i t i o n s i n the f i e l d as w e l l as to measure the o v e r a l l performance s p e c i f i c a t i o n s o f the system. Even though each o f the components of the system may be o p e r a t i n g s a t i s f a c t o r i l y on i t s own, t o g e t h e r , they may i n t e r a c t to cause problems with the system as a whole. A b r i e f d e s c r i p t i o n o f the t e s t s w i l l be given here but the d e t a i l s r e q u i r e lengthy d i s c u s -s i o n , and are l e f t to Appendix A7. As an example of a p o t e n t i a l d e f e c t t h a t was a meliorated at t h i s stage, f i l t e r s had to be i n s t a l l e d i n D.C. power d i s t r i b u t i o n l i n e s t o stop the 200 Hz phase s w i t c h i n g s i g n a l from l e a k i n g i n t o the s i g n a l l i n e s . Such leakage causes a f a l s e c o r r e l a t i o n s i g n a l to appear at the output. Once the p r o t o t y p e c o r r e l a t o r u n i t had passed these t e s t s , an i n t e r f e r o m e t e r was set up at s e v e r a l d i f f e r e n t spacings. S p e c i a l antenna phasing networks were b u i l t so that the elements were d i r e c t e d r i g h t at Cass A. Again, a few more problems developed and were c o r r e c t e d . Of course much of the d e s i g n o f the e l e c t r o -n i c s f o r the E.O.E. and the W.O.E. was a l s o t e s t e d at t h i s time. Other l a b o r a t o r y t e s t s were conducted as w e l l . One o f the fundamental and most d i f f i c u l t t e s t s f o r a c o r r e l a t o r system to pass i s long term r e j e c t i o n o f " c r o s s - t a l k " o r unintended leakage o f c o r r e l a t e d s i g n a l s . The l e v e l of the c r o s s - t a l k must be 121 s u f f i c i e n t l y low t h a t i t cannot be d e t e c t e d a f t e r an i n t e g r a t i o n time e q u i v a l e n t to the l e n g t h of time r e q u i r e d to produce a f u l l survey. A f t e r s a t i s f a c t o r y performance was achieved, the d e c i s i o n to go i n t o " p r o d u c t i o n " was made. I t was sometimes necessary to chance s t a r t i n g the p r o d u c t i o n of some p a r t s b e f o r e t e s t s were r e a l l y complete. F o r t u n a t e l y , t h i s d i d not r e s u l t i n any major mishaps. Even so, d e l a y s t o t a l l i n g about one year were encountered i n j u s t g e t t i n g p r i n t e d c i r c u i t boards f a b r i c a t e d . A few more minor d e l a y s were a l s o encountered i n o t h e r areas o f c o n s t r u c t i o n . A f t e r the v a r i o u s c i r c u i t boards became a v a i l a b l e , they were t e s t e d s e p a r a t e l y . Unwisely, the i n t e g r a t e d c i r c u i t s used had not been checked i n d i v i d u a l l y . Many had to be r e p l a c e d , e s p e c i a l l y 741 o p e r a t i o n a l a m p l i f i e r s and RTL f l i p - f l o p s . Then each c o r r e -l a t o r u n i t was assembled and t e s t e d i n the l a b o r a t o r y bench system b u i l t f o r the p r o t o t y p e . The d e l a y tap on the d i g i t a l d e l a y was setup to correspond to the p o s i t i o n o f the p a r t i c u l a r c o r r e l a t o r u n i t i n the system. The analog d e l a y , c o n s i s t i n g o f r o l l s o f RG58 c a b l e s i m i l a r to t h a t used i n the a r r a y , was a d j u s t e d a c c o r d i n g l y . With an i n t e g r a t i o n p e r i o d o f 2 seconds, the output was recorded i n nine d i f f e r e n t s t a t e s . A t y p i c a l r e c o r d i s shown i n F i g u r e 3.10.1. The f i r s t t e s t was the response to u n c o r r e l a t e d i n p u t s . T h i s checks f o r spurious c o r r e l a t i o n o r o f f s e t s , as w e l l as producing a b a s e l i n e . An in-phase broad-band c o r r e l a t e d s i g n a l was then a p p l i e d . The corresponding output i s a measure of g a i n and o v e r a l l response. Then, three c o r r e l a t e d s i g n a l s at d i f f e -CNJ CM A. 0 a 4-1 3 O u o 4J ca o u at N +J 3 a c HICO XI 01 C 0) <s 60 1 a> •o •o cd o o u m N CO S cy § <u <T 60 CN 01 • X) CM CM O N CO § 11 0> u in 60 CM 0) • -a CM CM O NJ 0) 0) VD 60 CM CU • XI CM CM O CO N 01 S «>' S M <r oi CM XI # CM O CM Oi CO CO XI CO N 0) N 01 c 01 SO) 01 Ctf 01 u Xi u 60 60 1 60 m o> 01 XI ai CM X) ' CM XJ cd X3 0 • • o u CM O CM o u O 01 CM O CM « N . - - ~ _ — 01 u u o o t F i g u r e 3.10.1: An output from a bench t e s t o f one of the c o r r e l a t o r u n i t s . Such a t e s t was administered to a l l c o r r e l a t o r s as they were b u i l t . The type o f input s i g n a l a p p l i e d i s shown f o r each time s l o t . 123 r e n t f r e q u e n c i e s from the frequency s y n t h e s i z e r were a p p l i e d . The f o u r t e s t s were operated with a 90 degree phase s h i f t i n the l o c a l o s c i l l a t o r . The c o r r e l a t o r s were r e j e c t e d i f any of the quadrature set produced a d e f l e c t i o n g r e a t e r than 10 per c e n t o f the c o r r e s -ponding in-phase s e t . 3.11 Design o f C a l i b r a t i o n System The i d e a l c a l i b r a t i o n would not i n t e r f e r e w i t h o b s e r v a t i o n s . i I t would i n j e c t the c a l i b r a t i o n s i g n a l i n such a way as to t r a v e l the same path as the r e a l s i g n a l . I t would a l s o have the same s p e c t r a l c h a r a c t e r i s t i c s , and s i m i l a r s t r e n g t h . The r e s u l t i n g s i g n a l - t o - n o i s e r a t i o f o r the c a l i b r a t i o n should be much h i g h e r than that o f the s i g n a l i t s e l f . Moreover, the s i g n a l i n j e c t e d should have a well-known, s t a b l e amplitude and phase. T h i s t e l e s c o p e c o n s i s t s o f about one hundred i n t e r f e r o m e t e r s a l l o p e r a t i n g at once. The system i s p h y s i c a l l y d i s t r i b u t e d , and sub j e c t to changes o f environment (such as, f o r example, tempera-t u r e g r a d i e n t ) across i t . In o r d e r to i n j e c t the s i g n a l as c l o s e to the " f r o n t end" as p o s s i b l e , the c a l i b r a t i o n system must be d i s t r i b u t e d as w e l l . T h e r e f o r e , i t must f i r s t o f a l l be funda-m e n t a l l y much l e s s s u b j e c t to these changes than the o b s e r v i n g system i t s e l f . Two designs were c o n s i d e r e d and t r i e d . The f i r s t was an o s c i l l a t o r on the top o f a nearby h i l l attached to a d i p o l e antenna. The p o s i t i o n o f the o s c i l l a t o r was a c c u r a t e l y surveyed so t h a t the d i s t a n c e to each o f the elements o f each i n t e r f e r o m e t e r i s well-known. The o s c i l l a t o r i t s e l f was powered 124 by b a t t e r i e s , and was remotely c o n t r o l l e d by r a d i o so t h a t i t c o u l d be turned on and o f f at w i l l . T h i s system has the disadvantage t h a t the c a l i b r a t i o n s i g n a l had to be added to the r e a l s i g n a l . T h i s means t h a t a f i t to nearby output p o i n t s i s needed to s u b t r a c t the s i g n a l p a r t from the c a l i b r a t i o n p a r t of the output d e f l e c t i o n . A l s o , t h e r e was the p o s s i b i l i t y t h a t r e f l e c t i o n s from the surrounding h i l l s o r even the ionosphere might produce erroneous r e s u l t s . The second design was a b i n a r y branching c a b l e system. In f a c t , both systems were used si m u l t a n e o u s l y i n e a r l y stages of b u i l d i n g the t e l e s c o p e . A block diagram o f the f i n a l c a l i b r a t i o n system i s shown i n F i g u r e 3.11.1. About h a l f o f the c a b l e came from p a r t o f the feed s t r u c t u r e of the 22 MHz t e l e s c o p e , and the o t h e r h a l f was added. As i s obvious from the s t r u c t u r e , the s i g n a l path l e n g t h from the c e n t r a l p o i n t ( l o c a t e d at the E.O.E.) to any o f the outputs i s approximately equal. There are a p p r o x i -mately 6.5 km of c a b l e i n the c a l i b r a t i o n system.. One of the d i f f i c u l t i e s i n b u i l d i n g such a system i s t h a t i f a l l the c a b l e s are i n c l o s e p r o x i m i t y as they thread back and f o r t h through the antenna a r r a y , then c a b l e s c a r r y i n g l a r g e s i g n a l s near the bottom o f the b i n a r y branching system w i l l induce c r o s s - t a l k s i g n a l s i n the c a b l e s c a r r y i n g weak s i g n a l s . The c r o s s -t a l k s i g n a l s w i l l add random phases and amplitudes to the f i n a l d e l i v e r e d c a l i b r a t i o n s i g n a l s . To overcome t h i s problem some o f the c a b l e s c a r r y i n g strong s i g n a l s were strung i n separate hangers about s i x i n c h e s away from the main c a b l e bundle. A l s o , as shown i n the diagram, the powerful s i g n a l s emanating from the power a m p l i f i e r at the E.O.E. are at h a l f the o b s e r v i n g frequency. To Di reef Zona./ Couf/ers in B.W. A. 8 Outputs 8 Outputs 8 Outputs To Receiver Co-/. /np«.t t t i t i i i i East Binary Branching System West Binary Branching System i i i t l i l i -zxas-o MHz 1 22.2SoMHz \ l/V.O.E. II.I2S MHz \ To Receiver \ \ Ca./. Inpu.t V I CCL It bra. fi'or\ Con fro I 11. US MHz Source i S o o K H z B«.r*t G e n e r a for //.U<T M H z . //.ns MHz B.o.a F i g u r e 3.11.1: A block diagram o f the c a l i b r a t i o n system. The d e t a i l s o f the E.O.E. and W.O.E. C a l . Sw i t c h i n g system are i n chapter 3 . 8 . There are phase-matched frequency d o u b l e r s at the W.O.E. and at the c e n t r e o f the main ar r a y . A f u r t h e r c r o s s - t a l k problem e x i s t f o r the W.O.E. Because down-conversion to the 5 MHz I.F. frequen cy does not occur u n t i l the s i g n a l from the W.O.E. reaches the E.O.E. , the p o s s i b i l i t y e x i s t s f o r c r o s s - t a l k between the cable c a r r y i n g the c a l i b r a t i o n s i g n a l to the W.O.E. and the r e t u r n i n g R.F. s i g n a l . Again the same p r e c a u t i o n s were taken. The v o l t a g e doublers r e q u i r e at l e a s t a 0 dbm s i g n a l to ope-r a t e e f f e c t i v e l y . T h i s s e t s a lower l i m i t t o the amount of power r e q u i r e d . T a k i n g i n t o account the c a b l e l o s s i n f r o n t o f the do u b l e r s , the power requirement f o r the c a l i b r a t i o n i n p u t s i g n a l i s about 1 watt. T h i s s i g n a l i s p r o v i d e d by a power a m p l i f i e r l o c a t e d i n the E.O.E. I t i s , o f course, important t h a t the l e v e l o f second harmonic from t h i s a m p l i f i e r be low enough t h a t leakage of the second harmonic i n t o the c a b l e s d i r e c t l y f e e d i n g c a l i b r a -t i o n s i g n a l t o the c o r r e l a t o r u n i t s i s much s m a l l e r than the c a l i b r a t i o n s i g n a l i t s e l f . The frequency doublers were equipped with bandpass f i l t e r s on both input and output. The inp u t f i l t e r r e j e c t s any remaining second harmonic; the output f i l t e r does not pass the fundamental frequency. I t i s u s e f u l at t h i s p o i n t to d i s c u s s j u s t what e r r o r s temperature g r a d i e n t s across the v a l l e y w i l l produce i n the c a l i -b r a t i o n . N o t i c e , by the way, t h a t a f t e r the c a l i b r a t i o n s i g n a l i s s p l i t f o r the f i r s t time t h a t no a c t i v e elements are used. Th( o n l y semiconductor components are the frequency doublers. They were phase matched and t h e i r temperature c o e f f i c i e n t o f phase i s about 1 degree f o r a 10°C change i n temperature. 127 A measurement was made o f the change i n e l e c t r i c a l l e n g t h o f the RG-8 polyfoam cable used i n the c a l i b r a t i o n system and was found to be -67 ppm/°C. Since each l e g o f the system i s about 1400 m long, the r e s u l t i n g phase e r r o r f o r a 1°C change o f tempe-r a t u r e f o r one l e g over another i s 3.1 degrees. I t i s not easy to estimate the temperature g r a d i e n t s across the length o f the a r r a y f o r a l l p o s s i b l e weather c o n d i t i o n s . The c a b l e s are not s h i e l d e d from s u n l i g h t , and ve r y l a r g e temperature g r a d i e n t s of the c a b l e can be expected when the sun i s s h i n i n g . F o r t u n a t e l y , o b s e r v a t i o n s never need to take p l a c e when the sun i s s h i n i n g . Otherwise, one expects two o t h e r types o f c o n d i t i o n s , cloudy o r c l e a r n i g h t s . On cloudy n i g h t s the c a b l e s w i l l be at a i r temperature. Unless the a i r i s u n u s u a l l y s t i l l one expects t h a t the c a b l e s w i l l be a l l at the same temperature w i t h i n a few degrees c e n t i g r a d e . On c l e a r n i g h t s t h e r e w i l l be c o n s i d e r a b l e r a d i a t i o n c o o l i n g , but, because the whole c a b l e system i s exposed to the c l e a r sky the temperature g r a d i e n t should be s m a l l . With r e s p e c t to the above, t h e r e f o r e , t h i s system seems to s a t i s f y the standards o f s t a b i l i t y f o r phase r e q u i r e d f o r a c a l i -b r a t i o n system. As f a r as amplitude i s concerned, the s t a b i l i t y depends upon the constancy o f the s i g n a l i n p u t , and upon the l o s s -temperature r e l a t i o n s h i p o f the c a b l e . The power a m p l i f i e r which p r o v i d e s the s i g n a l has an AGC loop. The d e t e c t o r diode upon which the gain " s e t - p o i n t " depends i s i n s u l a t e d from i t s surround-i n g s , and kept i n a t e m p e r a t u r e - c o n t r o l l e d box. Furthermore, u n l i k e much o f the e l e c t r o n i c equipment, the a m p l i f i e r i s i n s i d e an equipment t r a i l e r maintained a t approximately constant temperature. A measurement o f the peak-to-peak f l u c t u a t i o n s o f 128 output o f the a m p l i f i e r over a 12 hour p e r i o d with an R.F. power meter shows l e s s than .1 db v a r i a t i o n . A measurement o f o u t s i d e a i r temperature d u r i n g o b s e r v i n g i s used to compensate f o r v a r i a t i o n o f the c a b l e l o s s as a f u n c t i o n o f temperature. The i n j e c t i o n o f the c a l i b r a t i o n s i g n a l i n t o the system w i l l now be d e s c r i b e d . As p o i n t e d out e a r l i e r , i t i s to advantage to i n j e c t the s i g n a l as c l o s e to the f r o n t ends o f each o f the i n t e r f e r o m e t e r elements as p o s s i b l e . A l s o , i t i s d e s i r a b l e to " t u r n o f f " the s i g n a l from the sky while the c a l i b r a t i o n i s being done but to maintain the o v e r a l l s i g n a l l e v e l as i t was d u r i n g o b s e r v a t i o n s . In o t h e r words, d u r i n g c a l i b r a t i o n an u n c o r r e l a t e d s i g n a l component i s r e q u i r e d as w e l l as a c o r r e l a t e d component. P r o v i s i o n of an u n c o r r e l a t e d n o i s e source f o r each h a l f o f each i n t e r f e r o m e t e r might have been a problem had i t not been f o r the f a c t t h a t a l l the i n t e r f e r o m e t e r s share t h e i r West halv e s between two antennas. S i g n a l s from these two antennas are switched o f f and r e p l a c e d with outputs from a noise, generator (see chapter 3.8). The s i g n a l from the sky serves as an u n c o r r e l a t e d n o i s e source f o r the East h a l v e s . For the 96 East h a l v e s a l l t h a t i s r e q u i r e d i s a way of c o u p l i n g a small c o r r e l a t e d component o f s i g n a l i n t o the system. The o n l y disadvantage o f t h i s technique i s t h a t , d u r i n g the p e r i o d s o f strong i n t e r f e r e n c e , the incoming s i g n a l can s a t u r a t e one h a l f o f each i n t e r f e r o m e t e r . Because these i n t e r f e r e n c e s i g n a l s are not c o r r e l a t e d , they do not have as much of an e f f e c t as might be expected. But s h o r t b u r s t s o f i n t e r f e r e n c e f o r c e the r e c e i v e r s i n t o complete s a t u r a t i o n , g i v i n g 129 the impression t h a t something i s s p o r a d i c a l l y wrong with the system. One o f the uses o f the c a l i b r a t i o n system i s to be able to t e l l t h a t a l l c a b l e connections, e t c . , are i n t a c t . U n f o r t u n a t e l y , i t d i d not seem p r a c t i c a l to i n c l u d e the antennas, themselves, or p a r t o f t h e i r f e e d s t r u c t u r e i n the c a l i b r a t i o n loop. I t would have r e q u i r e d c o u p l i n g i n t o each d i p o l e , a procedure r e q u i r i n g a great d e a l o f e x t r a equipment. The c o u p l i n g i s done by means o f a very simple d i r e c t i o n a l c o u p l e r . The design i s s i m i l a r to th a t used at microwave f r e q u e n c i e s i n waveguide (see F i g u r e 3.11.2), but implemented with c a b l e s . I t i s necessary t h a t the c o u p l i n g be d i r e c t i o n a l because c a l i b r a t i o n s i g n a l s t r a v e l l i n g towards that antenna would f i n d t h e i r way i n t o nearby elements, c a u s i n g i n t e r -f e r e n c e i n nearby i n t e r f e r o m e t e r s . The c a l i b r a t i o n system must be operated by the master c o n t r o l system i n the o b s e r v a t o r y b u i l d i n g . The system used f o r most othe r s w i t c h i n g f u n c t i o n s ( u s i n g m u l t i p l e x e d codes f o r each func-t i o n ) was not used here c h i e f l y because i t does extend to the W.O.E. The source o f c a l i b r a t i o n s i g n a l i s a c r y s t a l o s c i l l a t o r , i n the o b s e r v a t o r y b u i l d i n g i n the master c o n t r o l rack. The c r o s s -over switches i n the W.O.E. and the E.O.E. are a c t i v a t e d by low frequency (500 kHz) tone b u r s t s sent down the c a l i b r a t i o n system i t s e l f . A l s o , the l o c a l o s c i l l a t o r i s switched from "in-phase" to "quadrature" by t h i s method. T h i s has been d i s c u s s e d i n chapter 3.8. One o f the most time consuming t a s k s i n v o l v e d with the c a l i -b r a t i o n system i s measurement o f the output amplitudes and phases. 1 2 0 CAL AV RF /A/ . RGS8 X 44 .OUT TO RCVR SOJU X . OUT To- /zcvfit F i g u r e 3.11.2: A dual d i r e c t i o n a l c o u p l e r made from RG58 c o a x i a l c a b l e to operate at 22.250 MHz. C o u p l i n g i s about 15 db; d i r e c t i v i t y , about 30 db. The c a p a c i t o r s are a l l 25 p f . These measurements are c r u c i a l , and must be repeated every time a major a l t e r a t i o n i s made. One must a l s o be extremely c a r e f u l not to a l t e r phase paths by i n s e r t i n g s l i g h t l y d i f f e r e n t l e ngths o f ca b l e o r d i f f e r e n t k i n d s o f adaptors. For t h i s reason a master diagram was made showing every p h y s i c a l l y removeable component, e s p e c i a l l y the small ones. A l s o , a l l the connectors were marked so t h a t p i e c e s removed t e m p o r a r i l y c o u l d be r e p l a c e d . Amplitudes a r e , o f course, much e a s i e r to measure than phases. A Hewlett-Packard R.F. power meter was used. In or d e r to accomp-l i s h t h i s measurement the c a l i b r a t i o n s i g n a l power had to be i n c r e a s e d g r e a t l y . Because the system (beyond the frequency d o u b l i n g stage) i s l i n e a r and p a s s i v e , the i n c r e a s e , produced by removing a t t e n u a t o r s a f t e r the doublers o r by a power a m p l i f i e r , d i d not a f f e c t the r e l a t i v e measurements. In two se t s o f such measurements made about 9% months a p a r t , there was an o v e r a l l l e v e l change o f about 1.0 db with a s c a t t e r o f .09 db. Since the c a l i b r a t i o n i s not an absolute one, t h i s l e v e l o f s c a t t e r i s q u i t e a c c e p t a b l e . Phase measurements are another matter. U l t i m a t e l y , the phase o f the c a l i b r a t i o n s i g n a l i n j e c t e d i n t o the East h a l f o f each i n t e r f e r o m e t e r must be known with r e s p e c t to t h a t i n t o the West h a l f (one of the shared elements). However, s i n c e i t i s almost i m p o s s i b l e to have both together at the same p o i n t , some method must be d e v i s e d f o r measuring them at a d i s t a n c e . Two methods have been d e v i s e d f o r t h i s purpose. The f i r s t , c a l l e d the Extended Probe method i s i l l u s t r a t e d i n F i g u r e 3.11.3. Two phase measurements with a Vector Voltmeter are r e q u i r e d . The Vector Vector Voltmeter Voltmeter ref. ref 0 I, b o.) t Osc. F i g u r e 3.11.3: The "extended probe" method o f measuring phases. -s— S i g n a l a.) t S i g n a l hi F i g u r e 3.11.4: The " c h a i n i n g " method o f measuring phases. two ends o f 1^, the unknown, cannot be brought together; otherwise, the problem would be t r i v i a l . A c a b l e 1 2, o f unknown l e n g t h , i s a l s o r e q u i r e d . The o s c i l -l a t o r s i g n a l i s s p l i t as i n F i g u r e 3.11.3 p a r t a ) , and the ends o f 1^ and l£ are a l s o connected. The r e s u l t i n g phase measurement i s ( a l l moduli are with r e s p e c t to 360 degrees) 9 a = Mod ( l a + 1 ) where 1^ i s the e l e c t r i c a l l e n g t h o f 1^ i n degrees ±2 i s the e l e c t r i c a l l e n g t h o f 1^ i n degrees 9^ i s the Vector Voltmeter r e a d i n g i n degrees The second measurement i s , as shown i n F i g u r e 3.11.3 p a r t b ) , e 2 = Mod ( l a - i 2 ) where 1^, 1 2 , 9 2 are as above. The r e q u i r e d phase i s Z » Mod (1^) S o l v i n g i a + i 2 - k T + e a y i e l d s 21^ « ( k ^ k ^ 360 + 9^ + 6 2 1^ — 1 2 — k 2 + 9 2 where k^, k 2 are i n t e g e r s . 9 1+9„ k.+k„ Mod ( 2 f o r Mod ( 2 d ) = 0 9+9 k +k Mod ( 1 2 2 ) + 180 f o r Mod ( 1 2 2 ) - 180 There i s a 180 degree ambiguity which can be r e s o l v e d i f the 134 process i s repeated with a half-wave l e n g t h o f c a b l e i n c l u d e d with 1^. T h i s method i s very u s e f u l i f a wander lead o f unknown length i s to be used, or i f the d i s t a n c e i s too f a r f o r a wander l e a d , but two c a b l e s e x i s t going to the same d e s t i n a t i o n . The second method, c a l l e d the C h a i n i n g method, because i t resembles s u r v e y i n g , i s d e p i c t e d i n F i g u r e 3.11.4. I t i s u s e f u l when there are a number of outputs f o r which mutual phase measurements are needed. Two such outputs are shown i n the f i g u r e . The f i r s t measurement a) y i e l d s 9 a = Mod ( 1 2 + i 3 - i a ) I ky. — k„ 9,. — 9 p the second one b) y i e l d s S. 1 0 - 1. = 0 — - + 2 1 ~ 2 2 9 2 - Mod ( l a + 1 3 - 1 2) S o l v i n g , as above, y i e l d s 8 - 6 k - k Mod (-^-g—-) f o r Mod (—±— -) » 0 9 1 " 62 k l " k 2 Mod (~^-s -) f o r Mod (—=-= -) « 180 Again, a 180 degree ambiguity e x i s t s , but, i n the case o f most o f the b i n a r y branching system, the outputs were c l o s e r to being in-phase r a t h e r than out-of-phase. The East p a r t o f the system was measured u s i n g the C h a i n i n g method. Cables normally used to tr a n s m i t s i g n a l s to the c o r r e l a -t o r s were used as "^^ 'S." f o r each s e c t i o n . Because measure-ments can o n l y be made from one output to the next, the accuracy decreases the f u r t h e r the output i s from the West end. By 135 c h a i n i n g from one end to the o t h e r , and then " c l o s i n g the loop" by c h a i n i n g back again, the loop e r r o r can be d i s t r i b u t e d evenly among a l l the outputs. The Extended Probe method was used to measure the phase o f the W.O.E. output r e l a t i v e to the E.O.E. output. Numerous oth e r m i s c e l l a n e o u s phase measurement must be made b e f o r e a l l o f the phases can be r e l a t e d . There i s much o p p o r t u n i t y f o r c o n f u s i o n i n r e l a t i n g the phases. The f i n a l measurements are entered i n t o a f i l e i n the computer f o r access by the r e d u c t i o n program. Because the c a l i b r a t i o n s i g n a l s are n o i s y , they w i l l i n c r e a s e the standard d e v i a t i o n s o f the measurements. I t i s n a t u r a l l y d e s i r a b l e to keep t h i s source o f n o i s e as small as p o s s i b l e without j e o p a r d i z i n g the " d r i f t - c o r r e c t i n g " e f f e c t s o f the c a l i -b r a t i o n . Three random processes are i n v o l v e d . There are: a) the measurement o f the s i g n a l , b) measurement o f the c a l i b r a -t i o n and c) the process d e s c r i b i n g the change o f i n s t r u m e n t a l parameters, namely net g a i n and phase o f f s e t of each i n t e r f e r o m e -t e r . Of course, they are not independent; the t h i r d p rocess a f f e c t s the f i r s t two. The measurement o f the c a l i b r a t i o n i s used to estimate the change o f parameters, and then to apply c o r r e c t i o n s to the measurement of the s i g n a l . I f an estimate o f the frequency spectrum o f the g a i n and phase changes i s a v a i l a b l e , then the minimum r a t e o f c a l i b r a t i o n s can be d e r i v e d a c c o r d i n g to sampling theory. However, because the c a l i b r a t i o n s are n o i s y e s t i m a t e s ( i n t h i s case about h a l f as n o i s y as the d a t a ) , i t i s necessary to c a l i b r a t e redundantly. In t h i s case, the phase and g a i n changes are r e l a t e d to 136 temperature changes. A rough estimate o f the time between changes i s about o n e - h a l f hour. A c c o r d i n g l y , c a l i b r a t i o n s are done about every 320 sec. , and du r i n g the p r o c e s s i n g a running mean o f 5 c a l i b r a t i o n samples i s formed. 3.12 System C o n t r o l and Data Logging O b v i o u s l y , a system such as the one d e s c r i b e d r e q u i r e s some k i n d o f a c o n t r o l l e r to c o o r d i n a t e data c o l l e c t i o n and to produce m u l t i f a r i o u s s w i t c h i n g s i g n a l s . Today, one would most l i k e l y purchase a small microprocessor f o r the job, but e a r l i e r , b u i l d i n g a s p e c i a l purpose d i g i t a l c o n t r o l l e r seemed the e a s i e s t way to accomplish the task at the time (1973). The q u a n t i t y o f data to be logged d u r i n g each o b s e r v a t i o n more o r l e s s r e q u i r e d the use o f magnetic tape. Paper tape was the o n l y o t h e r a l t e r n a t i v e a v a i l a b l e at the time, but was imprac-t i c a l because o f the amount o f data to be handled. P a r t o f the PDP-9 computer used f o r c o n t r o l l i n g the 1420 MHz s y n t h e s i s t e l e s -cope at D.R.A.O. was used on a time s h a r i n g b a s i s . Data was logged, s i m u l t a n e o u s l y with o p e r a t i n g the o t h e r t e l e s c o p e , on two magnetic tape u n i t s attached to the computer. T h i s scheme i m p l i e d , however, t h a t " i n t e r r u p t s " t o s e r v i c e the 22 MHz system would have to be on a low p r i o r i t y b a s i s . Consequently, the c o n t r o l l e r had to be designed with i n t e r i m storage c a p a c i t y f o r data. The b a s i c requirement o f the c o n t r o l l e r i s to gather and st o r e the outputs o f the c o r r e l a t o r u n i t s a f t e r each i n t e g r a t i o n p e r i o d . The c o r r e l a t o r u n i t s are spread out over the l e n g t h o f 137 the a r r a y , so t h a t i t was i m p r a c t i c a l to have a separate wire c a r r y each output to a s i n g l e l o c a t i o n . An e i g h t - w i r e "data bus" system was b u i l t ( f o r the e i g h t c o r r e l a t o r s i n each c o r r e l a t o r u n i t ) . Each u n i t i s assigned a "d e v i c e code", and an "address bus" a l s o connects a l l the c o r r e l a t o r u n i t s to the c o n t r o l l e r ( F i g u r e 3.12.1). At the end o f an i n t e g r a t i o n p e r i o d the c o n t r o l l e r sends out the d e v i c e codes, one a f t e r the ot h e r . Each c o r r e l a t o r u n i t c o n t a i n s a decoder c i r c u i t which r e c o g n i z e s i t s own code and switches the outputs o f the e i g h t c o r r e l a t o r s on to the "data bus". These outputs are d i g i t i z e d i n t u r n and s t o r e d i n the b u f f e r memory. The d e v i c e codes and the "address bus" can a l s o be used to t r i g g e r o t h e r f u n c t i o n s . As d i s c u s s e d i n Chapter 3.8, they are a l s o used to c o n t r o l the antenna s w i t c h i n g i n the E.O.E. and W.O.E. Because o f the p o s s i b i l i t y o f the c o n t r o l l e r and i t s asso-c i a t e d s w i t c h i n g s i g n a l s producing s p u r i o u s R.F. s i g n a l s , the system was designed to be completely q u i e t d u r i n g the i n t e g r a t i o n p e r i o d . The l e n g t h o f the readout p e r i o d was determined by the speed o f the FET bus switches, and by the time r e q u i r e d f o r the analog output v o l t a g e s t o s e t t l e . The r e s u l t i s t h a t a l l the d a t a i s c o l l e c t e d i n about 30 msec. Once the data i s i n the b u f f e r memory, i t can be t r a n s f e r r e d to the computer asynchronously over the next i n t e g r a t i o n p e r i o d . Address Bus C Corr. Corr, Unit Unit • 0 6 c Data Bus Calibration Signal Generator FT Line Drivers and Optical Isolators 5 T T Address Generator 4 Controller Calibration Control Address Bus Line Receivers and Amplifiers Data Bus Multiplex Switch 8 - Bit A/D Converter Data Storage Buffer Interrupt "Done" Flag to Computer Interface Combined Calibration and Control Signal Data Bus Level Converters and Line Drivers F i g u r e 2 . 1 2 . 1 E.O.E. Antenna Control "7 Optical Isolators > Data to Computer , Interface H i 139 The data i s s t o r e d i n 8 - b i t b y t e s , and two bytes packed i n t o a s i n g l e 1 6 - b i t word. The computer i s an 1 8 - b i t machine. The oth e r two b i t s are used to s t o r e the s t a t e o f the antenna switch and the s t a t e o f the phase-antiphase switch. The c o n t r o l l e r a l s o produces t i m i n g p u l s e s f o r the c a l i b r a -t i o n system. Every 32 i n t e g r a t i o n p e r i o d s the system goes through a c a l i b r a t i o n c y c l e . The d e t a i l s of the c o n s t r u c t i o n o f the c a l i b r a t i o n system have a l r e a d y been d i s c u s s e d . 1 4 0 Chapter Four  Data Reduction and Computation of Results 4.1 Data Reduction - Pre Map Stage As outlined e a r l i e r data i s collected on a PDP-9 computer which simultaneously c o l l e c t s data for the 1420 MHz Spectral Synthesis Telescope. The data i s logged on "DECTAPE". An assembly language routine was written to f i t i n with the online "foreground" operation of the computer i n "foreground background" mode. The observing program demodulates the phase switching, keeps track of data flowing from the East-West switching of the interferometers, checks f o r ce r t a i n errors i n the control c i r c u i t r y of the t e l e s -cope, as well as packing the data and logging i t on magnetic tape. With the generous help of CH. Costain, the program was made to f i t i n with the logging program for the 1420 MHz Synthesis Teles-cope. The data from one 12-hour period of observation occupies approximately 2 data tapes. After each observation period the data i s transferred v i a an interface to a data disk on the PDP-11' computer. Because the data i s acquired faster than i t can be reduced, i t i s then stored on magnetic tape. It i s on t h i s computer that a l l the actual map-making i s done. The computer i s a PDP-11/45 equipped with three 1.2 x 10 word disks, one terminal, a magtape drive, and an e l e c t r o s t a t i c p r i n t e r / p l o t t e r . Before the inversion of the u-v plane can begin, a number of 141 other operations must be performed on the data. Apart from such things as gridding and scaling, display of the data i s very import-ant. A great deal of time can be wasted operating on data c o l l e c t -ed with f a u l t y equipment. It i s convenient to coin a few terms here for use i n t h i s chapter. Because the data i s coll e c t e d more or less on an r, 9 grid i n the u-v plane, a string of data l y i n g along a l i n e of constant 9 i s c a l l e d a " r a d i a l " . A s t r i n g of data l y i n g along a l i n e of constant r i s ca l l e d a " v i s i b i l i t y " . A string of data coll e c t e d at the same time i s ca l l e d a "dump". The following steps i n the production of data ready to be inverted w i l l be dealt with i n turn. A. Stripping c a l i b r a t i o n s from the data. The structure and theory of the c a l i b r a t i o n system i s de s c r i -bed i n chapter 3.11. The c a l i b r a t i o n i s applied every 16th dump. It replaces the data for that dump ( i . e . i s not added to the data). Therefore, to avoid a system of holes i n the u-v plane shaped l i k e bent spokes of a wheel, these holes must be f i l l e d with interpola-ted data. Otherwise, the e f f e c t on the synthesized beam would be similar. The c a l i b r a t i o n s are stripped out of the data and stored i n a separate f i l e on disk. The re s u l t i n g holes are replaced with a 6 point Lagrangian interpolation. Of course, near the edges of the u-v plane some of these points w i l l be independent. This w i l l contribute some error to the interpolated value, but the eff e c t of the r e g u l a r i t y of the holes every 16th r a d i a l w i l l be masked. B. Smoothing the c a l i b r a t i o n data. The question of the signal-to-noise r a t i o of ca l i b r a t i o n s and i t s e f f e c t on the data i s studied i n chapter 3.11. In short, the c a l i b r a t i o n s should be as free of noise as possible, yet at the same time f u l l y represent the fluctuations of system parame-ters that they are meant to remove. Measurements were made of the time scale of the fluctuations by keeping the c a l i b r a t i o n system on continuously. These fluctuations are c h i e f l y the r e s u l t of thermal variat i o n s i n the ele c t r o n i c s . The time i n t e r v a l between ca l i b r a t i o n s i s approximately 5.33 minutes. The thermal variations are estimated to be on a time scale of about 25 minutes. Accord-ingly, the c a l i b r a t i o n data was smoothed with a 5 point running average. C. Display of c a l i b r a t i o n data. The most valuable tool for determining the state of the system has turned out to be the plots of the c a l i b r a t i o n data. As has been emphasized i n other places, t h i s system i s a very large one for one person to maintain. Once a f a u l t has been spotted, i t s t i l l can take many hours before i t i s located exactly and repair-ed, e s p e c i a l l y under adverse weather conditions. Some examples of c a l i b r a t i o n plots are shown i n Figure 4.1.1. Altogether, of course, 192 such plots are required for each observation. When the system i s operating each day, these plots provide a once a day look at a l l outputs. (This i s approximately the "turn around time" for repairing f a u l t s anyway.) Combining information on shared components of the system with sets of fa u l t y outputs, i t i s possible to t e l l i n which general area the fa u l t l i e s . F i g u r e 4 . 1 . 1 : P l o t s o f the c a l i b r a t i o n s f o r e i g h t c o r r e l a t o r s . The t i c k marks on the h o r i z o n t a l a x i s represent one hour i n t e r v a l s . The s o l i d l i n e s are outputs o f the in-phase c o r r e l a t o r ; the dot ted l i n e s , o f the quadrature one. 144 D. Calculation of correction c o e f f i c i e n t s . The algorithm for c a l c u l a t i n g the correction c o e f f i c i e n t s has been worked out i n chapter 4.2. Phase and amplitude measurements of the c a l i b r a t i o n signals are stored in a f i l e on disk. These serve as a reference upon which the c a l i b r a t i o n depends. These and the f i l e of c a l i b r a t i o n data are input to t h i s program. The output i s a f i l e of c o e f f i c i e n t s l a t e r used on the data. In other words, the application of the c a l i b r a t i o n to the data i s carried as far as possible here "so as not to be done r e p e t i t i v e l y l a t e r on. E. Application of correction c o e f f i c i e n t s to the data. Again the exact algorithm for t h i s operation i s derived elsewhere. Because the c a l i b r a t i o n c o e f f i c i e n t s are available only every 16 dumps, an interpolation i s also required here. This time a six point Newtonian Interpolation (for equally-spaced data) i s employed. This precision i s c e r t a i n l y much more than necessary, but because the amount of ca l c u l a t i o n i s t r i v i a l l y small, six points was used. F. Gridding data on a r a d i a l grid. Because one of the outer elements of each interferometer i s not on an East-West l i n e , one dump of data does not constitute a r a d i a l . Also, only every second interferometer spacing i s present on a p a r t i c u l a r dump. That i s , the even spacings w i l l be present on one dump; the odd ones, on the adjacent one. Carried with each dump i s a short "data status block" which has in i t , among other things, the sidereal time of observation and an indicator as to whether the even or odd spacings are being measured. The gridding system used i s as follows: The adjacent dumps 145 are merged to form one r a d i a l . Points on the outer part of the u-v plane are gridded to the request r a d i a l . This system may seem somewhat coarse but because the sampling rate i s higher than the minimum the small random s h i f t s introduced by the gridding process w i l l not normally be noticed. G. Optional averaging of adjacent r a d i a l s . Depending upon how many spacings are to be used for a given map, i t may be he l p f u l to average adjacent r a d i a l s so that time to compute maps i s reduced. H. Display and editing of data. About 80 percent of the observations obtained were rejected either at the time the c a l i b r a t i o n p l o t s were made or at t h i s point i n the processing. Most of the obvious instrumental f a i l u r e s were caught e a r l i e r , but other causes, c h i e f l y interference, make the data unsuitable. Also, more subtle problems with the equipment have been ironed out as a r e s u l t of being able to inspect the data. The programs involved transpose the r a d i a l s to v i s i b i l i t i e s , and plot them on the e l e c t r o s t a t i c p l o t t e r . Figure 4.1.2 shows examples of these plots for representative spacings. Also, a program was written to display data on an o s c i l l o s -cope, and to perform various operations. One i s able to delete interference, scale, smooth, subtract or replace f i t s to the data, etc. These operations can be performed on one record at a time or on sets of records. I. S h i f t i n g the observational phase centre. The ultimate diagnostic tools for making the system operation-SPACING 61 COR It II AT I ON UNIT 15 60 5 g 58 a l are strong radio sources. Unfortunately, the strongest one of a l l , CASS A, dominates the v i s i b i l i t i e s , but, because i t i s most-ly outside the f i e l d of view, i t s fringes are d i f f i c u l t to use for t h i s purpose. Also, ionospheric r e f r a c t i o n when CASS A i s at lower culmination can cause large random phase and amplitude fluctuations. Using programs developed for t h i s purpose, the v i s i b i l i t y phase corresponding to a p a r t i c u l a r assumed position can be calcu-lated. The phases of the v i s i b i l i t i e s are rotated so as to stop the fringes on a p a r t i c u l a r radio source. This rotation forces t h i s source to the centre of the map. I f i t i s a point source, the v i s i b i l i t y w i l l i d e a l l y be constant, and the quadrature compo-nent w i l l be zero. Of course, considerable f i l t e r i n g of fringes of other sources, i s necessary p a r t i c u l a r l y CASS A, before t h i s e f f e c t can be observed. 3C61.1, one of the strongest sources i n the f i e l d , was used f o r t h i s purpose. J. Source elimination. This program has been used to remove CASS A, and, hopefully, some of i t s deleterious e f f e c t s from the map. The method i s to s h i f t the source to the centre of the map, and then to high-pass f i l t e r each v i s i b i l i t y . Of course, sources at a given declination do not have constant fringe rates. In other words, some sources near the cutoff distance from the centre of the shifted map w i l l be affected at some hour angle ranges, but not at others. 148 4.2 Applying C a l i b r a t i o n Signals to Interferometer Data Even though an interferometer may be b u i l t to r i g i d s p e c i f i -cations, imperfections almost always arise which cause gains and phase paths to vary. Periodic c a l i b r a t i o n of the system, using f a i r l y simple standards, i s necessary to maintain the best possible accuracy and dynamic range of the instrument. The stand-ards required are a signal of known amplitude and phase, and an accurate means of providing a 90 degree phase rotation of the signal. Normally, there are one or more in-phase and quadrature outputs to the system. Ideally, the quadrature outputs measure components of the signal shifted by exactly 90 degrees. However, i n p r a c t i c a l systems t h i s s h i f t i s d i f f i c u l t to achieve accurately. Moreover, i f the above mentioned 90 degree phase rotation i s available, i t i s not necessary to have signal components i n actual quadrature. A degradation i n signal-to-noise r a t i o w i l l result from any departure from quadrature, but the degradation w i l l be proportional only to cos (0Q) (where 0Q. i s the angle between the in-phase signal components and the quasi-quadrature components -see Figure 4.2.1.). The following i s a procedure f o r correcting the above-mentioned e f f e c t s . (Refer to Figure 4.2.1). 1. Inject a signal with known phase and inte n s i t y , l e t A s» amplitude of c a l . signal 6 ss phase of c a l . signal Record outputs IP0, QU0 149 Cal, Signal Figure 4.2.1: A schematic diagram of a cor r e l a t i o n interferometer showing the aspects pertinent to c a l i b r a t i o n . 150 2. R o t a t e s i g n a l phase by 90 degrees a t a l l f r e q u e n c i e s Record o u t p u t s IP90, QU90 Because IP0 and IP90 a r e i n a c c u r a t e q u a d r a t u r e , t h e y can be r e p r e s e n t e d by t h e complex number ACP=IP0 + IP90 S i m i l a r l y , f o r IP90 and QU90 ASP=QU90 + QU0 The a c t u a l s i g n a l d e l i v e r e d t o t h e system i s CS = A e 1 9 T h e r e f o r e , a complex g a i n f o r each o u t p u t can be c a l c u l a -t e d i n t h e normal way. GC » ACP/CS = ot e l A 0 c c GS m ASP/CS = o/ se l A (*s where a i s the g a i n o f the i n - p h a s e system or i s t h e g a i n o f t h e q u a d r a t u r e system h<f>c i s t h e phase o f f s e t o f t h e i n - p h a s e system A 0 s i s t h e phase o f f s e t o f the q u a d r a t u r e system Note t h a t A$ - Ac* = 0 ^ - 90 (see f i g u r e 4.2.1) C S Q Now t h e s e f a c t o r s GC and GS may be used to c o r r e c t a r b i t r a r y o u t p u t d a t a . L e t TC, TS be c o r r e c t o u t p u t s and TCP, TSP be measured o u t p u t s . TC = B cos 0 TS = B s i n 0 TCP = or B c o s ( 0 + A 0 ) 151 TSP = a Bsin ( 0 + A 0 ) s s Rewrite as cos A 0 c - sin A 0 c sin A0 cos A0 s s Solve to y i e l d T , T g T c TCP/ c T s T S P / c s. 1 det TCP cos A0 TSP sin A0 s v c TSP cos A0 or s -TCP sin A0 s Cf where det = cos ( A 0 - A® ) c s In terms of GC, GS TCP Re(GS) TC TS :Re(GC.GS?) TSP Im(GC) TSP Re(GC) -TCP Im(GS) Four c o e f f i c i e n t s are found = Re (GS) / Re (GC.CS*) A 2 = Im (GC) / Re (GC.CS*) A 3 s Re (GC) / Re (Gc.CS*) A 4 a Im (GS) / Re (GC.GS*) A^ represents the* amount of in-phase information i n TCP; A^ " " '* " quadrature information i n TCP; A^ " '* " " quadrature information i n TSP; A. " " " " in-phase information i n TSP; 152 and GC.GS* represents the loss of amplitude due to • 0^ not being 90 degrees. Under perfect conditions A l = A 3 = 1 a n d A 2 = A 4 = 0. These quantities, although the most useful for computing, can also be represented i n terms of four more e a s i l y understood ones. Note that Re (GC.GS*) = a> a cos (A0 - Art ) c s c s and that A„ ce sin A0 <L C C tan A0 A_ ci cos A0 u v c 5 c c s i m i l a r l y A 4 tan A0 s -Also, Cf cos A0 A. = C 3 ca a cos (A0 - A0 ) c s c s therefore cos A0 a = c s A_ cos (A0 - A0 ) 3 c s S i m i l a r l y cos A0 s a = c A^ cos ( A 0 c - A0 g) The following parameters summarize the performance of the system. Gain = cf c 153 a c ~ . „ ,. In-phase System G a i n G a i n R a t i o = ——5—, i n r ~—=— »• — Quadrature System Gam a g Phase = A0 c Phase o f f s e t from Quadrature = A 0 c - A 0 g The t h e o r y o u t l i n e d here was used as d i s c u s s e d i n c h a p t e r 4.1 t o a p p l y t h e c a l i b r a t i o n measurements t o t h e map. 154 4.3 The S e n s i t i v i t y of Fringe Phase to Baseline Errors V i s i b i l i t y functions are an e a s i l y interpreted, d i r e c t output from each of the interferometers making up a synthesis telescope. Hence they are a useful tool for recognizing blunders i n the instrumentation or i n the computer reduction programs. Under id e a l conditions they can also be used to correct for small errors i n the geometrical parameters of the interferometers. It would be desi-rable to have several strong, well separated, unresolved sources in the f i e l d of view so that the v i s i b i l i t y function can be ana-lyzed without regard to amplitude changes. However, near the centre of the North Polar Cap there i s only one strong radio source, and i t i s s t i l l much weaker than the residual from CASS A. Also, ionospheric variations can change the apparent positions of sources, thereby making the analysis of the v i s i b i l i t y d i f f i c u l t . Therefore, as outlined i n chapter 3.2, the approach has been to make careful measurements of the baselines independently. What follows i s a discussion of the s e n s i t i v i t y of the fringe phase to changes i n geometrical parameters. The re s u l t translates surveying errors into phase errors. The fringe phase i s as outlined i n chapter 4.4: ; 0 = 2TT^ (sin6 sind + cos6 cosd cos(H-h)) where D i s the length of the interferometer 1s baseline X i s the wavelength d i s the angle between the North C e l e s t i a l Pole and the a x i a l plane of the interferometer h i s the angle between the meridian plane and the baseline (measure with same sign as hour angle) 155 H i s the hour angle of the source 6 i s the declination of the source The parameters of the baseline are the three coordinates, D, d, and h and the wavelength, \. Also, since h appears only i n H-h, an error i n h i s equivalent to an hour angle or time error. Further-more, the equation i s isomorphic with respect to interchanging d and 6. Errors i n each of these parameters w i l l be considered i n turn. a) Error i n h ( e f f e c t i v e l y a time error) Let be the error. Instead of the above v i s i b i l i t y , the observed one w i l l be -0 ' » 2TT^ ( s i n 6 sind + cos 6 cosd c o s ( H - ( h - e h ) ) Let A 0 be the phase error produced by e^. A 0 = 0 - 0 ' = 2TT^ cos6 cosd cos(H-h) - c o s ( H - h + e h ) Since e, « 1 cos e, s s l , s in e, sse, h h n h and A 0 ^ 2TT^ cos 6 cosd sin (H-h) b) Error i n d ( e f f e c t i v e l y a declination error) Let « d be the error. Using analysis similar to that i n a), A 0 ^ SB 2TT^ {sin6 cosd - cos6 sind c o s ( H - h ) } J c) Error i n D Let e Q be the error. Again using similar analysis eD A 0 D ss 2TT-y fsin6 sind + cos6 cosd cos(H-h)} 156 d) Error i n X With E X as the error: E X D A0^ «a - y 2TT^ {sin6 sind + cos6 cosd cos(H-h) } Four special cases are of i n t e r e s t : Case 1. Telescope i n the equatorial plane (d = 0) A0 h - e h 2TT5 cos5 sin(H-h) cosinusoidal (for E-W baselines) i n H A0^ a e d 2TT^ sin6 constant E D A0 D = 2TT-y cos6 cos (H-h) sinusoidal (for E-W baselines) i n H E X D A < * X = ~T 2 T T X " c o s ^ cos(H-h) Case 2. Small d approximation (d « 1) A0^ = 2TT^ cos 6 sin (H-h) A0. = 2TTY e. {sin5-d cos6 cos(H-h) } d - "T,X e d D -y fd 6 +E X D A0^ = - y 2TTT- fd sin6 + cos6 cos(H-h) } A0, i s the same as i n Case 1. A0, has a sinusoidal term added • h d to i t which i s s i g n i f i c a n t for low declinations. A0 D and A0^ have a constant term added to them which i s s i g n i f i c a n t for high d e c l i -nations. CASE 3. Small d and high declination approximation. Let p be polar distance (p « 1). A0^ = 2TT^ p sin(H-h) 157 A 0 d = 2 T T^ e d {l - .pd cos (H-h),} very small ~ 2 t t\ ed A 0 D = 2TT-y fd + p cos(H-h)} e> n A 0 X = -y 2TT£ fd + p cos(H-h)} Case 3 applies to the 22 MHz telescope. The error i n assuming p (polar distance) = cos6 i s a maximum at the edge of the f i e l d of view, and i s .007 for 6 = 70°. The inner 98 baselines are i n the equatorial plane where d « 0. Figures 4.3.1 - 4.3.4 show plots of the above phase errors. They generally increase towards the edge of the map. Using Table 3.2.1, ed and eh can be taken as about one arc minute; eD, as about .3m. The maximum frequency error i s determined by the accuracy of the e f f e c t i v e centre of the I.F. band i n the receivers. This i s about 3 kHz. Table 4.3.1 shows the r e s u l t i n g worst case phase errors. The average phase errors are very much smaller. Apart from A 0 d , they have an i n s i g n i f i c a n t e f f e c t on the synthesized beam. A 0 d i s a borderline case. I t i s independent of declination and or hour angle for a given baseline. This makes i t i n d i s t i n g u i s h -able from an instrumental phase o f f s e t . Of a l l the types of phase errors, t h i s i s the easiest to detect and remove. A l l that i s needed i s the average phase of the v i s i b i l i t y for a point source over a period of observing. Two sources, 3C61.1 and 3C390.3, are strong enough to allow averaging over the portion of the hour angle range not covered by CASS A near lower culmination. This 158 has been done s u c c e s s f u l l y f o r the i nne r spac ings , but has not been used so f a r f o r the ou te r ones. Table 4 . 3 . 1 A 0 h 7 degrees A 0 d 20 degrees A 0 D 4 degrees A 0 , .1 degrees 159 A F i g u r e 4 . 3 . 1 : Phase e r r o r as a r e s u l t o f an e r r o r i n d p l o t t e d as a f u n c t i o n o f spac ing . F i g u r e 4 . 3 . 2 : F i g u r e 4 . 3 . 4 : Phase e r r o r r e s u l t i n g from an e r r o r i n D p l o t t e d as a f u n c t i o n o f p o l a r d i s t a n c e . T h i s e r r o r i s a l s o dependent upon d. 161 4.4 Forming an Image from the Interferometer Data 4.4.1 Computation of Fan Beams One of the burdens of the synthetic aperture telescope i s that measurements of sky brightness are not d i r e c t , and brightness must be computed from separate interferometer observations. In f a c t , synthesis telescopes are image forming devices which produce a map of brightness temperature over a " f i e l d of view". The following i s a discussion of t h i s image forming process as i t pertains to the 22 MHz Synthesis Telescope. The Fourier transform relationship that e x i s t s between the f i e l d e x c i t a t i o n of an antenna and i t s far f i e l d pattern has long been known. Use was made of the Fourier series version to design the 22 MHz Synthesis Telescope elemental antennas. The fa c t that the i n d i v i d u a l Fourier components can be measured separately at d i f f e r e n t times ( f o r a time invarient source of radiation) was f i r s t recognized and used to make radio telescopes by Ryle (18). The measurements (the output) from an interferometer are made i n what has become commonly known as the u-v plane. For the case of a single antenna, i t i s the plane of the autocorrelation func-ti o n of the f i e l d e x c itation. For an interferometer, i t i s the plane of the cross-correlation function of the two f i e l d excita-tions of the elements. The conjugate Fourier transform plane i s the 4-m plane where & and m are d i r e c t i o n cosines. The 4-m plane i s a brightness d i s t r i b u t i o n . Expressed as a formula, 00 00 du dv — 00 — 00 F(u,v) i s complex, but, of course, B(4,m) must be r e a l . The r e s u l t i n g r e s t r i c t i o n on F(u,v) i s that i t must be Hermitian. It i s useful here to v i s u a l i z e i n more operational terms how senting the f i e l d of view containing an a r b i t r a r y brightness d i s t r i b u t i o n i n the 4-m plane. Now the kernel of the transform i s a p a i r of sinusoidal corrugations i n quadrature which multiply the brightness d i s t r i b u t i o n . The re s u l t i s one Fourier Component. Each value of u,v i n the kernel produces a corrugation at a p a r t i c u l a r wavelength, l//u* + v^, and position angle, t a n - 1 (v/u). These corrugations are, of course, models of the interferometer fringes which, as i s well known, also multiply the brightness d i s t r i b u t i o n i n the f i e l d of view. The r e s u l t i s that an i n t e r -ferometer of fixed spacing (as viewed from the centre of the f i e l d ) traces a c i r c u l a r path on the u-v plane. Unfortunately, however, rea l interferometers do not always produce the exact fringe pattern required for mathematical perfection. In f a c t , for the case at hand serious d i s t o r t i o n s at the edge of the map can result from these imperfections. Parenthetically, i t can be said that the brightness d i s t r i -bution i n the , m plane i s already a distorted version of what i s wanted. I and m are d i r e c t i o n cosines and not angles; for wide f i e l d s of view, objects of equal angular size w i l l not be the same size on the map. This d i s t o r t i o n can be overcome by p l o t t i n g the map on a non-linear scale. The re s u l t then i s that t h i s transform works. Figure 4.4.1 shows a c i r c u l a r region repre-e i2TT(u-£ + vm) a cos 2TT ( U £ + vm) + i sin 2TT (ui + vm) 163 F i g u r e 4 . 4 . 1 : A c i r c u l a r f i e l d showing the s i n u s o i d a l c o r r u g a t i o n s ( f r i n g e s ) which r o t a t e w i t h respec t to the & , m axes. The s o l i d l i n e s represent the in-phase f r i n g e ; the dashed ones, the quadrature f r i n g e s . 164 r e s o l u t i o n i s not c o n s t a n t a c r o s s the f i e l d . F i g u r e 4.4.2 shows the i n t e r f e r o m e t e r a t t h e c e n t r e o f t h e c e l e s t i a l sphere. A l l a r c s shown are g r e a t c i r c l e s . The s p a t i a l f r e q u e n c y p l a n e ( o r u-v p l a n e as i t i s o f t e n c a l l e d ) i s tan g e n t t o the c e l e s t i a l sphere a t S ( u s u a l l y t h e c e n t r e o f t h e f i e l d o f v i e w o f t h e t e l e s c o p e ) . The f r i n g e phase a t S can now be d e r i v e d as a f u n c t i o n o f the f o l l o w i n g p a rameters -H i s t h e hour a n g l e o f the c e n t r e o f t h e f i e l d o f view 6 i s t h e d e c l i n a t i o n o f the c e n t r e o f t h e f i e l d o f view h i s t h e a n g l e between the b a s e l i n e and t h e m e r i d i a n d i s t h e a n g l e between t h e b a s e l i n e and t h e e q u a t o r i a l p l a n e X i s t h e wavelength and 6 i s t h e a n g l e between S and t h e a x i a l p l a n e o f the i n t e r f e r o m e t e r U s i n g s p h e r i c a l t r i a n g l e NSB and t h e c o s i n e f o r m u l a f o r s p h e r i c a l t r i a n g l e s , c o s ( ^ - 9) = cos(£ - d) c o s ( J - 6) + s i n ( J - d) sin(£ - 6) cos (H-h) s i n 9 s* s i n d s i n 6 + cosd cos6 cos(H-h) Now t h e f r i n g e phase, 0, i s r e l a t e d t o 9 by: 2T T t s i n 9 where D i s t h e d i s t a n c e between the elements i n wavelengths The f r i n g e phase a t S i s t h e n 165 North C e l e s t i a l F i g u r e 4.4.2: Geometry o f an i n t e r f e r o m e t e r w i t h r e s p e c t t o t h e C e l e s t i a l S p h e r e . 0 = 2TT^ ( s i n 6 s i n d + cos 6 cosd cos (H-h)) F i g u r e 4.4.3 shows the u-v plane with b a s e l i n e p r o j e c t e d i t i n r e c t a n g u l a r c o o r d i n a t e s . In the f o l l o w i n g D, X, d, H, 6 are as above. From f i g u r e s 4.4.2 and 4.4.3 a s. TT—NSB « r i g h t ascension i i a ^ cos9 co so/ SB ^  cos9 cosNSB v = ^ cos9 since » - cos9 sinNSB Using the s i n e formula f o r s p h e r i c a l t r i a n g l e s on t r i a n g l e NSB cosd sin(H-h) sinNSB = cos 9 The c o s i n e formula y i e l d s cosNSB s s i n d - sin6 sin9 cos6 cos9 S u b s t i t u t i n g u - cosd sin(H-h) v: - ^ ( s i n d - sin6 sin9) S u b s t i t u t i n g f o r sin9 from above i n t o the equation f o r v y i e l d s the r e q u i r e d r e s u l t : u = ^ cosd sin(H-h) v a ^ ( s i n d cos6 - cosd sin6 cos(H-h)) These equations are, o f course, the p a r a m e t r i c equations o f an e l l i p s e . For 6 = 90 deg and d a 0, the l o c u s o f a p o i n t as a f u n c t i o n o f time i s a c i r c l e . For lower d e c l i n a t i o n s i t i s an 167 v A U -«3-F i g u r e 4.4.3: The u-v p l a n e s h o w i n g a p r o j e c t i o n o f t h e b a s e l i n e , D c o s 9 . The p r o j e c t i o n a n g l e i s 0. I n E a r t h r o t a t i o n s y n t h e s i s , a s t h e E a r t h t u r n s t h e a n g l e H c h a n g e s u n i f o r m l y . 9 i s a l s o a f u n c t i o n o f H. 168 e l l i p s e . I f the baseline i s i n the equatorial plane (d = 0), then the e l l i p s e s are centred on the North C e l e s t i a l Pole. I f not, then they are o f f s e t along the v axis by 2TT^ sind cos6 radians. Normally, u and v are calculated assuming that they are not a function of p o s i t i o n i n the sky, and that H and 6 are taken at the centre of the f i e l d . I f , however, the f i e l d i s wide enough that there i s a s i g n i f i c a n t v a r i a t i o n of fringe separation across the f i e l d , then the approximation breaks down. Moreover, t h i s means that the kernel of the Fourier transform i s no longer an exact model of the measurement being made by the interferometer. Three conditions must apply before there i s serious d i f f i c u l -ty. F i r s t l y , as mentioned above the f i e l d of view must be large enough that there i s a v a r i a t i o n of fringe spacing over the f i e l d . This r e s u l t s i n a map i n which there i s a s l i g h t d i s t o r t i o n of scale at the edges, but t h i s d i s t o r t i o n , of course, could be r e c t i f i e d by a change of coordinates. Secondly, the interferome-ters must each have a d i f f e r e n t value of d; that i s , each i n t e r -ferometer at a d i f f e r e n t spacing has a d i f f e r e n t orientation. I f a l l the interferometers are i n the equatorial plane, then d = 0, and a simple correction for t h e i r orientations i n the equatorial plane (correcting for h) s u f f i c e s to a l l e v i a t e any problem. I f a l l the interferometers have d i f f e r e n t d the situation i s s l i g h t -l y more complicated. An exaggerated case i s i l l u s t r a t e d i n Figure 4.4.4. Three sets of fringes are shown as cut by the plane contain-ing the baseline and the North C e l e s t i a l Pole (abbreciated NCP) (o f f s e t from each other for c l a r i t y ) . Sets one and two have the 169 NCP Fr inge Set Figure 4 . 4 . 4 : Fringe patterns as cut by the plane containing the baseline and the North C e l e s t i a l Pole. The f i r s t two fringe sets have the same centre of symmetry ( i . e . the value of d i s the same). The t h i r d set i s the same as the second except that i t has been shifted to a new value of d. These three sets cannot simultaneously be transformed to sine waves by a non-linear change of scale on the 9 axis. 170 same centre of symmetry (white l i g h t f r i n g e ) , but the centre of symmetry i s not at the North C e l e s t i a l Pole. The angle between the NCP and the centre of symmetry i s d. I f a l l the interferome-ters have the same value of d, a non-linear r e d e f i n i t i o n of the coordinate system w i l l restore sinusoidal fringes. I f , however, set two i s shifted to form set three, then no a l t e r a t i o n of the coordinate system can cause both fringe sets to become sinusoidal simultaneously. I t i s useful at t h i s point to continue the enquiry into how the Fourier transform works i n an operational sense. Expressed more d i r e c t l y , how does the Fourier transform go about forming a beam? At any given point, x, where a beam i s required ( i . e . where a radio brightness i s to be calculated from the data), the kernel of the Fourier transform adjusts the phase of the fringes so that there i s a maximum at that point. As the fringes of various spacings are added, they i n t e r f e r e constructively at that point and, more or l e s s , at random at a l l other points (providing, of course, that there i s some radiation emanating from point x). Obviously, what i s needed to form a beam with only quasi-sinusoidal fringes i s to mimic t h i s operation. In other words, we calculate an extra phase term to compensate fo r d so that each fringe has a maximum at the point i n question. The problem i s much more tractable i n one dimension. As w i l l be shown, there i s no loss of generality i n producing a fan beam at a p a r t i c u l a r orient-ation, and then using the fan beams at a l l orientations to construct the image. I f we set H-h - 0 i n the fringe formula, we get a cut through 171 the fringes perpendicular to the a x i a l plane of the interferometer. 0 = 2TT^ (sin& sind + cos6 cosd) = cos( 6-d) The fringes are cos0 and s in0 (quadrature p a i r ) . If t h i s function i s used at the kernel of an i n t e g r a l equation, then the beam forming process described above w i l l ensue as the int e g r a l i s evaluated i . e . U rmax I2T T D f(p) = J F ( u ) e X ^co sp sind J^J^inp co sdj ^ u o sin (p + d) where D, d are as above p i s polar distance u i s redefined as ^  and d - some function of D. Note that i f d = 0, t h i s equation reduces to the usual Fourier transform. Possibly the fringe functions do not form a complete, orthogonal set, but for small d and p r a c t i c a l l y attainable f i e l d s of view they are s u f f i c i e n t . The amount of the phase correction for the 22 MHz system i s shown i n Table 4.4.1 for representative baselines at several d i f f e r e n t polar distances. These phases have been calculated assuming that phase has been adjusted to zero at the NCP. As an example for the case where 70° , d = 4°, D . 97X D A0 m 2TT2 [ ( s i n 4° + sin 20°) - sin 24°] 172 TABLE 4.4.1 Length i n Phase Correction Baseline Wavelengths d 6=90° 6*80° 6=70° 98 97.50 4.674° 0 64° 212° 145 145.0 3.079° 0 56° 195° 193 192. 70 2. 256° 0 51° 183° 1 7 3 ss 3 . 0 7 radians Unfortunately, the above equation i s not solved as e a s i l y as a Fourier transform. A so-called " f a s t " method of computation does not seem possible. Several approaches are possible. The most obvious i s to simply evaluate the i n t e g r a l at each position of the fan beam. Another i s to use an FFT over a small range of positions, accepting a small error, and then to provide a phase s h i f t concomi-tant with an adjacent range of positions. The former method has been used for the entire f i e l d , but the l a t t e r i s useful for a quick look at the central portion of the map. 4 . 4 . 2 Computation of Maps It was mentioned above that the f u l l two-dimensional map can be computed from fan beam scans. It was also shown that with the unusual c h a r a c t e r i s t i c s of the 2 2 MHz telescope that i t was easier to calculate fan beam scans f i r s t rather than try i n g to do the equivalent of a two dimensional Fourier transform. The construction of two-dimensional brightness d i s t r i b u t i o n s from fan beam scans has a long hi s t o r y i n radio astronomy. Typi-c a l l y the problem arose when telescopes which actually had fan-shaped beams were used to observe sources such as the Sun ( 2 0 ) . More recently, these techniques have been adopted by people i n t e -rested i n Tomography under the name of "reconstruction from pro-jections" . Even though the synthesis telescope does not produce fan beam 174 scans d i r e c t l y , once they have been computed, the inversion problem i s si m i l a r to the above one. Bracewell and Riddle (21) have shown that the following theorem i s true, (Figure 4.4.5). Let f (i,m) be the required brightness d i s t r i b u t i o n . A fan beam scan along the l i n e AB w i l l r e s u l t i n the scan function f e ( R ) ~JJ~fU,m) 6Ucos6.+ msin9-R) dA dm. over f i e l d where 6(Acos9 + msin9) denotes a l i n e function. f(4,m) can be reconstructed from f Q ( R ) b y f i r s t finding h Q(R) = f 0 ( R ) -/ fg(R-r) M s i n e 2 (Mr) dr -Ceo and then adding the processed scans TT f(4,m) aJ~ h Q(X Cos9 + msin9) d( o , . s i n TTX where s ine x = TTX i s the maximum s p a t i a l frequency measured. Operationally, t h i s means that the scans are f i r s t to be 2 convolved with a sine (Mr) function. The r e s u l t i s subtracted from the scans, and the modified scans are added up at a l l posi-t i o n angles for each point on the map. In the 22 MHz case, the operation of modifying the scans can be combined with the c a l c u l a t i o n of the scans i n the f i r s t place. 2 Convolving with sine (Mr) function i n the -^m plane i s equivalent to multiplying by i t s Fourier transform, -A-(|!) , i n the u-v plane where 175 A Figure 4.4.5: Geometry of a fan beam reconstruction process. The fan beam i s scanned along the l i n e A-B at a l l angles 0. I f these fan beam scans are available as data, then the brightness d i s t r i b u t i o n i n the .£-m plane can be reconstructed. 1 7 6 I - I P I | P | < i o IP I >1 Since the mere fact that we can measure s p a t i a l frequencies only out to some l i m i t i n g value, M, means that the scan i n the u-v plane has been multiplied by a boxcar function Therefore, the modification of the scan i n the i-m plane proposed by Bracewell and Riddle i s equivalent to multiplying the scan i n the u-v plane by the " b u t t e r f l y " function shown i n Figure 4 . 4 . 6 (before Fourier transforming). It i s not known whether t h i s i s s t r i c t l y true for the modified transform used to compensate fo r the geometry of the 22 MHz system, but i t i s supposed that since both approaches are so s i m i l a r , that the proof should be l e f t to experiment. As part of any discussion of a p r a c t i c a l inversion scheme fo r producing maps, i t i s helpful to get an estimate for the number of computational operations involved. Let there be N points i n each scan i n the u-v plane. The data i s complex so that there are 2N numbers to deal with for each scan. Roughly speaking, i f the r a d i a l points are just at the sampling l i m i t , then the number of scans required i s For the 2 2 MHz case N = 1 9 2 ; K « 6 0 3 . In actual fact K has been made somewhat larger; K = 1 0 8 0 . Therefore, altogether there where K sa TTN Figure 4 . 4 . 6 : "Grading" function used to multiply data on " r a d i a l s " i n the u-v plane before transforming to fan beams. m 1 Output Figure 4 . 4 . 7 : The geometry of summing fan beams to output grid points i n the 4-m plane. An array of output points i s kept i n the computer. A single fan beam scan i s summed to a l l of these points before going on to the next scan. 178 are approximately 10^ numbers i n the u-v plane. In order to compute the i n t e g r a l to produce each fan beam 2 scan approximately N operations are required. Each operation requires the c a l c u l a t i o n of s i n , cos, 2 m u l t i p l i c a t i o n s and one 2 addition. Production of a l l the scans involves about KN such operations. These scans are then summed to a rectangular output grid. 2 Each scan must be summed to a l l N points. Figure 4.4.7 i l l u s t r a -tes t h i s process. An algorithm i s required for interpolating between points on the scan ( i f no redundant points are a v a i l a b l e ) . 2 Therefore approximately KN operations are required for the second phase. However, these are about 10 times faster than the previous ones and can be neglected i n c a l c u l a t i n g the o v e r a l l time 7 required. The t o t a l number of operations i s about 4 x 10 . _3 Allowing that each operation could be done i n 10 seconds, the whole computation would take about 11 hours, hardly a quick look at the r e s u l t s . This method has been used for the inversion of many data sets for the inner spacings of the u-v plane (spacings 2 - 97). Only a few sets of data for the outer part of the u-v plane have been reduced. Chapter 5 contains a summary of progress made so far i n reducing the observations. A comparison with other methods i s warranted here. The most common approach used i n synthesizing maps (where, naturally, the geometry i s more tractable) i s to simply interpolate the u-v plane data onto a rectangular g r i d , and then to do a two-dimensional fast Fourier transform. Again the gridding time i s smaller than the time taken to do the Fourier transform and the operation proportional to KN. Using the same time per operation t h i s would take about 3.5 minutes. An alternative to adding fan beams, then, i s to use the fast Fourier transform method on small sub-fields. The phase errors are r a t i o n a l i z e d to the centre of each sub-field. The size of each piece i s governed by a l i m i t of acceptable phase error on i t s edge. For example, a sub-field with a radius of 2 degrees would have a maximum phase error of 5.8 degrees. I f the whole f i e l d of view were done i n pieces, problems with joining them might arise. For t h i s reason t h i s method has not been put to use so f a r . 5.1 The Observations Chapter F i v e 180 At the time o f w r i t i n g i t has not been p o s s i b l e to make a map with the f u l l r e s o l u t i o n o f the t e l e s c o p e . There i s a v a i l a b l e , however, a map made with the i n n e r h a l f o f the u-v plane. I t , t h e r e f o r e , has a 30 arc minute beam. Approximately 160 observa-t i o n s were made a l t o g e t h e r , o f these about 70 were deemed to be devoid o f equipment f a i l u r e . Computing f a c i l i t i e s allowed the r e d u c t i o n o f the data i n t o maps at the r a t e o f about one i n two days. Of the 70 o b s e r v a t i o n s approximately 12 maps contained u s e f u l r e s u l t s . Owing to i n t e r f e r e n c e , i o n o s p h e r i c s c i e n t i l l a t i o n , o r r e f r a c t i o n , many o f the o t h e r maps showed no r e a l f e a t u r e s at a l l . The averaged r e s u l t i s shown i n F i g u r e 5.1.1. More s o p h i s t i -cated r e d u c t i o n techniques w i l l e v e n t u a l l y be a p p l i e d to the data to improve the map. T h e r e f o r e , any remarks made below about d e f e c t s apply o n l y to i t s c u r r e n t s t a t e . N e v e r t h e l e s s , a l a r g e body o f a s t r o n o m i c a l l y s i g n i f i c a n t data i s a v a i l a b l e d i r e c t l y from t h i s map. I t i s mainly c o n f u s i o n l i m i t e d at the c e n t r e , and s e n s i t i v i t y l i m i t e d at a d e c l i n a t i o n o f about 70 degrees. I t i s q u i t e proba-b l e t h a t some str o n g sources south o f t h i s d e c l i n a t i o n are detec-t a b l e , but so f a r the map has been s y n t h e s i z e d o n l y n o r t h o f 70 degrees. Over c e r t a i n areas s i d e l o b e s o f the str o n g e r sources and the g r a t i n g r i n g o f Cygnus A l i m i t the s e n s i t i v i t y . The two most prominent sources are 3C61.1 and 3C390.3. They have l a r g e n e g a t i v e s i d e l o b e s l y i n g on a l i n e p a s s i n g through the source and p e r p e n d i c u l a r to the l i n e c o n n e c t i n g the source to • I.*., F / , , c« ? a t e 16-MAR-78 Time 10:18:49 Sizes. E 256 < 1 256 1> , R 256 < t 256 1> F I f 1 i I i i Type C No of contours 20 Minimum -500.0 Max mum f i B « k « . *2 R e f ° : ^ t * p ? i 1 Contours -499 -87 298 69-5 , n ? Tccc B.1B00E+05 Log contr1b0.60 • , , 6 9 3 1 1 1 2 1 5 6 5 2 0 5 9 2 6 g 2 2 2 0 0 3 B & ? « S _ 9 1 6296 7289 8390 9610 10962 12461 14121 15961 182 CASS A. T h i s i s a "hour angle" e f f e c t and i s probably due to a n o n - l i n e a r c o r r e l a t o r response o c c u r r i n g while CASS A i s i n lower t r a n s i t . The e f f e c t may have been a m p l i f i e d somewhat by a c o r r e c -t i o n technique ( o u t l i n e d i n chapter 4.1) used on the source 3C61.1. SOURCES The most i m p a r t i a l way t h a t sources can be d e t e c t e d on the map i s by means o f a " s o u r c e - f i n d i n g " computer program. Develop-ment o f t h i s k i n d o f program w i l l be the next step i n the produc-t i o n o f a f i n a l source l i s t . However, because the g r e a t e s t i n t e r e s t i s i n the s p e c t r a o f weak sources, the f o l l o w i n g method was employed to f i n d sources. O v e r l a y s o f the p o s i t i o n s o f sources i n the survey done by Branson (4) at 81.5 MHz with 12 a r c minute r e s o l u t i o n were produced. T h i s r e s o l u t i o n i s b e t t e r than t h a t at 22 MHz so that problems of c o n f u s i o n a r i s e f o r about 68 sources. The maps from which the sources were s c a l e d are i n Appendix A8. F i g u r e 5.1.2 i s a g r i d showing how the o v e r a l l map has been d i v i d e d and the p o s i t i o n s of the p i e c e s . The c e n t r e o f each p i e c e has been l a b e l l e d A l , A2, e t c . on the g r i d i n F i g u r e 5.1.2. The map was d i v i d e d i n t o o v e r l a p p i n g p i e c e s each about 11 degrees square. O v e r l a y s to the same s c a l e were a l s o made with dots r e p r e s e n t i n g the p o s i t i o n of 81.5 MHz sources. A sample o v e r l a y i s shown i n F i g u r e 5.1.3. Contour i n t e r v a l s were s e l e c t e d e m p i r i c a l l y t o produce maps which show some n o i s e (or c o n f u s i o n ) and the weakest sources. F i g u r e 5.1.2: A g r i d showing how the map was d i v i d e d so that f l u x e s c o u l d be read. Each i n d i v i d u a l map i n Appendix A8 covers f o u r squares i n the r e c t a n g u l a r g r i d . The maps are l a b e l l e d by the g r i d p o i n t s at t h e i r c e n t r e s . co u> F i g u r e 5.1.3: An o v e r l a y o f the p o s i t i o n s o f sources measured by Branson at 81.5 MHz on one o f the maps made with present instrument. Sources were i d e n t i f i e d i n t h i s mahner. oo 185 T h i s turned out to be about 1.5 Jansky approximately c o n s i s t e n t with the t h e o r e t i c a l c o n f u s i o n l i m i t . A base contour l e v e l was set at a n e g a t i v e value equal to 2 percent o f the peak value on the map. T h i s base l e v e l was estimated to account f o r the f a c t t h a t the z e r o t h o r d e r spacing and some of the low o r d e r spacings are m i s s i n g . A l s o , each source has some n e g a t i v e s i d e l o b e component cau s i n g a g e n e r a l d e p r e s s i o n o f the base l e v e l . Strong sources have been allowed to s a t u r a t e . An i d e n t i c a l set o f maps with l o g a r i t h m i c contour i n t e r v a l s was used to s c a l e the f l u x e s o f these sources. Table 5.1.1. shows the l i s t of sources c o i n c i d e n t with sources i n the Branson ca t a l o g u e . F l u x d e n s i t i e s i n t h i s l i s t should be m u l t i p l i e d by 1.32 to convert to Janskys. The f o l l o w i n g c r i t e r i a were used f o r p o s i t i v e d e t e c t i o n o f a given source: A l o c a l base l e v e l was e s t a b l i s h e d around each source. Good p o s i t i o n a l c o i n c i d e n c e with an i s o l a t e d , beam-shaped, s i n g l e contour i s the s m a l l e s t f l u x value l i s t e d (before c o r r e c t i o n f o r the p o l a r diagram). Sources with p o s i t i o n a l e r r o r g r e a t e r than 10 a r c minutes r e q u i r e two o r more contours to be l i s t e d . Sources w i t h more than 20 a r c minutes p o s i t i o n a l e r r o r but s t i l l i s o l a t e d and having f o u r o r more contours are l i s t e d with a "P" a n n o t a t i o n . Sources showing enough c o n f u s i o n to s e r i o u s l y impair measurement of the f l u x are l i s t e d with a "C" a n n o t a t i o n . These sources are l i s t e d twice with the same f l u x . A l s o i n the l i s t are the Branson p o s i t i o n s , the s p e c t r a l index, i t s s p e c t r a l c l a s s i f i c a t i o n (see d i s c u s s i o n below) and a comment c o n t a i n i n g a t e n t a t i v e i d e n t i f i c a t i o n . RV:PDSPEC.SRC DATE 28-MAY-78 TIME 21s42:05 PAGE 1 Table 5 .1 .1 R.A. DEC. 22 MHZ FLUX ANNOTATION SPECTRAL SOURCE BRANSON POSITION INDEX 70 DEGREES 1 00H 13M 46S 70D 52.2M 4.1 -.3 CI NB 70.01 2 03H 30M 03 S 70D 43.4M 22. 1.2 CI 4C 70.3 3 05H 29M 54S 70D 13.0M 10. P .87 4C 70.4 4 06H 09M 56S 70 D 59.2M 4.5 .40 4C 70.5 5 07H 33M 44S 70D 29. 9M 35. .65 3C 184 6 09H 29M 53S 70D 03. IM 18. 1.13 4C 70.7 7 09H 49M 53S 70D 39.8M 16. P 4C 70.8 8 1 IH 11M 19S 70D 51 . IM 21 . 1.4 NB 70.11 9 1 IH 44M 50S 70D 54.0M 5.2 1.4 C1 4C 70.11 10 12H 10M 54S 70D 34. 7M 21 . 1.6 C1 4C 70.12 11 12H 37M 10S 70D 45.0M 5.2 1.4 CI 4C 70.13 12 14H 47M 37S 70D 26. 9M 5.3 1.11 4C 70. 15 13 15H 09M 42S 70D 57.5M 73. 1 .2 CI 3C 314.1 14 15H 49M 23S 70D 21 .0M 1 1 . .8 4C 70. 18 15 15H 57M 53S 70D 46.9M 34. 1 .33 4C 70.19 16 18H 07M 22S 70D 42.2M 24 . .74 4C 70.20 17 18H 18M 27S 70D 40.6M 4.6 1.4 4C 70.21 18 20H 05M 19S 70D 40. 2M 4.5 1.5 NB 70.26 19 23H 31M 38S 70D 24.9M 4.3 C NB 70.30 20 23H 35M 37S 70D 34.IM 4.2 C 4C 70.25 21 23H 40M 18S 70D 34.8M 4.2 C 4C 70.26 71 DEGREES 22 01H 44M 25S 71D 04. 2M 8.0 .66 NB 71.3 23 02H 36M 58S 71 D 47.2M 7.2 .74 CT 4C 71.3 24 07H 14M 52S 71D 27.6M . 8.7 .67 4C 71.5 25 08H 16M 28S 71D 30.9M 8.7 .64 4C 71.6 26 1 IH 20M 30 S 71D 34. IM 23. 1.5 NB 71.12 27 11H 34M 53S 71D 30.3M 14. C NB 71.13 28 1 IH 36M 58S 71D 16.4M 15 . C NB 71.14 29 1 IH 55M 14S 71D 59.5M 38. 1 .0 4C 71.12 30 13H 31M 05 S 71D 14.0M 4.7 .33 NB 71.19 31 14H 55M 53S 71D 50.8M 46. P .48 3C 309. 1 32 17H 45M 56S 71D 14.5M 30. 1.3 4C 71.17 33 22H 48M 37S 71D 1 1.8M 3.9 .92 CI 3C 454. 1 34 00H 02M 58S 72D 14.2M 72 DEGREES 3.3 .32 PART OF CTA1 -NB 72.1 H i 03 tn 35 RV:PDSPEC.SRC DATE 28-MAY-78 TIME 21:42:05 PAGE 2 35 00H 11M 16S 72D 20.2M 3.2 .36 PART OF CTA1 36 01H 06 M 13S 72D 55.7M 30. .66 3C 33. 1 37 01H 23M 42S 72D 28.8M 13. 1.1 CI 4C 72.2 38 03 H 10M 32S 72D 08.5M 10. .62 4C 72.4 39 03H 10M 57S 72D 59.8M 3.1 .29 4C 73.2 40 03H 19M 23S 7 2D 39.2M 9.7 . 73 4C 72.5 41 04H 28M 31S 72D 20.9M 28. .70 4C 72.7 42 06H 10M 24S 72 D 28. IM 7.2 .71 4C 72.11 43 06H 36M 28S 72D 20. 2M 3.7 . 10 NB 72.13 44 07H 02M 07 S 72D 57.IM 6.8 .70 4C 72.12 45 08H 29M 22S 72 D 50.0M 11 . .57 4C 72. 13 46 10H 48M 51S 72D 14.5M 4.5. 1.0 4C 72. 15 47 1 IH 42M 49S 72D 50.4M 11. .92 NB 72. 19 48 12H 27M 12S 72D 22.0M 8.0 P .68 4C 72. 17 49 15H 20M 39S 72D 36.7M 66. 1 .1 4C 72 .20 50 15H 50M 24S 72D 17.8M 12. -P 1.2 NB 72.24 51 16H 00M 30S 72D 53. 6M 17. 1. 1 4C 72.21 52 17H 33M 05 S 72D 35.9M 7.0 1.2 CI 4C 72.23 53 17H 50M 58S 72D 1 1 . 9M 15. .75 4C 72.24 54 18H 45M 32S 72D 03. 4M 15. .73 4C 71.18 55 19H 08M 59S 72D 14.5M 14. .84 4C 72.26 56 21H .05M 56S 72 D 27. 3M 6.6 .51 4C 72.29 57 21H 21M 10S 72D 47. IM 9.5 .75 4C 72.30 58 22H 21M 07S 72D 02. 8M 10. .46 4C 72.32 73 DEGREES 59 00H 40M 42S 73D 27. 6M 14. .73 CI 4C 73. 1 60 03H 28M 42S 7 3D 59.2M 13. .74 4C 74.5 61 05H 07M 51S 73D 36.0M 8.8 1.1 4C 73.3 62 06H 47M 16S 73D 23.7M 3.2 .75 CI 4C 73.4 63 07H 06M 42S 73D 38.5M 6.2 C 4C 73.5 64 08H 04M 50S 73D 32.6M 6.5 .65 4C 73.6 65 09H 24M 19S 73D 09. 2M 3.5 C 4C 73.7 66 09H 25M 12S 73D 04.3M . 3.5 C NB 73.8 67 09H 44M 20S 73D 28.5M 73. .38 4C 73.8 68 1 IH 57M 36S 73D 18.2M ' 63. .65 3C 268. 1 69 12H 32M 57S 73D 59. 6M 22. 1.0 4C 74. 19 70 13H 18M 53S 73D 17.7M 10. .93 4C 73. 13 71 13H 43M 06 S 73D 32 .0M 13. .75 4C 73.14 72 17H 28M 34S . 73D 54.2M 21 . .75 4C 73. 15 73 19H 18M 51S 73 D 49. 2M 14. . 92 NB 73. 18 74 19H 28M 48S 73D 52.7M 11 . .70 4C 73. 18 75 20H 19M 06 S 73D 14. 5M 9.0 .52 4C 73. 19 76 RV: PDSPEC.SRC DATE 28-MAV-78 TIME 21:42:05 PAGE 3 76 20H 49M 32S 73D 05. 7M 9.0 .78 4C 73.20 77 23H 01M 15S 73D 38.7M 2.7 .71 CI 4C 73.23 74 DEGREES 78 00 H 42M 34S 74D 58. 7M 4.6 C .31 NB 74. 1 79 00 H 49M 36S 74D 39.6M 4.8 .35 4C 74.2 80 01H 02M 27S 74D 1 9 . 1M 2.5 1.6 C1 4C 74.3 81 01H 13M 15S 74D 35.2M 14. P .81 4C 74.4 82 03H 40M 47S 74D 28. IM 7.7 .74 4C 74.6 83 03H 45M 13S 74D 51 .6M 20. P 1.2 NB 74.6 84 03H 57M 24S 74D 46.8M 15. 1. 1 CI 4C 74 . 7 85 04H 06M 58S 74D 43.7M 7.5 .59 CI 4C 74.8 86 04H 51M 12S 74D 20. IM 1 1 . .82 4C 74.9 87 07H 02M 99S 74D 53.M 45. .69 3C 173.1 88 07H 35M 28S 74D 18.7M 52. 1.5 4C 74. 13 89 08H 20M 15S 74D 17.8M 15. P .74 4C 74.14 90 09H 46M 41S 74D 30. 5M 5.7 .64 NB 74. 15 91 09H 52M 00 S 74D 58.6M 8.2 .61 4C 74. 15 92 10H 09M 56S 74D 52. 8M 38 . . 84 4C 74.16 93 1 IH 19M 52S 74D 03. 9M 25. 1 . 1 4C 74. 18 94 12H J0T9M 14S 74D 36 . 7M 8.6 .45 NB 74.21 95 15H 01M 37S 74D 31 .0M 49. 1.3 4C 74.20 96 16H 35M 06 S 74D 1 1 . IM 17. .78 4C 74.21 97 17H 18M 31S 74D 21 .7M 5.6 .52 4C 74.22 98 18H 25M 46S 74D 19. IM 30. . 69 3C 379.1 99 19H 19M 41S 74D 08.0M 14. .90 NB 74.26 100 20H 43M 58S 74D 55.9M 14 . .84 4C 74.26 101 21H 18M 49S 74D 57.3M 14. .61 4C 74.27 102 21H 28M 39S 74D 30. 8M 2.5 .03 NB 74.29 103 23H 04M 59S 74D 08. IM 5.1 C 4C 74.28 104 23H 06M 14S 740 26.3M 4.9 c NB 74 . 32 105 23H 46M 27S 74D 59.7M 2.3 -.04 NB 74.33 75 DEGREES 106 00H 02M 31S 750 46.0M 4.2 c NB 75. 1 107 00 H 07M 02 S 75D 45.5M 4.2 c NB 75.2 108 00 H 42M 14S 75D 27. IM 2.2 c NB 75.4 109 01 H 08M 26S 7 5D 35. 7M 6.4 1.0 NB 75.5 110 01H 47M 34S 75D 34.7M 8.7 .75 4C 75. 1 111 02H 28M 02 S 75D 07. 2M 4.6 1.0 NB 75.7 112 03H 03M 43S 75D 30.9M 6.6 1.0 NB 75.8 113 04H 07M 03S 75D 59. 3M 4.3 .37 4C 76.4 114 04H 34M 00 S 75D 52. 3M 1 1 . 1.3 NB 75.10 115 RV: 1 »DSPEC.SRC DATE 28-MAY-78 TIME 2U42.-05 PAGE 4 115 04H 54M 08S 75D 20.IM 7.1 1.3 NB 75.11 116 05H 41M 47S 75D 57. IM 2.2 .29 NB 75. 12 117 06H 12M 43S 75D 31. 7M 4.7 .62 NB 75. 13 118 JH6H 29M 35S 75D 01 . 9M 5.0 1.4 CI 4C 75.2 119 08H 01M 33S 75D 57.6M 3.8 C NB 75. 17 120 09H 17M 03 S 75D 03. 7M 16. 1.5 NB 75. 19 121 10H 31M 48S 75D 33.2M 13. C NB 75.20 122 10H 35M 07S 75D 11 .9M 13. C 4C 75.3 123 1 IH 52M 26S 75D 47.8M 10. .74 4C 75.4 124 13H 24M 35S 75D 48.4M 4.9 .75 NB 75.23 125 15H 00M 46S 75D 33. IM 23. .84 4C 75.5 126 16H 49M 54S 75D 49.9M 24 . .73 4C 75.6 127 19H 45M 53S 750 06. 9M 4.7 .58 4C 75.8 128 20H 53M 04S 75D 12.2M 9.2 C 4C 75.9 129 20H 56M 58S 75D 04. 2M 9.4 C 4C 75 . 10 130 22H 27M 03S 75D 12.3M 2.3 .22 4C 75.11 131 22H 49M 44S 75D 41 .7M 2.1 C NB 75.38 132 23H 01M 08S 75D 33.3M 2.2 -.02 NB 75.39 133 23H 42M 29S 75D 46 .0M 2.1 P .42 NB 75.42 76 DEGREES 134 00 H 38M 35S 76D 50. 7M 5.6 .95 NB 76. 1 135 00 H 43M 20S 76D 19.5M •2.0 .37 NB 76.2 136 02H 19M 14S 76D 37.2M 3.9 .55 CI 4C 76. 1 137 05H 10M 30S 76D 44.2M 10. .74 NB 76.7 138 05H 28M 24S 76D 29. 5M 10. .71 NB 76.8 139 06H 09M 21S 76D 08. 7M 2.2 .18 NB 76.9 140 06H 23M 00 S 76D 33. 2M 1.9. .52. 4C 76.6 141 06H 35M 34S 76D 07. 9M 474 .67 NB 76. 11 142 08H 52M 04S 76D 13. 9M 4.6 P .97 NB 76. 13 143 1 IH 52M 35S 76D 28.3M 4.6 .97 NB 76. 15 144 12H 43M 32S 76D 28. 7M 12. C NB 76. 19 145 12H 48M 33S 76D 17. 4M 12. C NB 76.20 146 12H 49M 30S 76D 54 . 5M 6.5 .87 NB 76.21 147 14H 17M 24S 76D 00. IM 24. C NB 76.22 148 14H 20M 14S 76D 1 1 .4M 24. C 4C 76.7 149 16H 18M 31S 76D 51 .7M 8.4 1.3 NB 76.25 150 16H 18M 36S 76D 28.6M 13. 1.3 NB 76.26 151 16H 50M 58S 76D 38.6M 11 . 1.3 NB 76.27 152 17H 15M 45S 76D 14.3M 20. .87 4C 76.9 153 18H 47M 27S 76D 47.0M 8.0 .97 NB 76.30 154 20H 46M U S 76D 08. 2M 15. 4C 76. 12 155 21H 04M 24S 76D 22. IM 62. .55 3C 427. 1 156 RV:PDSPEC.SRC- DATE 28-MAY-78 TIME 21J42:05 PAGE 5 156 21H 22M 51S 76D 30. 6M 5.9 NB 76.37 157 21H 56M 59S 76D 38.5M 1.9 1.1 Cl 4C 76 .14 158 22H 35M 00 S 76D 32.0M 9.7 .90 4C 76. 15 159 22H 48M 46S 76D 02. 6M 12. .97 NB 76.40 160 23H 26M I3S 76D 03. 1M 4.1 .43 4C 76. 16 77 DEGREES 161 00H 06M 51S 77D 06. 4M 7.2 C 4C 77.1 162 00 H 11M 37S 77D 34.8M 10. 1.3 Cl 4C 77.2 163 02H 23M 31S 77D 28.4M 1 .8 .90 Cl 4C 77.3 164 03H 54M 30S 77D 47.7M 5.3 P 1 . 1 NB 77.4 165 04H 18M 12S 77D 42.9M 7.1 .62 NB 77.5 166 04H 21M 46S 77D 01 .7M 37. .93 4C 77.4 167 05H 05M 36S 77D 27.4M 17. 1 . 3 4C 77.5 168 06H 38M 16S 77D 58 .0M 24. .88 4C 77.6 169 07H 13M 43S 77D 51.5M 5.6 P .67 NB 77.9 170 08H 19M 35S 77D 02. 6M 8.4 .77 4C 77.7 171 09H 53M 06 S 77D 22. 2M 8.2 1.0 NB 77. 11 172 10H 06M 01S 77D 02. 2M 38. 1 .2 4C 77.8 173 1 IH 00M 22S 77D 14.6M 54. .80 3C 249. 1 174 1 IH 010M 28S 7 7D 10. 9M 8.4 .55 4C 77. 10 175 1 IH 19M 49S 77D 48 . 1M 20. 1.2 4C 77.11 176 12H 32M 30S 77D 46.7M 12. .87 4C 77. 12 177 14H 44M 40S 77D 18. 3M 20. c 3C 303. 1 178 14H 47M 41S 77 D 07. 7M 21 . c 3C 305. 1 179 17H 04M 04S 77 D 09. 7M 8.0 .74 4C 77. 15 180 17H 28M 15S 77D 27. 5M 1.9 .74 Cl 4C 77.16 181 19H 00M 33S . 77D 40. 2M 11 . .87 4C 77. 17 182 19H 25M 00 S 77D 47.0M 5.3 .58 NB 77.22 183 19H 33M 18S 77 D 16.4M 3.7 c NB 77.23 184 19H 41M 31S 77D 29.4M 9.2 c 4C 77. 18 185 20H 18M 00 S 77D 19.9M 7.4 1.3 NB 77.25 186 21H 58M 22S 77D 03. 7M 5.5 .59 4C 77.21 187 23H 24M 00 S 77D 54.8M 1 .7 0.0 NB 77.31 188 23H 27M 47S 77D 26 .0M 7.1 .58 NB 77.32 78 DEGREES 189 00H 13M 29S 78D 59. 4M 17. 190 00 H 15M 21S 78D 09. 5M 4.9 191 02H 45M 08 S 78D 57. 2M 7.8 192 02H 55M 30S 78D 46. 1M 4.8 193 03H 51M 22S 78D 33. 8M 4 . 9 194 04H 37M 46S 78D 32. 5M 6.7 .18 3C 6.1 .18 NB 78.02 .49 4C 78.2 .43 4C 78.3 .47 4C 78.4 ^ .71 4C 78.5 MO O RV:PDSPEC.SRC DATE 28-MAY-78 TIME 21:42:05 PAGE 6 195 06H 10M 26S 78D 21 . 1M 3.5 P .23 4C 78.6 196 06H 14M 38S 78D 49. 9M 1.7 .31 NB 78.7 197 07H 09M 27S 78D 24. 5M 5.3 P .90 NB 78.9 198 08 H 00M 20S 78D 51. 2M 3.4 .58 NB 78. 10 199 08H 41M 34S 78D 39. 6M 38. .95 4C 78.7 200 09H 32M 36S 78D 27.2M 9.0 .65 4C 78.9 201 10H 43M 59S 78D 39. 6M 7.2 1.3 NB 78.16 202 1 IH 31M 17S 78D 16. 7M 7.5 1. 1 NB 78.17 203 12H 05M 18S 78D 13. 4M 1.9 .18 NB 78.18 204 12H 18M 40S 78D 34. 5M 9 .0 1.5 NB 78.19 205 13H 22M 15S 78D 22. 3M 1.8 .29 NB 78.20 206 15H 31M 08 S 7 8D 55. 4M 3.4 .55 NB 78.. 22 207 16H 00M 39S 78D 25. 2M 8.9 1 .0 NB 78.23 208 16H 58M 47S 78D 03. 4M 1.8 -.02 NB 78.25 209 17H 06M 10S 78D 44-. 0M 44. 1.5 NB 78.26 210 18H 03M 23S 78D 25. 6M 3.4 P .67 NB 78.27 211 19H 46M 21S 78D 07. 7M 3.4 P .18 NB 78.28 212 20H 44M 00 S 78D 43. 2M 1.6 .12 NB 78.29 213 22H 16M 51S 78D 43. 5M 3 . 1 .40 NB 78.31 79 DEGREES 214 00H 55M 40S 79D 37. 8M 2.9 .29 4C 79. 1 215 02H 11M 56S 79D 33. 6M 7.4 P .71 4C 79.3 216 03H 44M 16S 79D 56. 9M 7.3 .47 4C 79.4 217 03H 57M 56S 79D 48. 6M 10. .92 NB 79.7 218 04H 59M 03 S 79D 07. 4M 9.6 .62 4C 79.5 219 05 H 34M 25S . 79D 58. 0M 4.5 .98 NB 79. 10 220 05H 48M 08 S 79D 58. 2M 1 1 . 1. 1 NB 79.11 221 06H 55M 46S 79D 00. 6M 1 . 7 . 12 NB 79.14 222 07H 20M 03 S 79D 01 . 2M 5.0 1 .1 NB 79. 16 223 09H 26M 07S 79D 16. 9M 60. .78 3C 220. 1 224 09H 40M 07 S 79D 51 . 2M 8 .0 .71 4C 79.7 225 09H 52M 35S 79D 20. 8M 6.7 .71 4C 79.8 226 10H 24M 56S 79D 05. 9M 5.2 1 .2 Cl 4C 79.9 227 10H 29M 13S 79D 38. 7M 3.3 C .55 NB 79.22 228 10H 47M 13S 79D 29.0M 23. 1. 1 4C 79. 10 229 11H 09M 04S 79D 51 .0M 4.9 1 . 1 NB 79.25 230 12H 17M 48S 79D 43 . 2M 6.6 .69 4C 79. 12 231 13H 10M 52S 79D 25. 8M 13. C NB 79.27 232 13H 15M 54S 7 9D 08. 8M 14. c NB 79.28 233 13H 37M 55S 79D 29. 5M 5 .0 .43 NB 79.29 234 13H 57M 25S 79D 57. 4M 1 1 . .71 4C 79. 13 235 14H 15M 26S 79D 18. 3M 6.7 .69 4C 79. 14 236 RV:PDSPEC.SRC DATE 28-MAY-78 TIME 21:42:05 PAGE 7 236 17H 00M 42S 790 32.0M 3.2 C 4C 79.16 237 17H .33M 35S 79 D 50. 6M 27. .82 4C 79.17 238 18H 45M 41S 79D 42.4M 0. 12E+03 .58 3C 390.3 239 19H 25M U S 79D 12. IM 9.4 1 . 1 NB 79.37 240 19H 37M 35S 79D 48. 7M 10. .58 4C 79 .20 241 21H 08M 14S 79D 56.6M 5.8 .49 4C 79.21 242 22H 49M 49S 79D 37.5M 5.9 PC 1 243 23H 52M 51S 79D 38.0M 28. .57 3C 469.1 80 DEGREES 244 00H 16M 46S 80D 21 .9M 5.5 C .52 NB 80. 1 245 00H 18M 15S 80D 06. 8M 5.6 C 1.1 NB 80.2 246 00 H 32M 23S 80D 09. 3M 4.2 .59 NB 80.3 247 02H 21M 36S 80D 32.9M 4 . 1 P .59 NB 80.5 248 04H 09M 28S 80D 39.0M 8.3 1. 1 NB 80.7 249 05H 55M 18S 80D 05. 6M 10. .92 NB 80. 11 250 06H 33M 25S 80D 31 .5M 1 . 4 -.51 NB 80. 14 251 07H 34M 29S 80D 32.5M 45. .65 3C 184.1 252 08H 25M 10S 800 15.IM 12. P 1.5 NB 80. 17 253 09H 14M 47S 80D 29.3M 4.5 .55 NB 80.18 254 10H 17M 31S 800 47.2M 46. 1 .0 NB 80. 19 255 12H 41M 04 S 80D 17.4M 4.6 1 .0 NB 80.20 256 13H 05M 23S 80D 25. IM 14. .74 NB 80.21 257 13H 36M 32S 800 45.9M 10. P .82 NB 80.22 258 16H 05M 01S 80D 23.2M 33. .80 NB 80. 25 259 17H 1 IM 17S 80 D 09. 8M 6.0 .55 NB 80.26 260 19H 1 IM 18S 80D 54.0M , 6.9 .51 NB 80.27 261 19H 31M 44S 80D 51 . 9M 9.6 1.2 NB 80.28 262 22H 15M 40S 80D 14 .0M 2.8 .51 NB 80.30 263 22H 32M 12S 80D 24.3M 2.7 .71 NB 80.32 81 DEGREES 264 00 H 02M 23S 81D 16.3M 2.6 C NB 81.1 265 01H 56M 02S 81D 00. 5M 9.3 .90 NB 81.2 266 02H 24M 24S 81D 26. 2M 1.3 -.12 NB 81.3 267 02H 58M 35S 81D 48.6M 8.9 1.43 NB 81.4 268 05H 32M 54S 810 15.5M 2.7 .71 NB 81.6 269 07H 04M 26S 81D 55.2M 8.0 .70 NB 81 .9 270 07H 47M 44S 81D 58.4M 4.0 c NB 81.11 271 08H 40M 05S 81D 24.3M 4.2 1. 1 NB 81.12 272 09H 16M 21S 810 27.3M 11 . 1.2 NB 81.13 273 10H 00M 51S 8 ID 45.3M 30. .97 NB 81.14 274 RV: 1 PDSPEC.SRC DATE 28-MAY-78 TIME 21:42?05 PAGE 8 274 10H 44M 17S 81D 35.6M 5.6 .82 NB 81.15 275 1 IH 15M 06 S 81D 04. 4M 7.3 .97 NB 81.16 276 1 IH 50M 49S 81D 14.3M 8.7 .88 NB 81.17 277 12H 22M 24S 81D 00. 3M 10. 1.2 NB 81.18 278 12H 59M 45S 81 D 10.2M 38. .97 NB 81.19 279 14H 18M 22S 81D 12.7M 4.3 .22 NB 81 .20 280 15H 15M 47S 810 53. 6M 2.7 -.14 NB 81.21 281 16H 27M 29S 81D 23. IM 4. 1 .95 NB 81 .22 282 17H 55M 29S 81D 48.2M 2.6 .19 NB 81.28 283 18H 49M 59S 81D 48.6M 6.5 .40 NB 81 .29 284 22H 38M 06S 81D 33.8M 2.5 -.04 • NB 81.31 285 23H 56M H S 81D 08 .5M 2.6 C .41 NB 81 .34 82 DEGREES 286 02H 27M 14S 8 2D 24.7M 8.5 .89 NB 82. 1 287 02H 57M 21S 82D 03 .6M 8.7 1.5 NB 82.2 288 03H 32M 16S 82D 1 1 .0M 5.0 C NB 82.3 289 03H 40M 20S 82D 04. 6M 5.0 C NB 82.4 290 06H 36M 25S 82D 17.3M 1.3 -.45 NB 82.6 291 07H 26M 51S 82D 04. 7M 12. 1.3 NB 82.8 292 07H 28M 47S 82D 52.5M 14. C NB 82 .9 293 07H 40M 45S 8 2D 48 .0M 14. C NB 82. 10 294 10H 49M 56S 82D 36 . IM 10. 1.4 NB 82.12 295 1 IH 16M 43S 82D 01 .4M 5.4 1.4 NB 82. 14 296 1 IH 20M 04 S 82D 52.4M 3.8 .69 NB 82.15 297 1 IH 52M 10S 82D 12.7M 1.3 C NB 82.16 298 • 1 1 H 52M 59S 82D 5 2.0M 6.4 .69 NB 82. 17 299 13H 05M 06 S 82D 1 1 .4M 5.4 C NB 82. 19 300 13H 17M 39S 82D 34. IM 29. .90 NB 82.20 301 16H 10M 59S 82D 08. 5M 9.2 C NB 82.21 302 16H 34M 49S 82D 41.0M 22. 1. 1 NB 82.22 303 18H 03M 16S 82D 00. 8M 2.6 .30 NB 82 .24 304 18H 09M 05 S 82D 18. 8M 6.3 .70 NB 82.25 305 19H 51M 05 S 82D 51.8M 8.5 C NB 82.26 306 20H 01M 59S 82 D 41 .2M 8.5 C NB 82.27 307 20H 33M 20S 82D 15.2M 2.5 .36 NB 82.29 308 21H 13M 20S 82D 42.7M 8.4 .75 NB 82.31 309 21H 41M 18S 82D 52.5M 4.7 .75 NB 82.33 310 22H 23M 40S 82D 07. 4M 6.2 1.2 NB 82.34 311 23H 25M 05S 82D 14.7M 4.9 -.09 NB 82.35 312 23H 39M 15S 82D 50. 7M 3.5 .57 NB 82.36 83 DEGREES v£> 313 RV:PDSPEC.SRC DATE 28-MAY-78 TIME 21:42:05 PAGE 9 313 00H 46M 17S 83D 55 .4M 6.7 .36 NB 83.1 314 01H 15M 45S 83D 13 .3M 5.8 .47 NB 83.2 315 01H 57M 30S 83D 1 1 .6M 5.8 .54 NB 83.3 316 04H 16M 04S 83D 05 . 9M 1.2 .16 NB 83.4 317 05H 07M 38S 83D 55 .7M 3.5 .87 NB 83.5 318 05H 51M 10S 83D 26 . 8M 1 .2 0.0 NB 83.6 319 06H 36M 44S 83D 12 . 9M 2.4 .80 NB 83.7 320 07 H 00M 57S 83D 05 .8M 1.2 .29 NB 83.8 321 08H 58M 51S 03 D 56 . 6M 2.4 .81 NB 83. 10 322 09H 30M 55S 83D 28 . 1M 59. .69 3C 220.3 323 10H 21M 56S 83D 04 . 2M 1 .3 .32 NB 83.12 324 10H 59M 45S 83D 43 .3M 11 . C NB 83.13 325 11 H 11M 31S 83D 51 .3M 11 . C NB 83. 14 326 12H 56M 59S 83D 57 . 2M 2.4 0.0 NB 83. 15 327 14H 02M 24S 83D 34 .3M 4.9 .59 NB 83.16 328 15H 35M 16S 83D 00.4M 3.8 .36 NB 83. .1 8 329 18H 34M 31S 83D 03 .2M 3.6 .92 NB 83. 19 330 20H 31M 15S 83D 59 . 5M 5.7 .84 NB 83.22 331 21H 33M 57S 83D 43 . 6M 25. c NB 83.23 332 21H 42M 04 S 83D 27 .7M 25. c NB 83.24 333 22H 14M 15S 83D 37 .6M 1 1 . .80 NB 83.25 84 DEGREES 334 00 H 07M 09S 84D 08 . 6M 4.5 .53 NB 84.1 335 00 H 28M 15S 84D 33. .8M 7.6 c NB 84.2 336 00H 37M 28S 84D 33, .5M 7.6 c NB 84.3 337 04H 03M 33S 84D 16. .5M 11 . .82 NB 84.5 338 05 H 46M 41S 84D 04. . 1M 5.8 1.5 NB 84.6 339 . 06H 24M 51S 84D 12. ,8M 8.0 .78 NB 84.8 340 08H 18M 31S 84D 34. , 1M 5.7 .54 NB 84.9 341 09H 07M 41S 84D 54 , . 8M 5.7 .54 NB 84. 11 342 10H 17M 04S 84D 22. . 3M 8.2 1.2 NB 84.12 343 12H 02M 10S 84D 10. . 6M 3.6 .55 NB 84.14 344 12H 22M 21S 84D 51 .0M 8.0 1.3 NB 84. 15 345 12H 36M U S 84D 13. ,2M 5.9 .51 NB 84.16 346 12H 36M 42S 84D 46. . 1M 8.1 1.5 NB 84.17 347 13H 57M 20S 84D 26. . 3M 3.5 .52 NB 84.18 348 15H 44M 06S 84D 32. 8M 8 .0 .78 NB 84. 19 349 17H 47M 13S 84D 46. 5M •17. .88 NB 84.20 350 19H 01M 22S 84D 31 . 4M 2.2 -.10 NB 84.22 351 19H 50M U S 84D 54. 4M 15. .65 NB 84.23 352 20H 03M 55S 84D 10. 1M 5.7 .74 NB 84.24 353 21H 34M 25S 84D 39. 8M 5.5 p -. 14 NB 84.25 RV:PDSPEC.SRC DATE 28-MAY-78 TIME 21s42:06 PAGE 10 85 DEGREES 354 00H 09M 37S 85D 26. 9M 4.2 .43 NB 85.1 355 04H 09M 03 S 85D 37.7M 4.3 1 . 1 NB 85.2 356 05H 03M 09 S 85D 55. 9M 4.3 .41 NB 85.3 357 07H 11M 26S 85D 49. 8M 4.3 .85 NB 85.4 358 10H 48M 39S 85D 56.7M 2.2 .35 NB 85.5 359 1 IH 59M 59S 85D 52.4M 3.3 .87 NB 85.6 360 13H 09M 17S 85D 59. 9M 6.6 .34 NB 85.7 361 16H 15M 45S 85D 09. 1M 7.8 .67 NB 85.8 362 16H 31M 00 S 85D 55.7M 4.3 -. 18 NB 85. 10 363 17H 21M 55S 85D 47.6M 5.4 1.0 NB 85.11 364 18H 47M 05 S 85D 1 1 . 0M 7.6 .46 NB 85. 12 365 19H 15M 26S 85D 31 .7M 7.6 .25 NB 85.13 366 21H 58M 17S 85D 26.0M 5.3 .45 NB 85. 15 367 22H 48M 40S 85D 41 .4M 8.4 .62 NB 85.16 86 DEGREES 368 02H 10M 50S 86D 04.7M 95. .65 3C 61.1 369 06H 19M 03S 86D 27.6M 3.2 C NB 86.2 370 06H 41M 41S 86D 36 . 9M 3.2 C NB 86.3 371 08H 03M 51S 86D 23.9M 2.1 .98 Cl RN 30 372 09H 06M 18S 86D 41 . 1M 18. 1. 1 RN 32 373 10H 03M 10S 86D 08. 8M 7.6 .78 RN 35 374 12H 23M 29S 86D 24.8M 7.6 C RN 44 375 12H 43M 01S 86D 30. 1M 7.5 C RN 46 376 13H 47M 13S 86D 15. 8M 5.4 C NB 86.10 377 14H 05M 35S 86D 2 5.0M 5.4 C RN 51 378 16H 54M 00 S 86D 40.0M 1 . 1 .04 RN 63 379 20H 53M 34S 86D 24.9M 6.2 .87 RN 75 87 DEGREES 380 05H 05M 00 S 87D 27.8M 5.1 C RN 19 381 05H 55M 40S 87D 20.2M 2.1 C RN 21 382 07H 01M 30S 87D 16.8M 5.2 C RN 27 383 07H 46M 50S 87D 09.1M 4.2 C RN 28 384 1 IH 45M 00 S 87D 57. 5M 6.2 .97 RN 41 385 13H 38M 50S 87D 05. 7M 15. 1.0 RN 49 386 15H 19M 40S 87D 16.7M 3.1 .65 RN 59 387 16H 26M 00 S 87D 56. 8M 3.1 C RN 62 388 20H 53M 50S 87D 46.4M 2.0 c RN 74 389 21H 18M 50S 87D 27.6M 2.0 c RN 78 390 RV: PDSPEC.SRC DATE 28-MAY-78 TIME 21:42:05 PAGE 11 390 22H 44M 50S 87D 58. 9M 3.0 1.2 CI RN 85 391 23H 20M 20S 87D 33. 8M 2.0 .97 RN 86 88 DEGREES 392 05H 39M 30S 88D 43. 6M 3.0 1.2 RN 20 393 09H 59M 20S 88D 09. 7M 2.1 .58 RN 34 394 12H 46M 00 S 88D 1 1 . 5M 2.1 .45 RN 47 395 19H 58M 20S 88D 04. 9M 2.0 .47 RN 72 395 22H 43M 20S 88D 52. 7M 5.0 . C RN 84 89 DEGREES 397 00H 38M 20S 89D 12. 6M 3.0 -.14 RN 3 THE FLUX SCALE The f l u x s c a l e i s based on sources measured at 22 MHz by-Roger, C o s t a i n , and Lacey (1) with the T a r r a y at D.R.A.O. Table 5.1.2 shows a l i s t o f sources n o r t h o f 6 = 70 degrees measured with t h i s system. Of these, about f i v e appear to be m i s - i d e n t i f i -c a t i o n s . A l s o , sources i n s i d e the range of Right Ascension between 22 Hours and 4 Hours below a d e c l i n a t i o n of 80 degrees have been excluded as being too near the powerful r a d i o source CASS A. F i g u r e 5.1.4 shows a p l o t of f l u x d e n s i t i e s as measured with the T system i n Jansky's versus those measured i n a r b i t r a r y u n i t s w i t h the s y n t h e s i s system. There may be some tendency f o r the weak f l u x v a l u e s (approx. < 70 J.) to be overestimated because o f c o n f u s i o n . The very s t r o n g sources on the s y n t h e s i s map seem to have been degraded by the c o r r e c t i o n process a p p l i e d to 3C61.1. Although 3C61.1 has negative s i d e l o b e s , they are more c o n f i n e d than those f o r 3C390.3 and 3C427.1. T h i s suggests t h a t the procedure may not apply e q u a l l y over the map. T h i s l i k e l y accounts f o r the low f l u x d e n s i t i e s f o r these sources. For some reason, however, t h i s does not seem to apply f o r weak sources. Again, the problem may be a n o n - l i n e a r i t y i n the system which a f f e c t s strong sources more than weak ones. E r r o r s i n the e s t i m a t i o n o f the f l u x d e n s i t i e s vary as a f u n c t i o n o f d e c l i n a t i o n because o f the a p o d i z i n g e f f e c t o f the p o l a r diagram. The response used to c o r r e c t the source f l u x e s i s shown i n F i g u r e 5.1.5. I t i s an average i n the f o u r c a r d i n a l d i r e c t i o n s o f the expected response o f the beam d e r i v e d i n chapter T a b l e 5.1.2: 22 MHz T Sources North o f DEC=:70 Degrees  Source Name 22 MHz F l u x (Jansky) . 3C184 55 + 19 3C314.1 97 ± 5 3C454.1 90 + 6 3C309.1 51 ± 4 4C72.15 57 ± 11 4C72.07 71 ± 12 4C72.06 58 ± 7 4C72.13 30 + 7 3C33.1 83 ± 23 3C268.1 69 + 22 4C74.13 51 3C379.1 45 + 5 4C74.05 38 ± 2 NB74.15 76 ± 10 4C74.08 61 ± 2 4C74.16 37 + 5 3C173.1 87 + 11 4C75.05 52 ± 12 4C75.07 42 ± 12 3C427.1 167 ± 10 4C77. 7 42 ± 7 3C249.1 52 ± 10 4C78.7 55 + 10 3C6.1 71 ± 10 3C220.1 70 + 22 3C390.3 277 + 28 3C184.1 60 ± 4 3C61.1 125 ± 35 199 F i g u r e 5.1.4: The p l o t o f f l u x d e n s i t i e s o f the c a l i b r a t i o n sources as measured with the o r i g i n a l 22 MHz T system i n Jansky versus those measured with the present system i n a r b i t r a r y u n i t s . The l e a s t squares f i t . i s shown as a l i n e with a slope o f 1.32. F i g u r e 5.1.5: The p o l a r diagram o f the elemental antennas as estimated from t h e o r y (dark l i n e ) . The p o i n t s are the f l u x e s o f the c a l i b r a t i o n sources p l o t t e d i n f i g u r e 5.1.4 b e f o r e being c o r r e c t e d f o r the p o l a r diagram shape. 201 3.1. The maps i n Appendix A8 have not been c o r r e c t e d f o r the p o l a r diagram. An independent check on the slope o f the primary p o l a r diagram has been done u s i n g the c a l i b r a t i o n sources. F l u x d e n s i t y v a l u e s u n c o r r e c t e d f o r the p o l a r diagram have been p l o t t e d i n F i g u r e 5.1.5 f o r the c a l i b r a t i o n sources used i n determining the f l u x s c a l e . Except f o r a few p o i n t s , t h i s t e s t confirms the estimate o f the p o l a r diagram curve. I f the whole survey were s e n s i t i v i t y l i m i t e d , and i f there were no a r t e f a c t s on the map, i t would be r e l a t i v e l y easy to c a l -c u l a t e the rms d e v i a t i o n over a r e l a t i v e l y blank area to f i n d the no i s e component. However, i n . t h i s case t h e r e i s a combination o f co n f u s i o n l i m i t at the ce n t r e spreading to s e n s i t i v i t y l i m i t at the edges. At the c e n t r e , t h e r e f o r e , averaging many o b s e r v a t i o n s t o g e t h e r does not improve the l i m i t i n g f l u x d e n s i t y . As more o b s e r v a t i o n s are averaged, the r a d i u s from the centre at which c o n f u s i o n l i m i t t u r n s to s e n s i t i v i t y l i m i t i n c r e a s e s . In the l i m i t o f a very l a r g e number o f o b s e r v a t i o n s , the l i m i t i n g f l u x d e n s i t y as a f u n c t i o n o f r a d i u s on the map w i l l be constant u n t i l a c e r t a i n r a d i u s at which p o i n t i t w i l l r i s e v ery s h a r p l y to i n f i n i t y at the f i r s t zero o f the p o l a r diagram. T h i s p a r t i c u l a r case, however, i s not as s t r a i g h t f o r w a r d as d e s c r i b e d above because t h e r e are enough a r t e f a c t s to make i t d i f f i c u l t to estimate the n o i s e . By i n s p e c t i n g the map c a r e f u l l y i t seems t h a t t h i s e f f e c t seems to extend to a d e c l i n a t i o n - o f about 75 degrees. Table 5.1.3 g i v e s estimated e r r o r s f o r three d e c l i n a t i o n ranges and f o r f o u r f l u x d e n s i t y ranges. 202 Tabl e 5.1.3. Estimated Average E r r o r s i n F l u x D e n s i t y F l u x D e n s i t y D e c l i n a t i o n Percentage Range (Jy) Range (Degrees) E r r o r S>50 70 - 72 20 73 - 75 15 75 - 90 10 15SS<50 70 - 72 25 73 - 75 20 75 - 90 15 5£S<15 70 - 72 30 73 - 75 25 75 - 90 20 S<5 70 - 72 40 73 - 75 30 75 - 90 25 i 203 SPECTRAL INDICIES Low frequency s p e c t r a f o r most of the sources have been p l o t t e d u s i n g , where p o s s i b l e , p o i n t s at 178 MHz, 81.5 MHz, 38 MHz, and 22 MHz. These have been measured by the Cambridge 4C group (27), Branson ( 4 ) , W i l l i a m s e t a l (28), and the present t e l e s c o p e r e s p e c t i v e l y . For sources with s t r a i g h t s p e c t r a , o r f o r those with o n l y two p o i n t s a v a i l a b l e , a s p e c t r a l index has been i n c l u d e d i n the t a b l e . About h a l f o f the sources have been catalogued o n l y by Branson, and t h e r e f o r e w i l l have o n l y two p o i n t s on the s p e c t r a . Sources which have been l i s t e d i n Table 5.1.1 with an "NB" d e s i -g n a t ion are i n t h i s category. Except f o r about 5 cases i n which 38 MHz f l u x d e n s i t i e s are a v a i l a b l e , these s p e c t r a have been d e t e r -mined f o r the f i r s t time. Cases which show low frequency t u r n - o v e r are l i s t e d with a CL anno t a t i o n . Since o n l y peak f l u x e s are l i s t e d , some "CL" sources may a c t u a l l y have s t r u c t u r e l a r g e r than the: » beam. The c o r r e c t i o n f a c t o r s p u b l i s h e d by Roger, C o s t a i n , and B r i d l e were used f o r the 38 MHz and 178 MHz f l u x e s . F i g u r e 5.1.6 shows a p l o t o f source f l u x e s common to the Branson survey and the Artyukh (29) survey at 86 MHz. T h i s p l o t y i e l d s a s c a l e change o f 1.3 between the two surveys ( t a k i n g i n t o account the s l i g h t change i n f r equency). Roger, C o s t a i n , and B r i d l e suggest a s c a l e change o f .96 f o r the Artyukh f l u x e s . Branson f l u x e s have, t h e r e f o r e , been s c a l e d by 1.25. T h i s agrees w i t h i n the e r r o r s w i t h S c o t t and Shakeshaft (30) who suggest an upward r e v i s i o n o f the Kellerman, P a u l i n y - T o t h , and W i l l i a m s (31) s c a l e on which the Branson s c a l e was based. F i g u r e 5.1.7 shows examples o f the s p e c t r a l index p l o t s f o r Figure 5.1.6: A plot of the flux densities of two surveys near 80 MHz used to determine the f l u x scale of the Branson polar cap survey. 205 10 100 10 10 0 10 100 10 1 i • i i 4C74.13 i j 3C 173.1 • • t • i 1 i ! i • 1 3C379.1 f • • i 3C249.1 i 1 i i i 1 • 1 4C74.16 i 10 100 10 1 0 0 1000 MH: F i g u r e 5.1.7 a ) : Well determined s p e c t r a o f str o n g sources u s i n g the 4C, Branson, WKB, and 22 MHz f l u x e s from the present survey. 1 * i 1 • • • • 1 J • 4C78.7 • • 3C61.1 • $ 1 • • 1 1 3 C220.1 • • • t 1 1 1 m 1 3C184.1 * 206 10 1 0 0 F i g u r e 5.1.7 b) 10 1 0 0 1 0 0 0 M H z 207 1 • 1 1 • 1 1 ' 1 . 3 C 1 8 4 • X 1 • 1 1 • 1 i i 4 C 72 .15 • • • • • t 1 • 1 1 1 3C314.1 • • 1 i • 1 • • 3 C 2 6 8 . 1 1 • • t 1 i , • i • 3 C 3 0 9 . 1 i 10 1 0 0 10 1 00 1 0 0 0 M F i g u r e 5 .1 .7 c) 208 14 sources f o r which there are f o u r f l u x d e n s i t y measurements at 178 MHz, 81.5 MHz, 38 MHz, and 22 MHz. One o f the sources, 4C74.13, has a steep s p e c t r a l index. S e v e r a l o t h e r s show evidence of t u r n i n g over. F i g u r e 5.1.8 i s a histogram o f the s p e c t r a l i n d i c i e s i n Table 5.1.1. Sources which show a low frequency c u t - o f f are not i n c l u d e d . The mean s p e c t r a l index f o r t h i s sample i s .72. The standard d e v i a t i o n of the sample i s .37. The " t a i l " o f s p e c t r a l i n d i c i e s e xtending from 0.0 t o -0.5 may be a p o p u l a t i o n o f G a l a c t i c thermal sources. I f these are excluded, the mean becomes .78 and the standard d e v i a t i o n .34. At t h i s (low) frequency one expects a s e l e c t i o n e f f e c t a g a i n s t f l a t spectrum sources and f o r steep spectrum ones. Only the sources which have p r e v i o u s l y been catalogued at 81.5 MHz have been i n c l u d e d i n t h i s sample. Although they have not been catalogued y e t , i t i s obvious from the work which has been done so f a r t h a t t h e r e i s a comparatively s m a l l , but s i g n i f i c a n t number of new sources on the 22 MHz map. I f p l o t t e d on F i g u r e 5.1.8 they would add a " t a i l " o f h i g h s p e c t r a l index sources. 50 40 30-20 • -.5 0 1.0 1.5 F i g u r e 5.1.8: A histogram o f s p e c t r a l i n d i c i e s as determined from T a b l e 5.1.1. The c u t o f f at 1.5 i n d i c a t e s the f l u x d e n s i t y l i m i t o f the Branson 81.5 MHz survey. Chapter Six d L  Conclusions This project has demonstrated the a p p l i c a b i l i t y of aperture synthesis techniques to low frequency radio astronomy. The ef f e c t of solar a c t i v i t y on the ionospheric l i m i t s the useful observing periods to the solar minima. Moreover, the ionosphere has i r r e -gular variations during these periods which further l i m i t observing time. Therefore, for high resolution observations at low frequen-c i e s , i t i s usefu l to have an instrument capable of making a map over a f i e l d i n a short time compared with ionospheric variations. Also, c o l l e c t i n g the data at the le v e l of in d i v i d u a l v i s i b i l i t i e s rather than combining them i n an antenna system allows phase and amplitude corrections to be made "a p o s t e r i o r i " . This instrument was designed and b u i l t around an antenna which already existed f o r another purpose. The design of a new telescope based upon sim i l a r p r i n c i p l e s might not be exactly the same. There was some d i f f i c u l t y encountered i n pointing the elemental antennas very f a r from the zenith. A new system would u t i l i z e a design which would avoid t h i s problem, perhaps involving a combination of physical movement and array phasing. Also, an antenna capable of being adjusted i n Hour Angle would be useful so that other areas of sky could be mapped (as outlined i n chapter 2.1). A new system design might include some redundant spacings and possibly enough correlators to be able to put "phase closure" constraints on the measurements. The phase closure technique has been used in long-baseline interferometry systems. I t i s similar i n nature to the "chaining" method of measuring phases described i n chapter 3.11. So f a r , however, straight-forward methods of applying the constraints have not been developed, e s p e c i a l l y for complex situations such as described i n t h i s thesis. More research i s required i n t h i s area. Complex systems such as the one described here are d i f f i c u l t to maintain with a small s t a f f ( i n t h i s case one person). It i s , therefore, worth spending extra e f f o r t i n the design stage incor-porating quick methods of te s t i n g . A means of quickly displaying the general state of the system i s also useful. The advent of cheap microprocessors i n the past couple of years should make these things easier to accomplish than before. One of the greatest maintenance problems involved the cabling systems used to d e l i v e r l o c a l o s c i l l a t o r , clock, and c a l i b r a t i o n signals to the correlator units. There are hundreds of cable connections involved. These connections were the main source of equipment f a i l u r e . A more e f f i c i e n t use of cable and connectors could e a s i l y be designed now with the aid of new developments i n el e c t r o n i c s . Although i t was not intended at the outset, most of the observing was done "b l i n d " . In other words, i t was not possible to compute even a rough map i n order to assess observing conditions and instrumental e f f e c t s . In any new system i t would be an improvement to determine more accurately the amount of e f f o r t required to make maps, and to ensure that s u f f i c i e n t computing f a c i l i t i e s are available. Although the processing of the observations made with t h i s instrument i s not complete, the r e s u l t s obtained so f a r are encouraging. The source l i s t contains about 300 isola t e d sources. The spectral index at low frequencies has been defined for many of them for the f i r s t time, e s p e c i a l l y those between declinations of 80 and 87 degrees. Some problems s t i l l e x i s t , however, such as the large sidelobes near the strongest sources (see chapter 5), and the grating r i n g of Cygnus A. These problems are currently under inv e s t i g a t i o n , and w i l l l i k e l y be soluble with modest e f f o r t More sophisticated processing techniques may allow an increase i n dynamic range. The observations made in the outer part of the u-v plane have not been reduced to maps as yet. This part of the system was not operating as early as the rest of i t . Consequently, there are not as many observations made. Also, because of the geometry of the system, the maps made with t h i s part of the u-v plane take much longer to compute. However, the v i s i b i l i t i e s obtained with these interferometers look reasonable, and there i s a good chance that several observations made with t h i s part of the system w i l l y i e l d maps with a resolution of 15 arc min. Because t h i s map i s a sort of "snapshot" of the sky (12 hour exposure), i t i s suitable for finding independent positions of sources, e s p e c i a l l y for those not previously catalogued. This procedure requires source finding software which w i l l be developed at the Dominion Radio Astrophysical Observatory f o r t h i s purpose. As the map stands, there i s some v a r i a t i o n i n the shape of the beam across the map. This v a r i a t i o n can be removed to a large extent, thus enabling source positions to be found more e a s i l y . It should be noted that for source surveys done with T instruments ionospheric r e f r a c t i o n , and the problem of joining scans make 213 finding independent positions d i f f i c u l t . The data as presented here are optimized for detection of unresolved or p a r t i a l l y resolved sources. Although no e f f o r t has been applied so f a r , i t i s conceivable that large scale, low brightness Galactic components are v i s i b l e . Removal of point sources would aid i n the detection of these components. F i n a l l y , i t i s hoped that the r e s u l t s obtained with t h i s instrument, combined with others, w i l l lead to a greater under-standing of the nature of radio sources. Also, i t i s hoped that t h i s experiment has led to a greater understanding of the techniques needed to observe at low frequencies. 214 References (1) CH. Costain, J.D. Lacey, and R.S. Roger, "Large 22 MHz Array for Radio Astronomy", IEEE Transactions on Antennas and  Propagation, Vol. AP-7, No. 2, 162-196, March 1969. (2) A.H. B r i d l e and P.A. Feldman, "Radio I d e n t i f i c a t i o n s of Weak Extragalactic X-ray Sources", Nature Phy. Science, Vol. 235, February 19 72. (3) M. Ryle and A.C. N e v i l l e , "A Radio Survey of the North Polar Region with a 4.5 Minute of Arc Pencil-Beam System", Mon. Not. R. astr. Soc., Vol. 125, No. 1, P.39, 1962. (4) N.F.B.A. Branson, "A Radio Survey of the Sky North of Declination 70° at a Frequency of 81.5 Mc/s", Mon. Not. R. astr. Soc., Vol. 135, Pp. 149-174, 1967. (5) M.S. Longair, "The Counts of Radio Sources", Soviet Physics-Uspekhi, Vol. 12, No. 5, P. 673, A p r i l 1970. (6) N.M. McKay, " P r a c t i c a l Solutions to Phase and Delay Problems in a Compound Interferometer", Ph.D. Thesis, School of E l e c t r i c a l Engineering, 1969. University of Sydney. (7) F.K. Bowers and R.J. Klinger, "Quantization Noise of Correla-t i o n Spectrometers", Astron. Astrophs. Suppl., Vol. 15, Pp. 373-380, 1974. (8) A. Hewish, "Extrapolation of the Number-Flux Density Relation of Radio Stars by Sheuer's S t a t i s t i c a l Method", Mon. Not. R. astr. Soc., Vol. 123, No. 2, Pp. 167-181, 1961. (9) P.A.G. Sheuer, "A S t a t i s t i c a l Method f o r Analyzing Observations of Faint Radio Stars", Proc. Camb. P h i l . Soc. , Vol. 53, Part 3, Pp. 764-773, 1957. (10) CH. Costain and R.S. Roger, 22 MHz Survey, unpublished data. (11) I. Wolff, "Determination of the Radiating System which w i l l Produce a Specified Directional C h a r a c t e r i s t i c " , Proceedings of the Ins t i t u t e of Radio Engineers, Vo1. 2 No. 5, 1937. (12) I.S. Sokolnikoff and R.M. Redheffer, "Mathematics of Physics and Modern Engineering", McGraw-Hill, 1958. (13) S.A. Schelkunoff and H.T. F r i i s , "Antennas, Theory and Practice", Wiley, 1952. (14) J.D. Kraus, "Antennas", McGraw-Hill, 1950. (15) R.E. C o l l i n , "Foundations for Microwave Engineering", McGraw H i l l , 1966. (16) E.J. Wilkinson, "An N-Way Hybrid Power Divider", I.R.E. Transactions on Microwave Theory and Techniques, p. 116 January 1960. (17) H. Jones, Geodetic Survey of Canada, private communication. (18) M. Ryle and A. Hewish, "The Synthesis of Large Radio Telescopes", Mon. Not. R. astr. Soc. , Vol. 120, P. 220, 1960. (19) W.N. Christiansen and J.A. Hogbom, "Radiotelescopes", Cambridge University Press, 1969. (20) W.N. Christiansen and J.A. Warburton, Australian J. Phys., Vol. 6, P. 262, 1953. (21) R.N. Bracewell and A.C. Riddle, "Inversion of Fan-Beam Scans i n Radio Astronomy", Astrophys. J . , Vol. 150, Pp. 427-434, November 1967. (22) R.H. Frater, Ph.D. Thesis, School of E l e c t r i c a l Engineering, 1966. University of Sydney. (23) M. Born and E. Wolf, " P r i n c i p l e s of Optics", Perqamon Press, 1969. 216 (24) A.H. B r i d l e , "The spectra of Galactic and Extragalactic Radio Sources" Ph. D. Thesis, University of Cambridge, 1967. (25) J.D. Kraus, "Radio Astronomy", McGraw-Hill, 1966. (26) R.S. Roger, A.H. B r i d l e , and CH. Costain, "The Low-Frequency Spectra of Non-Thermal Radio Sources", Astron. J . , Vol. 78, No. 10, December 1973. (27) J.F.R. Gower, P.F. Scott, and D. W i l l s , "A Survey of Radio Sources i n the Declination Ranges -07° to 20° and 40° to 80°", Mem. R. astr. Soc., Vol. 71, Pp. 49-144, 1967. (28) P.J.S. Williams, S.Kenderdine, and J.E. Baldwin, "A Survey of Radio Sources and Background Radiation of 38 Mc/s", Mem. R. astr. Soc., Vol. 70, Pp. 53-110, 1966. (29) V.S. Artyukh, V.V. Vitkevich, R.D. Dagkesamanskii, and V.N. Kozhuklov, "Flux Densities and Spectral Indicies for the Sources i n the 3C and 3CR Catalogues", Soviet Astronomy-AJ, Vol. 12, No. 4, February 1969. (30) P.F. Scott, and J.R. Shakeshaft, "The Flux Density Scale for Radio Sources at 81.5 MHz", Mon. Not. R. astr. Soc., Vol. 155, P. 19p, 1971. (31) K.I. Kellerman, I.I.K. Pauliny-Toth, and P.J.S. Williams, "The Spectra of Radio Sources i n the Revised 3C Catalogue", Astrophys. J . , Vol. 157, P. 1, 1969. (32) C.C.I.R. Report AM/2, "Ionospheric Limitations to Ground-Based Radio Astronomy Below 20 MHz", 1976. (33) W.M. Smart, "Spherical Astronomy", Cambridge University Press, 1956. (34) W.A. Rheinfelder, "Design of Low-Noise Transistor Input C i r c u i t s " , Hayden Book Co. , 1964. (35) A. Papoulis, "Probability, Random Variables, and Stochastic Processes", McGraw-Hill, 1965. (36) R.M. Bracewell, "The Fourier Transform and Its Application" McGraw-Hill, 1965. (37) Van Vleck, Radio Res. Lab., Harvard University Report #51, 1943. (38) C.H. Costain, A.H. B r i d l e , and P.A. Feldman, "Decametric Radio I d e n t i f i c a t i o n of an Extragalactic X-ray Source" Astrophys. J . , Vol. 175, No. 1, 1972. (39) P. Kissam, "Surveying", McGraw-Hill, 1947. 218 Appendix A l Derivation of the C e l e s t i a l Orientation of the Telescope The following i s a derivation of the formulae for d and h (defined i n chapter 4.4.1) expressed as a function of the angles NX and ZZ'. NX and ZZ' are measurable d i r e c t l y using surveying techniques. Figure A l . l defines these angles with respect to the lo c a l horizontal plane; Figure A1.2 defines them with respect to the c e l e s t i a l sphere. A l l arcs i n figure Al.2 are great c i r c l e s . The horizontal plane i s defined by great c i r c l e ENW with pole Z (the l o c a l zenith). The a x i a l plane of the interferometer i s defined by Z'BX. The equatorial plane i s defined by ERW with pole P (the north c e l e s t i a l pole). The la t i t u d e of point Z i s defined 0 a PN. The l o c a l meridian c i r c l e i s PZRN. Its upper branch i s PZ (from which longitude i s measured). The zeroth meridian i s d e f i -ned as PM. Therefore, the longitude of Z i s X rs MR + TT One of the angles to be found i s d, the angle PB between the north c e l e s t i a l pole and the a x i a l plane of the interferometer. The other angle i s h, the angle between the l o c a l meridian and the meridian containing the west end of the baseline. i - TT _ _ h . j - RQ i g u r e A l . l : D e f i n i t i o n s o f angles NX and ZZ' i n the l o c a l a l t i t u d e - a z i m u t h coord ina t system. 220 A l l Arcs Great C i r c l e s 1 F i g u r e A l . 2 : The C e l e s t i a l Sphere. The two angles that can be measured are ZZ', the zenith angle of the a x i a l plane of the interferometer, and NX, the angle by which the a x i a l plane i s skewed i n the l e v e l plane from the north-south l i n e . This angle i s considered p o s i t i v e i n a counter clockwise d i r e c t i o n when viewed from the zenith. Consider the following spherical trigonometry ( a l l reference to formulae can be found i n "Spherical Astronomy" (33). t In Triangle NXZ: NZ = -| ZX - -| NZX = NX 1 In Triangle ZZ'N: ZX = | Z'X = | Z'XZ = ZZ' 2. In Triangle ZCX: Z'XZ = CXZ = ZZ' from 2. 3. CZX m NZX « NX from 2. 4. ZX — „ • 5. Using the polar formula (33) and 3., 4., 5.: -cosZCX = cosCZXcosCXZ - sinCZXsinCXZcosZX y i e l d s cosZCX = -cosNXcosZZ'. 6. Using the law of sines (33) twice: sinCX sinZX sinCZX " sinZCX sinNX y i e l d s sinCX = and sinZCX sinZC sinZX sinCXZ sinZCZ y i e l d s sinZC = sinZZ' sinZCX 222 Using the law of cosines (33) cosZC = cosCXcosZX + sinCXsinZXcosCXZ Yields cosZZ- = f f f § 9 . Using 6., 7. , 8., 9. , tanZZ * t a n Z C " IlnNX- 1 0 • In Triangle PCB: Using the law of sines: sinPB sinPC sinPCB * sinPBC 1 1 * by d e f i n i t i o n PBC = -J, PB - d 12. By summation of angles on a plane tangent to the c e l e s t i a l sphere at C PCB = TT - ZCX 13. Using 11. , 12. , 13. : sin d = sinPC sinZCX 14. By summation of great c i r c l e angles: NZ - = PN + PC + ZC 15. By d e f i n i t i o n PN s 0 16. Using 14., 15., 16.: sin d - cos (0 + ZC) sinZCX 17. Therefore, sin d can be found from NX and ZZ' by 17., 10., and 6. 223 In Triangle RCQ; QRC = -| 18. from 13. PCB = RCQ = TT - ZCX Using the polar formula and 18. : -cosRQC = cosQRC cosRCQ - sinQRC sinRCQ cosRC yi e l d s cosRQC = sin ( TT - ZCX) cosRC 19. By d e f i n i t i o n RP = By summation of spherical angles RC » + PC 21. Using 15., 16. , 21: RC ss TT — 0 — ZC 22. Using 19., and 22.: cosRQC = -sin(ZCX) cos(0+ZC) 23. Using the law of sines: sinRQ sinRC sinRCQ ~ sinRQC from 18., 22., 24.: TT 24. d„T>n sin (0 + ZC) sinZCX sinRQ = : — T , - , - 25. sinRQC By d e f i n i t i o n h =. -j - RQ 26. Using 25., and 26.: 224 cos(h) - s i n ( 0 + ZC) sinZCX sinRQC T h e r e f o r e , u s i n g 6., 10., 19.,.and 27.,cos(h) Can be found from ZZ' and NX. 225 Appendix A2  P r o p e r t i e s o f a 1 B i t by Analog C o r r e l a t o r I t i s o f i n t e r e s t f o r t h i s p r o j e c t to know how q u a n t i z a t i o n at the one b i t l e v e l o f one o f the i n p u t s to a s i g n a l m u l t i p l i e r i n c r e a s e s the v a r i a n c e o f the output over the " p e r f e c t " analog c o r r e l a t o r . In t h i s i n s t a n c e the v a r i a n c e can be d e r i v e d f o r a l l l e v e l s o f c o r r e l a t i o n c o e f f i c i e n t without approximation. The s i g n a l s x ( t ) and y ( t ) ( F i g u r e A2.1) are assumed to be normal random pro c e s s e s ( s t a t i o n a r y and e r g o d i c ) . z ( t ) i s the output o f a m u l t i p l i e r i n which one o f the s i g n a l s has been d i g i -t i z e d at the 1 b i t l e v e l . z ( t ) . ( s i g n x ( t ) ) - y ( t ) » ^ ( t ) ^ At any given time x and y can be co n s i d e r e d to be samples from normal d i s t r i b u t i o n s with zero mean and standard d e v i a t i o n s a = /R (o)' and a * /R (o)' , R ( t ) and R„„(t) are the auto-c o r r e l a t i o n f u n c t i o n s o f the processes x ( t ) and y ( t ) . x and y are a l s o j o i n t l y normal and have c o r r e l a t i o n c o e f f i c i e n t R ( T ) r ( T ) = xy yy /R (O)R TOT V xx I t i s r e q u i r e d to f i n d E{z} and E(z } where "E{ }" denotes "expected v a l u e " . These can be found u s i n g the general formula E { g i ( x ) g 2 ( y ) ) « E { g i ( x ) E { g 2 ( y ) [ x } } (35) where E { g 2 ( y ) | x ] i s read "expected value o f g 2 ( y ) giv e n x". 226 x(t) X 1-Bit D i g i t i z e r F i g u r e A2.1: A 1 b i t by a n a l o g c o r r e l a t o r . The o u t p u t o f the s i g n a l m u l t i p l i e r i s z ( t ) . The o u t p u t o f t h e i n t e g r a t o r i s q( t ) . g l ( x ) = |x| 9 2 ( y ) ** Y z = 9 1 ( x ) g 2 ( y ) E(z} « Ef-^-} - E f ^ E f y l x } } r a x but E[y|x} = XY y - found by d i r e c t i n t e g r a t i o n x r ..a. 2 E f | x j 5 = J ^ * a x - found by d i r e c t i n t e g r a t i o n E{;Z} « J T a r Y xy E{z 2} = E { ^ } - E f ^ i - E{y 2 |x}} Ix x E f y 2 | x } = a 2 ( l - r 2 ) + r 2 a 2 x 2 - found by d i r e c t y xy xy y J 2 . - - .-• CTx i n t e g r a t i o n E{-f^} - E{|x( 2} = a 2 | x r S u b s t i t u t i n g g i v e s E{z 2} = a  2 y From E[z} we have t h a t the mean value o f the output i s u, = /— a r z v TT y xy From E{z} and E(z } we have the v a r i a n c e o f the output. 228 a 2 „ 0 2 _ 2 2 c t 2 = 2 ( 1 _ 2 2 ) z y T T x y y y TT xy The r a t i o o f (1) and (2) i s t h e s i g n a l - t o - n o i s e r a t i o s/ W r x y v TT 2~» z  TT "xy A comparison can now be made w i t h a p e r f e c t " a n a l o g by a n a l o g " m u l t i p l i e r w i t h t h e same i n p u t s i g n a l s x ( t ) and y ( t ) . We w i l l c a l l t h e p r o d u c t p ( t ) . E{p] = E { x y ] = r a c xy x y E{p 2 } « a 2 a 2 * 2r 2 a 2 a  2  c x y xy x y mean = (j, = r a a (3) p xy x y V a r i a n c e « a 2 = E ( p 2 } - E 2 f p ] =» a 2 a 2 - r 2 a 2 c r 2 p K l F x y xy x y I n t h i s case the s i g n a l - t o - n o i s e r a t i o i s 7, (4) s/ - r x v N f ^ ~ ^ v xy 2 F o r t h e a p e r t u r e s y n t h e s i s case the r x y « l . Terms i n can be i g n o r e d , and t h e d e g r a d a t i o n i n s i g n a l - t o - n o i s e i s J'~ ' f o r a o n e - b i t by a n a l o g c o r r e l a t o r . N o t i c e t h a t t h e mean v a l u e o f t h e o u t p u t i s l i n e a r i n r f o r ^ xy th e o n e - b i t by a n a l o g c o r r e l a t o r . There i s no Van V l e c k c o r r e c t i o n ( 3 7 ) . Note a l s o t h a t i n the case i n wh i c h a d d i t i v e n o i s e dominates t h a t 2 CT ~ s a 2 n r epresen ts s i g n a l power represen ts no i se power. Appendix A3 Design, C o n s t r u c t i o n and T e s t i n g o f the Receivers The d e s i g n o f the I.F. a m p l i f i e r s was based upon t h a t deve-loped by R.H. F r a t e r (22) f o r use with the F l e u r s Radio Telescope The method b a s i c a l l y produces a good approximation to a maximally f l a t response u s i n g a common i n t e r s t a g e t r a n s f o r m e r d e s i g n . The design can be r e a l i z e d u s i n g a cascode a m p l i f i e r at each stage. O b v i o u s l y , b e i n g able to use a s i n g l e c i r c u i t f o r a l l t h r e e stage o f f e r s c o n s i d e r a b l e p r o d u c t i o n advantages. An o u t l i n e of the tuned c i r c u i t d e s i g n i s as f o l l o w s : Pole p o s i t i o n s f o r a maximally f l a t response o f bandwidth Ato occur on c i r c l e c e n t r e d at <D on the imaginary a x i s o f the p o l e - z e r o plane with diameter Auu. T h i s assumes ( f o r Att> «uo„) t h a t the c o n t r i b u -t i o n s from the zeros at the o r i g i n c a n c e l those from the p o l e s i n the n e g a t i v e h a l f - p l a n e ( F i g u r e A3.1). of a doubled-tuned c i r c u i t shown i n F i g u r e A3.2. L l ' L 2 ' a n d M a r e n o t d i r e c t l y measurable parameters o f the transformer. They are r e l a t e d to the measurable short c i r c u i t and open c i r c u i t inductances: o T h i s p o l e zero c o n f i g u r a t i o n can be r e a l i z e d with the model L L po so s: L = L 1 2 + M + M L L ps ss - L a + L2||M - L 2 + L j |M where X||Y » XY/(X+Y) and p, s denote primary, secondary A F i g u r e A3.1: Pole-zero p o s i t i o n f o r a maximally f l a t f i l t e r . gure A3.2: Model o f a doubly tuned c i r c u i t . . and inductances and M L are the "leakage"  i s the "mutual" i n d u c t ance. r e s p e c t i v e l y . I t i s necessary, then, to f i n d equations r e l a t i n g the p o l e - z e r o plane parameters Au>, iu , and a to R , C , L„ , M, L_, C , R . They o p p 1 2 s s are found i n terms o f two parameters, K J l - ^ , yl P S the c o u p l i n g c o e f f i c i e n t , and T = 2 0 ^ Y 5 1 a parameter r e l a t i n g primary and secondary damping where T + R C and T = R C . P P P s s s The f o l l o w i n g u s e f u l r e l a t i o n can e a s i l y be d e r i v e d from the above M a Ky"li _L po so The g e n e r a l equations are given i n R.H. F r a t e r ' s Ph.D. T h e s i s , and are v ery unwieldy. Only s i m p l i f i e d v e r s i o n s w i l l be r e q u i r e d here Y i s a f r e e parameter ( f o r the c i r c u i t o f F i g u r e A 3 . 2 ) , and must be s e l e c t e d on the b a s i s o f the output impedance o f the generator which d r i v e s the tuned c i r c u i t . S i nce the cascode c i r c u i t , o f f e r i n g advantages to be d i s c u s s e d l a t e r , w i l l be used, Rp must be h i g h i n order to match the output impedance of the common case t r a n s i s t o r . An approximation i n which T s 00 and P Y = 1 i s s u i t e d to t h i s a p p l i c a t i o n . I f , furthermore, AID « co the f o l l o w i n g e quations r e s u l t : 233 K = 2a where a = Ato/2 s " 4a in C sine*/ o s In t h i s case Aco = . 3 MHz and u> » 5 MHz, so t h a t o 7 — = . 0 6 . o T h e r e f o r e , a and or a f f e c t o n l y R , the o n l y c i r c u i t change r e q u i r e d from one stage to the next. T h i s makes sense i n t u i t i v e l y , because f o r narrow bandwidths, the c o u p l i n g o f the transformer i s very s m a l l . T h e r e f o r e , the primary and secondary inductances are r e l a t i v e l y independent of each o t h e r . The most p r a c t i c a l method o f making the c o i l s i s by experiment. T h i s process i s r a t h e r easy i f a few c o i l s with known p r o p e r t i e s are a v a i l a b l e as models. For narrow bandwidths i t i s sometimes d i f f i c u l t to achieve high enough Q. In t h i s case t u b u l a r ceramic c o i l forms were used. A f t e r each t r i a l the open c i r c u i t and short c i r c u i t parameters are measured, and v a l u e s o f C , C , and R , ^ ' p s s are c a l c u l a t e d . I t i s important to have v a l u e s o f and C g which are much l a r g e r than the t r a n s i s t o r and " s t r a y " c a p a c i t a n c e s . R g should be small enough t h a t leakage r e s i s t a n c e and c o i l l o s s e s are not an important p a r t o f the c i r c u i t . In o t h e r words, the Q o f the c o i l s should be hig h enough t h a t a r e s i s t o r i s needed i n the secondary c i r c u i t o f each stage. 234 S e v e r a l t o o l s are needed to make s u c c e s s f u l t r a n s f o r m e r s . A t e s t j i g i s very u s e f u l i n which c o i l s can be q u i c k l y i n s e r t e d and "tuned up" to ev a l u a t e i t s c e n t r e frequency and damping. A c o i l winding d e v i c e which can r e p e a t a b l y produce m e c h a n i c a l l y s t a b l e c o i l s i s necessary. Subsequent d i s c u s s i o n w i l l d well more thoroughly on the t o p i c o f f a b r i c a t i o n . The p r i n c i p l e of t h i s s o r t o f a c t i v e f i l t e r i s th a t the stages of t u n i n g are independent o f each o t h e r , i n oth e r words, th a t the a c t i v e elements p r o v i d e enough i s o l a t i o n f o r adjustments to be made on one stage without a f f e c t i n g neighbouring ones. The cascode a m p l i f i e r i s a well-known c i r c u i t which p r o v i d e s t h i s s o r t o f i s o l a t i o n . In terms o f small s i g n a l admittance parameters, ^11' ^12' Y 2 1 ' ^ 22' ^ n P u t admittance and output admittance can be expressed as f o l l o w s : _ y 2 1 Y 1 2 22 T j rL 'out "* '22 " y a i + y s where y L , y g are load and source admittances r e s p e c t i v e l y . For a cascode a m p l i f i e r Y-j^' the i n t e r n a l feedback parameter, i s about 2 o r d e r s o f magnitude lower than f o r a s i n g l e common e m i t t e r t r a n s i s t o r . The r e s u l t i s that y. and y . are r e l a t i v e l y inde-l n J o u t J pendent o f y L and y g r e s p e c t i v e l y . Furthermore, because y ^ 2 i s sm a l l , the t r a n s i s t o r i s much l e s s l i k e l y to o s c i l l a t e . I n t e g r a -ted c i r c u i t s are a v a i l a b l e which can be used as a cascode p a i r . An MC 1550 was s e l e c t e d f o r use i n the I.F. s e c t i o n . I t has reasonably good bandwidth, has an e x t r a t r a n s i s t o r which can be used f o r gain c o n t r o l , and i t has i n t e r n a l b i a s i n g . I t i s , however, too n o i s y to use i n the p r e a m p l i f i e r stage. These tuned a m p l i f i e r stages must be connected t o g e t h e r , and so t h a t the i n p u t impedance o f the stages must a l s o be ev a l u a t e d . The cascode a m p l i f i e r can be d e s c r i b e d r o u g h l y as a common-emitter t r a n s i s t o r c o n f i g u r a t i o n o p e r a t i n g i n t o a s h o r t - c i r c u i t , f o l l o w e d by a common base c o n f i g u r a t i o n d r i v e r by a c u r r e n t source. T h i s i s t r u e because the output impedance o f a common-emitter t r a n s i s -t o r i s much h i g h e r than the i n p u t impedance o f a common base t r a n s -i s t o r . T h e r e f o r e , the input to the cascode behaves as a common e m i t t e r t r a n s i s t o r . The b i a s s t a b i l i z i n g e f f e c t o f unbypassed e m i t t e r r e s i s t a n c e as w e l l as i t s e f f e c t upon i n p u t impedance are w e l l known. T h i s c o n f i g u r a t i o n i s shown i n F i g u r e A3.3 along with an approximate model f o r the lower t r a n s i s t o r . The i n p u t r e s i s -tance i s R. « h. + ( l + h ^ ) R I, i i e f e e b With modest v a l u e s o f h. , 1100 A , and o f h,. , 50, R. i s e f f e c t -i e ' . ' f e ' ' x i v e l y double h. f o r R =* 20 A. Measurements were made at 5.0 MHz i e e o f input impedance with an Hewlett Packard Vector Impedance Meter. For R e =s 20 A a complex impedance o f 2.3K /-45° ohms corresponding to a p a r a l l e l R. » 3.3K and C. =9.8 p f . ^ xn i n ^ With t h i s i n f o r m a t i o n i t i s now p o s s i b l e to proceed with the des i g n o f the tuned c i r c u i t . Of course, a number o f c o n d i t i o n s must be si m u l t a n e o u s l y met. The Q o f the primary c o i l must be hi g h , meaning t h a t the primary inductance cannot be too high. On the o t h e r hand, i f the primary inductance i s too low, i t i s d i f f i -c u l t to wind a c c u r a t e l y . The transformer f i n a l l y used had a primary open c i r c u i t inductance o f 10.2 \xh, and an a d j u s t a b l e secondary inductance o f about 16.2 p-h. The adjustment o f the 236 Vj —AAA " r 1 1 ^ 'b J|Re(T)hf e'o F i g u r e A 3 . 3 : The input c i r c u i t o f a cascode a m p l i f i e r . Z=» F i g u r e A 3 . 4 : An impedance t r a n s f o r m i n g c i r c u i t to go between the secondary tuned c i r c u i t o f one stage to the i n p u t of the f o l l o w i n g stage. secondary inductance was a l s o arranged to a f f e c t the c o u p l i n g but not the primary inductance. The r e s u l t i n g primary Q was c a l c u l a -ted to be about 312 u s i n g the quoted output r e s i s t a n c e o f 100 K A. The loaded Q o f the primary inductance as d e r i v e d from the band-width o f the resonance when the secondary tuned c i r c u i t i s tuned away i s about 50. The a c t u a l unloaded Q i s t h e r e f o r e somewhere between 50 and 300. The f i n a l proof o f whether t h i s i s high enough comes when the c i r c u i t i s used to d e f i n e the p a i r of p o l e s at a m 15°. The c a l c u l a t e d primary and secondary c a p a c i t a n c e s are 99 pf and 62.4 p f r e s p e c t i v e l y . A 75 p f c a p a c i t o r i n p a r a l l e l with a 5.5 - 15 pf v a r i a b l e c a p a c i t o r was used. The remaining c a p a c i t a n c e was produced by the output o f the t r a n s i s t o r . Note t h a t there i s no q u e s t i o n t h a t changes i n the output c a p a c i t a n c e o f the t r a n s i s -t o r can o n l y be very small i n comparison with the t o t a l primary c a p a c i t a n c e . The secondary c a p a c i t a n c e i s another matter. I t must be c o n s i d e r e d i n r e l a t i o n t o the f o l l o w i n g stage. From the above design equations The p a r a l l e l i n put impedance o f s e v e r a l K.n. p r o v i d e s f a r too much damping. A l s o , there i s a 10 pf i n p u t c a p a c i t a n c e which i s small by comparison with the 62.4 pf c a p a c i t o r . T h i s problem can be avoided by t r a n s f o r m i n g impedance as i l l u s t r a t e d i n F i g u r e R s = C ( p f ) s i n a s 265 K 16.5 K f o r cv = 15° 6.0 K f o r cv a 45° 4.4 K f o r a = 75° A3.4. 238 The f o l l o w i n g approximate formula can be d e r i v e d u s i n g s t a n -dard c i r c u i t theory: 2 2 c +c c Real(Z) = R h = R. (^) 1 1 1 s C C 1 2 where C = — i s the e f f e c t i v e t u n i n g secondary c a p a c i t a n c e . Using then Real(Z) = 32K, R± = 3K, and C g = 62.4 p f C0 = 204 p f , and C = 90 p f . The 204 pf c a p a c i t o r swamps the i n p u t c a p a c i t a n c e o f the next stage, and the e f f e c t i v e l o a d i n g o f 32K upon the p r e v i o u s tuned stage i s not too l a r g e compared with 16.6K. T h i s step completes the d e s i g n o f the tuned stages. A method f o r measuring the bandshape o f each stage i s necessa-r y to be able to a l i g n i t . There are t h r e e stages. For obvious reasons they are c a l l e d underdamped, c r i t i c a l l y damped, and over-damped f o r a = 15°, 45°, 75° r e s p e c t i v e l y . The band shapes o f each o f these stages as w e l l a s t t h a t o f the f i n a l bandshape are shown i n F i g u r e A3.5. A marker generator was c o n s t r u c t e d to generate frequency markers at 1 MHz and at 100 kHz i n t e r v a l s . Each stage was a l i g n e d to the c a l c u l a t e d r a t i o o f the c e n t r e f r e -quency g a i n to t h a t at the frequency o f the 3 db p o i n t s o f the f i n a l f i l t e r . These r a t i o s can be d e r i v e d as f o l l o w s : (see F i g u r e A3.6): For t r i a n g l e s STQ and PQR the f o l l o w i n g two r e l a t i o n s h o l d r e s p e c t i v e l y 1 2 m 2a sin?5 1^ + \ 2 a ( 2 a ) 2 239 Underdamped Stage C r i t i c a l l y Damped Stage Overdamped Stage F i g u r e A3.5 a ) : The bandshapes of the th r e e stages of the r e c e i v e r . The th r e e c e n t r a l markers are at 22.150 MHz, 22.250 MHz, and 22.450 MHz. The amplitude s c a l e i s l i n e a r i n power, t h a t i s , h a l f o f the peak value i s the 3 db p o i n t . Figu re A3 .5 b ) : The f i n a l product o f the three bandshapes i n pa r t a) of t h i s f i g u r e . 241 F i g u r e A 3 . 6 : Geometry o f po le p o s i t i o n s hear the resonance o f the doubly tuned c i r c u i t s tage. 242 The gains at the centre frequency and at the f i n a l 3 db p o i n t s 2 are r e s p e c t i v e l y p r o p o r t i o n a l to a and l ^ ^ * T h e i r r a t i o i s G3db 1 1 1 2 ~G~~ : 2~ c a S u b s t i t u t i n g the above equations i n t o the r a t i o formula g i v e s 2 s i n a For the three s e t s o f p o l e s these r a t i o s are 5.72 db f o r a = 15° -3.00 db f o r a « 45° -5.72 db f o r a = 75° Adjustments are made to each stage u n t i l the frequency markers are p o s i t i o n e d a p p r o p r i a t e l y . A wide dynamic range, square law d e t e c t o r was used so that power could be measured d i r e c t l y . S e v e r a l methods of alignment were t r i e d . The most s u c c e s s f u l was to a l i g n the l a s t stage f i r s t ; then the l a s t two were a l i g n e d , e t c . The stages were arranged so th a t the underdamped stage i s i n the middle, and the c r i t i c a l l y damped stage at the end. In t h i s manner, each stage was set up " l o o k i n g i n t o " i t s f i n a l impedance. With o n l y three adjustments f o r each stage, the task c o u l d be completed very q u i c k l y . Because o f the high gain o f the I.F. s t r i p , i n a d v e r t a n t l y c r e a t e d feedback paths may le a d to o s c i l l a t i o n . I t i s t h e r e f o r e common to s h i e l d one stage from the next. An i n t e r e s t i n g e f f e c t was n o t i c e d a f t e r the f i r s t I.F. s t r i p was a l i g n e d . When the 243 cover was put on top, i t had a d r a s t i c e f f e c t on the bandshape. The d i s c o v e r y was e v e n t u a l l y made that the s h i e l d s on e i t h e r s i d e o f each stage o f the I.F. s t r i p were c o u p l i n g with the transformer to form a shorted t u r n . T h i s was c o r r e c t e d by s l i c i n g a small p i e c e o f f the top o f each s h i e l d so th a t i t d i d not co n t a c t the l i d . One o f the keys to being a b l e to phase match the r e c e i v e r s i s making them i d e n t i c a l to the l a s t d e t a i l . In p a r t i c u l a r , the I.F. c o i l s are probably the most important. S o l e s o i d a l c o i l forms made o f ceramic were used. About 150 were r e q u i r e d . T h e i r diameters were measured i n two p e r p e n d i c u l a r d i r e c t i o n s as i n F i g u r e A3.7. As shown, t h e i r c r o s s - s e c t i o n a l area i s approximately p r o p o r t i o n a l to the sum o f the d e v i a t i o n s from a nominal diameter. A histogram o f 6^  + 6^  was p l o t t e d f o r a l l the c o i l forms. The c e n t r a l 150 were s e l e c t e d f o r the I.F. stages. The nominal diameter, d, was .260 inches; the mean diameter was .2599 inches; the ranges of 6^ + 6^ was approximately ± .004 inches. The c o i l s were wound with #40 AwG wire w i t h an o u t s i d e diameter ( i n c l u d i n g i n s u l a t i o n ) o f .003 i n c h e s . S e v e r a l batches of wire were t r i e d b e f o r e one c o u l d be found t h a t was s u f f i c i e n t l y u niform. The spacing between the c o i l s was e q u i v a l e n t to 49 t u r n s . At f i r s t c o i l s were made by winding 89 tu r n s f o r the f i r s t winding, then s t a r t i n g the next 40 tu r n s f o r the second winding adjacent to the f i r s t . The l a s t 49 t u r n s on the f i r s t winding were then unwound. T h i s p r o c e s s , although a c c u r a t e , was very l a b o u r i o u s . A spacer was subsequently f a b r i c a t e d to clamp over the c o i l form. The c o i l s were then s t a r t e d i n the ce n t r e and wound toward the o u t s i d e s . 244 a ss d + 6, b x d + 6. , A r e a ceabce d + d(6„ + 6_) + 6 „ 6 n b 1 ^ 1 2 A r e a a 6^ + 6^ F i g u r e A3 . 7: C o i l form c r o s s - s e c t i o n . 0 245 The cascode c i r c u i t has another a p p l i c a t i o n i n use f o r t h i s r e c e i v e r . The base b i a s o f the common base t r a n s i s t o r can e a s i l y be a l t e r e d by a l o c a l o s c i l l a t o r s i g n a l . The f i r s t I.F. stage has an e n t r y p o i n t p r o v i d e d f o r the L.O. s i g n a l . The L.O. power requirement i s q u i t e high at 50 ohms impe-dance. A 4:1 impedance transformer was used t o reduce t h i s power requirement to approximately .4 mw. The design o f the p r e a m p l i f i e r stage a l s o uses the cascode c o n f i g u r a t i o n . Here, however, s e l e c t i v i t y and n o i s e f i g u r e are o f paramount importance. A l s o the input impedance must be 50 J V . F i g u r e A3.8 shows a schematic o f the c i r c u i t . A thorough treatment of the design o f input networks f o r low-noise a m p l i f i e r s i s given by R h e i n f e l d e r (34). Of course, unbypassed e m i t t e r r e s i s t a n c e i s p a r t o f the s i g n a l i n p u t c i r c u i t , and cannot be used i n the f i r s t stage. A l s o , i t i s very important t h a t the bypass c a p a c i t o r be a low impedance to ground. In t h i s case a s e r i e s s e l f resonant c a p a c i t o r was used. E m p i r i c a l adjustments o f C^, C^, L, and I g were made to reduce n o i s e f i g u r e while m a i n t a i n i n g some s e l e c t i v i t y b e f o r e the f i r s t t r a n s i s t o r . L and were always set f i r s t , then was adjust e d t o p r o v i d e the input match. I was then a d j u s t e d f o r minimum n o i s e f i g u r e . Because I a f f e c t s the in p u t c a p a c i t a n c e o f the t r a n s i s t o r , L and were r e a d j u s t e d . The r e s u l t i n g band-shape was measured u s i n g a sweep s i g n a l generator. A bandwidth of about 4 MHz was f i n a l l y accepted. 246 J F i g u r e A 3 . 8 : The inpu t c i r c u i t to the r e c e i v e r s . 247 The i n p u t impedance was adjusted to 50 si u s i n g a Vector Impedance Meter. The p r e a m p l i f i e r bandshape was d i s p l a y e d on a l o n g - p e r s i s t a n c e o s c i l l o s c o p e by means of two sweep o s c i l l a t o r s , one on the s i g n a l i n p u t ; the o t h e r , on the L o c a l O s c i l l a t o r i n p u t . The sweep r a t e of the s i g n a l input was a d j u s t e d to be about ten times f a s t e r than that f o r the L o c a l O s c i l l a t o r i n p u t . The r e s u l t -i n g d i s p l a y i s the f r o n t end bandshape convolved by the r e l a t i v e l y narrow I.F. bandshape. T h i s d i s p l a y was used f o r a l l f r o n t end adjustments. Once a l l the r e c e i v e r s had been c o n s t r u c t e d (as i d e n t i c a l l y as p o s s i b l e ) , each one had to be a d j u s t e d so t h a t i t s phase match met s p e c i f i c a t i o n s . One o f the r e c e i v e r s was d e c l a r e d the "master r e c e i v e r " , and a l l o f the o t h e r s were compared with i t . A t e s t arrangement was set up so that comparisons c o u l d be made q u i c k l y between the r e c e i v e r under t e s t and the master r e c e i v e r . Hybrids and a t t e n u a t o r s were used to s p l i t the shared s i g n a l s so that i n t e r a c t i o n between them c o u l d not occur. Before t h i s was done, the r e c e i v e r s were allowed to "age" f o r s e v e r a l months. They were a l s o temperature c y c l e d by o c c a s i o n a l l y moving them back and f o r t h between the summer s u n l i g h t and an under-ground t u n n e l , a tempera-t u r e range o f about 10 - 40°C. Most of the phase e r r o r p l o t c o u l d be accounted f o r by a l i n e a r f i t . The phase slope i s a t t r i b u t a b l e to a bandwidth d i f f e -rence; the phase o f f s e t , to a c e n t r e frequency d i f f e r e n c e . The former e r r o r was most o f t e n c o r r e c t e d u s i n g the c r i t i c a l l y damped I.F. stage; the l a t t e r by a l t e r i n g the p r e a m p l i f i e r t u n i n g s l i g h t l y . Because the p r e a m p l i f i e r bandwidth i s much l a r g e r than the I.F. 248 bandwidth, a l t e r i n g the slope of the wide band s h i f t s the phase more or l e s s u n i f o r m l y a c r o s s the I.F. band. F i g u r e A3.9 shows p l o t s of phase versus frequency f o r 5 r e c e i v e r s , i n c l u d i n g the one with the worst peak-to-peak phase d e v i a t i o n . T h i s p r o c e s s had to be executed at l e a s t twice at a s i n g l e " s i t t i n g " f o r each r e c e i v e r . A f t e r the phase was roughly matched, the i n p u t impedance was checked. Then the f i n a l phase adjustments were made; i n p u t impedance, re-checked. A t o l e r a n c e o f ± 3 ohms and i 3 degrees was set f o r the complex in p u t impedance. The r e c e i v e r s are s e n s i t i v e d e v i c e s r e q u i r i n g a c e r t a i n amount of p r o t e c t i o n a g a i n s t r a p i d temperature changes, shock, f o r e i g n p a r t i c l e s and other environmental changes. I t i s h e l p f u l to have the c i r c u i t board mounted i n a robust c h a s s i s . At the same time, however, i t should a l s o be made so that access to the c i r c u i t board i s quick. Many r e c e i v e r c h a s s i s i n v o l v e much machining and m i l l i n g . The c h a s s i s used f o r t h i s p r o j e c t s a t i s f y most of the above c r i t e r i a . They are made from two p i e c e s o f aluminum exten-si o n s which happen to f i t t o g e t h e r very snugly. The f a b r i c a t i o n i n v o l v e s s l i c i n g o f f the r i g h t length o f e x t e n s i o n , d r i l l i n g adjustment h o l e s f o r a d j u s t i n g the tuned c i r c u i t s and screw h o l e s f o r mounting, and making end p l a t e s . Automatic g a i n c o n t r o l was c o n s i d e r e d f o r these r e c e i v e r s , but, because most o f the outputs are d i g i t i z e d i n t o a one b i t s i g n a l , g a i n v a r i a t i o n s are not s e r i o u s . Manual gain c o n t r o l i s p r o v i d e d as o u t l i n e d above. S e v e r a l o t h e r measurements were made on one o f the r e c e i v e r s . Image r e j e c t i o n i s 62 - 66 db. The l o c a l o s c i l l a t o r power emana-M H z Figu re A 3 . 9 : Across- the-band phase measurements o f f i v e r e c e i v e r s . ro t i n g from the s i g n a l input p o r t i s -97 to -107 dbm. The thermal time constant o f the r e c e i v e r i s about 55 minutes. Gain s e n s i t i -v i t y to temperature i s approximately -.08 db/°C. Phase s e n s i t i v i -t y i s about .6 degrees C. T h i s r e c e i v e r d e sign has been s u c c e s s f u l and a t t e n t i o n has been p a i d to the p o s s i b i l i t y t h a t they c o u l d be u s e f u l i n subse-quent p r o j e c t s . W i t h i n reasonable l i m i t s both the R.F. and the I.F. f r e q u e n c i e s c o u l d be changed. 251 Appendix A4 Measuring P o s i t i o n s on Aperture S y n t h e s i s Maps The i n v e r s i o n process i n producing a s y n t h e s i s map from data taken on the u-v plane i n v o l v e s a F o u r i e r t r a n s f o r m o f the f o l l o w -i n g form: -R where 9 i s the angular d i s t a n c e from the c e n t r e o f the f i e l d o f view. The conjugate v a r i a b l e s i n t h i s t r a n s f o r m are u and sine9. T h e r e f o r e , d i s t a n c e s on the map are l i n e a r i n s i n 9 , not 9. For very small f i e l d s o f view, the approximation t h a t i s o f t e n used. However, f o r the 22 MHz system the e r r o r i s l a r g e enough near the edge o f the f i e l d to be a s i g n i f i c a n t f r a c t i o n o f one beamwidth. The e r r o r can be expressed as f o l l o w s : f ( 9 ) sin9 a » 9 e 9 - sin9 BW where e i s the f r a c t i o n a l e r r o r 9 i s the r a d i u s o f the f i e l d BW i s the s y n t h e s i z e d beamwidth In the prese n t case e = .8 f o r 9 = 20 degrees and BW = 30 arcmin 252 and e = 1.6 f o r 9 = 20 degrees and BW a 15 arcmin For h i g h s i g n a l - t o - n o i s e r a t i o s i t i s q u i t e common to r e p o r t p o s i t i o n s to w i t h i n one t e n t h o f a beamwidth. Sometimes tan9 i s used i n s t e a d o f 9. T h i s r e s u l t s i n a much l a r g e r e r r o r than u s i n g 9. The f o l l o w i n g i s a d e r i v a t i o n o f formulae used t o convert l i n e a r measurements on aperture s y n t h e s i s maps to Right Ascension and D e c l i n a t i o n c o o r d i n a t e s . F i g u r e A4.1 i s the c e l e s t i a l sphere with p o l e at P. Suppose the c e n t r e o f the f i e l d i s at C; the p o s i t i o n to be determined, at S. The map i s a plane tangent to the c e l e s t i a l sphere at C. A and D are the Right Ascension and D e c l i n a t i o n o f p o i n t C; a and 6, of p o i n t S. The p r o j e c t i o n o f the l i n e s PC and CS d e f i n e s t r a i g h t l i n e s on the plane, and the angle between the p r o j e c t e d l i n e s i s 9. (T h i s p r e s e r v a t i o n o f angles holds o n l y at the tangent p o i n t . ) Two ortho g o n a l axes T| and 5 are d e f i n e d . The T| a x i s p o i n t s towards the North C e l e s t i a l Pole and i s the p r o j e c t i o n o f PC. The 5 a x i s p o i n t s towards i n c r e a s i n g Right Ascension. The p r o j e c t i o n o f CS, t h e r e f o r e , has or t h o g o n a l components p a r a l l e l to the § and Tl axes. The d i s t a n c e o f S from C on the §-T) plane i s s i n 0 , and the c o o r d i n a t e s o f S are s i n 0 s in9 1. 2. 253 F i g u r e A4.1: C e l e s t i a l Sphere. N.C.P. i s the North C e l e s t i a l P o l e . The c e n t r e o f the f i e l d i s at C; the p o s i t i o n to be determined, at S. 254 U s i n g the s p h e r i c a l t r i a n g l e s PCS, the f o l l o w i n g r e l a t i o n s h o l d sin0 _ sin(90-6) sinH ~ sine sin© cose = cos(90-5)sin(90-D)-sin(90-6)cos(90-D)cosH T h e r e f o r e , § s = s i n 0 s i n 0 = cos6sinH 3. T) = sin0cos9 = s i n 6cosD-cos 6sinDcosH 4. which i s the r e q u i r e d r e s u l t . The i n v e r s e problem i s to f i n d CY and 6 given § s , 7] , A and D. ( S u b s c r i p t S i s dropped i n the f o l l o w i n g ) By d e f i n i t i o n g tan9 » ^ 5. from which 9 can be found. U s i n g 1. above, s in0 = „f^yr or sin0 = c sine ~' - cos9 from which 0 can be found assuming without l o s s o f g e n e r a l i t y t h a t -9O°<059O° Using the t r i a n g l e PCS cos(90-D)cos9 = sin(9O-D)cot0-sin9cotH cotH = c o sDcot0-sinDco s9 sin9 255 tanH « cosDcos^-sinD' T) 7. from which H can be found. U s i n g 3. and 4. above, ][ s i n 6co sD-co sS sinDco sH § 8 3 sinHcos6 y i e l d i n g , . TlsinH+EsinDcosH tan 6 = — 1 = — s — = r 8 §cosD the r e q u i r e d r e s u l t from which 6 can be found. I f § rs 0, then the t r i a n g l e c o l l a p s e s , and sin0 a T] from which 0 can be found-, and 6 ss 0 + D Cf a A I t i s a l s o u s e f u l t o know how much f r i n g e phase s h i f t i s r e q u i r e d to s h i f t the p o s i t i o n o f a source from one p o s i t i o n to another on the §-11 plane. T h i s can be d e r i v e d by a p p l y i n g the " S h i f t Theorem" o f F o u r i e r transforms (36) to the two-dimensional case: F(§-A§, Tl-AT)) <=> e -2TT1A?*U -2TTiATl'V x e 1 f ( u , v ) where denotes " F o u r i e r i n v e r s e o f " are conjugate c o o r d i n a t e s v,Tj are conjugate c o o r d i n a t e s 256 Therefore, a displacement i n the §-T| plane corresponds to a fringe phase s h i f t of A 0 = 2TT( A§«U+AT|. V ) 9. From chapter 4.4, u ss ^  cosdsin(H-h) 10. v = ^ (sindcosfi - cosdsin6cos(H-h) 11. where D, X., d, h are defined as i n chapter 4.4, and 6 and H are the declination and hour angle of the p o s i t i o n p r i o r to s h i f t i n g . Substituting 10. and 11. into 9., A 0 = - ^ - j — (A|cosdsin(H-h) + AT|sindcos6 - AT|cosdsin6cos(H-h)) Note that i f the orientation of the baseline i s East-West, and i n the equatorial plane, d sa 0 and h a 90 degrees then A 0 =s 2TT^ ( A § C O S H + AT|sinSsihH) the required r e s u l t . A § and AT] can then be found from equations 3. and 4. i n terms of Right Ascension and Declination. Small angle approximations can also be used here with the same errors as outlined at the beginning of t h i s Appendix: 257 AT] = A5 A? = -Ao/cosS T h i s produces an approximate formula: ~ D A0 « 2TT^ (A6sin5sinH - A C Y C O S5C O S H ) which i s o n l y u s e f u l f o r small f i e l d s o r small s h i f t s i n p o s i t i o n . 258 Appendix A5  The E f f e c t s o f R.F. Bandwidth on R e s o l u t i o n The c h o i s e o f R.F. bandwidth f o r a t e l e s c o p e a f f e c t s c h i e f l y i t s s e n s i t i v i t y . However, th e r e are a l s o o t h e r c o n s i d e r a t i o n s f o r image-forming t e l e s c o p e s which p r o v i d e r e s t r i c t i o n s on the maximum bandwidth. T h i s d i s c u s s i o n w i l l c o ncentrate i n i t i a l l y upon the theory o f these e f f e c t s f o l l o w e d by the a p p l i c a t i o n to the 22 MHz t e l e s c o p e . The image i s formed from a s e r i e s o f i n t e r f e r o m e t e r measure-ments. The s i z e o f the f i e l d o f view i s determined to be the angular d i s t a n c e from i t s c e n t r e at which the s e n s i t i v i t y decrea-ses to some a r b i t r a r y l e v e l ( u s u a l l y about 30 percent o f maximum). The aperture f u n c t i o n , which governs the s i z e o f the f i e l d , can be f a c t o r e d i n t o a product o f two f u n c t i o n s . One i s the antenna p a t t e r n o f the elements of the i n t e r f e r o m e t e r ( i f the elements are d i s s i m i l a r , i t i s the geometric mean of the two antenna p a t t e r n s ) ; the o t h e r , the F o u r i e r transform o f the R.F. bandshape ( i . e . the power spectrum o f t h e R.F. s i g n a l ) . T h i s r e s u l t can be simply d e r i v e d u s i n g the f a c t t h a t the a u t o c o r r e l a t i o n f u n c t i o n o f a s i g n a l i s the F o u r i e r transform o f i t s power spectrum. S i g n a l s emanating from a p o i n t P an angular d i s t a n c e 9 from the c e n t r e o f the f i e l d w i l l be delayed by D s i n 9 DX . . T = = — s i n 9 C V 259 where i s the l e n g t h o f the i n t e r f e r o m e t e r i n wavelengths v i s the c e n t r e frequency o f the instrument c i s the v e l o c i t y o f l i g h t I t i s w e l l known t h a t S ( f ) <=> B ( T ) (<=> denotes F o u r i e r transform) where S ( f ) i s the power spectrum o f the s i g n a l emanating from P and B ( T ) i s the a u t o c o r r e l a t i o n f u n c t i o n of the s i g n a l . For a r e c t a n g u l a r bandshape o f width Av t h i s f u n c t i o n B(Av,G,D x) i s TTAV D s i n ( v sinB X) v s i n 9 X where 8 i s the angular d i s t a n c e from the c e n t r e o f the f i e l d i s the r a d i a l d i s t a n c e from the c e n t r e of the u-v plane Av i s the R.F. bandwidth Although bandshapes can be o n l y approximately r e c t a n g u l a r , the e r r o r committed by assuming the r e c t a n g u l a r shape i s u s u a l l y s m a l l . At the c e n t r e o f the f i e l d B has no e f f e c t on the r e s o l u -t i o n . But f o r sources at the edge o f the f i e l d , B produces a tapered weighting o f the c o r r e l a t i o n c o e f f i c i e n t s on the u-v plane. A c c o r d i n g to a w e l l known theorem f o r F o u r i e r transforms (36), the e q u i v a l e n t width o f the bandshape i s the i n v e r s e o f the 260 e q u i v a l e n t width o f B. For many i n t e r f e r o m e t e r s used i n image-forming t e l e s c o p e s Av i s small enough t h a t the aperture f u n c t i o n i s determined almost e n t i r e l y by the i n t e r f e r o m e t e r elements. But f o r maximum s e n s i t i v i t y , i t i s advantageous to use the maximum p o s s i b l e bandwidth. For the 22 MHz t e l e s c o p e the f i e l d i s r e l a t i v e l y wide. I t i s p o s s i b l e to achieve a much wider f i e l d width with aperture s y n t h e s i s t e l e s c o p e s at low f r e q u e n c i e s than at high ones. The reason i s t h a t not much elemental c o l l e c t i n g area i s needed.-th a t i s sources are strong and the ge n e r a l b r i g h t n e s s temperature of the sky i s the l i m i t i n g f a c t o r i n s e n s i t i v i t y f o r a s i n g l e element. The wide f i e l d , t h e r e f o r e , l i m i t s the a v a i l a b l e band-width u n l e s s s p e c i a l p r e c a u t i o n s are taken. P a r e n t h e t i c a l l y , t h i s d e c o r r e l a t i o n i n the f i e l d o f view can be overcome at the expense o f b u i l d i n g more c o r r e l a t o r s . The s o l u t i o n can be implemented e i t h e r i n the frequency domain or i n the time domain. In the frequency domain the R.F. band can be d i v i d e d i n t o s u i t a b l y small p a r t s , each with a c o r r e l a t o r . The outputs o f the c o r r e l a t o r s are averaged f o r each sample a f t e r undergoing a p p r o p r i a t e phase s h i f t s a c c o r d i n g to the ce n t r e f r e -quency o f each p a r t . The s i z e o f the p a r t s i s c a l c u l a t e d to produce no more than a s p e c i f i e d d e c o r r e l a t i o n . I f , f o r example, t h i s l i m i t i s taken as 5 percen t , then the channel bandwidth i s . . 18v A V as : " s i n G where v i s the centre frequency o f o b s e r v a t i o n 9 i s the angular f i e l d r a d i u s 261 i s the maximum spacing i n wavelengths The same r e s u l t can be accomplished i n the time domain by a r r a n g i n g c o r r e l a t o r s along a d e l a y l i n e i n the f a s h i o n o f a c r o s s - c o r r e l a t i o n spectrometer. In t h i s case, a s e l e c t i o n o f an a p p r o p r i a t e output can be made f o r any g i v e n s l i c e o f the f i e l d o f view. A l t e r n a t i v e l y , the F o u r i e r t r a n s f o r m can be used to produce the above r e s u l t i n the frequency domain. Table A5.1 summarizes the e f f e c t o f d e c o r r e l a t i o n on the r e s o l u t i o n o f the 22 MHz t e l e s c o p e f o r v a r i o u s bandwidths and p o l a r d i s t a n c e s . The beamwidths are e q u i v a l e n t widths, s l i g h t l y narrower than half-power widths. They are c a l c u l a t e d on the b a s i s of a Gaussian a p o d i z i n g f u n c t i o n t r u n c a t e d at the 20 percent l e v e l at the edge o f the f i e l d . Because the f u n c t i o n B i s not a x i a l l y symmetric on the u-v plane, the beam near the edges o f the f i e l d w i l l be broadened by the amount shown i n T a b l e A5.1 i n one dimen-s i o n o n l y . A bandwidth of 300 kHz was s e l e c t e d as a reasonable compromise, g i v i n g o n l y a 16 percent decrease i n r e s o l v i n g power at the edge o f the f i e l d . In any case, f o r the 22 MHz t e l e s c o p e , a c o r r e c t i o n f o r B can be made d u r i n g the i n v e r s i o n p r o c e s s . For reasons o u t l i n e d i n chapter 4.4, the b r i g h t n e s s temperature at each p o i n t i s c a l c u l a t e d as an i n t e g r a l , thereby a l l o w i n g the compensating f a c t o r to be a p p l i e d to a g i v e n p o i n t without a f f e c t i n g the o t h e r p o i n t s i n the f i e l d . T h i s k i n d o f c o r r e c t i o n i s not p o s s i b l e i f f a s t F o u r i e r transform techniques are used. The procedure c a n c e l s any decrease i n r e s o l v i n g power l e a v i n g o n l y a s l i g h t l o s s i n s e n s i t i v i t y near the edge o f the f i e l d . The d e c o r r e l a t i o n near the edge o f the f i e l d a l so has the advantage tha t i n t e r f e r e n c e and s t rong sources near hour angles 6H and 18H do not i n t e r f e r e w i t h obse rva t ions ( p r o v i d i n g they do not sa tura te any o f the e l e c t r o n i c dev ices i n f ron t o f the co r re l a t o r i t s e l f ) . TABLE A5.1 Av 400 kHz 0° 5 10 15 E q u i v a l e n t Width o f B 248X 240 219 190 Beamwidth 13.9 ' 14. 3 15. 7 18.1 % Decrease R e s o l u t i o n 0% 3% 13% 30% 300 kHz 0° 5 10 15 248X 243 231 213 13.9 ' 14.1 14.9 16.1 0% 1% 7% 16% 200 kHz 0° 5 10 15 248X 246 241 232 13.9 ' 14.0 14. 3 14.8 0% 1% 3% 6% 264 Appendix A6 The E f f e c t on S e n s i t i v i t y o f the Sampling D i s t r i b u t i o n  and A p o d i z i n q i n the u-v Plane The random f l u c t u a t i o n s on an a p e r t u r e s y n t h e s i s map are a r e s u l t of measurement e r r o r s i n the data d i s t r i b u t e d i n the u-v plane. The " n o i s e " on the map has a s p a t i a l spectrum which depends upon t h i s d i s t r i b u t i o n . Each data p o i n t w i l l have a standard d e v i a t i o n which depends upon the amount o f time spent o b s e r v i n g t h a t p a r t i c u l a r p o i n t . For an e a r t h r o t a t i o n s y n t h e s i s t e l e s c o p e , the d i s t r i b u t i o n o f o b s e r v i n g time i s u s u a l l y i n v e r s e l y propor-t i o n a l to the r a d i u s i n the u-v plane. The a p o d i z i n g or window f u n c t i o n determines the shape o f the s y n t h e s i z e d beam. L e t the window f u n c t i o n be w(u,v). I t can be c o n s i d e r e d to be a product of two components. The f i r s t , r e f e r r e d to above, w i l l be c a l l e d the " n a t u r a l " component, n(u,v). Each o r d i n a t e at n(u',v') i s determined by how many independent measure-ments were averaged together to produce the data p o i n t at u',v'. For the 22 MHz system n(u,v) i s approximately 1 n(r)c? e « l r+ e where r i s the d i s t a n c e to the o r i g i n i n the u-v plane. The second component, w'(u,v), i s a p p l i e d to a l t e r the n a t u r a l compo-nent i n o r d e r to produce an a c c e p t a b l e s y n t h e s i z e d beamshape. The r e l a t i o n s h i p between w, w', and u i s g i v e n by w(u,v) = n(u,v) w'(u,v) - . In the f o l l o w i n g d e r i v a t i o n the f u n c t i o n s n,w, and w' w i l l be 265 used to c a l c u l a t e a f a c t o r i n the o v e r a l l s i g n a l - t o - n o i s e r a t i o on the s y n t h e s i z e d map. Assume t h a t the u-v plane can be d i v i d e d up i n t o elemental areas with n^.. samples o f data taken i n each one. Each sample has a mean x and a standard d e v i a t i o n a , and r o o n. . IT2AVT . . where Av i s the R.F. bandwidth i s the t o t a l o b s e r v i n g time spent measuring the ^ t h ^ j t h s p - ^ i a i F o u r i e r component. A p o i n t source i n the A-m plane (plane o f b r i g h t n e s s d i s t r i -b u t i o n ) w i l l have a component from each p o i n t i n the u-v plane weighted by n^... The mean v a l u e , "x, o f the p o i n t i'jvn' at the cen t r e o f the p o i n t source i s the mean o f a l l the p o i n t s i n the u-v plane. ^N. M. „ N M X = ? a ? a * i j = N M ^ £ n i j *o N M where N i s the number o f elements on the u a x i s M i s the number o f elements on the v a x i s N M N M a 2 m £ £ CT..2 1 ^ 2 n . . a i=7i u i 1 J N M 1 J c N M •CT CTQ J N M. where S/N i s s i g n a l - t o - n o i s e r a t i o . °/N might be c a l l e d the " n a t u r a l " s i g n a l - t o - n o i s e r a t i o because i t 266 involves only n ^ . I f w'(u,v) i s applied to the data before Fourier transforming i t , N M N M N M <~ -C. ! J X J NM I J I J O N M N M i < <" / 2 2 i < r ^ / 2 • NM < < W i j : G i j = NM 2. < W i j " i j ao a N M x s < < , o / w . . n. . 7N CTo / N M _ • It i s useful to convert t h i s equation to a r a t i o of signal-to-noise r a t i o s . Q _ signal-to-noise r a t i o with w'(u,v)  / ~ signal-to-noise r a t i o with w'(u,v) = 1 Also, since the f i n a l window function, w^j, i s the important independent variable, i t can be substituted into the formula for Q . The r e s u l t i s In i n t e g r a l form, j^J~ w(u,v) dudv 267 If n:(u,v) and w(u,v) are a x i a l l y symmetric (a function only of radius i n the u-v plane), and using n(r) = -and ignoring the discontinuity at the o r i g i n , r Q s o w(r)rdr 1 l g t M o m e n t o f w ( r ) 7 n C T R 1% ( 2 n d Moment of w 2 ( r ) ) ^ J~RI I w 2(r)r 2drJ Figure A6.1 shows the factor ^ s / n for various window func-tio n s , including the Gaussian one used i n the 22 MHz system. As discussed i n Appendix A5, i f there i s some decorrelation within the f i e l d of view, then n(u,v) w i l l be a function of posi-t i o n i n the f i e l d . Near the edges of the f i e l d , ^ s / n w i l l be somewhat smaller than near the centre. 268 w(r) 1 1.0 r/R F i g u r e A 6 . 1 : The s i g n a l - t o - n o i s e r e d u c t i o n f a c t o r , Q s / n > f o r v a r i o u s apod iz ing func t i ons i n the u -v plane (assuming a V r " n a t u r a l " component). 269 Appendix A7  The Prototype System As o u t l i n e d i n chapter 3.10, a number o f measurements and t e s t s were made on a prototype system. The experimental arrange-ment and v a r i o u s measurements are d e s c r i b e d h e r e i n . A l a b o r a t o r y bench system was e s t a b l i s h e d to t r y to simulate a c t u a l c o n d i t i o n s i n the f i e l d as w e l l as t o check as many as p o s s i b l e o f the o v e r a l l parameters o f the r e c e i v e r s , c o r r e l a t o r s , e t c . T h i s setup was l a t e r expanded, and used as a " p r o d u c t i o n " setup f o r f i n a l adjustments to a l l the e l e c t r o n i c s . A l l o f the measurements d i s c u s s e d here were done without the phase switch i n s t a l l e d i n the c o r r e l a t o r u n i t (see chapter 3.9). The i n s t a l l a t i o n o f the phase switch r e s u l t e d i n improved p e r f o r -mance o f the c o r r e l a t o r over a wider range o f temperatures. An a d j u s t a b l e analog d e l a y l i n e was b u i l t to simulate the long c a b l e s c a r r y i n g the quasi-baseband s i g n a l . I t was b u i l t u s i n g m-derived f i l t e r s e c t i o n s o f .85 (j,sec each, approximately the d e l a y o f one s e c t i o n o f the d i g i t a l d e lay l i n e . F i g u r e A7.1 i s a block diagram o f the i n s t r u m e n t a t i o n . Only major elements are shown. Numerous a m p l i f i e r s , a t t e n u a t o r s , h y b r i d s , and f i l t e r s were a l s o r e q u i r e d . Depending upon r e q u i r e -ments, v a r i o u s t h i n g s were changed or added to s u i t the a p p l i c a -t i o n . The f i r s t measurement to be d e s c r i b e d i s a d i r e c t measurement o f the a u t o c o r r e l a t i o n f u n c t i o n o f the c o r r e l a t e d component o f 270 Frequency Synthesizer' Analog Delay L i n e Noise Generator B 27.25 MHz I L o c a l -1 O s c i l l a t o r •4-4 4.7 MHz L o c a l O s c i l l a t o r | Chart Recorder D i g i t a l Delay L i n e I n t e g r a t i o n | P e r i o d | Timer i F i g u r e A 7 . 1 : A l a b o r a t o r y system f o r deve lop ing the pro to type and f o r t e s t i n g the c o r r e l a t o r u n i t s . 271 s i g n a l . The arrangement o f F i g u r e A7.1 was used with the n o i s e generator B connected to supply the c o r r e l a t e d s i g n a l . Generators A and C were not used so t h a t the experiment was done at a high s i g n a l - t o - n o i s e r a t i o . F i g u r e A7.2 shows the measured a u t o c o r r e -l a t i o n f u n c t i o n . T h i s measurement r e q u i r e d a number o f d i f f e r e n t arrangements o f the d e l a y l i n e , a l l o f which were not c a l i b r a t e d w e l l with r e s p e c t to one another i n delay. The best match o f the measurements at v a r i o u s d e l a y taps i s p l o t t e d . An o f f s e t v o l t a g e o f approximately -100 mV i s apparent. With t h i s o f f s e t the f i r s t s i d e l o b e l e v e l i s about 20 percent o f the peak; the second, about 10 percent. T h i s corresponds to 22 percent and 13 percent f o r a s i n x r. , . f u n c t i o n . x The next few measurements i n v o l v e a frequency sweeping sine wave generator as a c o r r e l a t e d s i g n a l . A d e l a y o f f s e t was used so that " f r i n g e s " were produced on the output of the s i g n a l m u l t i -p l i e r . An x-y r e c o r d e r was used on the output to p l o t frequency as the x - c o o r d i n a t e . A good i n d i c a t i o n o f the phase l i n e a r i t y o f the system i s given by a quadrature set o f " f r i n g e s " ( F i g u r e A7.3). A l s o , the t e s t was performed over a wide range o f c o r r e l a t i o n c o e f f i c i e n t s . Because of the AGC a m p l i f i e r the output i s a measure of c o r r e l a t i o n c o e f f i c i e n t ( i . e . c o r r e l a t e d p ower/total power) d i r e c t l y . For l a r g e s i g n a l i n p u t s the c o r r e l a t e d power i s a s i g n i f i c a n t f r a c t i o n o f the t o t a l power. F i g u r e A7.4 shows outputs f o r a 10 db range o f c o r r e l a t e d power. F i g u r e A7.4 i s a l s o a p l o t o f the expected bandshape.' At 22.10 MHz the c o r r e l a t o r response i s about 0.8 db down, approximately 17 percent. (Note that the band i s r e v e r s e d by the h i g h - s i d e f i r s t l o c a l o s c i l l a t o r ) . T h i s slope i s thought to r e s u l t from an asymmetry o f the p o s i t i v e and volts 1.04 0 Jerroi F i g u r e hi.2-. The a u t o c o r r e l a t i o n f u n c t i o n o f the i n p u t n o i s e measured by a d j u s t i n g the length of the d i g i t a l d elay l i n e . — 1 — : 1 : •• 1 22 . 10 2 2 . 2 5 22 . 4 0 MHz F i g u r e A7.3: A set o f a r t i f i c i a l " f r i n g e s " produced i n quadrature by two c o r r e l a t o r ou tputs . U ) 22.10 22.25 22.40 MHz Figure A7.4: Correlator outputs for a 10 db range of input power. The error bars are the absolute value of the negative peaks. The o v e r a l l bandshape i s the l i n e through the po s i t i v e peaks and the error bars. n e g a t i v e t r a n s i t i o n s o f zero c r o s s i n g d e t e c t o r on the d i g i t a l s i d e . T h i s d e t e c t o r , t o g e t h e r with the sampling f l i p - f l o p , form a mixer at 5 MHz. A f a s t gate on the output o f the d e t e c t o r was found to improve the response. In the next t e s t , the bandwidth of the c o r r e l a t o r was measured up to 14 MHz, the l i m i t o f the AGC a m p l i f i e r . The sweep s i g n a l was i n j e c t e d a f t e r the second l o c a l o s c i l l a t o r as i l l u s t r a t e d i n F i g u r e A7.5. The bandwidth of the c o r r e l a t o r was found to be g r e a t e r than 14 MHz. The f o l l o w i n g s e n s i t i v i t y measurement i s an important one. The c o r r e l a t e d component i s p r o v i d e d by a n o i s e generator; the u n c o r r e l a t e d components, by the i n p u t n o i s e o f the r e c e i v e r s . T h e i r g a i n was turned up a p p r o p r i a t e l y . As d e r i v e d i n Appendix A2, the s i g n a l - t o - n o i s e r a t i o f o r t h i s type of c o r r e l a t o r i s g i v e n by . jT r /2B7 CT \j TT xy J q 1 * where mean output CT = q standard d e v i a t i o n o f the output r = xy c o r r e l a t i o n c o e f f i c i e n t B bandwidth T = i n t e g r a t i o n p e r i o d . The i n t e g r a t i o n timer was set to 20 sec. so that T = 20. With B = 300 kHz i Comparator Correlator Analog Delay Line AGC Ampl i f i e r F i g u r e A7.5: T e s t i n g the "back end" o f the c o r r e l a t o r system. I f peak-to-peak f l u c t u a t i o n s are co n s i d e r e d to be f i v e times rms f l u c t u a t i o n s , r . 1.8 x 10~ 3 xy c o rresponding to The i n p u t n o i s e o f the r e c e i v e r s i s approximately 700° K. The peak-to-peak f l u c t u a t i o n s should t h e r e f o r e be e q u i v a l e n t to 1.27° K. F i g u r e A7.6 shows the r e s u l t s o f the t e s t . W i thin the accuracy o f the measurement the t h e o r e t i c a l s e n s i t i v i t y i s c o n f i r -med. A t e s t o f l a r g e s i g n a l l i n e a r i t y was made u s i n g the noise generator as a c o r r e l a t e d component o f s i g n a l . C o r r e l a t i o n coef-f i c i e n t s o f 6 and 12 percent were used. The output o f the i n t e g r a t o r was set up to be near s a t u r a t i o n at the hi g h e r o f these two l e v e l s . The r e s u l t s are p l o t t e d i n F i g u r e A7.7. A " z e r o - c o r r e l a -t i o n " o f f s e t o f about .4 v o l t s i s pr e s e n t . Numerous t e s t s f o r the presence o f leakage o r c r o s s - t a l k were made. In f a c t , with such a s e n s i t i v e d e v i c e i t i s a r o u t i n e to check f o r c r o s s - t a l k a f t e r any s i g n i f i c a n t change has been made. I t can o f t e n be i s o l a t e d by the use o f independent l o c a l o s c i l l a -t o r s f o r the two ha l v e s o f the c o r r e l a t o r . For example, i f the equipment i s arranged as i n F i g u r e A7.1, and no " o f f i c i a l " c o r r e l a t e d s i g n a l i s present, i t should be p o s s i b l e to s u b s t i t u t e two independent f i r s t l o c a l o s c i l l a t o r s f o r the one shown. The output w i l l change i f there i s s i g n i f i c a n t c r o s s - t a l k i n the Jc 1 2 K 1 F i g u r e A 7 . 6 : System s i g n a l - t o - n o i s e r a t i o measurement. Peak-to-peak f l u c t u a t i o n s i n the output o f the c o r r e l a t o r cor responding to a change of 1.2K i n c o r r e l a t e d inpu t power. co 279 Figure A7.7: Large signal test of correlator. 280 system b e f o r e o r at the f i r s t l o c a l o s c i l l a t o r . I t i s l i k e w i s e p o s s i b l e to do the same with second l o c a l o s c i l l a t o r . A number o f s p e c t r a were taken w i t h ai'.Hewlett Packard spectrum a n a l y z e r at c r i t i c a l p l a c e s to look f o r s p u r i o u s responses, over-l o a d i n g , o r s i g n a l s which might produce f a l s e c o r r e l a t i o n . A wide range spectrum o f the output o f one of the r e c e i v e r s i s shown i n F i g u r e A7.8. The output shows a harmonic l e v e l o f -50 db1. Otherwise the spectrum i s c l e a n . F i g u r e A7.9 shows a spectrum o f the output o f the a m p l i f i e r which d r i v e s the analog s i d e o f the c o r r e l a t o r s , the quasi-baseband a m p l i f i e r . A wide range spectrum i s d i s p l a y e d i n F i g u r e A7.10. The second l o c a l o s c i l l a t o r i s present at about the -36 db l e v e l . The wide band low l e v e l p e d e s t a l i s i n p u t n o i s e of the quasi-baseband a m p l i f i e r . No c o r r e l a t i n g e f f e c t c o u l d be t r a c e d to the second l o c a l o s c i l l a t o r . I t i s very u n l i k e l y t h a t t h i s s i g n a l c o u l d c o r r e l a t e . Even i f the f o u r t h harmonic of the d e l a y l i n e c l o c k were present on the output of the r e c e i v e r s , the sampling f l i p - f l o p a c t s as a mixer. The r e s u l t i n g product would be a d.c. s i g n a l which c o u l d not c o r r e l a t e with the quasi-baseband s i g n a l on the analog s i d e . The next few t e s t s are longer term ones intended to look f o r long term d r i f t and low l e v e l c r o s s - t a l k . The c o r r e l a t o r u n i t , under the command o f the c o n t r o l l e r , was attached to the computer e x a c t l y as would be the case i n a c t u a l use, except t h a t the c o r r e -l a t o r was i n s i d e the l a b o r a t o r y . The f i r s t t e s t c o n s i s t e d o f r e c o r d i n g the output with uncor-r e l a t e d i n p u t s f o r j u s t over 9 hours (12 hours would have been 284 more a p p r o p r i a t e , but the r e s u l t s are not expected to have been s i g n i f i c a n t l y d i f f e r e n t ) . Of the e i g h t c o r r e l a t o r s t e s t e d , one was not f u n c t i o n i n g p r o p e r l y . A histogram of a t y p i c a l output o f one o f the c o r r e l a t o r s i s shown i n F i g u r e A 7 . l l . 2 A x t e s t was done on each sample to t e s t the h y p othesis t h a t the outputs were withdrawn from a normal d i s t r i b u t i o n . The r e s u l t was c o n s i s t e n t with the h y p o t h e s i s to the 5% l e v e l f o r most o f them. T h i s l e d to s e v e r a l d i s c o v e r i e s o f c r o s s - t a l k paths, and some problems with i n t e r a c t i o n . A f t e r a phase-switching system was i n t r o d u c e d the d i f f i c u l t i e s were r e s o l v e d . As a check upon the read-out system, a channel was recorded to which no c o r r e l a t o r was attached. A l l outputs produced zero. The second t e s t done was to c y c l i c a l l y apply a strong c o r r e -l a t e d s i g n a l to some of the c o r r e l a t o r s , more than enough to s a t u -r a t e the c o r r e l a t o r s . T h i s was done to two c o r r e l a t o r s . The o t h e r outputs were t o t a l i z e d i n two l o t s , one i n which the c o r r e -l a t e d s i g n a l was a p p l i e d ; the o t h e r , while i t was o f f . T h i s t e s t was designed to t e s t the i s o l a t i o n between c o r r e l a t o r s . T a b l e A7.1 shows the r e s u l t s f o r the f i r s t t e s t . The t o t a l i n t e g r a t i o n time was 11 hours. C o r r e l a t o r s 1 and 3 were r e c e i v i n g c o r r e l a t e d s i g n a l . The r e s u l t shows measurable i n t e r a c t i o n among the c o r r e l a t o r s , e s p e c i a l l y c o r r e l a t o r 2. The l e v e l o f c o r r e l a t e d s i g n a l a p p l i e d was s e v e r a l times that r e q u i r e d to s a t u r a t e the c o r r e l a t o r s . The i n t e r a c t i o n , t h e r e f o r e , at the < 1 p ercent l e v e l was not c o n s i d e -red a s i g n i f i c a n t problem. A c o n t r o l t e s t was run i n which the c o u n t s 4 4 0 0 + 2 0 0 + -128 F i g u r e A 7 . l l : 0 4—so- bins 1 2 8 A h i s t r o g r a m o f c o r r e l a t o r o u t p u t n o i s e i n a 9 hour t e s t on u n c o r r e l a t e d i n p u t s . ro co cn TABLE A7.1 Average D i f f e r e n c e Between "ON" & "OFF" 119. 4.9 116. 2. 2 .56 .50 .13 Estimated Standard D e v i a t i o n o f Standard the Mean o f D e v i a t i o n the Two L o t s 4. 3 3.6 1. 7 3. 2 2.9 .13 .11 .05 .10 .09 T o t a l number o f samples = 2112 equipment and o t h e r c o n d i t i o n s were the same, but the c o r r e l a t e d s i g n a l was turned o f f a l t o g e t h e r . These r e s u l t s are shown i n T a b l e A7. 2. T h i s r e s u l t was r a t h e r s u r p r i s i n g i n that i t showed a d i f f e -rence between the two h a l v e s o f the c y c l e at about the 2a l e v e l . Moreover, a l l the c o r r e l a t o r s showed t h i s d i f f e r e n c e i n the same sense. P o s s i b l y the switch s i g n a l used to t u r n the c o r r e l a t e d s i g n a l on and o f f was a f f e c t i n g the c o r r e l a t o r s . Whatever the cause, the e f f e c t i s to reduce the s i g n i f i c a n c e o f the p r e v i o u s r e s u l t s t i l l f u r t h e r . I t was p a r t l y f o r t h i s reason t h a t the phase switch d e s c r i b e d i n chapter 3.9 was added to the c o r r e l a t o r u n i t s . TABLE A7.2 Average D i f f e r e n c e Between Standard "ON" & "OFF" D e v i a t i o n .51 .59 .43 . 76 .46 .50 .55 T o t a l number of 1.8 2.3 1.9 2. 5 1. 7 2.0 2.1 samples = 960 Estimated Standard D e v i a t i o n o f the Mean .08 .10 .09 .11 .08 .09 .10 Appendix A8 The maps i l l u s t r a t e d here were used to produce the source l i s t (Table 5.1.1). They are evenly spaced contour maps o f f l u x d e n s i t y , 1.32 Jy apart. The coverage o f each map i s i n F i g u r e 5.1.2, repeated here f o r easy access. These maps have not been c o r r e c t e d f o r the p o l a r diagram o f the elemental a r r a y s . F i g u r e 5.1.2: A g r i d showing how the map was d i v i d e d so t h a t f l u x e s c o u l d be r e a d . Each i n d i v i d u a l map i n Appendix A8 c o v e r s f o u r squares i n the r e c t a n g u l a r g r i d . The maps a r e l a b e l l e d by the g r i d p o i n t s a t t h e i r c e n t r e s . lo 291 292 29 3 2 9 4 295 29 7 298 299 300 301 302 303 305 306 307 308 310 311 312 313 315 3 1 6 317 318 319 320 322 323 324 325 326 327 329 330 3 3 1 332 335 3 3 6 t 337 338 339 

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