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Factors of merit for radiation detectors Unwin, Alexander Matthew 1953

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FACTORS OF MERIT FOR RADIATION DETECTORS by ALEXANDER MATTHEW UNWIN A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of PHYSICS We accept t h i s thesis as conforming to the standard required from candidates for the degree of MASTER OF SCIENCE Members of the Department of Physics THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1953 V ABSTRACT A discussion i s given of the many uses of photo-conductive c e l l s , e s pecially of those of the lead sulphide type. A Factor of Merit f o r r a d i a t i o n detectors as pro-posed by Clark Jones i s presented, which i s intended to cover a l l types of detectors, and which i s applied to the lead s u l -phide c e l l s studied. Other Factors of Merit are also mentioned. From information obtained the Factors of Merit are evaluated for the c e l l s . These Factors of Merit are found to vary with the temperature of the c e l l layer. I t i s found that l i m i t i n g noise i s not due to Johnson noise, but rather to r a d i a t i o n f l u c t u a t i o n s ; and that the ultimate sen-s i t i v i t y has been reached i n some c e l l s . The c e l l s are assumed to be type I I detectors according to Clark Jones's c l a s s i f i c a t i o n . I t Is found that the engineering l i m i t pro-posed by R. J . Havens does not apply here. P a r t i c u l a r l y good agreement between various expressions for the Factor of Merit i s shown, assuming a type I I detector. A description of the apparatus i s given i n some de-t a i l . A black body radiator and associated temperature con-t r o l , a 900 cycles per second tuned a m p l i f i e r , a wide band preamplifier and a multivibrator used i n measuring time con-stants of such c e l l s are described. v i The methods of measurement of responsivity to noise r a t i o , of noise, of time constants, frequency response curves and spectral response of a detector are outlined. I t i s found that the black body i s o p t i c a l l y aligned; tests show that the response of a c e l l i s d i r e c t l y proportional to the i n t e n s i t y of the i l l u m i n a t i o n . ACKNOWLEDGEMENTS The author wishes to thank Dr. A. M. Crooker fo r his help and encouragement i n d i r e c t i n g t h i s research. Thanks are also due to Mr. P. A. Lee for much assistance and for many invaluable sugges-t i o n s . The author wishes to acknowledge his indebtedness to the Defence Research Board for use of the 900 cycles per second tuned a m p l i f i e r , and for permission to use some of the c e l l s studied. i i i CONTENTS Page ABSTRACT I INTRODUCTION 1 I I FACTORS OF MERIT 7 I I I THE APPARATUS 19 IV THE EXPERIMENTAL PROCEDURE 33 V THE RESULTS 54 VI DISCUSSION 67 BIBLIOGRAPHY 70 ACKNOWLEDGEMENT ILLUSTRATIONS FIGURE 1 The Black Body Radiator 2 Optical System of the Black Body 3 V i r t u a l Source Theory 4 The 900 c/s Amplifier 5 Response v. Frequency of 900 c/s Amplifier 6 Response v. Input of 900 c/s Amplifier 7 The Wide Band Preamplifier 8 Response v. Frequency of Preamplifier 9 C e l l Mounting 10 The Measurement of Time Constants 11 Signal v. Intensity of Illumination 12 Block Schematic of Time Constants 13 C e l l 293 Spectral Response 14 Response v. Modulation Half Width Chapter I INTRODUCTION Much attention has been given to photoconductive c e l l s as infrared detectors i n the past few years, e s p e c i a l l y to those operating i n the region between one and s i x microns. Such c e l l s , which were developed mainly during the war years, now find many interesting applications i n pure and applied research. A b r i e f summary of such research w i l l now be given, fo r i t i s the purpose of t h i s research to study the properties of several such detectors with a view to evaluating t h e i r r e l a t i v e merits and demerits i n a single comprehensive "Factor of Merit". Many applications, together with a summary of perform-ance: of such c e l l s , are given i n a review a r t i c l e by Simpson and Sutherland (1). Detectors to be considered are sensitive above one micron; those with a cut-off i n t h i s region are already w e l l known and include thallium sulphide c e l l s , whereas such detectors as are studied here extend our present knowledge i n many f i e l d s . Three substances, photoconductive beyond one micron, are of greatest interest and form the basis of the most research; 2 lead sulphide, lead selenide and lead t e l l u r i d e . Such mater-i a l s are normally deposited i n t h i n layers from IO"4" to 10~^cm. , • i* thickness on glass or some other non-conductor, by evaporation or a chemical process. Dark resistances so f a r encountered 4 f t are from 10 to 10 ohms, and response times are found to be between 10"^ and 10"^ seconds. I t w i l l be seen i n Chapter V that a l l measurable properties of the c e l l s encountered i n th i s research f a l l within the ranges given. I t i s also immed-i a t e l y apparent that one great att r i b u t e of such detectors, compared to bolometers, thermocouples and other heat detecting devices, i s t h e i r r e l a t i v e l y short time of response. An excellent a r t i c l e by Sosnowski, Starkiewicz and Simpson (2) describes the preparation of lead sulphide c e l l s and also the main aspects of the theory. Many such c e l l s have been made, which operate at room temperature and are ex-posed to the atmosphere. However, most layers' are kept i n vacuo; a further betterment i n t h e i r responsivity being obtained by cooling the layer, either to s o l i d carbon dioxide or l i q u i d oxygen temperatures. This i s also known to extend the long wave l i m i t of such c e l l s from about 3 .3 microns to about 3-6 microns. On the other hand, lowering the tempera-ture also raises the resistance and increases the time constant; consequently a cooled c e l l i s not always advantageous. Selenide and t e l l u r i d e c e l l s must be cooled to the neighbourhood of dry ice temperatures before photoconductivity takes e f f e c t . At present, only lead sulphide c e l l s are commercially 3 available. Each of the semiconductors hitherto mentioned has i t s own response versus wavelength curve, c h a r a c t e r i s t i c of the material i n the layer and also of the method of prep-aration. Such a curve i s shown i n figure (13), for three d i f f e r e n t temperatures of the same detector. For lead s u l -phide c e l l s , the/peak i n the curve generally occurs at two microns, for lead selenide between three and four microns, for lead t e l l u r i d e a l i t t l e beyond four microns. I t i s i n t e r e s t i n g to observe how such detectors approach/their t h e o r e t i c a l ultimate s e n s i t i v i t i e s . This l i m i t , determined by the responsivity and the noise of any detector, i s discussed i n several of the papers quoted, the most important of which i s that by Clark Jones (3); t h i s paper i s discussed at some length i n Chapter IV, section (1). F e l l g e t t (4) calculates the l i m i t i n g s e n s i t i v i t y imposed by rad i a t i o n fluctuations on a lead sulphide c e l l , from i t s measured responsivity wavelength c h a r a c t e r i s t i c s , assuming the c e l l s to have been cooled and exposed to a s o l i d angle 2TT of rad i a t i o n (from surroundings taken to be at 15° C). The ultimate s e n s i t i v i t y was then calculated to be 2.1 x l O " 1 ^ watt at the optimum wavelength, compared with an actual meas--13 ured noise equivalent power per unit bandwidth of 4.9 x 1G watt. These results indicate that the t h e o r e t i c a l l i m i t f or the lead sulphide c e l l had been reached; the t o t a l noise being only twice as great as that due to the r a d i a t i o n f l u c t u a -tions alone. 4 Moss (5) has also studied the ultimate s e n s i t i v i t y and i t s dependence on the spectral response curve. For photo-conductive detectors, the background ra d i a t i o n i s normally of greater wavelength than the wavelength at maximum response. Upon cooling a c e l l , Moss found the l i m i t i n g s e n s i t i v i t y to deteriorate from 5.2 x 1 0 " 1 4 watt at 273°K to 17 x 1 0 " 1 4 watt at 90°K at 2 .3 microns. This i s because of the p r e f e r e n t i a l increase of the response at longer wavelengths upon cooling. On the other hand, at 3«5 microns the s i t u a t i o n i s reversed. The l i m i t i n g s e n s i t i v i t y for the same detector improved from -11 -14 2 x 10 watt to 15 x 10 watt. I t i s then of p a r t i c u l a r importance, i n choosing a detector for some s p e c i f i c purpose, to define a suitable Factor of Merit for detectors i n general. Without such a simple c r i t e r i o n , i t would be necessary to compare the performance of a l l available types of detector under the proposed experimental conditions. This long standing need for a Factor of Merit has been met by many workers, notably Clark Jones (6) and Daly and Sutherland ( 7 ) . These references are discussed i n the next chapter. Some of the i n t e r e s t i n g applications for photoconduc-t i v e c e l l s i n pure physics are i n the f i e l d of infrared spectro-scopy. By using photoconductive c e l l s , notable progress has been made i n resolving power and scanning speed; the point having been reached, where the infrared spectrometer i s becoming limited by o p t i c a l considerations and not by the detecting 5 element as heretofore.' Sutherland, Blackwell and F e l l g e t t (8) reported that they achieved a resolving power of 30,000 i n the water vapour spectrum near 2.5 microns, whereas pre-viously only a resolving power of 7,000 had been attained i n th i s region. Advances have also been made, using photocon-ductive c e l l s , i n the observation of spectra of extraterres-t r i a l objects. Rapid changes i n spectra occurring i n explosions or i n the early stages of a chemical reaction are often items of Interesting study. With a fast bolometer, the scanning time for the range of a few microns i s of the order of several sec-onds i f resolving power i s to be maintained ( 9 ) . Bullock and Silverman ( 1 0 ) , by using photoconductors, are able to scan a range of two microns between one and f i v e microns i n some thousandths of a second and with a resolving power of 100 near three microns. In t h i s way they have been able to study the f i r s t stages of the explosive reaction between oxygen and car-bon monoxide. Infrared spectroscopy has already made a vlarge con-t r i b u t i o n to the study of the atmospheres of planets. Kuiper (11) , using photoconductive c e l l s , has shown that the polar caps on Mars do not consist of s o l i d carbon dioxide but are almost c e r t a i n l y composed of i c e . In industry, lead sulphide c e l l s open up new possi-b i l i t i e s i n radia t i o n pyrometry. Lee and Parker (12) have shown that temperatures as low as 100°C can be measured t h i s 6 way with f a i r accuracy, and those of 5 0 0 ° C, sometimes encountered i n the rapid braking of locomotive wheels, can be followed con-tinuously and measured to an accuracy of one per cent. The purpose of t h i s research w i l l be to study the prop-erties of several photoconductive c e l l s , and evaluate several Factors of Merit for them. Any inconsistencies i n these w i l l be noted, the whole with a view to enabling future workers i n the f i e l d to choose the best of these detectors on merits of size of sensitive layer and time constant. Chapter I I FACTORS OF MERIT 1. The Clark Jones Factor of Merit (6) In his paper cn" Factors of Merit, Clark Jones (6) points out the need for " ... a s i n g l e , quantitative Factor of Merit f o r use i n comparing the s e n s i t i v i t y of various radiation detectors." A c r i t e r i o n i s needed for comparison of s i m i l a r detectors, such as an evaporated thermocouple and a wire thermocouple, as also f o r the comparison of d i s s i m i l a r detectors, such as a Golay pneumatic heat detector and a lead sulphide photoconductive c e l l . This Factor of Merit must be capable of comparing detectors with greatly d i f f e r e n t sensitive areas, response times and spectral response curves, when measured with an ampli-f i e r having any given frequency-response curve. In part I. of the second of. three papers dealing with radiation detectors, (3> 13? 6) Clark Jones defines a type n detector as one whose noise equivalent power (defined i n 13) P m i n the reference condition A depends upon the reference time constant t: and the sensitive Area A according to where k n i s a parameter independent of A and.T, but which has 8 d i f f e r e n t values for d i f f e r e n t detectors. Clark Jones (6) pro-poses a suitable multiple of k n as a numerical Factor of Merit. For type 1 detectors Clark Jones uses equation (3.8) of paper I (3 ) . For a detector whose quantum e f f i c i e n c y i s unity at every rad i a t i o n wavelength, equation (3.8) states that the minimum value of the noise equivalent power i s given by w ^ - - • ' < 2 ) where k i s Boltzmann's constant, cr i s the Stefan Boltzmann radiation constant, and where T i s the absolute temperature of the detector and of the surrounding r a d i a t i o n f i e l d . At the temperature T = 300 aK. the l a s t equation may be written where P m i s i n watts, A i s i n square millimeters, and "C i s i n seconds. I f a detector s a t i s f y i n g the above i s considered to have a Factor of Merit equal to unity then the Factor of Merit for any other type I detector may be wr i t t e n = VO_V2-where P i s i n watts, A i s i n square millimeters, t- i s i n m seconds, k i s In the units r e s u l t i n g from using the units just mentioned i n equation (6) and R Q i s i n watt 9 Equation (4) i s Clark Jones's proposed Factor of Merit f or a type I detector. For type I I detectors, Clark Jones (6) bases his multiple, chosen f o r k 2, on Havens's L i m i t . This l i m i t — based on an estimate of the minimum value of the noise equiva-lent power which could be obtained with thermocouples and bolometers with currently available materials and techniques — was made i n 1946, by R. J . Havens (4) for a detector at room temperature. This l i m i t , which i s of an opt i m i s t i c engineer-ing and not of a fundamental nature, has been very we l l con-firmed . Havens * s Limit i s ? ^ , s > . i o - " - ( K * / t . ) <» where P i s i n watts, A i s i n square millimeters, and ~c i s i n m seconds. I f a detector which s a t i s f i e s equation (5) be consid-ered to have a Factor of Merit equal to unity, then the Factor of Merit for any other type I I detector may be written = 3 x l o - ^ ( K k 2 / ^ V ( 6 ) where P m i s i n watts, A i s i n square millimeters, X i s i n seconds, k 2 i s i n the units r e s u l t i n g from using the units 10 just mentioned i n equation (1) and R is, i n watt o Equation (6) i s the proposed Factor of Merit for a type I I detector. In discussing the significance of the Factors of Merit, Clark Jones (6) then goes on to show that two detectors with the same Factors of Merit and of the same type ( e.g. both bolometers) but with d i f f e r e n t sensitive areas and d i f f e r e n t time constants w i l l not i n general y i e l d the same results i n any p a r t i c u l a r a p p l i c a t i o n . However, i f the two detectors are so reconstructed that they each have the o p t i -mum sensitive area arid the optimum time constant for the p a r t i c u l a r a p p l i c a t i o n , then the performance of the two w i l l be the same. This point cannot be stressed too greatly, since t h i s i s the great significance — and explains i n the best fashion the importance and usefulness -- of Clark Jones's proposed Factor of Merit. Thus with a knowledge of the Factors of Merit of d i f f e r e n t types of r a d i a t i o n detectors, one may, by knowing the optimum value of sensitive area and of time con-stant, choose a detector type of the appropriate size and response time which has a Factor of Merit close to unity, re-gardless of whether the detector be a bolometer, thermocouple, or photoconduetive c e l l . Thus a knowledge of the Factor of Merit of many di f f e r e n t detectors of known area and time con-stant seems highly desirable. This has been attempted for 11 several photoconductive c e l l s i n t h i s research. Clark Jones (6) carries the argument further, i n that i f the two detectors have d i f f e r e n t Factors of Merit and are constructed so that each has the optimum sensitive area and time constant for a p a r t i c u l a r a p p l i c a t i o n , the signal to noise r a t i o s so obtained w i l l be d i r e c t l y i n pro-portion to t h e i r Factors of Merit. For detectors such as bolometers and thermocouples, where i t i s assumed that the only source of noise i s the Johnson Noise associated with the resistance of the detector, M may be written (6) 2 KA-2. s0.O4-<£>* K / W ) ^ ( 7 ) where S D i s the effective zero frequency responsivity, meas-ured i n v o l t s per watt, A the sensitive area i n square m i l l i -meters, R the resistance i n ohms, and t i s the reference time a constant i n seconds. In the case of pbjotoconductive c e l l s , the noise i s not limited by Johnson noise only, and where the noise i s act u a l l y measurable, the following Factor of Merit i s obtained. Let P_ be the steady incident power which produces a steady output voltage equal to the noise voltage under the actual conditions of measurement. Where the measurement i s made with a squarely modulated s i g n a l , P i s obtained by reducing the o measured r e s u l t to zero frequency by making use of the measured square wave frequency response curve of the detector. 12 The quantity A f i s the noise equivalent band width i n the actual measurement, and A and T~ denote the sensitive area and the reference time constant. Clark Jones then shows (6), that M 2 may be written where P Q i s i n watts, A i s i n square millimeters, i s i n cycles per second, and "X i s i n seconds. A l l the Factors of Merit have been stated f or detec-tors operating at room temperature. The values for detectors operating at the dry ice and l i q u i d oxygen temperatures, 201°K. and 90°K., are given i n Chapter V, r;; i . . . { /„ In his discussion, Clark Jones (6) notes that no thermopile or bolometer operating at room temperature has a Factor of Merit as large as unity. . Only the super-conducting bolometers and the Golay pneumatic heat detector have Factors of Merit greater than unity ( v i z . , from 1.29 to 13.9» and 4.69 respectively). The Golay detector operates at room temperature, but since i t i s a type I detector (3) i t i s not permissible to state the Factor of Merit M 2 f o r t h i s detector. The Factor of Merit f or the Golay heat detector i s 0.30. Clark Jones also notes that the maximum attainable Factors of Merit at room temperature are s u b s t a n t i a l l y the same for thermocouples and bolometers. The s u i t a b i l i t y of his proposed Factor of Merit i s 13 also borne out, according to Clark Jones (6) by the results obtained for three thermistor bolometers, which use the same type of sensitive element, but employ greatly d i f f e r e n t coefficients of thermal conductivity between the sensitive element and i t s surroundings. The time constant for a bolo-meter i s defined as the r a t i o of the heat capacity per unit area to the thermal conductivity. In spite of the hundred to one range of time constant, the largest Factor of Merit for these thermistor bolometers i s only 15 per cent greater than the smallest. Clark Jones also states the need f o r the proper s p e c i f i c a t i o n of the relevant properties of radi a t i o n detectors. He states what he considers to be the necessary information about detectors: a) whose only source of noise i s the Johnson noise associated with t h e i r resistance as 1. The e l e c t r i c a l resistance 2. The sensitive area 3. The curve of r e l a t i v e responsivity versus frequency. I f the frequency response may be characterized by a single time constant, a statement of i t s value i s s u f f i c i e n t . 4. . The r e l a t i v e response to d i f f e r e n t r a d i a t i o n wave lengths 5 . The responsivity ( i n v o l t s per watt) at a single frequency with a specified spectral energy d i s t r i b u t i o n . and b) for detectors other than the above as 1. The sensitive area 14 2. A curve of r e l a t i v e responsivity versus frequency 3. A curve of the r e l a t i v e noise power per unit band width versus frequency, under the same conditions used to determine item 2 4. ,The r e l a t i v e response to d i f f e r e n t r a d i a t i o n wavelengths 5. A single measurement of the signal to noise r a t i o under f u l l y defined conditions* In the case of photoconductive c e l l s , the necessity of 4 i n both a) and b) i s due to the large v a r i a t i o n of s e n s i t i v i t y as a function of wavelength. I t i s worthwhile to consider further the c l a s s i f i c a -t i o n system proposed by Clark Jones (3). A detector i s defined to be a type n detector for a given range of reference time constants i f over that range of reference time constants the zero frequency responsivity to noise r a t i o n R Q depends upon the A and the reference time constant "C i n accordance with where k n i s a constant which i s independent of A and X. Clark Jones then l i s t s eight d i f f e r e n t kinds of rad-i a t i o n detectors (3) which he can c l a s s i f y as either type I or (9) 14 type I I detectors on the basis of t h e o r e t i c a l considerations. The l i s t i s as follows:-Range of x In seconds Detector - Type I Golay pneumatic heat detector Vacuum phototubes limited by shot noise Gas phototubes limited by shot noise Photomultiplier tubes l i m i t e d by shot noise Dipole antenna limited by temperature noise = shot noise - Type I I Bolometers Thermocouples and Thermopiles Photographic plates li m i t e d by grain structure 10~2 - co 10" J - oo 2.5 x 10" - oo 10"9 - co 10-3 - l 10 -1 Reciprocity law This paper w i l l t r y to assess the type number of the various types of photoconductive c e l l s under consideration purely on the basis of experimental evidence. The actual reference condition of measurement proposed by Glark Jones (3) i s the following. I t s a t i s f i e s these condi-tions :-1. The noise equivalent power of the detector i s measured i n the presence of the noise i n a manner such that the band width of the noise i s approximately equal to the band width of the detector. 2. The band width of the detector i s measured after the amplifier gain has been equalized so that the noise spectrum i s f l a t . 1 5 Then follows a pr e s c r i p t i o n for the adjustment of the amplifier and for the measurement of the noise equivalent power. However, t h i s has not been carried out i n the present work, but i t i s f e l t that time and material do not j u s t i f y such a step as the measurements carried out allow enough lee-way for e f f e c t i v e values to be obtained at the expense of only s l i g h t loss i n precision and generality. The above i s men-tioned as a further step necessary only to the absolute f u l f i l l m e n t of a l l the conditions l a i d down by Clark Jones (3) for the assignment of Factors of Merit. However, since Clark Jones (6) has assigned Factors of Merit to various detectors on the basis of previous published reports on t h e i r characteris-t i c s which do not follow his unique s p e c i f i c a t i o n s , and since he has assumed certain evidence to be able to convert published figures to his own specifications", i t i s thought to be s u f f i c -ient merely to do the same. Further, Clark Jones uses such above mentioned evaluations of Factors of Merit i n straight-forward comparisons between detectors, which i s e s s e n t i a l l y the purpose of t h i s paper. In summary, Clark Jones (6) has devised a thoroughly practical, and widely applicable method for assigning to ce r t a i n types of radi a t i o n detectors a number, called t h e i r Factor of Merit, which when properly interpreted allows complete comparison of a l l detectors covered, and which also indicates the best detector available for a thoroughly specified purpose. To a large extent, t h i s paper seeks to extend his d e f i n i t i o n to the large number of photoconductive c e l l s now being developed or 16 already i n use, i n order to aid workers i n f i e l d s associated with t h e i r use i n choosing s a t i s f a c t o r y detectors. 2 . The Daly and Sutherland Factor of Merit (7) One may express (7) the mean square f l u c t u a t i o n v o l -tage at the detector output as V (10) where Jx i s c h a r a c t e r i s t i c of the detector alone and ^ f i s ch a r a c t e r i s t i c of the ampl i f i e r (and display) alone. Further, defining O" as the responsivity i n microvolts per microwatt and "C as the time constant of the detector, Daly and Sutherland (7) propose taking (11) as the Figure of Merit of a detector, when s e n s i t i v i t y , speed, and noise l e v e l have a l l been taken into account. To compare the Daly and Sutherland Figure of Merit with that proposed by Clark Jones, the inverse of the former must be considered, since i t i s i t s e l f proportional to the minimum detectable power, whereas the number proposed by Clark Jones i s inversely proportional to the minimum detectable power. Also, Daly and Sutherland omit reference to the sensitive area, 17 which, being combined with the above remarks, gives as a s u i t -able Factor of Merit as proposed by Daly and Sutherland 3. Other Factors of Merit. The Hornig and O'Keefe Factor of Merit (15) Hornig and O'Keefe propose a factor of Merit (15) for thermal detectors which employ thermoelectric properties i n thermocouples of various materials. They propose a figure where Q i s the thermoelectric power of a thermoelectric junc t i o n attached to the receiver, k i s the thermal conductivity material. Denoting the two wire materials by the subscripts 1 and 2, a precise Factor of Merit i s established, of the form A ^ <T/^-O (12) (13) of the wire material, and f the r e s i s t i v i t y of the wire (14) Q i s measured i n microvolts per degree Centigrade, k i n watts per centimeter degree Centigrade, and ^ i n ohm centimeters. 18 I t i s f e l t that the Factor of Merit given by Clark Jones carries the greatest weight since i t i s universal, applying to a l l types of detector, whereas both the above are specialised cases. I t also considers the sensitive area, which i s a matter merely of adjustment to the above figures. However, Clark Jones's Factor of Merit i s chosen on the basis of t h e o r e t i c a l prediction, and i s not merely a good guess, and embodies considerations such as minimum detectable power, proper time constant and class of detector. Chapter I I I THE APPARATUS The apparatus must be able to measure responsivity to noise r a t i o , time constant, and also the sensitive area. The l a t t e r may be measured by the usual means of t r a v e l l i n g microscope, since for most detectors i t i s impossible for a detailed examination of the sensitive area to be made, as the detectors are i n vacuum. The responsivity to noise r a t i o i s measured by using a 900 cycles per second tuned amplifier with properties des-cribed i n section (3) of t h i s chapter. The measurement of time constants i s performed by using a neon f l a s h bulb as a source of variable modulation frequency (square wave modulated) radiant energy, a wide band preamplifier a f t e r the detector whose time constant i s being measured, and an oscilloscope, a l l of known frequency response, a plot then being made of response versus frequency from which the time constant i s determined. A detailed description of the above-mentioned i n s t r u -ments follows. 1. The Black Body Radiator. The radiator i s shown i n figure (1). A i s a s t e e l 20 cylinder 10 centimeters long and 6 centimeters i n diameter. A conical hole subtending an angle of f i f t e e n degrees i s bored i n one face (the cylinder then being thoroughly baked f o r oxidisation purposes) and i s surrounded by a dis c of a i r of 6 centimeters diameter and 1 centimeter thickness. I t i s covered with a c i r c u l a r aperture of 1 centimeter d r i l l e d i n a brass discB. Another brass disc i s placed i n a symmetrical p o s i t i o n , 1 centimeter from the l a t t e r face of the s t e e l cylinder. The whole i s enclosed i n an alundum cylinder C which i s .wound non-inductively with a nichrome heater E. A resistance thermometer F i s then wound over the heater, shorts being avoided by having a l l wires E and F embedded i n alundum cement. This c y l i n d r i c a l r o l l i s then covered by a r o l l of several thicknesses of asbestos sheeting D, surrounded by rock wool, which constitutes a rectangular f i l l i n g of a wooden box, whose inner dimensions are 12 cm. by 12 cm. by 20 cm. The front end of t h i s box i s covered by a thickness of aluminum J with a 1 cm. aperture. A hole was bored through the back brass disc B and the s t e e l cylinder A to the apex of the conical hole as shown i n figure (1). This hole contains.: the thermo-couple, which i s of i r o n constantan. The thermocouple c a l i -bration curve was plotted, i n d i c a t i n g close agreement with the c a l i b r a t i o n curve f or such a couple found i n the Wheelco tables. The resistance thermometer has a temperature co e f f i c i e n t of .0045 per degree Centigrade. The wire used has a length of 20 feet, resistance at 0° C. being 24.6 ohms, and at 200° C. 25 ohms. 21 In figure ( 2 ) , the o p t i c a l system of the black body radiator i s shown. A l l plates of aluminum are highly polished on the side facing the source, and painted with a mixture of lamp-black and methyl hydrate on the side away from the source. O r i g i n a l l y , the b a f f l e system consisted of two baffles of type A (figure (2) ), and two b a f f l e s made of single aluminum plates, of the dimensions i l l u s t r a t e d and of square area. The present system, which necessitated removal of a l l b a f f l e s except that shown at A, was due to standardization of the length of separa-t i o n between the sensitive area of the detector and the v i r t u a l source to 20 centimeters. The asbestos used i n shield A i s of the sheet type. F i s a s l i d i n g shutter of aluminum, also o r i g i n a l l y of several a i r separated aluminum plates with polished and blackened sides, now consisting of a single plate of alumi-num. The chopper disc B (figure (2) ) may be used either " for sinusoidal modulation or square wave modulation of the incom-ing r a d i a t i o n , depending on the desired app l i c a t i o n . This i s effected by having holes and spaces of equal widths for square wave modulation, or i n a specified r a t i o f o r sinusoidal modula-t i o n . There are 30 holes i n the chopper wheel at a radius of 10.2 centimeters. The chopper motor D i s an 1800 r.p.m. synchronous motor, and i s mounted below a brass tube J , blackened on the i n s i d e . C i s an aperture d i s c , with eight holes d r i l l e d i n i t . The diameters of these holes, as measured by a t r a v e l l i n g micro-scope, are . 7 9 8 , .631 , .577, . 4 8 2 , . 3 6 9 , . 3 , .189 and .109 22 centimeters respectively. The aperture standard normally used.is 3 millimeters i n diameter. The detector i s held by means of clamps with i t s sensitive area at K. Great care was exercised i n designing t h i s o p t i c a l system, so that a l l c e l l s would be uniformly . radiated from the black body, for a l l sensitive areas encount-ered. The maximum radius f or the sensitive area of a detector c e n t r a l l y mounted on the axis of the o p t i c a l system i s of 1 centimeter radius f o r an aperture of 3 millimeters required to act as a v i r t u a l source. A b r i e f digression i s i n order here to explain how the c i r c u l a r 3 millimeter aperture acts as a v i r t u a l source. A complete treatment i s given by Roberts (16) on page 390 and i s as follows with reference to figure ( 3 ) . The small hole cd i s the 3 millimeter aperture i n question, the receiver i s ab, and the radiator i s a'b 1. The essential feature i s that the l i n e s ad and be produced intersect the radiator, taken as the 1 centimeter conical hole. This condition ensures that the ra d i a t i o n received by any and every point on the receiver i s the same as i f the radiator were of the same area as the aperture cd i n the screen and were situated i n the plane of the aperture. For proof of t h i s , consider the. radiation received by an i n f i n i t e s i m a l area at the point P on the receiver. As far as the point P i s concerned, the only part of the radiator : which i s ef f e c t i v e i s represented by c'd'. I f A,is the area of cd, and A J that of c'd 1, 23 K M - C ^ / C o - " ) * ( 1 5 ) that i s , the areas are proportional to the squares of t h e i r distances from the point P. But the i n t e n s i t y of rad i a t i o n f a l l s o f f inversely as the square of the distance from the source. Since t h i s i n t e n s i t y i s also proportional to the area of the source, the increase i n area compensates for the increased distance, and the rad i a t i o n at P from the surface c'd 1 i s the same as the radia t i o n from a surface of the size of ed situated i n the plane of the screen would be. Under experimental procedure i n Chapter IV, section (6) i t w i l l be seem.that an experiment was performed to test whether the source was ac t u a l l y a v i r t u a l one. The whole framework containing the black body may be mounted either v e r t i c a l l y or h o r i z o n t a l l y , depending on whether c e l l s which have to be cooled have side or end windows, since the c e l l s must always be mounted v e r t i c a l l y to allow t h e i r being cooled. 2. Temperature Control for the Black Body Radiator. The standard setting of the black body i s 5 0 0 ° K., and to ensure that t h i s temperature i s produced with no change over long durations of measurements, i t was found necessary to use a temperature control of the type described. 24 A bridge network i s made up, of which two arms are the resistance thermometer already described i n the preceding section, and a control, R t t l and R^ . respectively. The control i s made up of two wire-wound potentiometers i n series; one has a value of 2G0 ohms and acts as the coarse con t r o l , the other being a 5 ohm resistance i n series with i t which may be used as the fine control. E s s e n t i a l l y , the function of the c i r c u i t i s the mix-ing of two a.c. voltages, one of which has a constant amplitude . and a constant phase, the second having varying amplitude and approximately constant phase. When the amplitude of the second voltage i s varied, the output signal varies i n phase and i t s amplitude increases. This signal i s applied to the grid of an F.G. 57 thyratron. The f i r s t signal i s provided by an a.c. network across the 6.3 vo l t heater, supply, and can be adjusted to have a phase varying within plus or minus of 120° with respect to the a.c. voltage supplied to the thyratron anode. This phase i s adjusted by means of a 5G* kiloohm potentiometer so that, when the bridge i s i n balance, the signal which i s applied to the grid of the thyratron gives exactly the current through the heater winding of the black body needed to maintain the black body radiator at i t s balance temperature. I f the R v setting i s above the present black body temperature, the bridge goes o f f balance and t h i s additional signal produced across the temperature bridge i s added to the 25 network s i g n a l , increasing the grid voltage i n amplitude and changing i t s phase. This phase change i s such that the on period of the thyratron i s increased, which i n turn gives an increase i n the heater current. The heater i s i n the anode load of the thyratron. I f the black body i s too hot, however, the phase angle varies such that the on period decreases. A 6K6 tube i s linked i n the c i r c u i t as a cathode follower to provide a low impedance signal to the grid with l i t t l e or no d i s t o r t i o n . The o v e r a l l c i r c u i t gain i s about 3 0 , 0 0 0 , and regula- :. O ^ o t i o n has been found better than 0 . 1 K. f o r 500 K. operation, by measurements made with a thermocouple. The thermocouple which measures the ef f e c t i v e black body temperature may be read on a small m i l l i v o l t m e t e r marked "Centigrade" on the apparatus. For higher accuracy than t h i s , an external potentiometer must be used for the temperature measurements. The advantage of t h i s type of control unit over other types i s that the black body can be brought from room tempera-ture to anywhere i n the (400-600)° K. region i n a matter of one and one-half hours without having to bring the radiator to within a few degrees f i r s t , as i s necessary with most other con-ventional types. 26 3. The 900 cycles per second tuned am p l i f i e r . The amplifier was b u i l t a f t e r a design by Brown ( 1 7 ) and i s i l l u s t r a t e d i n figure (4). The merits of the ampli-f i e r are that i t has a f l a t peak of several cycles to compen-sate mains voltage changes af f e c t i n g the chopping frequency, a high gain and a l i n e a r response. There are three main stages of a m p l i f i c a t i o n i n the o r i g i n a l c i r c u i t , each consisting of three tubes. The cathodes of the f i r s t and t h i r d tubes are connected to give negative feedback. An attenuator i s placed between the f i r s t and second group of three tube stages, to step up the a m p l i f i c a t i o n by convenient factors of three. A tuned anode load i s placed' on the t h i r d tube i n each of the f i r s t two stages, one tuned at 880 cycles per second and the other at 920 cycles per second, to give a flat-topped frequency response curve at 900 cycles per second. The c o i l s are t o r o i d a l , and are mounted i n mumetal cases to give magnetic and e l e c t r o s t a t i c screening. The output i s fed through a transformer with a 1 : 1 r a t i o from the primary to each half of the secondary.. The present amplifier i s e s s e n t i a l l y the same as the above with the following modifications. F i r s t l y , a low noise twin triode 12AY7 replaces the f i r s t two pentodes i n each of the three groupings. Secondly, some positive feedback i s employed between the cathodes of the second and t h i r d tubes of each ring of three. T h i r d l y , the output twin diode has been replaced by two 1N34 r e c t i f i e r s . The heater voltage i s adjusted to give 27 l e a s t hum by means of a 150 ohm potentiometer across the heater winding connected to some point on the power supply. The output i s shown on a 0-200 microammeter whose f u l l - s c a l e d e f l e c t i o n corresponds to 10 m i l l i v o l t s output. The data for the amplifier i s as follows. The gain = (50) + (50) + (24) = (124) db = 1.5 x 1 0 7 With input terminals shorted the noise l e v e l i s equivalent to ( .22) j>V. No noticeable change on the output meter i s noted for a mains voltage range 90 - 135 v o l t s on amplifier scale 11 . On open c i r c u i t - n o i s e l e v e l i s equivalent to ( 1 .53) jA v o l t s . Figure (5) shows the frequency-response curves f or inputs of 2.5 m i l l i v o l t s and of 5»01 microvolts respectively. Figure (6) shows the l i n e a r i t y of response for a gain setting of ( 11) . The peak of the frequency-response curve occurs at a frequency of 895 cycles per second. The bandwidth i s 44 cycles per second at minus 3 db. Considering R 2 as the dynamic impedance of the tuned load at the operating frequency, the gain per ri n g of three stage i s R2/R]_, where R-^  i s the cathode load of the t h i r d tube. With desired values of the tuning c o i l and the "Q" of the tuned load, Brown (18) has shown that R 2 i s approximately equal to 40 kiloohms at the required operating frequency. To obtain maximum gain, one must make R^ small, which c a l l s for a tube of short grid base and high g m i n both the t h i r d and f i r s t tubes. Brown (18) shows that a f r a c t i o n a l change of loop gain dA/A and the f r a c t i o n a l change of gain dG/G are related by 28 Thus, for A = 999 > a 10$ change i n A gives a 0.1% change i n G . The amplifier gives long-term s t a b i l i t y of gain, low noise l e v e l , and l i n e a r i t y of response, and i s therefore i d e a l l y suitable i n the work attempted here. 4. Time Constants Apparatus. The time constants are measured by a method explained under Experimental Procedure, chapter IV, section (2). A neon 30 tube i s used whose time of response i s characterised by a time constant of 'v/lO sec. I t s response curve was obtained using the method outlined i n chapter IV, section (5). Neon, as the gas for discharge, was chosen because although the time constants of such tubes may be some-what longer than for other gases, notably hydrogen, hydrogen sources lead to other complications due to the s c a r c i t y of in f r a -red l i n e s obtainable from them. The l i m i t i n g factor to be scrutinised i n choosing a suitable source of infra-red r a d i a t i o n , i s the i o n i s a t i o n time of the gas, which for the tube used was found to be<lo~ Q sec.. 2 9 The Multivibrator used consists of s i x tubes, and employs a plate-to-grid coupling. The signal i s taken from a cathode follower to give a low impedance source for switch-ing the neon. The range of the multivibrator extends for square waves with half-widths from 5 microseconds to 10 m i l l i -seconds, and the edges of the square waves are less than 0 . 5 microseconds long; a figure good i n comparison to that quoted by Elmore and Sands (19) on page 81 , who give a steepness of 0 . 1 microseconds as a t h e o r e t i c a l l y attainable l i m i t , f o r a multivibrator using two pentodes and having a large consumption of power; a s i m i l a r scheme to that used i n t h i s multivibrator as mentioned i n t h i s paragraph. The frequency of o s c i l l a t i o n can be varied f a i r l y conveniently.in steps, each step having a continuous range overlapping those of other steps, and covering the t o t a l range' of 5 to 10,000 microseconds mentioned above. Voltages are supplied by an e l e c t r o n i c a l l y regulated power pack. Special attention has been given to the building and design of t h i s power pack, to enable use of various neon tubes with a large v a r i a t i o n of s t r i k i n g voltages. A wide band preamplifier was designed for use with the apparatus for measurement of time constants. O r i g i n a l l y , a single stage preamplifier was b u i l t with a gain of 50; t h i s was not of high enough gain for measuring time constants of some of the lead selenide and lead t e l l u r i d e c e l l s , whose out-put i s smaller than that of most lead sulphide c e l l s , f o r which 30 l a t t e r t h i s amplifier was o r i g i n a l l y intended. Therefore a new wide band preamplifier was b u i l t with a gain of 2000, which could be used to measure time constants of most of the detectors studied i n t h i s research. The c i r c u i t i s shown i n figure (7)> and consists of two high g m sharp cut-off 6AG5 miniature pentodes and a cathode follower. The output i s put either d i r e c t l y on the plates of a double-beam o s c i l l o -scope, or through the low gain amplifier on the oscilloscope, which has a f l a t response out to seven megacycles per second. The frequency range of the preamplifier i s governed at the low end by the condition that 1/RC be very much less than 50 where R and C afe as i n figure 7'• The values of R (3 .3 Megohms) and C ( 0 . 5 microfarads) s a t i s f y t h i s condition. At high frequencies, the value of R must be much larger than 1/Cw, where C i s the input capacitance of the 6AG5 tube, and w i s the highest angular frequency used. This condition i s also f u l f i l l e d . Decoupling between stages has been used to eliminate p o s i t i v e feedback, and the screens of the two pentodes are decoupled by 8 microfarad e l e c t r o l y t i c condensers as shown. Use of negative feedback has not been found necessary (by the removal of the 250 microfarad cathode s e l f - b i a s con-densers). The grid of the cathode follower has been put at 150 volts to allow output pulses of t h i s height to be seen on the oscilloscope. The actual maximum signal into the o s c i l l o -scope i s 22 v o l t s . 31 Figure (8) shows the frequency-response curve for the wide band preamplifier, which covers the range of square wave signals from the multivibrator f a i r l y adequately and with no d i s t o r t i o n , as has been found by using a frequency adjusted attenuator for using the 120 v o l t multivibrator output as an input signal to the preamplifier, and comparing the input and the ouput by means of the double-beam oscilloscope. 5. C e l l Mountings Most of the c e l l s studied were either lead sulphide or lead t e l l u r i d e . The lead sulphide Admiralty c e l l s were used at room temperature, and mounted i n brass shielding (figure ( 9 ) ) with coaxial cable connectors. The other lead sulphide, lead t e l l u r i d e and lead selenide c e l l s were either commercial ones and already mounted with a tube base (e.g. the B.T.H. lead sulphide and lead t e l l u r i d e c e l l s ) and thus re-quired a metal screen with the tube socket i n one side and a coaxial connector i n the other with a screened lead carrying the signal inside the can, or the c e l l s were sometimes of glass with two tungsten electrode leads at one end and a window at the other, i n which case a screened lead with brass connectors was used, and the whole screened i n a r o l l of grounded t i n f o i l . 6. Spectral Response Measuring Equipment The equipment consisted of a Brown recording potentio-32 meter, whose f u l l scale reading corresponds to 10 m i l l i v o l t s , a Perkin and Elmer model 12C infra-red monochromator with a rocksalt prism, a globar for a source of black body r a d i a t i o n , a standard Perkin Elmer thermocouple detector and associated d.c. a m p l i f i e r , and a 900 cycles per second tuned a m p l i f i e r , a chopping wheel and motor. The globar operates with a current of 2 .25 amps, at a temperature of 1400° K. and with an emissivity of about .9-More d e t a i l s are given i n section (4) of chapter IV dealing with the experimental procedure. Chapter IV THE EXPERIMENTAL PROCEDURE The Factor of Merit M2> as defined i n Clark Jones's paper (6) uses the following measureable properties of a detector, namely: responsivity, minimum detectable energy, time constant, the e l e c t r i c a l resistance and the sensitive area. Dealing with each of the above i n order, i t may be said that the measurement of the e l e c t r i c a l resistance and the sensitive area poses no great d i f f i c u l t y , only i n certain cases of high resistance or of unusual envelopes and surfaces of detectors may d i f f i c u l t i e s be encountered. 1. Responsivity and Responsivity to Noise Ratio For the measurement of the responsivity, defined as the r a t i o of the output voltage of a detector with an e l e c t r i -c a l output to the power incident upon the detector (13), and written as S, a standard r a d i a t i o n signal i s the f i r s t require^ ment. To obtain t h i s , use i s made of Stefan's Law of ra d i a t i o n from a p e r f e c t l y black body, that the t o t a l emissive power of such a body i s proportional to the fourth power of i t s absolute temperature, £he constant of pro p o r t i o n a l i t y , v T , being Stefan's constant, and numerically equal to 5*672 x 10"^  ergs cm"2 34 degrees s e c - J v The amount of rad i a t i o n i n the form of energy received per second by a pe r f e c t l y black receiver of area A 2 (the chopper wheel being at a temperature of T-L °K.) from a radia t i o n of pe r f e c t l y black body type at temperature T 2° K., where A-^  i s the area of the v i r t u a l aperture mentioned i n chapter I I I , section ( 1 ) i s an amount Q V L T S - T ^ K K ^ ( 1 7 ) where D i s the distance of the receiver from the aperture. 1 From ( 1 7 ) ? usingCr= 5 . 6 7 x 1 0 ~ 1 2 joules cm.^degree'^sec."1, T 2 = 5G0 0 K., T x = 3 0 0 ° K., A X = C T V 4 ) ( . 3 ) 2 cm.2 and D = 2 0 cm., Q/A 2 may be obtained, and w i l l be i n units of watts per square centimeter. A number of standard values are seen to have been used. The black body i s heated to a temperature of 5 0 0 ° K., the c i r c u l a r aperture i s made to be 3 millimeters i n diameter, and the distance used from the aperture to the sensitive layer of the c e l l i s made equal to 20 centimeters. (The c e l l s are worked at the temperatures of l i q u i d oxygen ( 9 0 ° K . ) , a mix-ture of dry ic e and methyl hydrate ( 2 0 1 ° K.) and at room temper-ature ( 3 0 0 ° K.) ) . The exact amount of ra d i a t i o n received by any detector placed at the standard distance and centered on the o p t i c a l axis of the black body system i s thus known, making the following assumptions. The source must be a v i r -t u a l one, and that t h i s i s so may be seen by reference to the 35 experiment mentioned i n section (6) of t h i s chapter. Second-l y , the optical-system must be perf e c t l y aligned; t h i r d l y , the black body must be black and at a temperature of 500° K. Tests have not been performed as to the blackness of the black body, an assumption of 0.9 t o t a l black body emission as a mini-mum conservative estimate seems to be quite j u s t i f i a b l e , and ce r t a i n l y not an unreasonable fi g u r e . The temperature control i s accurate to 0.1° K. i n 500° K. (see chapter I I I , section (2) ), and the temperature scale i s calibrated by means of an accurate Leeds and Northrup potentiometer, using the calibrated i r o n constantan thermocouple of the black body. The values of the detector's sensitive area (A 2 i n equation (17) ) and of A i are the least w e l l known, A 1 i s known to approximately one per cent, A 2 to w i t h i n as l i t t l e as ten per cent. The incident power must be corrected f o r modulation; since t h i s i s square wave then the root mean square value of the incident power f a l l i n g on the radiator i s equal to one h a l f of the value given i n equation (17) • The photoconductive c e l l i s also a poor black body receiver for wavelengths greater than the neighbourhood of r3 to 5 microns, which corresponds to a very small percentage of the t o t a l power from the black body, of the order of one per cent. Therefore equation (17) must also be corrected by multiplying i t by a factor of the order of 1/100. These corrections are applied i n the next chapter. The detector i s connected to the 900 cycles per 36 second tuned low noise amplifier by means of a short coaxial cable going d i r e c t l y to the input condenser of the am p l i f i e r , bypassing any input connectors, and i s shielded, as shown i n figure (9) by a brass cylinder. The sensitive layer l i e s inside the tube J of figure (2), which i s blackened inside by a mixture of lamp-black, alcohol and a small trace of sh e l l a c . The amplifier passes a current through the detector (a photoconductive c e l l ) producing a voltage across i t of some number of microvolts. The detectors have resistances of the order of kiloohms, and the current used i s of the order of microamps. The detector "sees" the black body through a suc-cession of baffles and the aperture, which l a t t e r are a l l at room temperature. A chopper wheel, painted black, cuts the radiation into approximately square bursts at a frequency of 900 cycles per second; each burst of radiation changes the conductivity of the c e l l by some f r a c t i o n of the zero frequency change of conductivity from 300° K. to 500° K. (or from the operating c e l l temperature to 500°K.). This f r a c t i o n may be taken as unity, and i s ac t u a l l y given i n chapter V. Thus a signal i s generated, at a frequency of 900 cycles per second, and i s amplified and r e c t i f i e d by the amplifier to give a reading equivalent to the root mean square value of vo l t s i n -put (or v o l t s output from the detector). The reading taken i s on a microammeter calibrated f o r each scale to give root mean square v o l t s input from the detec-t o r . 37 The amplifier has the following c h a r a c t e r i s t i c s 1. A bandwidth of 44 cycles per second at minus 3 db. 2. A peak centered at 895 cycles per second on a l l ranges (see figure (10) ) 3. A f l a t response from 890 to 900 cycles per second on a l l ranges (see figure (10) ) 4. Linear response on a l l ranges (see figure (11) ) 7 5. A gain of (124) db = 1.5 x 10 on scale 11 6. An open c i r c u i t signal of (1.53) microvolts 7. A shorted input signal of (.22) microvolts 8. No detectable change i n output on the top of scale 11 for a v a r i a t i o n i n mains voltage from 90 to 135 vo l t s 9. Good r e p r o d u c i b i l i t y at a l l times These considerations make the amplifier i d e a l f or measuring signals from the detectors under study, and mean that the amplifier can be used for detectors with short time constants and of resistance ranges from 50,000 to 1,000,000 ohms, and which have noise appreciable i n comparison with the noise value of the amplifier ( i . e . with (.22) microvolts). A change i n mains frequency w i l l change the chopper frequency but w i l l not change the output signal because of the f l a t amplifier response. A change i n mains voltage i s also seen to have ne g l i g i b l e effect on the output. Stray r a d i a t i o n i s eliminated by having a tuned a m p l i f i e r . L i n e a r i t y of response ensures single-valued-ness of output as a function of 38 the input, and speaks for i t s e l f . S t a b i l i t y , which i s achieved by the use of a great amount of negative feedback, cannot be overemphasised i n importance. The fact that a tuned am p l i f i e r (or a.c. amplifier) i s used eliminates the p o s s i b i l i t y of d r i f t encountered i n d.c. a m p l i f i e r s , and enables the achievement of a very high gain. The f l a t top of the frequency-response curve f o r the amplifier has been achieved by the use of two tuned stages, each of three tubes, and having equal gain but centered at d i f f e r e n t frequencies. The disadvantages are seen to be that the amplifier i s a very serious proposition i n b u i l d i n g , and i n achieving low noise. This means great care i n soldering j o i n t s , d i f f i -c u l t y i n replacing low noise tubes, careful grounding, and only at one point i n the c i r c u i t , careful screening between stages and use of screened interstage leads, and the use of expensive and bulky paper and o i l condensers rather than elec-t r o l y t i c ones (except for screen decoupling purposes). I t i s also necessary to use wire-wound r e s i s t o r s i n the f i r s t stage, which have very low noise of the order of the Johnson noise of the r e s i s t o r . Avoidance of 60 cycle per second pickup i s also of the utmost importance, not only i n the ampli-f i e r i t s e l f , but on the detector too. In the case of the detector, t h i s i s accomplished by very careful screening, and care i s taken to ensure well-soldered j o i n t s on the detector. On the a m p l i f i e r , the c o l l s used as plate loads are also 39 screened, as are input lead and output for oscilloscope t e s t -ing and the d.c. output. The bottom of the chassis i s ' t i g h t l y covered, and the power supply i s kept as remote as possible from the ampl i f i e r i t s e l f . Any audio-frequency a m p l i f i e r , such as t h i s one, i s also very prone to hum and motorboating, besides which any 900 cycles per second harmonics of the main voltage, unless very c a r e f u l l y kept removed and i s o l a t e d , w i l l cause o s c i l l a t i o n s to develop. O s c i l l a t i o n s between stages must also be avoided at a l l costs, by keeping inputs and out-puts of stages w e l l removed from each other. The heater v o l t -age windings of the transformer are therefore c a r e f u l l y biased by means of a 150 ohms potentiometer (figure (4) ) to give least noise for the amplifier output under shorted input condition of operation. Another problem i s microphonics, which at audio-frequencies frequently cause havoc i n the readings. These too must be avoided, or measurements made under conditions of least l o c a l i n terruption (preferably at night). The attenuator i t s e l f must be c a r e f u l l y designed so that the grid input of the second stage of am p l i f i c a t i o n i s never l e f t f l o a t i n g . For t h i s i t i s useful to obtain an atten-uator which has shorting spacers such that when the amplifier i s on no range (between ranges) the grid of the f i r s t tube of the second stage (ring of three) i s shorted to ground. For calculating' responsivity to noise r a t i o (R, an accurate determination of the noise voltage needs to be made. Clark Jones (13) defines R as U 3 s/M- (18) where N denotes the noise power per unit band width. The noise power may be defined as the mean, square value of the noise voltage. In discussing the noise, reference must be made to the following sources of noise. Clark Jones (3) describes these appropriately as; a) The Radiation Background This i s due to the black body r a d i a t i o n f i e l d from the detector i t s e l f and from the surroundings. The noise due to t h i s background i s called temperature noise (3, 13)> and i s due to the fluctuations i n temperature of the heat detecting element. Since photoconductive c e l l s are not temperature detectors, i . e . do not operate by changes i n t h e i r temperature caused by the incident r a d i a t i o n , t h i s aspect need not be con-sidered. The photoconductive c e l l does not operate by changes of i t s temperature, exchanging energy with i t s surroundings only by r a d i a t i o n . Thus fluctuations i n the output of such a photoconductive c e l l are due e n t i r e l y to fluctuations i n the ra d i a t i o n , and thus the re s u l t s quoted by Clark Jones (3) w i l l hold, since he derives these on just such an assumption of fluctuations i n the r a d i a t i o n . The results obtained by him hold for detectors whose size i s large compared to the wave-lengths of the radiation being detected, and which obey Lam-bert's Law. This radiation background i s seen to give r i s e to a minimum detectable power of the detector, H m, equal to i t s noise equivalent power, where for a detector with an emissivity of unity at a l l frequencies ' ^ 4 ' L o - T * K T / t ^ / ^ ( 1 9 ) where ^ s i s the absorption c o e f f i c i e n t , taken as unity, A i s the area of the detector, T i s i t s temperature, ~C- i s i t s time constant, and c r and k are Stefan's constant and Boltzmann's constant, respectively. The factor (^u./^s") has been taken equal to unity. b) The Internal Background This type of background i s introduced w i t h i n the detector i t s e l f , and consists of Johnson noise, Current noise and perhaps Semiconductor noise. c) Signal Noise Whereas the r a d i a t i o n background i s due to the black body noise of the detector i t s e l f and of i t s surroundings, i n detecting small changes i n steady signals, the s t a t i s t i c a l v a r i a t i o n i n the signal may, i f large, determine the smallest 42 detectable change. This i s of l i t t l e concern i n t h i s paper. The amplifier i s used to measure the noise when a black shutter (figure (2) ) i s placed across the black body source. The amplifier noise i s subtracted from t h i s noise, but i s usually too small with the amplifier used to be con-sidered at a l l compared to the detector noise.. The shutter must be cooled or kept cool, and the chopper need not be oper-ated since only the noise i n the amplifier bandwidth w i l l appear at the output, and the chopper frequently causes severe microphonics due to vibrations i n the system containing the chopper motor and the detector. A scheme exists therefore, for the experimental determination of the responsivity, the noise, and thus of the responsivity to noise r a t i o . 2. The Measurement of Time Constants Figure (12) shows i n block schematic form the arrangement of apparatus used to measure time constants of the range which these photoconductive c e l l s under consideration possess.. The multivibrator mentioned i n chapter I I I , section (4) has two outputs. One i s applied to the neon 30 tube ( I I I , (3) ), the other d i r e c t l y to the plates of a double beam oscilloscope. The square wave 120 v o l t s on-off voltage applied to the neon causes infra-red r a d i a t i o n to f a l l on the photoconductive c e l l , which i s e l e c t r o s t a t i c a l l y screened 43 from the neon by a fine wire mesh. The speed of response of the neon i s demonstrated by a procedure outlined i n sec-t i o n (5) of t h i s chapter. The photoconductive c e l l i s attached to the input of the wide band preamplifier, whose output i s then displayed on the Y 2 plates of the oscilloscope. The preamplifier i s provided with a variable gain control, and has a frequency-response curve covering the range of multivibrator frequencies adequately, as shown i n figure (10). t h i s method may be outlined as follows. With reference to figure (12), consider a detector receiving a square wave radia-t i o n signal of modulation frequency f cycles per second. The half-width t i s then seen to be equal to l / 2 f . Considering f i r s t l y a r i s e i n response of the detector to the s i g n a l , figure (10b), The theory of the measurement of time constants by (20) But from figure (10a) 3 _ k - c (21) a — c Therefore a - L — c ) 44 which gives _-t/-t (22) S i m i l a r l y , f o r a f a l l i n response, with reference to figure (10c) ( 2 3 ) Combining equations (22) and (23) C a-\=> > (24) which holds f o r b - c. Thus the response exponential wave i s symmetrically placed between the zero and peak amplitudes of the incident square wave, or of the t h e o r e t i c a l l y a t t a i n -able output wave f o r "C approaching zero. A, the observed amplitude, i s given by / U ( a - W ) ( l - e - W , . ( 2 5 ) Since 14- e and our f i n a l r e s u l t i s 45 Q \ —-c (26) V 4- ^ There are two important l i m i t i n g eases. For low frequencies, where t i s very large compared to "C, A becomes equal to a. At high frequencies, "C i s very large compared to t , the exponential approaches 1, and A may be written (27) When a plot of the response A versus the half-width t i s made, a frequency-response type curve r e s u l t s , which approaches the value a at the high t end, and has the form of a straight l i n e given by equation (27) at the low t end. These l i n e s meet when (28) where t = t , the value at the i n t e r s e c t i o n of these l i n e s , o and f i s the corresponding value of the frequency f 0 . Thus the time constants of detectors may be c a l c u l a -ted from the value t o / z . ( 2 9 ) or - C = 1 / 4 - S r o (30) 46 In pr a c t i c e , the preamplifier gain i s set so that at low frequencies the Y^  and Y 2 traces (signal and response) have the same amplitude. A graph with several points at low t values of A versus t i s then plotted, t 0 i s found from the inte r s e c t i o n of the best low t l i n e with the l i n e A = a, from which "C i s calculated. The method outlined i s limi t e d only by the range of the multivibrator, the range of the wide band preamplifier, and the range oyer which the oscilloscope may be triggered. Also, the neon i o n i s a t i o n time constant, i f large, may enter i n the l i m i t a t i o n s of t h i s method. In chapter I I I , section (4) , the range of multivibrator half-widths i s given as being from 5 microseconds to 10 milliseconds, which means that the the o r e t i c a l l i m i t s over which time constants may be measured i s f or X between 2.5 microseconds and 5 milliseconds. In practice, most of the detectors encountered had time constants well within t h i s range. The neon has a very short time constant (see section (5) belo\*) and does not enter i n for purposes of range consid-erations f o r the measurements of time constants. The preamplifier has a range from 0 cycles per second to 1 megacycle per second. The range of the multivibrator, expressed i n cycles per second for square waves, i s from 50 cycles per second to 100 k i l o c y c l e s per second, and the range of the preamplifier i s , f o r sinusoidal frequencies from 0 cycles per second to 1 megacycle per second. This gives a 47 factor 1G at either end of the range for conversion between square waves and sinusoidal waves, that i s , the preamplifier responds to signals of 5 cycles per second s i n waves, and w i l l therefore respond to square waves of 50 cycles per second f r e -quency with l i t t l e or no d i s t o r t i o n ; s i m i l a r l y a square wave signal of 100 k i l o c y c l e s per second, when going into the pre-amplifier with a f l a t response out to 1 megacycle per second, w i l l show l i t t l e or no d i s t o r t i o n . The preamplifier has been designed for photoconduc-t i v e c e l l s , and supplies them with current, i t may also be used i n the measurement of bolometer time constants, and, by removing the 1 megohm input to high tension l i n e r e s i s t o r , and adding more stages i f required, the amplifier may be used with high speed thermocouples and other detectors too. Thus a s a t i s f a c -tory method for the measurement of time constants has been described, and the procedure outlined. 3. The Frequency-Response Curves of a Detector The above method, section (2), for the measurement of time constants conveniently yields curves of r e l a t i v e res-ponse versus frequency. I f any sources of noise and otherrTad-i a t i o n e x i s t , small i n comparison with the si g n a l achieved, then the curves w i l l intersect the response axis at some posi-t i v e value f o r half-widths t equal to zero. This does not a l t e r the time constant when the extraneous radi a t i o n or s i g n a l 48 i s small and steady, also the r e l a t i v e response versus f r e -quency curve may be corrected for t h i s defect, knowing the appropriate time constant. This i s so because the slope of the low t straight l i n e i s known (and equal to and since X i s known and a more accurate determination of a may be made using a shutter between the neon and the detector, and subtracting such a signal from a at low frequencies giv-ing a 1 . Thus, with these curves, the responsivity to noise r a t i o CR may be converted to i t s zero frequency value ^RQ, since the neon output i n watts i n the sensitive region of microns of the detector i s not presumed to change with i t s mod-ulat i o n frequency, and the noise of the c e l l s i s constant over a l l chopping frequencies due to the narrow band width of the amplifier. 4. The Measurement of Spectral Response of a Detector. The detector i s placed at the focus of the model 12C Perkin Elmer monochromator ( I I I , (6) ), and i t s output, which i s from a high gain 900 cycles per second tuned a m p l i f i e r , i s displayed on a Brown recording potentiometer. The source of radiation i s a 1400° K. 900 cycles per second chopped globar source. The wavedrive i s set for a certai n speed, the Brown recorder i s attached, and a spectral curve for each detector 49 i s obtained, f o r any previously chosen s l i t width. The same procedure, using the same monochromator settings of s l i t width, wave drive speed, and a Perkin Elmer thermocouple and i t s associated d.c. amplifier ( I I I , (6) ) i s repeated. The graphs are marked at convenient wave drive numbers, which may be converted to wavelengths from a rocksalt c a l i b r a t i o n curve of wavelength versus wave drive setting obtained f or the rocksalt prism used i n the monochromator. The procedure then i s to take the r a t i o s of the detec-tor and thermocouple curves at many points (corresponding to many wavelengths), and to draw a graph of r e l a t i v e response of detector to that of the thermocouple, plotted against wave-length i n microns; taking the point at long wavelengths at which t h i s r e l a t i v e response has f a l l e n to ha l f of i t s maximum value as the cut-off point. Such a curve may then be replaced by one having uniform response, equal to maximum response for wavelengths up to the cut-off wavelength, at which the detector wavelength may be conisdered to f a l l abruptly to zero. The assumption has been made that the Perkin Elmer thermocouple i s a perfect black body ra d i a t i o n detector. That t h i s i s so for long wavelengths of the order of 4 microns and higher i s known, but for lesser wavelengths corrections may be necessary. Therefore the procedure followed i s not altogether s a t i s f a c t o r y . However, large errors are not foreseen i n t h i s method, and i t may be considered as being within the l i m i t s of 50 other experimental errors, sueh as the measurement of sensi-t i v e areas and also of time constants. 5. Measurement of the Neon Response The procedure followed here was to put the neon and a photomultiplier tube of known short time constant inside a l i g h t - t i g h t enclosure (to minimise photomultiplier noise). The neon was covered by a brass disc containing a fine pin-hole (to prevent flooding of the photomultiplier tube) and was connected to the multivibrator output. I t was placed at a variable distance from the photocathode of the photomultiplier, and the photomultiplier output was connected to the input of the preamplifier. The preamplifier output was then put on the Y 2 plates of the oscilloscope, the other output of the multivibrator output was connected to the Y^ plates of the o s c i l -loscope, as before, the only difference from figure (12) being that the photoconductive c e l l was replaced by the photomulti-p l i e r tube. The results obtained were, that upon varying the photomultiplier tube to neon tube distance to give a large enough output s i g n a l on the oscilloscope to be seen e a s i l y , i t was found when the two oscilloscope traces were matched i n amplitude at the lowest frequencies, they remained so matched to the highest frequency, and the Y 2 (neon tube) trace was seen to remain square to the very highest frequency. 5 1 These results c l e a r l y indicate the s u i t a b i l i t y of the neon tube used. They do not indicate what might be the sit u a t i o n at higher frequencies, since a multivibrator going to much higher frequencies (with 120 v o l t s output) than the one used here was not ava i l a b l e . 6. Measurement of Signal versus Area of V i r t u a l Source (Intensity of Illumination versus Signal) The disc with the variable aperture, used with the black body, and labelled C In figure (2), was used here i n various p o s i t i o n s , and the re s u l t i n g signals f o r various detectors were measured. For each detector, a plot of area of source versus output from a certain detector was made f o r many detectors. These plots were o r i g i n a l l y parabolic i n shape, the signal f a l l i n g o f f rapidly with large source areas. The black body was consequently reassembled to give a true v i r t u a l source, even when the aperture diameter was 8 m i l l i -metres, for the c e l l sizes i n question (see the requirement i n chapter I I I , section (1) f o r v i r t u a l sources). The results showed a straight l i n e graph (figure (in.) ) for a l l c e l l s tested and for v i r t u a l sources of up to 8 millimeters i n diam-eter. The conclusions to be drawn from t h i s , neglecting the p o s s i b i l i t y of pure coincidence, are the following:-1. The black body system i s o p t i c a l l y balanced for v i r -t u a l sources of up to 8 millimeters i n diameter, which covers 52 the standard setting of 3 millimeters diameter, a l l at 20 cm* 2 . The detectors give a signal proportional to incident watts; i . e . v o l t s per watt r a t i o i s independent of power incident on the detector 3 . The radiation i s black body, since according to Lam-bert ts law a black body i s equally bright i n a l l directions ( i . e . f o r a l l sizes of v i r t u a l source), as was found to be the case here. 7. The Measurement of the Sensitive Area and of the Elec-t r i c a l Resistance-This has already been discussed above at the begin-ning of t h i s chapter. The sensitive area i s defined as the average length of the two outside electrodes times t h e i r aver-age separation, expressed i n millimeters squared. Since the sensitive layers of most.of the c e l l s used are f l a t t h i s i s the sensitive area. For other d e f i n i t i o n s of area, where the sensitive area i s not f l a t , other prescriptions must be given for the d e f i n i t i o n of t h i s quantity ( 3 ) . The area i s assumed independent of the temperature of the c e l l . The e l e c t r i c a l resistance i s measured at the temper-ature of the c e l l coolant, for coolants such as dry ice or l i q u i d oxygen and also at room temperature. With some detec-t o r s , i t i s found that on cooling, the s t a t i c temperature equilibrium i s reached only a f t e r several seconds or even 53 several minutes, and not immediately. This has been taken into consideration both i n the measurement of the resistance, and i n the measurement of the signal to noise r a t i o . Both the resistance and the area have possible errors as great as 10 per cent, the area because of the vague d e f i n i t i o n of the electrode boundaries, the resistance because of the d i f f i c u l t y of accurate measurement of high resistances, as with an ordinary ohmmeter. Chapter V THE RESULTS Nine photoconductive lead sulphide c e l l s were the main items under study. Four of these were from the Admir-a l t y Research Laboratory (A.R.L.), numbers 7 3 , 1 1 9 , 1 2 3 and 1 3 1 . Five were B r i t i s h Thomson-Houston Company (B.T.H.) c e l l s . The chemically deposited one which i s not i n vacuo but i s open to the atmosphere i s label l e d "chemical"; the other four are i n vacuo and may be cooled; these are numbered 2 9 2 , 293> 3 6 7 and 3 9 5 . The A.R.L. c e l l s cannot be cooled, although they are evacuated. The measurement of the time constants as described i n Chapter IV, section ( 2 ) , was carried out and yielded the results shown i n Table I. TABLE I Time Constants of Various Lead Sulphide C e l l s at Three Temperatures ( i n microseconds) C e l l C e l l No. ( 3 0 0 ° K) No. ( 3 0 0 ° K) ( 2 0 0 ° K) ( 9 0 ° K) 73 1 6 5 2 9 2 93 1 0 0 0 1 0 5 0 1 1 9 1 3 5 2 9 3 79 2 9 2 1 7 5 0 1 2 3 1 5 1 3 6 7 72 7 7 5 980 1 3 1 8 2 3 9 5 1 2 5 1 8 0 0 1 8 0 0 Ch. 79 — — 55 A t y p i c a l plot f o r evaluating X i s shown (for c e l l 131) i n figure (14). Most of the measurements, when repeated, showed very s i m i l a r r e s u l t s ; time was allowed f or cooled c e l l s to reach a temperature equilibrium. In chapter IV, section (3)> mention was made of graphs which showed posi t i v e response when extrapolated to zero hal f width ( i . e . to i n f i n i t e frequency). I t has already been pointed out that t h i s w i l l not a l t e r the value of T?. In cases where such a s i t u a t i o n existed, i t was found on subsequent measurement that normal curves were obtained y i e l d i n g the same order of value of time constant. In his second paper, Clark Jones (13) points out that where the response-frequency curve corresponds to the existence of a single time constant, the following r e l a t i o n between f r e -quency and responsivity to noise r a t i o w i l l hold, namely ( 3 D Assuming that the value of the noise power per unit band width i s constant with the frequency f, t h i s r e l a t i o n w i l l hold f o r the response plotted against frequency. This proposition was checked for several detectors by replacing f i n ( 3 D by l/2h, where h i s the halfwidth as i n figure (14). In a l l cases only a very small error was found. This i s a good i n d i c a t i o n that the detectors studied may be characterised by a single time con-stant. 56 A very i n t e r e s t i n g measurement was made of the time constant of a lead selenide c e l l produced here. This was found to have a time constant of 225 microseconds, and showed the v e r s a t i l i t y of the time constants apparatus. The response-frequency curves as mentioned i n chap-ter IV, section (3) are obtained from those used to measure X by replacing h the half-width by l / 2 f (see figure (14)J. The factor (1 + ( 2-ftf-c) 2)^ was investigated, being close to unity for some c e l l s with short time constants, and as high as 10.25 for others. The values obtained are shown i n Table I I . TABLE I I Frequency Correction Factor for Various Lead Sulphide C e l l s at Three Temperatures C e l l ^ C e l l ^ ^ ' J No. (300° K) No. (300° K) (200° K) (90 K) 73 1 .367 292 1.130 5.736 6.024 119 1.257 293 1.095 1.930 9.940 123 1.314 367 1.080 4.492 ' 5.619 131 1.102 395 1.224 10 .25 10 .25 Ch. 1 .095 — The spectral response curves, obtained using the Perkin-Elmer thermocouple as a standard, and described i n chapter IV, section (4), yielded curves such as the ones ob-tained for c e l l 293 (figure (13) ) . The four admiralty c e l l s gave curves indentieal i n 57 shape, with a strong peak at approximately 2 . 5 microns. The cut-off (taken at half the maximum) varied from 2.8 to 2 .95 - 5 microns; the absolute (10" ) cut-off wavelength varied from 3.1 to 3.4 microns. The B.T.H. evacuated c e l l s have a rather d i f f e r e n t c h a r a c t e r i s t i c shape of spectral response curve. In chapter I , reference was made to the fact that d i f f e r e n t methods of preparation yielded d i f f e r e n t spectral curves. Whereas the admiralty c e l l s had a strong maximum at 2 .5 microns, the B.T.H. c e l l s and the chemical button c e l l , a l l of which are prepared chemically, have two strong peaks; one i s at 2.15 microns and the other at from 1.2 to 1.5 microns. I t i s noted that decreasing the temperature of the layer increases the cut-off f o r the B.T.H. c e l l s , as shown i n figure ( 1 3 ) . This effect i s not very great, however. Purely as a matter of i n t e r e s t , two A.R.L. lead t e l -l u r i d e c e l l s were also studied. Changing t h e i r temperature from 200° K down to 90° K extended the cut-off i n one case from 4.65 to 5.4-5 microns. The other c e l l gave apparently negative r e s u l t s . The peak of the good c e l l shifted from 3 . 8 to 4.6 microns. The i n e f f e c t i v e c e l l had a very large (100$) absorp-t i o n at 3 microns, and i t may have been receiving stray radia-t i o n i n one case. These results are quoted as a matter of interest only. Using the 900 cycles per second amplifier (chapter I I I , section (3) ), a series of measurements was performed on a l l 58 the c e l l s , p l o t t i n g the v a r i a t i o n of the responsivity to noise r a t i o R (f) as a function of the c e l l current. R(f) was found to be very constant with the c e l l current, which was measured by means of a very accurate microammeter. The signal was always found to be l i n e a r with the c e l l current; the noise was also often l i n e a r , explaining the constancy of R ( f ) . However, i n some cases the noise was parabolic, causing the value of R(f) to be f l a t only i n the middle range of c e l l currents. A f a i r l y wide range of c e l l currents may therefore be used. Typical values are from 20 to 100 microamps. Reproducibility of s i g n a l to noise r a t i o s was found to be good, being affected by the cell-to-source distance, and by the centering of the c e l l layer about the o p t i c a l axis of the black body system. Care must be taken to avoid heating the shutter, as t h i s increases the noise considerably. Q, the power incident upon the c e l l , i s obtained from equation ( 17) . The value so obtained i s 17.4 microwatts/ cm . This value must be halved to give an r.m.s. value for square wave modulation of the power. Another correction must be applied for the spectral response curve of each detector. The cut-off i s taken at half the maximum, and the response i s assumed to be unity up to t h i s wavelength. The t o t a l percent-age of Q/A which corresponds to the cut-off wavelength i s then calculated. A 500° K black body curve has i t s peak at 5 .8 microns. The radia t i o n up to t h i s value corresponds to 25$ of Q/A. Cut-offs encountered are of the order of 3 microns 59 corresponding to approximately 1% of Q/A. These corrections are applied i n Table V as shown. Q i s also shown. The s i g -nal voltage divided by the corrected Q i s then shown and gives the estimated value of the responsivity i n volts/watt (S), values ranging from 200 to 30,000 volts/watt being encountered. S Q i s obtained by using the correction factor shown i n equation ( 3 D . The noise equivalent power P m i s obtained by d i v i d i n g the noise voltage by SQ. To get the noise equivalent power per unit bandwidth, t h i s value must be divided by AJA^- where = 44 cycles/second, and i s the bandwidth of the amplifier used. Table I I I shows that c e l l s 293 and 367 have a value of t h i s quantity equal to 1.69-and 1-75 ( x l O - 1 ^ watt) respectively, a value close to the t h e o r e t i c a l l i m i t for such c e l l s (4 , 5 ) . TABLE I I I Noise Equivalent Power per Unit Band Width as a Function of the C e l l Temperature (watt x l O - ^ ) C e l l No. ( 3 0 0 ° K ) (200° K ) (909 K) 292 446 10.8 18.3 293 573 45.5 1.69 367 844 11.4 1.75 * 395 1270 52.6 22.8 6 0 The optimum wavelengths ( 5 ) for these B.T.H. c e l l s o occur when the c e l l s are at 90 K. with the exception of c e l l 2 9 2 , where t h i s occurs at 2 0 0 ° K. . I t i s suggested that the A.R.L. c e l l s would have better c h a r a c t e r i s t i c s and properties, i f they were b u i l t l i k e the B.T.H. c e l l s , which provide for cooling. Table IV shows the evaluated Factors of Merit. Clark Jones ( 6 ) proposes a value of for type I detectors, (where the numerical factor depends on the temperature as shown) and proposes ( 6 ) for type I I detectors; no correction i s made to equation ( 6 ) for the layer temperature. Equation ( 6 ) may also be written - ^ I O J l ( k V " P « . t \ ( 6 a ) as i n chapter I I , section ( 1 ) . A derivation i s given by Clark Jones ( 1 3 ) . There Is a difference between these two - 2 expressions of a factor 1 0 , as seen i n Table IV. Since the low frequency cut-off of the detectors has not been consid-ered, t h i s might be thought to be the cause. However, the 61 percentage of the black body radia t i o n below 1 micron i s only 0.0001$ of the whole. The difference between th i s value and 1% (corresponding to the long wavelength cut-off at 2 .9 mic-rons) i s n e g l i g i b l e compared to 1%. The proposed reason i s as follows. Clark Jones (13) prescribes adjusting the frequency response curve of the ampli-f i e r so that the noise power per unit band width i s constant at a l l frequencies, whereas i n t h i s research t h i s has not been done (chapter I I , section (1) ). From t h i s equalised ampli-f i e r , a frequency response curve for the detector i s to be drawn from which the time constant i s to be determined. The noise equivalent power for the detector i s to be determined with the amplifier now governed by a high frequency RC cut-off which i s added, where RC i s equal to the time con-stant . Since t h i s has not been done, a constant factor of 2 approximately 10 has been neglected throughout, and equations (6) and (6a) d i f f e r by t h i s amount. The values of t and P m as predicted by Clark Jones (13) w i l l also have t h e i r product d i f f e r i n g from the product obtained by t h i s factor. Equation (7)» assuming that the only noise i s Johnson noise, gives a Factor of Merit 62 Equation (8) given i n chapter I I , section (1) may e a s i l y be shown to be i d e n t i c a l with equation ( 6 ) . In chapter I I , section (2), Daly and Sutherland's proposed Figure of Merit has been modified by the author to give ^ (12) This may also be shown to be equivalent to equations ( 6 ) and (8). These results are shown i n Table IV. Table V shows the values of Q, P , R etc.. ' in ' 6 3 TABLE IV The Factors of Merit of Lead Sulphide Photoconductive C e l l s 3 0 0 ° K. M 2 M 2 2 M 2 M 2 C e l l ( 6 a ) ( 6 ) ( 8 ) ( 1 2 ) n ( 7 ) ( 4 ) No. 1 0 4 73 2 . 2 6 421 420 7 6 7 8 1 . 0 3 1 1 9 1 . 7 3 3 2 3 3 2 2 5 . 3 5 2 5 0 . 6 5 1 2 3 1 . 6 8 3 1 6 3 1 8 5 . 2 5 5 4 5 0 . 7 0 6 1 3 1 2 . 3 4 3 8 2 3 8 4 6 . 3 8 825 0 . 5 3 3 2 9 2 . 3 4 6 5 9 . 3 . 5 9 . 2 . 9 8 6 83 0 . 0 8 9 5 2 9 3 . 3 2 6 5 2 . 9 5 2 . 6 . 8 7 7 1 2 1 0 . 0 7 1 3 6 7 . 2 3 1 3 6 . 4 3 6 . 4 . 6 0 6 6 7 0.046 3 9 5 . 0 8 4 9 1 5 . 5 1 5 . 4 . 2 5 6 2 5 . 3 0 . 0 2 9 3 Ch. . 2 7 1 4 3 . 6 4 4 . 7 3 3 6 0 . 3 0 . 0 5 9 0 2Q0° K. 2 9 2 1 . 3 3 146 146 2 . 4 3 2 5 7 1 . 3 5 2 9 3 1 . 1 1 1 9 5 1 9 6 3 . 2 6 1 7 0 . 3 2 8 3 6 7 1 . 5 9 1 9 9 1 9 8 3 . 3 2 3 0 1 . 2 6 3 9 5 .141 1 1 . 7 1 1 . 7 . 1 9 5 2 8 . 6 . 2 5 9 9 0 ° K. 2 9 2 . 7 4 7 8 0 . 8 8 0 . 6 1 . 3 4 2 1 2 . 1 0 9 293 7 . 4 6 624 6 2 6 1 0 . 4 2 7 6 1 . 8 3 6 7 8 . 2 9 1 2 9 1 2 15 . 2 5 5 0 1 . 1 1 3 9 5 . 3 2 6 2 6 . 9 2 7 . 1 . 4 5 1 1 2 8 . 0 8 1 5 TABLE V Showing Corrected Values Needed to Calculate M 2 for the lead Sulphide Cell s •c K Conredr ^ Cootrt/c(nn S C00AU0'Comi. 300° K. 73 165 400 24 550 2.9 0.95 8.26 O.87 1.98 480 3.32 2.63 0.396 1.367 119 135 130 24 440 2.95 1.1 9.58 0.5 2.30 220 1.20 4.17 0.629 1.257 123 1 5 1 540 24 3 1 2 2.8 0.75 6.53 1.08 1.57 33 7 2.82 3.82 0.576 1.314 1 3 1 82 560 24 3 3 5 2.86 0.9 7.83 1.37 1.88 458 2.70 5.09 0.767 1.102 292 93 190 22.8 23.8 2.58 0.4 3.48 0.52 0.794 124 0.176 29.6 4.46 1.130 293 79 155 24 17.5 2.55 0.35 3.04 0.77 0.730 1 3 . 5 0.202 38.0 5.73 1.095 3 6 7 72 212 22 1 0 . 1 2.52 0.32 2.78 0.72 0.612 7.3 0.128 56.0 8.44 1.080 395 125 25 20 7.6 2.62 0.45 3.92 0.22 0.784 1.68 0.0261 84.1 12.7 1.224 Ch 200° K. 292 79 380 1000 3 5 0 0 25 22.8 14 202 2.53 2.6 0.33 0.42 2.87 3.65 0.72 2.28 0.717 0.832 10.1 460 0.154 31.8 46.6 O.718 7.02 0.108 1.095 5-736 293 292 3500 24 150 2.6 0.42 3.65 1.13 0.876 170 3.74 3.02 0.455 1.930 367 775 1550 22 198 2.55 0.35 3.04 1.01 0.669 200 13.4 0.755 0.114 4.492 3 9 5 1800 80 20 20.4 2.6 0.42 3.65 0.48 0.730 9.8 1.38 3.49 0.526 10.25 TABLE V continued 9 0 ° K. 2 9 2 1 0 5 0 3 5 0 0 2 2 . 8 293 1 7 5 0 10000 24 3 6 7 9 8 0 5 0 0 0 2 2 3 9 5 1 8 0 0 2 7 0 20 1 2 3 2 . 6 2 0 . 4 5 3 . 9 2 2 1 0 2 . 8 0 . 7 5 6 . 5 3 2 2 0 2 . 8 0 . 7 5 6 . 5 3 5 0 . 3 2 . 6 2 0 . 4 5 3 . 9 2 2.28 0.895 280 18.9 0.65 0 . 1 5 7 1 3 7 86.6 0.65 0.144 143 55.8 1 . 1 5 0.784 58 7 . 6 1 . 2 1 0.183 6.024 0.074-9 O .O I69 9 . 9 4 0 . 1 1 6 0 . 0 1 7 5 5 . 6 1 9 1 . 5 1 0 . 2 2 8 1 0 . 2 5 Chapter VI DISCUSSION Table IV leads to the conclusion that the best detec-tor i s c e l l 367 at 90° K. Other useful detectors are c e l l 293 at 90° K., the A.R.L. c e l l s , and c e l l s 292, 293 and 367 at 200° K.. The chemical c e l l and c e l l 395 (at a l l three temperatures), and the rest of the B.T.H. c e l l s at room temperature show the poorest Factors of Merit. Such conclusions are drawn from a l l columns except those marked (4) and (7)» which do not show the close agreement of the other columns. Both M2 and Mi are shown for purposes of comparison. Column ( 7 ) 5 by i t s disagreement, shows that the l i m i t i n g noise for photoconductive c e l l s i s not Johnson noise. Clark Jones, i n his f i r s t paper (3)> points out that f o r detectors which are cooled by r a d i a t i o n , as these are, the temperature fluctuations would be zero i f there were no fluctuations i n the transfer of heat by the ra d i a t i o n . He concludes that output fluctuations i n t h i s case are due to r a d i a t i o n f l u c t u a t i o n s . He gives as the mean square f l u c t u a t i o n i n power per unit frequency band-width (32) 6 8 For the size of detector used here t h i s gives 7*36 x l O " 1 ^ watt, which i s of the order obtained i n many cases (see Table IV). See also chapter I , where i t was quoted ( 4 , 5 ) that the measured noise approaches the l i m i t imposed by radiation f l u c t u a t i o n s . I t i s proposed that the detectors studied be c l a s s i -f i e d as type I I detectors (13). This i s because g.^  i s n°t independent of T, as for type I detectors. However, a d e f i n i t e statement on c l a s s i f i c a t i o n cannot be made, since k 2 of equation (1) corresponding to M 2 i s found to vary with temperature. I f i t , remained constant with temperature f or the B.T.H. c e l l s , could be plotted againstJC*, a straight l i n e establishing that the type number i s I I . This follows from equation (33) from the second paper by Clark Jones (13) (33) Since k i s not a constant, and i s derived from 2 equation (33)? t h i s equation can give no clue as to the proper value of n. Another reason f o r taking n as 2 i s the good agreement between the f i r s t four columns of Table IV. M]_ i s seen to behave properly, never greatly exceed-ing unity. M 2 on the other hand i s much greater than unity, showing that Havens's l i m i t w i l l have to be revised. I t i s not a fundamental l i m i t , and i s seen to hold for other types of detector (chapter I I , section (1) ). 69 The B.T.H. c e l l s are i d e a l i n t h i s work since they can be used at three d i f f e r e n t temperatures, and since t h e i r areas and other physical properties are unchanged by cooling. For t h i s reason, i t had been hoped a d e f i n i t e statement on type number could have been made. The A.R.L. c e l l s could c e r t a i n l y be much improved i f they could be cooled. This i s indicated because of the improvement cooling makes on the B.T.H. c e l l s (Tables I I I and IV). Photoconductive c e l l s have the great advantage over most temperature detectors that they have a selective spectral response, so that used as detectors i n the one to f i v e micron region, t h e i r ultimate s e n s i t i v i t y i s attainable. In the i n f r a red above f i v e microns, they are no better than thermo-couples or bolometers for the same reason. 70 BIBLIOGRAPHY 1. Simpson, 0 . , and Sutherland, G.B.B.M., Science. 115, 1 (1952) . 2. Sosnowski, L., Starkiewicz, J . , and Simpson, 0 . Nature, 159, 818 (1947). 3 . Jones, R. C., J . Optical Soc. Am., 3 7 , 879 (194-7). 4 . F e l l g e t t , P. B., J . Optical Soc. Am., 3 9 , 970 (194-9). 5. Moss, T. S., J . Optical Soc. Am.. 40, 603 (1950) . 6. Jones, R. C., J . Optical Soc. Am., 3 9 , 344 (1949). 7. Daly, E. F., and Sutherland, G.B.B.M., Proc. Phys. S o c London, A, 6 2 , 205 (1949). 8. Sutherland, G.B.B.M., Blackwell, D. E., and F e l l g e t t , P.B., Nature, 158, 873 (1946). 9 . Daly, E. F., and Sutherland, G.B.B.M. Proc. Phys. Soc.. London, 59, 77 (1946) . 10 . Bullock, B. W., and Silverman, S., J . Optical Soc. Am., 40, 608 (1950). 11. Kuiper, G. P., Rept. Progress Phys.. 13 , 247 ( 1950) . 12. Lee, E., and Parker, R. C, Nature, 158, 518 (1946). 13 . Jones, R. C., J . Optical Soc. Am., 3 9 , 327 (1949). 14. Havens, R. J . , J . Optical Soc. Am., 3 9 , 327 (1949). 15. Hornig, D. F., and O'Keefe, J . , Rev. S c i . Inst., 18, 474, (1947) . 16. Roberts, J . K., Heat and Thermodynamics, London, Blaekie, (1945) . 17 Brown, D.A.H., J . S c i . Inst., 29 , 292 (1952) . 18 Brown, D.A.H., T. R. E. Memo., 330. 19 Elmore, W. G., and Sands, M., El e c t r o n i c s , New York, McGraw H i l l (1949). T H E B L A C K B O D Y H 0 ° o 0 o 0 Q ° r , 0 0 ° r , ° r , o ^ ° ^ ° o 0 o 0 o 0 o 0 Q 0 o 0 Q 0 o 0 o ° Q -D-H F I G U R E I R A D I A T O R A S T E E L C Y L I N D E R B B R A S S D I S C S C A L U N D U M C Y L I N D E R D A S B E S T O S S H E E T I N G E N I CH R O M E H E A T E R F R E S I S T A N C E T H E R M O M E T E R G R O C K W O O L H WOOD C O N T A I N E R J A L U M I N U M K TH ER M O C O U P L E T H E O P T I C A L S Y S T E M O F T H E B L A C K B O D Y R A D I A T O R A A S B E S T O S SHIELD B E T W E E N ALUMINUM P L A T E S B CHOPPER C A P E R T U R E DISC D C H O P P E R M O T O R E B L A C K BODY F SLIDING S H U T T E R G BRASS DISC K S E N S I T I V E L A Y E R O F C E L L H S T E E L C Y L I N D E R S C A L E I INCH E Q U A L S IO C M S -2 0 0 K W W J _ 2 C J20 2 0 _ ] _ £ 4 ( ™ I LQO( O S C I L L O S C O P E T E S T P O I N T ® ^ ZJ200ZIM7IOOW II 1 16AUI 20 I 20 I 20]^ I O K 4 7 K • 4 7 K I W K I O O K > IOOKSS6K< [ 3L' ^ , f .Ol f - T - 5 I N 3 4 -H-N 3 4 7 2 0 K > 5 Q O ^ 1 2 0 0 0 : | 3 ^ . 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L F I G U R E 6 360 V IOOK I O O K IOOK O U T F I G U R E 7 W I D E B A N D P R E A M P L I F I E R 6 A G 5 -FIGURE e F R E Q U E N C Y RE S P O N S E INPUT O F O F W I D E 9 S O mv BAND P R E A M P L I F I E R O U T P U T 2 0 V O L T S • — O IS IO 5 O I O ° 1 0 ' 1 i o 2 1 3 IO 1 4 IO 1 5 IO 1 6 V 1 0 a 1 ^ ' ° F R E Q U E N C Y c / s P b - S C E L L M O U N T I N G F I G U R E 9 T H E M E A S U R E M E N T O F T I M E C O N S T A N T S > MU L T 1V 1 BRA • nji_n_n_r N E O N > P H O T O C O N D U C T I V E W I D E B A N D > T O R C E L L P R E A M P L 1 FIEP D O U B L E B E A M O S C I L L O S C O PE Y . P L A T E S Y- P L A T E S FIGURE 12 R E S P O N S E V E R S U S M O D U L A T I O N F R E Q U E N C Y H A L F W I D T H C E L L 131 F I G U R E 14 R E S P O N S E IN V O L T S I O O 200 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 B O O 

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