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Television picture transmission and optical signal processing Meier, Otto 1968

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TELEVISION PICTURE TRANSMISSION AND OPTICAL SIGNAL PROCESSING by OTTO MEIER D i p l . El.-Ing., Swiss Federal In s t i t u t e of Technology, 1965 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of E l e c t r i c a l Engineering We accept t h i s thesis as conforming to the required s-tandard Research Supervisor Members of Committee , Head of Department Members of the Department of E l e c t r i c a l Engineering THE UNIVERSITY OF BRITISH COLUMBIA JULY, 1968 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of Brit ish Columbia, I agree that the Library shall make it freely available for reference and Study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by hits representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of F,Z*c£ricA^ ^f^e^-^ The University of Brit ish Columbia Vancouver 8, Canada Date ZZ , M*t ABSTRACT O p t i c a l s i g n a l processing i s introduced as a t o o l f o r i n v e s t i g a t i o n s i n the f i e l d of t e l e v i s i o n compression research. An o p t i c a l s i g n a l processing system i s designed, which performs the F o u r i e r transform of a p i c t u r e s i g n a l F[B(x,y)] and i t s r e - co n s t r u c t i o n F ^"{F [B(x,y)]j . Some basic o p t i c a l f i l t e r i n g ex- periments are performed i n the s p a t i a l frequency plane, and the o p t i c a l analogue of the frequency sampling theorem i s demonstrated. The F o u r i e r transforms of t e s t p a t t e r n p i c t u r e s show lar g e gaps which can be used f o r compression. Observation of com- plex spectra of continuous tone p i c t u r e s i s found to be impaired by noise e f f e c t s . A p h y s i o l o g i c a l experiment i s c a r r i e d out, which i n v e s - t i g a t e s the r e l a t i o n s h i p between t o l e r a b l e f l i c k e r frequency and s p a t i a l frequency of a t e l e v i s i o n p i c t u r e . I t i s found that the t o l e r a b l e f l i c k e r r a t e f decreases as the s p a t i a l frequency f ^ i s increased, according to the e m p i r i c a l equation f = f e x p ( - k f x ) . f and k are parameters depending on f a c t o r s l i k e c o n t r a s t r a t i o , kind and s i z e of p i c t u r e , e tc. Compression systems using the above r e s u l t s are found to have a l i m i t of obtainable compression r a t i o of approximately 3 to 1. i i TABLE OF CONTENTS Page 1. INTRODUCTION 1- 2. THEORY OF OPTICAL SIGNAL PROCESSING 4 2.1 Fundamental o p t i c a l systems 4 2.2 O p t i c a l f i l t e r i n g 8 3. DESIGN OF THE OPTICAL SYSTEM... 11 3.1 Basic considerations .. ^ 3.2 C a l c u l a t i o n s 3.3 The l i q u i d c e l l 1 8 3.4 Frequency sampling arrangement '. 19 3.5 D e s c r i p t i o n of the system 20 4. FOURIER TRANSFORMS AND SPATIAL FILTERING . 24 4.1 'Two-dimensional F o u r i e r transforms 24 4.2 One-dimensional F o u r i e r transforms 27 4.3 R e l a t i o n to video s i g n a l 30 4.4 Frequency sampling ^ ; 4.5 Coarse f i l t e r i n g 6̂ 5. SPATIAL FREQUENCY FLICKER EXPERIMENTS 41 5.1 Basic idea 41 5.2 Test arrangement 42 5-3 Results 44 5.4 A t e n t a t i v e law 51 6. CONCLUSIONS AND FUTURE WORK 54 REFERENCES 57 APPENDIX 59 i i i LIST OF ILLUSTRATIONS Figure Page 1 Optical system for two-dimensional m u l t i p l i - cation and integration . 4 2 Optical Fourier transformer 6 3 Multichannel one-dimensional Fourier transformer.. 7 4 Successive Fourier transformers 8 5 Variable scale Fourier transformer 12 6 Basic o p t i c a l system 13 7 D i f f r a c t i o n grating 14 8 Liquid c e l l 19 9 Adjustable sampling grating 20 10 The f i n a l o p t i c a l system 22 11 ROWI test chart 25 12 Two-dimensional Fourier transform of Figure 11.... 25 13 D e t a i l of ROWI test chart 26 14 Two-dimensional Fourier transform of Figure 13-... 26 15 One-dimensional Fourier transform of ROWI test chart ?3 16 Marconi resolution chart No. 1 29 17 One-dimensional Fourier transform of Marconi chart 29 18 One-dimensional Fourier transform of an aperture.. 31 19 Part of the same transform as i n Figure 18, only showing higher s p a t i a l frequencies 31 20 Fourier transform of aperture with empty transparency 32 21 Fourier transform of aperture with empty trans- parency i n l i q u i d c e l l 32 22 String of output pictures after frequency sampling 34 23 Single output picture without sampling 34 iv 24 Central (zero order) output picture after frequency sampling 35 25 Enlarged part of sampled s p a t i a l frequency plane.... 35 26 Output picture displayed on closed c i r c u i t t e l e v i s i o n monitor 37 27 Effect of lowpass f i l t e r 38 28 Effect of highpass f i l t e r 38 29 Mask f i l t e r i n Fourier transform plane of eq. 13.... 38 30 Output from mask f i l t e r i n Figure 29 39 31 Fourier transform of a continuous tone picture .... 40 32 Sine wave response of the human eye 41 33 . F l i c k e r test arrangement 42 34 Optical f l i c k e r frequency as a function of s p a t i a l frequency for judgement "good" 45 35 C r i t i c a l f l i c k e r frequency as a function of s p a t i a l frequency for judgement "acceptable" 46 36 C r i t i c a l f l i c k e r frequency vs. contrast r a t i o 4-6 37 C r i t i c a l f l i c k e r frequency with picture area as parameter 48 38 "Face" 49 39 "Group" • : 49 40 C r i t i c a l f l i c k e r frequency of two half tone pictures 50 41 Bandlimited picture 50 42 & 43 View of test apparatus used for present work 53 A 1. Two-dimensional Fourier transformer 59 A 2 Geometrical relations 61 ACKNOWLEDGEMENT Many persons have helped i n one or the other way during the course of t h i s research p r o j e c t , and rny thanks go to a l l of them. In p a r t i c u l a r I would l i k e to thank .my supe r v i s o r , Dr. M. P. Beddoes, f o r many f r u i t f u l d i s c u s s i o n s and h e l p f u l suggestions, as w e l l as f o r h i s i n v a l u a b l e a s s i s t a n c e i n prepar- i n g the t h e s i s . I would a l s o l i k e to thank Dr. A. D. Moore f o r reading and c o r r e c t i n g the t h e s i s . Further thanks g>* to Mr. P. D. Carman and Mr. J . N. Cairns from NRC Ottawa, who provided the high q u a l i t y lenses needed f o r t h i s p r o j e c t . I am g r a t e f u l to Miss L. R a t c l i f f e and Mr. W. D. Ramsay f o r proofreading, and to Miss A. Hopkins f o r t y p i n g the t h e s i s . F i n a l l y , I. would l i k e to thank the a d m i n i s t r a t i o n of the U n i v e r s i t y of B r i t i s h Columbia f o r my exchange Fellowship, and NRC.for the f i n a n c i a l support of t h i s work. 1 1. INTRODUCTION A considerable amount of work has been done i n the f i e l d of image compression research, starting almost immediately after the invention of t e l e v i s i o n . Numerous systems and techniques have been proposed to reduce the bandwidth required for the trans- mission of t e l e v i s i o n signals, as becomes clear from Pratt's bib- l i o g r a p h y ^ ^ . But, as Schreiber put i t i n a recent a r t i c l e : "The (2) results are meager, indeed". . The work continues, because the need for a more e f f i c i e n t transmission system s t i l l e x i s t s . And, even though the p r a c t i c a l results.have been l i t t l e , we at least begin to understand the problem. Most of the present day work to reduce redundancy i n t e l - evision picture transmission i s done on the basis of some d i g i t a l techniques, investigating e f f i c i e n t coding and quantizing methods. Wide use of computer simulation i s made to " r e a l i z e " the coding methods, and only a very small part of the proposed systems have actually been b u i l t ^ " ^ . In the l a s t few years a new method of analysing and pro- cessing signals of various kinds has been developed, which makes use of coherent l i g h t , easily available today from lasers: Op- t i c a l signal processing systems find increasing application i n numerous f i e l d s of research and p r a c t i c a l use. Optical systems possess two degrees of freedom, i . e . , two independent variables, as opposed to electronic systems with only one independent variable, time. In addition, o p t i c a l systems show the property that a Fourier transform r e l a t i o n exists between the l i g h t amplitude d i s t r i b u t i o n at the front- and back-focal planes of a lens used i n the system. The o p t i c a l system i s capable of 2 performing F o u r i e r transforms or r e l a t e d mathematical operations instaneously i n two dimensions; or, by use of as t i g m a t i c lenses, i n one dimension with a number of independent channels. This makes i t s uperior to an e l e c t r o n i c system, which would have to use scan- ning or time sharing procedures to achieve the same r e s u l t s . The very l a r g e number of points which can e a s i l y be pro- cessed i n p a r a l l e l f a s h i o n i s another f a c t o r i n favour of the op- t i c a l method. A point against i t i s the noise, generated by the f i l m m a t e r i a l which c a r r i e s the o p t i c a l s i g n a l . With o p t i c a l methods, s p a t i a l frequency f i l t e r i n g i s a simple operation i n p r i n c i p l e , • and the research reported here uses- such f i l t e r i n g as a t o o l to i n v e s t i g a t e some p o s s i b i l i t i e s of bandwidth re d u c t i o n f o r a p i c t u r e s i g n a l . There may be l a r g e gaps i n the spectrum of a p i c t u r e , which could be used f o r compression purposes, as suggested by vocoder methods'in speech compression. An attempt was made to check on t h i s point i n Chapter 4 . Mertz and Gray f i r s t showed that the t e l e v i s i o n spec- trum i s comb-like i n s t r u c t u r e , with empty spaces i n between ("3) each clump of energy. (This f a c t i s made use of i n c a r r i e r i n t e r l a c e d c o l o r t e l e v i s i o n ) . Thus, we expect to be able to red- uce bandwidth merely by c l o s i n g up the spaces. In f a c t , the frequency v e r s i o n of the sampling theorerr/^ suggests s i m i l a r meth- ods; a basic experiment described i n t h i s t h e s i s shows that the s p a t i a l frequency spectrum of a s t i l l p i c t u r e can be made i n f i n - i t e s i m a l i n t o t a l , without a f f e c t i n g appreciably the p i c t u r e qual- i t y . For an a c t i v e l i n e of a normal t e l e v i s i o n d i s p l a y , 300 3 spectral spikes have to be used i n a frequency sampled signal, as w i l l be shown i n chapter 3.2. In p r i n c i p l e , each l i n e may be en t i r e l y uncorrelated, i n which case the bandwidth, needed for each spectral spike i s roughly the number of picture l i n e s times the picture r e p e t i t i o n frequency: 525x30 = 15,750 Hz, assuming single sideband modulation. Thus, although one single l i n e of a s t i l l picture needs zero bandwidth, (in the l i m i t ) , the t e l e - v i s i o n case-needs 300x15,750 Hz = 4-725 MHz; t h i s happens to be the normal actual bandwidth. Limitations i n the -perception of the human eye may be exploited to reduce television' bandwidth. One such l i m i t a t i o n i s examined i n t h i s thesis. I t i s concerned with the question: What i s the minimum rate at which the s p a t i a l frequencies must be pres- ented on a TV-screen, for f l i c k e r to be just not apparent? I t i s shown that the minimum rate, or tolerable f l i c k e r frequency, decreases as the s p a t i a l frequency i s increased. Thus, a band reduced system could be designed, using different transmission rates for low and high frequency compon- ents of a t e l e v i s i o n signal. The present thesis deals with three problems: (a) The design of o p t i c a l signal processing equipment, which can be used as a to o l to investigate t e l e v i s i o n compression prob- lems (chapter 3 ) ; (b) The performance and results of some exploratory f i l t e r i n g experiments. These are not complete, but intended as a.guide to further work (chapter 4-) ; (c) The results of f l i c k e r experiments, which investigate the temporal response of-the human eye to s p a t i a l frequencies (chapter 5)• 4 2. THEORY OP OPTICAL SIGNAL PROCESSING 2.1 Fundamental o p t i c a l systems An e x c e l l e n t d i s c u s s i o n of the theory of o p t i c a l data (5 ) processing i s given by Cutrona et a l . . For the purpose of t h i s t h e s i s a b r i e f d e s c r i p t i o n of the basic components and r e l - a t i o n s of an o p t i c a l system i s given here, d i s c u s s i n g mainly the theory as i t a p p l i e s to i n v e s t i g a t i o n s of the frequency domain. Let us f i r s t consider an example of a non coherent l i g h t system, as i t i s shown i n F i g . 1: y y F i g . 1 O p t i c a l system f o r two dimensional m u l t i p l i - c a t i o n and i n t e g r a t i o n A given s i g n a l of two v a r i a b l e s may be represented by a s p a t i a l l y v a r y i n g transparency, such as a photographic f i l m , whose transmittance i s t 1 ( x , y ) , with O-t.^-1. Light of uniform i n t e n - s i t y I passes through t h i s transparency and i s s p a t i a l l y modul- ated to give the output i n t e n s i t y I t ^ ( x , y ) . I f we now l e t t h i s l i g h t pass through a second transparency of transmission t 2(x-X,y) f o r example, where X i s a displacement of the transparency o f f the axis of the l i g h t path, then the transmitted l i g h t w i l l be of the inte n s i t y I t^(x,y)t^(x-X,y). Thus a two dimensional multiplica- t i o n i s performed. Let a second lens Lg focus the l i g h t to a point, summing up a l l i n t e n s i t i e s to a t o t a l i n t e n s i t y I : I p = Jj I Q t 1(x,y) t 2(x-X,y) dx dy 2.1 A A i s the t o t a l aperture area i n plane P.̂ , and attenuation and ef- fects of f i n i t e lens size have been ignored. This i n t e g r a l has the form of a two dimensional convol- ution or cross-correlation. We defined the transmission function to be positive only. If we desire to represent a negative going sign a l , we must write i t on a dc-bias, represented by a constant c i n the transmission function. We may also have to introduce a scaling factor a for the o r i g i n a l signal function. ^ + â ĵ  ^ ( x j ) 2.2 Evaluating an i n t e g r a l of the form of equation 2.1 w i l l then pro- duce undesired cross terms. In many applications i t i s possible to remove the dc- bias by using a "coherent" o p t i c a l system. Such a system requires the use of p a r a l l e l , s p a t i a l l y ' coherent and monochromatic l i g h t . A Fourier transform of the transparency i s obtained o p t i c a l l y i n t h is system, where the dc part of the signal i s concentrated at one s p e c i f i c location. It may then be removed by a simple stop, and a second Fourier transform reconstructs the o r i g i n a l signal without the dc b i a s . Pigure 2 shows the necessary o p t i c a l arrangement. Plane P P i g . 2 O p t i c a l F o u r i e r transformer L i g h t of the complex amplitude d i s t r i b u t i o n U^(x^,y-^) emerges from plane P^. We can w r i t e U-]_(x1,y1) = U 1 ( x 1 > y 1 ) . 3 x p T j a ( x 1 , y 1 ) 2.3 U-^(x-py^) i s the amplitude of the wave f r o n t and a(x^,y^) i s the phase d i s t r i b u t i o n . The amplitude may be regarded as represented by the photographic density of a transparency i n plane P^, the phase by v a r i a t i o n s i n transparency t h i c k n e s s . The complex amplitude d i s t r i b u t i o n ^2^x2'^2^ a"t plane P^ i s given by +C+D _ U n ( x n , y n ) e x p ( - j w x x 1 ) e x p ( - j w y1)dx1dy1 2.4 U 2 ( x 2 , y 2 ) = -C-D For a proof of equation 2.4 see appendix. The s p a t i a l frequencies wx and to are defined by r e l a - t i o n 2.5: to -2jtx, to -2%yr 2.5 where \ i s the wavelength of the l i g h t used. We see that i - s 'the Fourier transform of U , l y i n g within the l i m i t s -C, -D. Plane P^ i s the s p a t i a l frequency plane, The usefulness of a system according to Figure 2 can be seen im- mediately: Besides being a to o l for spectrum analysis, f i l t e r i n g i s e a s i l y accomplished by placing appropriate stops i n the f r e - quency plane to block any part of the spectrum. To simulate and process the equivalent of a scanned s i g - nal, we need only a one -dimensional system. The second dimension can then be used.to accommodate a large number of independent channels for one dimensional signals, thus not wasting the capac- i t y of the system. 2̂ Fig. 3 Multichannel one-dimensional Fourier transformer 8 The lens system of Figure 3 focuses only i n one dim- ension, performing an imaging i n the other dimension, such that y 2 i s an inverted image of y^. The Fourier transform obtained with t h i s system therefore becomes +r - U 2(x 2,y 2) = J U 1(x 1,y 1)exp(-j(o xx 1) dx 1 -C 2.6 Two or more Fourier transforming systems may be cas- caded to perform successive transforms. The conventional Fourier transform theory requires the kernel function exp(-jwt) for the transform from time to frequency domain, and the function exp (j cot) for the inverse transform from frequency to time. An opti c a l sys- tem ( i . e . , a lens) always introduces the kernel function exp 0 x 1 y 1 We can obtain the right sign for the ker- nel function of the inverse transform by merely l a b e l l i n g the co-ordinates appropriately, as shown i n Figure 4 . 1 Fig. Successive Fourier transformers 2.2 Optical f i l t e r i n g It i s possible to introduce f i l t e r i n g action on a signal 9 i n the frequency plane of an o p t i c a l system (plane T^, Figure 4). The r e s u l t i n g e f f e c t can be observed immediately i n the plane of the r e c o n s t r u c t i o n (P^, Figure 4). B a s i c a l l y there are two kinds of f i l t e r s that may be introduced i n the frequency plane: ampli- tude f i l t e r s and phase f i l t e r s . Together they can e f f e c t a com- plex f i l t e r f u n c t i o n . An amplitude f i l t e r i s obtained by v a r y i n g the o p t i c a l d e n s i t y of a transparency. A phase f i l t e r i s r e a l i z e d by v a r y i n g the th i c k n e s s , which i n t u r n v a r i e s the phase r e t a r d - a t i o n . A simple form of an amplitude f i l t e r might be a s l i t , whic corresponds to a s p a t i a l bandpass f i l t e r ; a stop represents a r e j - e c t i o n f i l t e r . Complex f i l t e r f u n c t i o n s appear to be p o s s i b l e , although more d i f f i c u l t to r e a l i z e p r a c t i c a l l y . A hologram, c o n t a i n i n g amplitude and phase information of a p i c t u r e , can be used as a complex f i l t e r . Examples f o r t h i s technique are to be found main- (6) l y i n the f i e l d of pattern r e c o g n i t i o n . . The one-dimensional F o u r i e r transform plane may be sampled by narrow s l i t s ( i n f i n i t e l y narrow i n the l i m i t ) , spaced at reg- u l a r i n t e r v a l s , to produce a perfect r e c o n s t r u c t i o n . This i s the • o p t i c a l analog of the frequency sampling theorem, which states tha a time l i m i t e d f u n c t i o n can be represented by i t s uniform samples i n the frequency domain.^ ̂ For each point i n a l i n e of a scanned p i c t u r e , time has a d i s t i n c t correspondence with each point i n the x - d i r e c t i o n i n plane P-̂  of the o p t i c a l system (Figure 3)- The input s i g n a l w i l l be a p i c t u r e of f i n i t e s i z e , placed i n t o t h i s plane, thus f u l f i l - l i n g the c o n d i t i o n of a time l i m i t e d s i g n a l . Now we can proceed to introduce some kind of a comb f i l t e r i n the F o u r i e r transform or s p a t i a l frequency plane P 2. The e f f e c t , observed at 10 the output plane (see Pigure 4 ) , w i l l be a d i f f r a c t i o n due to the grating-like action of the comb f i l t e r , producing a string of diffra c t e d output pictures. A coarse f i l t e r produces overlapping output images; the spacing of the grating l i n e s has to be made fine enough (according to d i f f r a c t i o n theory) i n order to get the f i r s t maximum of the d i f f r a c t i o n pattern at least one picture width off the op t i c a l axis (see chapter 3 ) - 11 3. DESIGN OP THE OPTICAL SYSTEM 3•1 Basic considerations In the op t i c a l system described here Ronchi rulings were used as a comb f i l t e r to v e r i f y the frequency sampling theorem. These rulings are o p t i c a l l y f l a t glass pieces with engraved,, met- a l - f i l l e d l i n e s of high precision, giving a 50/50 opaque/transpar- ent grating. They are readily available only with 500 l i n e s per inch, which imposes some l i m i t s on . the physical size of the whole system, because of the quite large d i f f r a c t i o n length needed to get the di f f r a c t e d output pictures separated i n a_ one to one imaging system (see chapter 3-2.). One to one imaging was found to be desirable i n order to allow easy observation of the output. A system using long focal length lenses i s also better with res- pect to lens aberrations, because the "thin lens" concept i s more closely r e a l i z e d . Further l i m i t a t i o n s of the physical dimensions are given by the width of the laser beam available, which provides the <-.o- herent l i g h t . Here a commercially available beam expander was used, giving a beam of 50 millimeters diameter, with gaussian phase d i s t r i b u t i o n over the aperture. Standard 35 millimeter s l i d e s , which could be illuminated quite uniformly with the expanded beam, were used i n the input plane. The laser beam1can be made p a r a l l e l or converging by ad- justing the expander telescope. This feature was used to get the f i r s t two dimensional Fourier transform of the input transparency, by focusing down the beam with the telescope, according to Figure 5. 12 Such a.n arrangement i s described by Vander Lugt as the "variable scale" Fourier transform system. The input plane P-̂ may be moved a x i a l l y without disturbing the exact Fourier trans- form r e l a t i o n between plane P-̂  and P 2; only the scale of the transform i s varied. This system has also the advantage of being space invariant i n the sense that a l l the l i g h t emerging from lens L, f a l l s on the input plane. Fig. 5 Variable scale Fourier transformer A spherical lens, placed right behind the Fourier trans- form plane, can be used to perform a second transform, giving an approximate one to one imaging onto the output plane. Two c y l i n - d r i c a l lenses, inserted at the appropriate places make the sys- tem one-dimensional. The basic setup i s shown i n Figure 6. 13 p. Pig. 6 Basic o p t i c a l system 3.2 Calculations The computations of the physical dimensions of the sys- tem according to Figure 6 w i l l be based on the few desirable prop- erties and given dimensions discussed above, such as size of i n - put picture, beam width, imaging conditions, size of .Ronchi r u l - ings . Let us f i r s t determine the d i f f r a c t i o n length needed to get the output pictures well separated. The 500 l i n e s per inch Ronchi rulings w i l l be used to perform the s p a t i a l frequency sam- pli n g , and 1:1 imaging i s assumed. This dimension w i l l give us an idea of the t o t a l length, of the f i n a l system. The general equation for the in t e n s i t y d i s t r i b u t i o n at a point behind a grat- (8) ing according to Figure 7 i s given by equation 3-1 • K P ) = sin-kNdp 2 X . kdp 3-1 where sinG - sin9 o 3-2 14 N s l i t s d Fig. 7 D i f f r a c t i o n grating L i s the length of a s l i t , k = 0, 1, 2 . . . The inte n s i t y d i s t r i b u t i o n I(p-) w i l l have maxima due to the period d of the grating, represented by the f i r s t bracket i n equation 3.1. These maxima w i l l occur at P m \ d (m = 0,-1,-2 ) 3-3 m i s the order of interference, i t represents the path length difference i n wavelengths i n the dire c t i o n of the maximum, from corresponding points i n neighbouring s l i t s . The f i r s t order ma.x- , X lmum occurs at p = ^ . In our case we have 9 =0, which means that the l i g h t o to i s normally incident on the grating. p l - s i n e i = d 3.4 ©]_ j s the angle of the f i r s t order d i f f r a c t e d picture with respect to the zero order picture on the opti c a l axis. We may replace sin9^ by the l a t e r a l separation b of the f i r s t order picture, divided by the d i f f r a c t i o n length 1 of the system. 15 s i n G i = i = a 3 ' 5 We are now able to determine the d i f f r a c t i o n length 1 from the given dimensions b, d, and X. b = 35 mm d = 25.4 500" m m X = 632.8 10~ 6 mm 1 = 2.8 m If we want to accommodate the whole p a r a l l e l beam of 50 mm d i a - meter, 1 comes out to be 4 meters. This value was used i n the actual system. The 35 mm picture i n input and output plane corresponds to a t e l e v i s i o n picture scanned by an electron beam, to give an electronic signal of a certain bandwidth. The standard t e l e v i s - ion system used here has 525 l i n e s , of which 21 are used for f i e l d blanking; t h i s leaves 504 active l i n e s . The time for one l i n e scan i s 63-5 us, of which 10.8 us are l i n e blanking time, leaving 52.7 us for one active l i n e . . Introducing a Kell. factor of 0.73, the v e r t i c a l resolution of the system i s 368 l i n e s per screen height. A 4 to 3 aspect r a t i o results i n 490 l i n e s horizontal resolution. These 490 l i n e s are t e l e v i s i o n l i n e s , corresponding to 245 complete cycles black - white, which i s the standard used to define resolution of f i l m , and also the s p a t i a l frequency. 245 f u l l cycles ( i n the worst case) are scanned by the t e l e v i s i o n system i n 52.7 us. This leads to a highest necessary bandwidth of the t e l e v i s i o n channel: 16 f 245 m a x 52.7x10' = 4.65 M H z 3-7 To summarize, 245 l i n e s (black - white cycles) across a t e l e v i s i o n picture correspond to a frequency of 4.65 MHz of the video s i g - nal. In the opt i c a l system described here, t h i s i s equivalent to a s p a t i a l frequency of 245 l i n e s per 35 mm, according to the chos- en picture size. We r e c a l l equation 2.4, which relates the scale of the sp a t i a l frequency plane with the physical dimensions of the o p t i - c a l processing system. 2TCX * OJ i n radians per / 0 A\ wx = ~W unit length To convert into the s p a t i a l frequency f , we divide by 2it. The highest s p a t i a l frequency i n our o p t i c a l system should f a l l inside an area i n the Fourier transform plane given by the size of the Ronchi rulings. 500 l i n e rulings are made i n a size of one by two inches, with the l i n e s p a r a l l e l to the short side. Therefore, for the l a t e r a l displacement of the of the highest s p a t i a l f r e - quency component from the dc centre l i n e somewhat less than one inch can be allowed. From Figure 6 and the 1 to 1 imaging condi- tion we find that the d i f f r a c t i o n length of the output section i s also the focal length of the f i r s t Fourier transforming lens . V/e now can determine the point i n the s p a t i a l frequency plane, which corresponds to the upper l i m i t of 4.65 MHz actual bandwidth of a video signal, or 245 l i n e s per 35mm s p a t i a l frequency, i . e . , 7 l i n e s per millimeter. 17 1 2rc\f x, =. = — = 17.5 mm 3-8 1 2it x-̂  i s therefore well within the l i m i t of one inch or 25.4 mm given by the size of the Ronchi r u l i n g . Prom 3-8 we now find that 1 millimeter i n the s p a t i a l 7 frequency plane corresponds to ^ = 0.4 l i n e s per mm. This i s equivalent to an actual signal frequency f^ f f, =• = 266 kHz 3-9 1 x l The s p a t i a l frequency plane i s sampled by the Ronchi r u l i n g at an i n t e r v a l d, which corresponds to a sampling i n t e r v a l Af i n actual signal space. Af = f± d = 13.5 kHz 3-10 Taking the approach from the d i f f r a c t i o n theory, we can calculate the spacing of some grating l i n e s , which would corres- pond to separated output pictures at the chosen d i f f r a c t i o n length of 4 meters. Prom equation 3«5 we have sinQ = T = -r-k- d = K1 3.11 1 d max b max With 1 = 4 m, b = 35 mm, X = 632.8 10~9m, we get d = 0.072 mm. niQ,x Converting into frequency, t h i s corresponds to a sampling i n t e r v a l Af max Af = f, d = 1 9 kHz 3.12 max 1 max The sampling theorem implies that the sample i n t e r v a l 18 has to be smaller or equal ^ , with T being the duration of m the time limited s i g n a l . The time duration T for one l i n e scan • ^ m i n the actual t e l e v i s i o n system i s 52.7 us. The necessary sam- pl i n g i n t e r v a l therefore becomes f = 7K = 19 kHz 3-13 max T m This i s the same result as obtained from d i f f r a c t i o n theory. The 500 l i n e per inch Ronchi rulings used here, having a spacing equivalent to 13-5 kHz i n the 4 m long system, some- • what oversample the spatial frequency plane. This was introduced deliberately by taking 4m as the d i f f r a c t i o n length between Fourier transform and output plane, to ensure a f u l l beam dia- meter separation. The system could be shortened to the absolute minimum of 2.8 meters, i f only 35 mm separation were desired. 3.3 The l i q u i d c e l l An empty transparency, i . e . , a piece of transparent c e l l u l o i d , i n the input plane of the o p t i c a l system of Figure 6 produces a great amount of noise i n the Fourier transform plane ?2. The cause of t h i s noise i s interference due to the uneven f i l m surface, which acts i n the coherent illumination as a phase modulator. This undesired effect can be greatly reduced by a l i q u i d c e l l , shown schematically i n Figure 8. The uneven f i l m transparency i s immersed i n a l i q u i d , which i s contained i n a box made out of o p t i c a l l y f l a t glass. The l i q u i d has to be of the same ref r a c t i v e index as the f i l m material, which i s around 1.5, so that a change i n ref r a c t i v e index only 19 occurs at the o p t i c a l l y f l a t glass surfaces. Several components were tested for the l i q u i d , with pure turpentine giving the best r e s u l t s . A demonstration of the effectiveness of the l i q u i d c e l l i s given i n section 4.3- f i l m transparency l i q u i d , r e f r a c t i v e index equal to f i l m material o p t i c a l l y f l a t glass Pig. 8 Liquid c e l l 3.4 Frequency sampling arrangement To sample the s p a t i a l frequency plane at regular i n t e r - vals, 2 Ronchi rulings were used, providing a variable s l i t width of 50/50 black/ transparent to 100$ black. One r u l i n g was f i x e d - mounted, while the other one was l a t e r a l l y movable by a fine ad- justing screw. A t h i n o i l f i l m between the two ruled surfaces enabled them to s l i d e easily on each other. Figure 9 shows the arrangement of the sampling r u l i n g schematically. coherent l i g h t T i l II III n 1 I) I ' 1 4 111 n 11 J 20 f i x e d mounted g r a t i n g mounts spri n g V adjustable g r a t i n g metal f i l l e d , engraved r u l i n g , ( g r e a t l y exaggerated) o i l f i l m a d j u s t i n g screw F i g . 9 Adjustable sampling g r a t i n g 3•5 D e s c r i p t i o n of the system In the a c t u a l system of Figure 10 a two meter f o c a l length lens i s used as the second F o u r i e r transforming l e n s , and i t i s placed r i g h t behind t h e ' s p a t i a l frequency plane P 2, 4 meters from the input plane and 4 meters from the output plane. This arrangement gives a 1 to 1 imaging. I t i s e a s i l y converted i n t o a one-dimensional system by i n t r o d u c i n g the two c y l i n d r i c a l lenses L 2 and 1^. The f o c a l l e n g t h of these two lenses i s not c r i t i c a l as long as L^, t h e . s p h e r i c a l l e n s , i s placed r i g h t behind the F o u r i e r transform plane, thus being of almost n e g l i g i b l e e f f e c t on the imaging c o n d i t i o n between F o u r i e r transform plane and out- put plane. The standard equation 3•14, r e l a t i n g the imaging d i s - tance B and the object distance G with the f o c a l length F of a l e n s , may be app l i e d to c a l c u l a t e the dimensions r e l a t e d with the c y l i n d r i c a l lenses L„ and L . . 21 1 1 1 •? 1 A F = B + G J ' 1 A Their f o c a l lengths have to be shorter than one meter, to ensure an imaging s o l u t i o n w i t h i n the a v a i l a b l e 4 meters t o t a l d i s t a n c e . A f o c a l l ength of 0.8 meters was chosen f o r both lenses and , g i v i n g approximately 3 to 1 imaging between the y - d i r e c t i o n of input and F o u r i e r transform plane, and 1 to 3 e n l a r g i n g from F o u r i e r transform to output plane. The.one-dimensional F o u r i e r transform i s therefore compressed i n the y - d i r e c t i o n , and thus f i t s e a s i l y i n s i d e the one in c h v e r t i c a l space l i m i t given by the Ronchi r u l i n g . S l i g h t o f f s e t of the lens from the exact h a l f distance between input and output plane may be compensated by asymmetrical arrangement of the c y l i n d r i c a l l e nses, but only i n a l i m i t e d r e - gion. For an exact c a l c u l a t i o n of the general asymmetrical case (8) the equation 3-15 f o r a two.lens system should be used f o r the output s e c t i o n . — — — _ H _ F = P + F 2 F 1 F 2 : 5 , 1 5 F and F 2 are the f o c a l lengths of the two lenses, H i s t h e i r separation. For lenses i n contact, (H = 0), t h i s equation r e - duces to a simple a d d i t i o n of the powers of the lenses. In p r a c t i c e , the symmetrical system was found to be eas- i e s t to handle, because alignment procedures soon get very d i f - f i c u l t w i t h an asymmetrical setup, due to the l a r g e number of var- i a b l e s •involved and the p h y s i c a l dimensions of the system. Figure 10 shows schematically the f i n a l system. Laser 1 Beam Liquid expander c e l l 4m L Ronchi r u l i n g 1.1m 'Fourier transforming section 1.1m «33 4m Reconstructing section Fig. 10 The f i n a l o p t i c a l system L^: Beam expander telescope, adjusted to F - 4m, 50mm diam. '• C y l i n d r i c a l lens, F = 0.8m, 55mm diameter L^: Spherical lens, F = 2m, 55mm diameter L.: Same as L„ A l l lenses had to be of e x c e l l e n t ' q u a l i t y , ground to w i t h i n the order of a wavelength. Any kind of surface d i s t o r - t i o n was r e a d i l y observable i n the output plane. The c y l i n d r i - c a l lenses were mounted i n r o t a t a b l e rings to provide easy a d j u s t - ment of the o p t i c a l a x i s . The sc a l e of the s p a t i a l frequency plane i n t h i s system was as c a l c u l a t e d under 3-2., i . e . , 1 mm i n the s p a t i a l frequency plane corresponds to 0.4 l i n e s per mm i n the input plane, or to 266 kHz of an a c t u a l video s i g n a l . 24 4 . FOURIER TRANSFORMS AND SPATIAL FILTERING 4 . 1 Two-dimensional F o u r i e r transforms The f i r s t s e c t i o n of the o p t i c a l system according to Figure 10 i s converted i n t o a two-dimensional F o u r i e r t r a n s - forming arrangement by removing the c y l i n d r i c a l lens L^. Figures 11 and 12 show the ROWI t e s t chart and the corresponding two-di- mensional F o u r i e r transform as observed i n plane P,~,. The center- p a r t , representing the dc and low frequency content of the t r a n s - formed p i c t u r e , had to be somewhat overexposed, to show the weaker parts of the l i g h t d i s t r i b u t i o n . Plane P 2 may be l a b e l l e d i n s p a t i a l frequency by a polar co-ordinate system w (r,<p), with o r i g i n i n the c e n t r a l dc poin t . P The concentric f r i n g e p a t t e r n represents the transform of the r i n g s i n the o r i g i n a l , with strong harmonics at the s p a t i a l frequencies corresponding to the width and spacing of the r i n g s . The repet- i t i v e dot patterns are due to s p a t i a l d e t a i l i n the r e s p e c t i v e d i r e c t i o n s . Figures 13 and 14 show an o f f center d e t a i l of the same chart and i t s transform. Note here e s p e c i a l l y the strong, widely-spaced harmonics i n the h o r i z o n t a l and v e r t i c a l d i r e c t i o n s , corresponding to oval c l u s t e r s of f i n e v e r t i c a l and h o r i z o n t a l l i n e s . Although these transforms are not of primary i n t e r e s t f o r i n v e s t i g a t i o n s of a one-dimensional t e l e v i s i o n s i g n a l , they show some basic c h a r a c t e r i s t i c s . o f the performance of an o p t i c a l system. For example, they show c l e a r l y that only a small part of the t o t a l area of the frequency plane i s r e a l l y occupied by the l i g h t d i s t r i b u t i o n , at l e a s t f o r a two tone p i c t u r e l i k e the ROWI chart. Fig. 11 ROWI test chart Fig. 12 Two-dimensional Fourier transform of Fig. 11 (Center part overexposed) 26 Pig. 14 Two-dimensional Fourier transform of Fig. 13 27 Furthermore, the analogy "between the Fourier transform plane i n the op t i c a l system and the hologram plane of a Fraunhofer d i f f r a c t i o n hologram may be mentioned here again. By superimpos- ing a reference beam on the Fourier transform we get a hologram of the input picture, which could be recorded on an appropriate photographic emulsion. The reference beam i n holography i s needed to get a recording of the phase d i s t r i b u t i o n i n the hologram plane by means cf interference, because photographic emulsion only responds to int e n s i t y and not to phase. A hologram then i s able to f u l f i l l the condition that the phase information also has to be retained i n the Fourier•transform plane i f further proces- sing of the signa l , e.g., a second Fourier transform producing a (7) reconstruction of the o r i g i n a l , i s to be performed. On the other hand, f i l t e r s produced by holographic tech- niques may be introduced i n the Fourier transform plane to achieve complex f i l t e r i n g , as has been done i n some pattern recognition +. (6) experiments. 4.2 One-dimensional Fourier transforms Inserting the c y l i n d r i c a l lens at the appropriate place into the system of Figure 10, we obtain a one-dimensional, multichannel Fourier transform arrangement. Now an imaging^ con- d i t i o n relates the y-axis of the planes P^ and P^, while the x- axis i s unchanged- and s t i l l governed by the Fourier transform r e l a t i o n . Figure 15 shows the one-dimensional transform of the cen- t r a l part of the ROWI test chart; Figures 16 and 17 show the Marconi resolution chart No. 1 and i t s Fourier transform. Here i t i s easy to r e l a t e the l i g h t d i s t r i b u t i o n of the Four i e r transform to the o r i g i n a l p i c t u r e . As i t i s w e l l known from the g r a t i n g equation 3»3, the separation of the secondary maxima of a d i f f r a c t i o n p a t t e r n i s i n v e r s e l y p r o p o r t i o n a l to the spacing of the g r a t i n g ; the same r e l a t i o n may also be derived from the d e f i n i t i o n of the s p a t i a l frequency (equation 2.4). We are thus able to c a l i b r a t e Figure 17 very e a s i l y i n a s p a t i a l frequency s c a l e , with respect to the o r i g i n a l t e s t chart. The i n t e n s i t y maxima, f o r the d i f f e r e n t l i n e spacings from 100 up to 600 l i n e s per p i c t u r e width are c l e a r l y v i s i b l e , as w e l l as the s l o p i n g l i n e s corresponding to the fanning-out l i n e s i n the center part of the o r i g i n a l . 1 i f I I I ^ 0 250 500 ( l i n e s per p i c t u r e width) F i g . 15 One-dimensional F o u r i e r transform of ROWI t e s t chart (center part) P i g . 16 M a r c o n i r e s o l u t i o n c h a r t No. 1 I I I L 0 200 400 600 f x (lines/picture width) Fig. 17 One-dimensional Fourier transform of Marconi chart (centre part) 30 4 . 3 R e l a t i o n to video s i g n a l A t e l e v i s i o n s i g n a l i s produced by scanning a p i c t u r e , ( 3 ) l i n e by l i n e , at a c e r t a i n r a t e . As i t i s well.known, t h i s leads to a concentration of the power i n the frequency spectrum at the harmonics of the l i n e r e p e t i t i o n frequency. This f a c t i s based on the s u p p o s i t i o n of a time l i m i t e d s i g n a l of the d u r a t i o n of one l i n e scan, or a sequence of s i m i l a r s i g n a l s of equal l e n g t h . In our o p t i c a l system we f i n d an exact equivalent to the r e a l time s i g n a l . The one-dimensional system t r e a t s the i n - put p i c t u r e l i n e by l i n e , g i v i n g the immediate F o u r i e r transform of each l i n e . The h o r i z o n t a l a x i s of the p i c t u r e i s l a b e l l e d time, and the p i c t u r e width then determines the time f o r one l i n e scan, which, i n the F o u r i e r transform plane, w i l l give r i s e to power concentrations at the harmonics of the s p a t i a l frequency corresponding to the p i c t u r e width. The aperture given by an empty frame as the input p i c - ture produces a F o u r i e r transform as shown i n the Figures 18 and 19. This i s the w e l l known patte r n of a Fraunhofer d i f f r a c t i o n (8) at an. aperture i n o p t i c s . Here the secondary maxima are the analogue of the maxima i n the frequency spectrum of a t e l e v i s i o n s i g n a l , spaced at i n t e r v a l s corresponding to the inverse l i n e d u r a t i o n . The e f f e c t of the l i q u i d c e l l described i n s e c t i o n 3-3 i s demonstrated by the Figures 20 and 21, both showing the F o u r i e r transform of an aperture w i t h an empty transparency of c l e a r f i l m m a t e r i a l introduced. The severely disturbed l i n e pat- tern of Figure 20 i s restored i n Figure 21, which was taken with, the same transparency, immersed i n the l i q u i d c e l l . 0 190 kHz actual video signal 18 One-dimensional Fourier transform of an aperture (Center part overexposed) .9 Part of the same transform as i n Fig. 18, only showing higher s p a t i a l frequencies. Line spacing equivalent 19 kHz actual video signal. (Fringe pattern due to lens used for enlargement i n photographic process) Fig. 20 Fourier transform of aperture with empty transparency Fig. 21 Fourier transform of aperture with empty transparency i n l i q u i d c e l l 33 4 • 4 Frequency sampling; The s t r i n g of separated output pictures produced by the frequency sampling i s shown i n Figure 22. The input picture was a 35 mm frame containing the center part of the ROWI test chart. As calculated i n section 3-2, the rulings are able to sample a 50 mm picture without ambiguity, i . e . , without producing overlap- ping outputs. Figure 23 shows the output of the system without the sampling r u l i n g . The rounded off edges are due to the small size lens used for enlargement i n the photographic process. Figure 24 shows the same image of the output plane, but with the rulings inserted and adjusted to a quite narrow s l i t width of approximately 15 to 1 opaque to transparent r a t i o . The effect on the output picture i s merely a decrease i n overall i n - tensity (compensated here by longer exposure of the photography). Some s l i g h t degradations are caused by imperfections i n the r u l - ings, only v i s i b l e under a microscope, and are independent of s l i t width. Figure 24 thus i s a very convincing demonstration of the .frequency sampling theorem. Figure 25 shows an enlarged part of the Fourier trans- form plane with the sampling grating, adjusted to the same s l i t width as used for Figure 24. A l l sampling l i n e s are of equal width; the apparent broadening of some bright l i n e s i s due to overexposure of these l i n e s , which was necessary to show the weaker parts. 34 Fig. 22 String of output pictures after frequency sampling Fig. 23 Single output picture without sampling F i g . 24 C e n t r a l ( z e r o order) output p i c t u r e . a f t e r f r e q u e n c y s a m p l i n g Fig. 25 Enlarged part of sampled s p a t i a l frequency plane. (Apparent irre g u l a r sample width due to overexposure) 36 .4-5 Coarse f i l t e r i n g For the f o l l o w i n g experiments, f o r ease of observation, the output plane was viewed by a camera of a closed c i r c u i t t e l - e v i s i o n system and displayed on a monitor. The p i c t u r e on the monitor was n a t u r a l l y somewhat degraded, but much more convenient to observe. Figure 26 i s a photograph of the output p i c t u r e of Figure 24, displayed on the monitor. Some basic p r o p e r t i e s of the o p t i c a l system may be shown by very simple, coarse f i l t e r i n g , p l a c i n g stops i n d i f f e r e n t parts of the F o u r i e r transform plane. The e f f e c t of a low pass f i l t e r , r e a l i z e d by a 10 mm wide s l i t i n the F o u r i e r transform plane, pas- s i n g only the c e n t r a l dc and low frequency region, i s demonstrated by Figure 27. The d i f f e r e n c e i n r e s o l u t i o n of v e r t i c a l and hor- i z o n t a l l i n e s i s apparent. The v e r t i c a l r e s o l u t i o n i s not a f f e c t e d by t h i s f i l t e r i n the one-dimensional transform. A high pass f i l t e r i s r e a l i z e d by a stop i n the dc reg- i o n . The e f f e c t of a 5 mm wide stop i s demonstrated by Figure 28. H o r i z o n t a l l i n e s are completely l o s t because of the missing low frequency components. As i t can be seen from Figure 15, the frequency spectrum of the ROWI t e s t chart contains many empty and low i n t e n s i t y spots. A very crude f i l t e r , passing only some of the b r i g h t e s t parts of the F o u r i e r transform plane (Figure 29), gives a f a i r l y good recon- s t r u c t i o n , shown i n Figure 30. Note here, f o r instance, the per- f e c t r e c o n s t r u c t i o n of the f i n e checkerboard p a t t e r n , which i s contained i n the string of harmonics at the top of Figure 29. The reduction i n bandwidth f o r t h i s part of the p i c t u r e i s approxim- a t e l y 6 to 1. The lower h a l f of the c e n t r a l r i n g p a t t e r n i s r e - 26 Output picture displayed on closed c i r c u i t t e l e v i s i o n monitor Fig. 27 Effect of low pass f i l t e r F i g . 28 Effect of high p a s s f i l t e r (lines/picture width) Fig. 29 Mask f i l t e r i n Fourier transform plane of Fig. 13 (Broken l i n e s mark high intensity- regions i n spectrum) 39 Pig. 30 Output from mask f i l t e r of Fig. 29 produced much better than the top half. The two v e r t i c a l bars i n the f i l t e r of Figure 29 stop out parts of the Fourier transform, which are essential for the reconstruction of the ring pattern. In general, the reconstruction i s quite good, considering the very rough methods used to r e a l i z e the mask f i l t e r . (It was shaped by eye to match the brightest parts of the spectrum). It seems possible to save transmission bandwidth by omitting a l l the unused parts of the spectrum of the transmitted signal i n a s u i t - able t e l e v i s i o n system. It i s not possible to treat a continuous tone picture i n the same way. The spectrum of such a picture (Figure 30) i s shown i n Figure 31• High s p a t i a l frequencies were very low i n i n t e n s i t y , (not even recorded on the photograph), and were submerged i n noise. Their presence could only be inferred i n the reconstruction by masking i n the Fourier transform plane. Nothing d e f i n i t e can therefore be said about the actual shape of the Fourier transform F i g . 31 Fourier transform of a continuous tone picture ("Face" Figure 38) for t h i s class of pictures. 41 5. SPATIAL FREQUENCY FLICKER EXPERIMENTS 5 .1 Basic 'idea I t i s w e l l known t h a t image q u a l i t y i s a h i g h l y sub- j e c t i v e measure. There are q u i t e a number of p h y s i o l o g i c a l f a c - t o r s that determine the apparent q u a l i t y , e s p e c i a l l y f o r a r e a l time t e l e v i s i o n p i c t u r e . I t i s known, e.g., that a frame rep- e t i t i o n as high as 30 per second i s unnecessary f o r most t e l e - v i s i o n reproductions, even of f a s t moving scenes (9) Some sav- ings of transmission bandwidth could be achieved t a k i n g advantage of t h i s f a c t , or of r e l a t e d p r o p e r t i e s of the human e y e . ^ 1 0 ^ 1 1 ^ More r e l a t e d to our approach of i n v e s t i g a t i n g the s p a t i a l frequency domain i s the v a r i a t i o n i n response of the human eye to d i f f e r e n t s p a t i a l frequencies. Measurements of t h i s " s t a t i c " r e l a t i o n s h i p have been made by s e v e r a l workers . ; the r e s - u l t s found by Lowry and de P a l m a ^ 1 ^ seem most widely accepted at t h i s time. (Figure 32) Normalized response 1 (lines/mm on r e t i n a ) F i g . 32 Sine wave response of the human eye 42 With respect to a t e l e v i s i o n p i c t u r e d i s p l a y , one question seems of s p e c i a l i n t e r e s t to us: How i s the response of the human eye to s p a t i a l frequencies a f f e c t e d by the f a c t that the p i c t u r e i s presented only part of the time rather than c o n t i n - uously? Or, i n other words, what i s the c r i t i c a l f l i c k e r f r e - quency as a f u n c t i o n of s p a t i a l frequency? I f t h i s "dynamic" c h a r a c t e r i s t i c has the same g e n e r a l l y n e g a t i v e l y s l o p i n g r e l a - t i o n s h i p f o r high s p a t i a l frequencies as the " s t a t i c " one, then i t could be taken advantage of by presenting the high s p a t i a l frequencies of a t e l e v i s i o n d i s p l a y at a lower rate than the ac- t u a l frame r e p e t i t i o n r a t e . The r e s u l t s of some r e l a t e d i n v e s t i - n g ) gations seem to j u s t i f y a c l o s e r look i n t o that question. The o p t i c a l s i g n a l processing system may be used quite e a s i l y f o r a study of t h i s problem. The s p a t i a l frequencies are r e a d i l y a c c e s s i b l e i n the F o u r i e r transform plane. A simple chop- ping d i s c may be used to step out a l l s p a t i a l frequencies above a c e r t a i n 3.imit temporarily, at a v a r i a b l e r e p e t i t i o n rate, thus " f l i c k e r i n g " the higher s p a t i a l frequency content of a p i c t u r e . The e f f e c t on the p i c t u r e q u a l i t y can be judged simultaneously by the r e c o n s t r u c t i o n i n the output plane. 5.2 Test arrangement To get some general and reproducible measurements, a p i c t u r e c o n s i s t i n g j u s t of a v e r t i c a l bar patte r n was used here i n a number of s u b j e c t i v e t e s t s . The setup f o r these f l i c k e r t e s t s i s shown i n Figure 33- A chopping wheel i s rotated by a small dc motor, producing a v a r i a b l e f l i c k e r r ate of 50/50 on/ of f time r a t i o f o r a part of the F o u r i e r transform plane. The side band stop blocks out one h a l f of the spectrum, passing only a "dc plus one sideband" s i g n a l , which i s s u f f i c i e n t to recon- s t r u c t the l i n e s of the t e s t p i c t u r e . The t o t a l information i s contained i n e i t h e r side of the symmetrical F o u r i e r transform, as f o r the normal amplitude modulation spectrum. Only one s i d e - band was used i n the f l i c k e r experiment here, to avoid the nec- e s s i t y of two synchronous chopping wheels f o r the high s p a t i a l frequencies of both sides of the spectrum. Compensating Chopping d i s c L ' J TV-Camera input sideband stop output plane (ground glass) subject TV-monitor A^Y"3 viewing distance 1.5m • -«ss • • • F i g . 33 F l i c k e r t e s t arrangement The output plane was viewed by means of the t e l e v i s i o n camera and monitor, so that brightness and constrast r a d i o could be e a s i l y adjusted. The secondary f l i c k e r introduced by t h i s viewing arrangement i s n e g l i g i b l e i f the set i s w e l l adjusted with regard to storage time of v i d i c o n and monitor, and i f the f l i c k e r introduced by the chopping wheel i s not i n the same f r e - quency range of 60 per second ( h a l f frame r a t e ) , which would pro- 44 cluce some beat frequency e f f e c t s - As i t turned out, the c r i t - i c a l s p a t i a l frequency f l i c k e r was always below 30 per second, and no stroboscopic e f f e c t s were observed. An a u x i l i a r y l i g h t was provided by a Zeiss microscope i l l u m i n a t o r s h i n i n g through the chopper d i s c at the appropriate time. I t was found to be necessary to i l l u m i n a t e the output plane during the time when'the s p a t i a l frequency plane was par- t i a l l y obscured. The explanation f o r t h i s seems to be the f o l l o w i n g : For i n c r e a s i n g s p a t i a l f requencies, the impression of a grey surface r a t h e r than the l i n e s t r u c t u r e of the t e s t s l i d e seems to become more and more dominant i n the perceived image. C u t t i n g out part of the F o u r i e r transform plane n a t u r a l l y reduces the t o t a l i n t e n - s i t y i n the observed p i c t u r e by a c e r t a i n amount. This i s per- ceived as a change i n the o v e r a l l brightness of the p i c t u r e , i . e . , a f l i c k e r . Using Biernson's somewhat c o n t r o v e r s i a l feedback mod- e l of human v i s i o n ^ ^ , t h i s e f f e c t may be explained by the f a s t response of the s p a t i a l average feedback, which also produces the grey impression. The a u x i l i a r y , compensating l i g h t , superposed during the chopping time, eliminated t h i s e f f e c t , and the eye seemed to con- centrate on the l i n e s t r u c t u r e again, as can be seen, from the r e s u l t s of s e c t i o n 5-3> The i n t e n s i t y of the l i g h t was adjusted e a s i l y to the necessary value by the f o c u s s i n g system of the Zeiss i l l u m i n a t o r . 5.3 Results Using the arrangement of Figure 33, a s e r i e s of subjec- 45 t i v e t e s t s was c a r r i e d out, with 4 subjects, 3 male and 1 f e - male; t h e i r ages ranged from 20 to 28 years. The t e s t persons were asked to judge the image c o n s i s t i n g of a v e r t i c a l bar pat- t e r n (50/50 black/white r a t i o ) as "good" and "acceptable", while the f l i c k e r rate of the e s s e n t i a l f i r s t harmonic i n the s p a t i a l frequency plane was v a r i e d . The r e s u l t s of these t e s t s are sum- marized i n the Figures 34 and 35. The t e s t s were run 3 times, to check the consistency of the judgement. I t was found that the r e s u l t s between d i f f e r e n t runs v a r i e d only s l i g h t l y , mostly by no more than -1 c y c l e of f l i c k e r r a t e . F i g . 34 C r i t i c a l f l i c k e r frequency as a f u n c t i o n of s p a t i a l frequency f o r judgment "good". (Broken curve without brightness compensation) f (Hz c 16 100 -J . . ! 50 4-6 A: B: Contrast r a t i o 27:1 Contrast r a t i o 2^:1 ( l i n e s / p i c t u r e width) 200 300 100 150 -tar- f X F i g . 35 C r i t i c a l f l i c k e r frequency as a f u n c t i o n of s p a t i a l frequency f o r judgement "accep- t a b l e " The contrast r a t i o of the l i n e p a t t e r n was adjusted by measuring the l i g h t i n t e n s i t i e s f o r peak white and peak black d i r e c t l y on the screen with a l i g h t meter. The i n f l u e n c e of the contrast r a t i o on the r e s u l t s i s made c l e a r by the curves of Figure 36, which are based on "good" judgements l i k e the curves of Figure 34 ^ A ( H Z ) 16 8 f = 1 0 0 f v = 125 lines/mm on r e t i n a Contrast r a t i o F i g . 36 C r i t i c a l f l i c k e r frequency vs contrast r a t i o . 47 The c r i t i c a l f l i c k e r frequency appears to be a loga - r i t h m i c f u n c t i o n of the contrast r a t i o . Only f o r high s p a t i a l frequencies at low contrast r a t i o s i s there a s l i g h t d e v i a t i o n from the l o g a r i t h m i c behaviour. This may be due to the dominat- ing grey impression received under these c o n d i t i o n s . The background i l l u m i n a t i o n was held at a reduced l e v e l of approximately 180 l u x . V a r i a t i o n s i n room i l l u m i n a t i o n from 2 l u x to 700 l u x were te s t e d , but found to be of n e g l i g i b l e i n - fluence. A b r i g h t background increased the c r i t i c a l f l i c k e r frequency very s l i g h t l y , e s p e c i a l l y f o r high s p a t i a l frequencies. The i n f l u e n c e of the average brightness of the p i c t u r e was checked over a 9 to 1 luminance range, from approximately 40 to 350 cd/m . The e f f e c t of the contrast r a t i o dominates the brightness e f f e c t by f a r , but i t seems that the c r i t i c a l f l i c k e r frequency increases very s l i g h t l y with i n c r e a s i n g brightness. An 2 average screen luminance of 200 cd/m was used f o r the experiments of.Figures 3^ to 37. The i n f l u e n c e of the s i z e of the p i c t u r e area i s shown i n Figure 37; i t i s very small a l s o , and l i e s almost w i t h i n the un c e r t a i n t y of about -1 Hz b a s i c a l l y inherent i n the t e s t s . A trend to increased c r i t i c a l f l i c k e r frequency with l a r g e r area i s n o t i c e a b l e . A much l a r g e r mumber of t e s t s has to be c a r r i e d out to get more exact r e s u l t s , but t h i s was beyond the scope of t h i s t h e s i s . Generally, i t may be s a i d that the e f f e c t s of p i c t u r e area, brightness and background are only small and seem to be consistent with r e s u l t s f o r t o t a l r ather than p a r t i a l f l i c k e r i n g (17) found by Foley , which show b a s i c a l l y l o g a r i t h m i c behaviour. 48 f G | (Hz) A 24 B C 20 16 12 8 A B C P i c t u r e area 36 cm P i c t u r e area 9 cm P i c t u r e area 5 cm 4 100 200 100 50 (.lines/mm on r e t i n a ) P i g . 37 C r i t i c a l f l i c k e r frequency with p i c t u r e area as parameter F i n a l l y some s u b j e c t i v e q u a l i t y t e s t s were c a r r i e d out with the p i c t u r e s of Figures 38 and 39, f l i c k e r i n g the higher s p a t i a l f r e - quencies. Here i t was not necessary to r e s t o r e the average b r i g h t - ness during the chopping period; the power of the high s p a t i a l frequency components i s very low, and no change i n average b r i g h t - ness was observed. They show, f o r example, that the severely bandlimited p i c t u r e of Figure 41, which resolves only 50 l i n e s per p i c t u r e width, may be presented a l t e r n a t i v e l y with the o r i g i n a l p i c t u r e (Figure 38) at a r a t e of 19 Hz, to give a s u b j e c t i v e l y perfect image. For l e s s b a n d l i m i t a t i o n , the rate may be decreased below that value. to save transmission bandwidth i n a t e l e v i s i o n system. There i s , however, an obvious l i m i t to the compression that can be achieved t h i s way. I t i s given by the r a t i o of the t o t a l area of Figure 40 to the area under the curves, which comes out to be approximately The r e s u l t s of these t e s t s are summed up i n Figure 40. I t can be seen immediately that t h i s f a c t may be used F i g . .38 "Pace" (viewed on TV-monitor) ; H Z ) 50 241 \ 16* 8h F i g . 40 100 50 A; "Face" ( f i g u r e 38) B: "Group" ( f i g u r e 39 (Rating "good") 200 l i n e s per pi c t u r e width) 300 TOO" 150 x (lines/mm on r e t i n a ) C r i t i c a l f l i c k e r frequency of two h a l f tone p i c t u r e s F i g . 41 Bandlimited p i c t u r e (Resolution 50 l i n e s per p i c t u r e width) 5 1 5.4 A t e n t a t i v e law One may t r y to approximate the r e s u l t s shown i n the F i g - ures 34, 35, and 40 by a mathematical expression i n order to put them i n t o the form of a basic law. I t seems that some kind of an exponential f u n c t i o n would describe the behaviour of these curves quite w e l l . We may therefore t r y an expression of the form of equation 5.1 f = f exp(-kf ) 5.1 c o 1 x f denotes the c r i t i c a l f l i c k e r frequency, f the s p a t i a l f r e - quency i n l i n e s per m i l l i m e t e r on the r e t i n a . f i s an e x t r a p o l - ated, merely t h e o r e t i c a l value f o r f at a s p a t i a l frequency equal to zero. I t i s not of much p r a c t i c a l s i g n i f i c a n c e , because f o r very low s p a t i a l frequencies we approach the case of normal " t o t a l area" f l i c k e r , and judgements of q u a l i t y are a l s o very d i f f i c u l t to make i n t h i s region. The i n f l u e n c e of some para- meters changes as w e l l , the contrast r a t i o f o r example becomes a measure f o r the average brightness too. I t can be seen, from e x t r a p o l a t i o n of our curves, that f w i l l depend on the contrast r a t i o and n a t u r a l l y on the kind of judgement we are working with ("good", "acceptable"). The f a c t o r k i n the exponent w i l l a l s o be a parameter'depending on the ex- periment. I t i s , f o r example, apparent that k w i l l be d i f f e r e n t f o r the l i n e p a t t e r n experiments and f o r the p i c t u r e experiments, and i t may a l s o depend on the contrast r a t i o . The a c t u a l experimental values f o r f g e n e r a l l y l i e bet- ween 24 and 34 Hz. The f a c t o r k l i e s q u i te constantly around 0.012 f o r a l l l i n e p a t t e r n experiments, and at 0.02 f o r the p i c t u r e s , k g e n e r a l l y seems to increase very s l i g h t l y f o r i n - cre a s i n g contrast r a t i o . For curve A of Figure 35 we get the mathematical ex- p r e s s s i o n of equation 5.2 Curve B of Figure 40 obeys a law according to equation 5.3 f c 30 exp(-0.012 f ) 5.2 f c 28 exp(-.0.02 f ) 5.3 F i g s . 42 and 43 View of t e s t apparatus used f o r the present work 54 6. CONCLUSIONS AND FUTURE WORK An o p t i c a l s i g n a l processing system may be used con- v e n i e n t l y f o r i n v e s t i g a t i o n s i n the s p a t i a l frequency domain of an image s i g n a l . This has been the object of the present work, with s p e c i a l emphasis on image compression research. I t i s not po s s i b l e at the present time to incorporate an optical.system d i r e c t l y i n a bandwidth compression scheme; but the r e s u l t s of o p t i c a l s i g n a l processing research can be very u s e f u l f o r study and design of new compression methods. Some s t r a i g h t f o r w a r d p o s s i b i l i t i e s of bandwidth compres- si o n are apparent f o r c e r t a i n t e s t charts which contain, very def- i n i t e s p a t i a l frequencies; the l a r g e empty regions i n t h e i r spec- t r a can be omitted to achieve s u b s t a n t i a l savings i n bandwidth. The coarse f i l t e r i n g experiment i n chapter 4 showed quite good p i c t u r e q u a l i t y f o r compression r a t i o s ranging from 2 : 1 to 8 : 1 depending on the p i c t u r e complexity. The spectra of continuous tone p i c t u r e s could not be observed a c c u r a t e l y enough, because of noise e f f e c t s ; nothing can be s a i d about p o s s i b i l i t i e s of bandwidth compression using spec- t r a l gaps f o r t h i s c l a s s of p i c t u r e s . Savings i n bandwidth can a l s o be achieved by e x p l o i t i n g some c h a r a c t e r i s t i c s of' the human eye. The o p t i c a l system has been shown to be a very u s e f u l t o o l f o r i n v e s t i g a t i n g one ques- tion, concerning the v i s u a l perception of the eye. The r e s u l t s of these experiments, reported i n chapter 5, are very promising with respect to compression p o s s i b i l i t i e s . The decrease i n c r i t - i c a l f l i c k e r frequency'for high s p a t i a l frequencies of a t e l e v i - s i o n p i c t u r e can be used f o r compression by presenting the high . 55 s p a t i a l frequency content at a reduced r a t e . Some d e t e r i o r a - t i o n of p i c t u r e s of f a s t moving scenes w i l l probably occur, sim- i l a r to the e f f e c t s reported f o r a frame r e p e t i t i o n and r e p l e n - ishment system^"'. Here these e f f e c t s w i l l be l e s s severe, because the important low frequency content i s presented at the normal r a t e . The a p p l i c a t i o n of o p t i c a l s i g n a l processing to the f i e l d of image compression research has produced some i n t e r e s - t i n g r e s u l t s . A number of questions and problems, however, s t i l l remain and have to be l e f t f o r f u t u r e work. In p a r t i c u l a r , the f o l l o w i n g p o i n t s seem to be of immediate i n t e r e s t : a) A d d i t i o n a l i n v e s t i g a t i o n s w i l l have to analyse spectra of "continuous" tone p i c t u r e s , i n which the grey shades are pro- duced by a r e g u l a r l y spaced r a s t e r , thus concentrating the s p a t i a l frequency content at c e r t a i n s p e c i f i c p o i n t s i n the spectrum. b) Further t e s t s , i n v e s t i g a t i n g the c r i x i c a l f l i c k e r frequency, have to be c a r r i e d out, using v a r i a b l e chopping i n t e r v a l s (instead of 50/50 on/off time). A more d e t a i l e d study of the i n f l u e n c e of such parameters as c o n t r a s t , p i c t u r e area, b r i g h t - ness, etc. i s suggested as w e l l . c) There are many ways i n which, a compression system may be des- igned using v a r i a b l e p r e s e n t a t i o n rate f o r d i f f e r e n t s p a t i a l frequency content of a t e l e v i s i o n d i s p l a y . As a f i r s t exper- iment, a very simple system may be b u i l t , using only two d i f - ferent r e p e t i t i o n r a t e s : Two scanning spots, at d i f f e r e n t v e l o c i t i e s , would produce two s i g n a l s ; one corresponding to 5 6 a 1 MHz bandlimited transmission at normal r e p e t i t i o n rate ( 3 0 frames per second), and one conta i n i n g the s p a t i a l frequencies from 1 to 5 MHz, but at h a l f the r e p e t i t i o n r a t e . 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C., et a l • , "Subjective E f f e c t s of Frame R e p e t i t i o n and P i c t u r e Replenishment", BSTJ v o l . 46, 1, January 1967. 12. DeMott, D. W., "Direct Measures of R e t i n a l Image", JOSA v o l . 49, June 1959- 13. S t u l z , K. F., and Zweig, H. J . , " R e l a t i o n between Grain- iness and G r a n u l a r i t y f o r Black and White Samples with Nonuniform G r a n u l a r i t y " , JOSA v o l . 49 June 1959. 14. Lowry, E. M. , and dePalrua., J. J . , "Sine Wave Response of the V i s u a l System", JOSA v o l . 51, 7, J u l y .1961. 58 15. Budrikis, Z. L., Seyler, A. L., " D e t a i l Perception A f t e r Scene Changes i n T e l e v i s i o n Image Presentations", IEEE Trans, on Inf. Theory, v o l . IT-11, Jan.1965- 16. Biernscn, G., "A Feedback-control Model of Human V i s i o n " , Proc. IEEE, v o l . 54, 6, June 1966. 59 APPENDIX Fo u r i e r transform re I at i oil of a coherent o p t i c a l system Coherent l i g h t can be t r e a t e d as an electromagnetic wave and described by g i v i n g i t s amplitude and phase as a func- t i o n of the three space v a r i a b l e s . U = I(x,y,z)cos[~cot + 0(x,y,z)] A . l x , y , z For the f i e l d i n a plane perpendicular to the z-axis i n an o p t i c a l system, we can w r i t e U Q = l(x,y)cos[wt + 0(x,y)] A.2 As a convention, t h i s may a l s o be w r i t t e n i n the form U o = I(x,y)exp[j0(x,yj] - A.3 This r e p r e s e n t a t i o n i s j u s t i f i e d by the time invariance of a l l the s i g n i f i c a n t features of the o p t i c a l system, where CJ (the temporal radian frequency of the l i g h t ) acts i n a sense l i k e a c a r r i e r frequency. Let us now consider Figure 2 again (from chapter 2.1), which Is repeated here f o r convenience. F i g . A . l Two-dimensional F o u r i e r transformer 60 In plane P̂  a transparency of the complex transmission f u n c t i o n S(x,y) i s introduced i n the "beam of coherent monochrom- a t i c l i g h t . S(x,y) = t(x,y)exp ha( x , y ) l A.4 Emerging from P-̂  i s then the m u l t i p l i c a t i o n of the l i g h t wave wi t h S(x,y) t\ = S U A. 5 1 o This wave now i s summed up over P^ onto P^ by focussing- lens . C a l c u l a t i o n of Uv, requires f i n d i n g the o p t i c a l path length from x^Y-^ "to x^,y^. Up then i s the i n t e g r a l over P^ of U^, properly delayed i n phase according to the distance r . .2%T - D - T - dx^dy^ A. 6 X = wavelength of l i g h t d = amplitude a t t e n u a t i o n f a c t o r r e s u l t i n g from distance between P-̂  and P . 1 -f^cosQ _ o b l i q u i t y f a c t o r r = distance between x - j _ 5 v ] _ "to X p , y p . In our system, —• can be dropped because absolute phase and amplitude are of no i n t e r e s t , d i s dropped because the a t t e n - u a t i o n i s n e g l i g i b l e , and the o b l i q u i t y f a c t o r i s dropped because 0- i s always s u f f i c i e n t l y s m a l l , so that cosO We then get 61 JJ U^exp - 3 — r ( x 1 , y l f x 2 , y 2 . d x 1 d y 1 A.7 To c a l c u l a t e the distance r , consider Figure A.2 x x 1 1 9< 0 -BH-SJ -r- P P' ^ l X, F i g . A.2 Geometrical r e l a t i o n s A plane wave emerging from plane P-̂  at an angle 9 to the o p t i c a l a x i s i s brought to focus at x2,' where x 2 = f sin9. This i m p l i e s that the o p t i c a l distance between x 2 and any point on P^ i s a constant c. 2 2 2 1/2 2 c = r-^ +. r 2 = l|g - X Q C O S 9 + |f. + x 2 A.8 c = g + f , 2 \ x 0 1 + fi — + f 2f f o r small 9 and x x 0 o 2 A.9 ta k i n g g The distance from the plane P-̂  to x 2 i s obtained by adding the term X ] X2 -x^sin.9 = —j— A.10 The t o t a l distance from x-̂  to x 2 i s then r U j ,y 1 ,x 2 ,y In two dimensions, the same approach leads to \ x 2+y 2 x n x 2 y ny. 2 / = .const. I 1 - ^ 2f i l l 'f A.12 For the wave IL-, at P 2 we then get where U 1exp(-j x x 1 ) e x p ) - j y y ] _ ) d x 1 d 3 ^ 1 exp j (3 ( o , OJ ) A. 13 1 x 2JI;X2 ' ~ \ f ~ ' 2rty, oo = - , J y \± A.14 and P = 1 \ 2 2 &\ X2 + y 2 f 2f A.15 For the system of Figure A . l g i s equal to f, so that (3 = 0. Equation 2.4 i n chapter 2.1 fol l o w s immediately. The co n d i t i o n f = g i s necessary to obtain an exact F o u r i e r transform between P^ and P 2 i n t h i s system.

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