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UBC Theses and Dissertations

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 . E l . - I n g . , Swiss Federal I n 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 t h e s i s 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 p a r t i a l fulfilment of the requirements  for an advanced degree at the University of B r i t i s h 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^  The University of B r i t i s h Columbia Vancouver 8, Canada Date  ZZ  ,  M*t  ^f^e^-^  ABSTRACT O p t i c a l s i g n a l p r o c e s s i n g i s i n t r o d u c e d 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 t h e f i e l d o f t e l e v i s i o n compression r e s e a r c h . An o p t i c a l s i g n a l p r o c e s s i n g system i s d e s i g n e d , which performs the F o u r i e r t r a n s f o r m 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 c o n s t r u c t i o n F ^"{F  [B(x,y)]j  .  Some b a s i c o p t i c a l f i l t e r i n g ex-  periments a r e performed i n t h e s p a t i a l f r e q u e n c y p l a n e , and t h e o p t i c a l analogue o f t h e f r e q u e n c y s a m p l i n g theorem i s demonstrated. The F o u r i e r t r a n s f o r m s o f t e s t p a t t e r n p i c t u r e s show l a r g e gaps which can be used f o r compression.  O b s e r v a t i o n of com-  p l e x s p e c t r a of c o n t i n u o u s tone p i c t u r e s i s found t o be i m p a i r e d by n o i s e 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 t h e 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 f r e q u e n c y and s p a t i a l f r e q u e n c y of a t e l e v i s i o n p i c t u r e . tolerable f l i c k e r rate f  I t i s found t h a t t h e  decreases as t h e s p a t i a l f r e q u e n c y f ^  i s increased, a c c o r d i n g t o the e m p i r i c a l equation f f  = f  exp(-kf ).  and k a r e parameters depending on f a c t o r s l i k e c o n t r a s t  x  ratio,  k i n d and s i z e of p i c t u r e , e t c . Compression systems u s i n g t h e above r e s u l t s a r e found t o have a l i m i t of o b t a i n a b l e compression r a t i o o f a p p r o x i m a t e l y 3 t o 1.  ii  TABLE OF CONTENTS Page 1.  INTRODUCTION  2.  THEORY OF OPTICAL SIGNAL PROCESSING  4  2.1  Fundamental o p t i c a l systems  4  2.2  Optical f i l t e r i n g  8  3.  4.  5.  6.  1  DESIGN OF THE OPTICAL SYSTEM... 3.1  Basic considerations  3.2  Calculations  3.3  The l i q u i d c e l l  3.4  Frequency s a m p l i n g arrangement  3.5  D e s c r i p t i o n of the system  11 ..  ^  1  FOURIER TRANSFORMS AND SPATIAL FILTERING  -  '.  8  19 20 .  24  4.1  'Two-dimensional F o u r i e r t r a n s f o r m s  24  4.2  One-dimensional F o u r i e r t r a n s f o r m s  27  4.3  Relation to video signal  30  4.4  Frequency s a m p l i n g  ^  4.5  Coarse f i l t e r i n g  ^6  ;  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  CONCLUSIONS AND FUTURE WORK  54  REFERENCES  57  APPENDIX  59 iii  LIST OF ILLUSTRATIONS Figure  Page  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  2  O p t i c a l F o u r i e r transformer  6  3  Multichannel one-dimensional Fourier transformer..  7  4  Successive Fourier transformers  8  5  Variable scale F o u r i e r transformer  12  6  Basic o p t i c a l system  13  7  Diffraction grating  14  8  Liquid c e l l  19  9  Adjustable sampling g r a t i n g  20  10  The f i n a l o p t i c a l system  22  11  ROWI t e s t chart  25  12  Two-dimensional F o u r i e r transform of Figure 11....  25  13  D e t a i l of ROWI t e s t chart  26  14  Two-dimensional F o u r i e r transform of Figure 13-...  26  15  One-dimensional F o u r i e r transform of ROWI test  .  4  chart  ?3  16  Marconi r e s o l u t i o n chart No. 1  29  17  One-dimensional F o u r i e r transform of Marconi chart  29  18 19  One-dimensional F o u r i e r transform of an aperture.. Part of the same transform as i n Figure 18, only showing higher s p a t i a l frequencies  31 31  20  Fourier transform of aperture with empty transparency  32  21  F o u r i e r transform of aperture with empty t r a n s parency i n l i q u i d c e l l  32  22  S t r i n g of output p i c t u r e s a f t e r frequency  34  23  Single output p i c t u r e without sampling  iv  sampling  34  24  C e n t r a l (zero order) output p i c t u r e a f t e r frequency sampling  35  25  Enlarged part of sampled s p a t i a l frequency plane....  35  26  Output p i c t u r e displayed on closed c i r c u i t t e l e v i s i o n monitor  37  27  E f f e c t of lowpass f i l t e r  38  28  E f f e c t of highpass f i l t e r  38  29  Mask f i l t e r i n F o u r i e r transform plane of eq. 13....  38  30  Output from mask f i l t e r i n Figure 29  39  31  F o u r i e r transform of a continuous tone  32  Sine wave response of the human eye  33 34 35  p i c t u r e ....  40 41  . F l i c k e r t e s t arrangement O p 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 "good" 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 "acceptable"  42 45 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 p i c t u r e area as parameter  48  38  "Face"  49  39  "Group"  40  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  50  41  Bandlimited p i c t u r e  50  43  View of t e s t apparatus used f o r present work  53  A 1.  Two-dimensional  59  A 2  Geometrical r e l a t i o n s  •  :  49  42 &  F o u r i e r transformer  61  ACKNOWLEDGEMENT  Many persons have helped course  i n one o r t h e o t h e r way d u r i n g t h e  of t h i s r e s e a r c h p r o j e c t , and rny thanks go t o a l l of them. In p a r t i c u l a r I would l i k e t o thank .my s u p e 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 s u g g e s t i o n s , 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 p r e p a r ing the t h e s i s . I would a l s o l i k e t o thank Dr. A. D. Moore f o r r e a d i n g and c o r r e c t i n g the t h e s i s . F u r t h e r thanks g>* t o Mr. P. D. Carman and Mr. J . N. C a i r n s from NRC Ottawa, who p r o v i d e d t h e h i g h q u a l i t y l e n s e s needed f o r this project. I am g r a t e f u l t o Miss L. R a t c l i f f e and Mr. W. D. Ramsay f o r p r o o f r e a d i n g , and t o Miss A. Hopkins f o r t y p i n g t h e t h e s i s . F i n a l l y , I. would l i k e t o thank t h e a d m i n i s t r a t i o n of t h e U n i v e r s i t y o f B r i t i s h Columbia f o r my exchange F e l l o w s h i p , and NRC.for t h e f i n a n c i a l support  o f 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, s t a r t i n g almost immediately a f t e r the i n v e n t i o n of t e l e v i s i o n .  Numerous systems and techniques  have been proposed to reduce the bandwidth required f o r the transmission of t e l e v i s i o n s i g n a l s , as becomes c l e a r from P r a t t ' s b i b liography^^.  But, as Schreiber put i t i n a recent a r t i c l e : (2)  r e s u l t s are meager, indeed".  .  "The  The work continues, because the  need f o r 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 l e a s t begin to understand the problem. Most of the present day work to reduce redundancy i n t e l e v i s i o n p i c t u r e transmission i s done on the basis of some d i g i t a l techniques, i n v e s t i g a t i n g 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 a c t u a l l y been b u i l t ^ " ^ . In the l a s t few years a new method of analysing and processing s i g n a l s of various kinds has been developed, which makes use of coherent l i g h t , e a s i l y a v a i l a b l e today from l a s e r s :  Op-  t i c a l s i g n a l processing systems f i n d i n c r e a s i n g a p p l i c a t i o n i n numerous f i e l d s of research and p r a c t i c a l use. O p t i c a l systems possess two degrees of freedom, i . e . , two independent v a r i a b l e s , as opposed to e l e c t r o n i c systems with only one independent v a r i a b l e , time.  In a d d i t i o n , o p t i c a l systems show  the property that a Fourier transform r e l a t i o n e x i s t s between the l i g h t amplitude d i s t r i b u t i o n at the f r o n t - 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 p e r f o r m i n g F o u r i e r t r a n s f o r m s or r e l a t e d mathematical  operations  i n s t a n e o u s l y i n two dimensions; o r , by use of a s t i g m a t i c l e n s e s , i n one dimension w i t h a number of independent c h a n n e l s .  This makes  i t s u p e r i o r t o an e l e c t r o n i c system, which would have t o use s c a n n i n g or time s h a r i n g procedures t o a c h i e v e the same r e s u l t s . The v e r y l a r g e number of p o i n t s which can e a s i l y be p r o 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 f a v o u r of the opt i c a l method.  A p o i n t a g a i n s t i t i s the n o i s e , 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 s i m p l e o p e r a t i o n i n p r i n c i p l e , • and the r e s e a r c h r e p o r t e d here usessuch f i l t e r i n g as a t o o l t o 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 r e 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 c o u l d be used f o r compression purposes, as suggested by vocoder methods'in speech compression.  An attempt was made t o check on  t h i s p o i n t i n Chapter 4 . Mertz and Gray f i r s t showed t h a t the t e l e v i s i o n spectrum i s comb-like i n s t r u c t u r e , w i t h empty spaces i n between ("3)  each clump of energy.  ( T h i s f a c t i s made use of i n c a r r i e r  interlaced color television).  Thus, we expect t o be a b l e t o r e d -  uce bandwidth merely by c l o s i n g up the spaces.  I n f a c t , the  frequency v e r s i o n of the s a m p l i n g t h e o r e r r / ^ suggests s i m i l a r methods; a b a s i c experiment d e s c r i b e d i n t h i s t h e s i s shows t h a t the s p a t i a l f r e q u e n c y 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 q u a l -  ity. 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 s p e c t r a l spikes have to be used i n a frequency sampled s i g n a l , 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  e n t i r e l y uncorrelated, i n which case the bandwidth, needed f o r each s p e c t r a l spike i s roughly the number of p i c t u r e l i n e s times the p i c t u r e r e p e t i t i o n frequency: s i n g l e sideband modulation.  525x30 = 15,750 Hz, assuming  Thus, although one s i n g l e l i n e of  a s t i l l p i c t u r e needs zero bandwidth, ( i n 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 a c t u a l bandwidth. L i m i t a t i o n s i n the -perception of the human eye may be exploited to reduce t e l e v i s i o n ' bandwidth. examined i n t h i s t h e s i s .  One such l i m i t a t i o n i s  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 presented on a TV-screen, f o r f l i c k e r to be just not apparent?  It  i s shown that the minimum r a t e , or t o l e r a b l e 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 d i f f e r e n t transmission rates f o r low and high frequency components of a t e l e v i s i o n s i g n a l . The present t h e s i s deals with three problems: (a)  The design of o p t i c a l s i g n a l processing equipment, which can be  used as a t o o l to i n v e s t i g a t e t e l e v i s i o n compression prob-  lems (b)  (chapter 3 ) ;  The performance and r e s u l t s of some exploratory f i l t e r i n g experiments.  These are not complete, but intended as a.guide  to f u r t h e r work (chapter 4-) ; (c)  The r e s u l t s of f l i c k e r experiments, which i n v e s t i g a t e the temporal response of-the human eye to s p a t i a l frequencies (chapter 5)•  4  2. 2.1  THEORY OP OPTICAL SIGNAL PROCESSING  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 t h e t h e o r y of o p t i c a l d a t a (5)  p r o c e s s i n g i s g i v e n by Cutrona et a l .  .  F o r 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 b a s i c components and r e l a t i o n s of an o p t i c a l system i s g i v e n here, d i s c u s s i n g m a i n l y the t h e o r y as i t a p p l i e s t o i n v e s t i g a t i o n s of the f r e q u e n c y domain. Let us f i r s t c o n s i d e r an example of a non coherent  light  system, as i t i s shown i n F i g . 1: y  Fig.  1  y  O p t i c a l system f o r two d i m e n s i o n a l 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 g i v e n s i g n a l of two v a r i a b l e s may be r e p r e s e n t e d by a s p a t i a l l y v a r y i n g t r a n s p a r e n c y , such as a p h o t o g r a p h i c f i l m , whose t r a n s m i t t a n c e i s t ( x , y ) , w i t h O-t.^-1. 1  sity I  L i g h t of u n i f o r m i n t e n -  passes through t h i s t r a n s p a r e n c y and i s s p a t i a l l y modul-  ated t o g i v e t h e output i n t e n s i t y I t ^ ( x , y ) . l i g h t pass through a second for  I f we now l e t t h i s  t r a n s p a r e n c y of t r a n s m i s s i o n t ( x - X , y )  example, where X i s a d i s p l a c e m e n t  2  of the t r a n s p a r e n c y 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 intensity I  t^(x,y)t^(x-X,y).  Thus a two dimensional m u l t i p l i c a -  t i o n i s performed. Let a second lens Lg focus the l i g h t to a p o i n t , 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 ( x , y ) t ( x - X , y ) dx dy 1  2.1  2  A A i s the t o t a l aperture area i n plane P.^, and attenuation and eff e c t s of f i n i t e lens s i z e have been ignored. This i n t e g r a l has the form of a two dimensional convolu t i o n or c r o s s - c o r r e l a t i o n . We defined the transmission f u n c t i o n to be p o s i t i v e only. If we d e s i r e to represent a negative going s i g n a l , we must w r i t e i t on a dc-bias, represented by a constant c i n the transmission function.  We may a l s o have to introduce a s c a l i n g f a c t o r a f o r  the o r i g i n a l s i g n a l f u n c t i o n . ^  + a^j^ ^ ( 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 produce undesired cross terms. In many a p p l i c a t i o n s i t i s p o s s i b l e to remove the dcbias 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 F o u r i e r transform of the transparency  i s obtained o p t i c a l l y  i n t h i s system, where the dc part of the s i g n a l i s concentrated at one s p e c i f i c l o c a t i o n .  I t may then be removed by a simple stop,  and a second F o u r i e r transform reconstructs the o r i g i n a l s i g n a l  w i t h o u t the dc b i a s .  P i g u r e 2 shows the n e c e s s a r y  optical  arrangement.  Plane P Pig. 2  Optical Fourier transformer  L i g h t of the complex a m p l i t u d e d i s t r i b u t i o n U^(x^,y-^) emerges from p l a n e P^.  We can w r i t e  U- _(x ,y ) ]  1  =  1  U (x y ).3xp T ja(x ,y ) 1  1 >  1  1  2.3  1  U-^(x-py^) i s the a m p l i t u d e 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 a m p l i t u d e may be regarded as r e p r e s e n t e d  by the p h o t o g r a p h i c d e n s i t y of a t r a n s p a r e n c y i n p l a n e P^, the phase by v a r i a t i o n s i n t r a n s p a r e n c y t h i c k n e s s . The complex a m p l i t u d e d i s t r i b u t i o n  a"t plane P^  ^2^ 2'^2^ x  i s g i v e n by +C+D _ U (x ,y ) 2  2  2  U (x  =  n  -C-D  n  , y ) e x p ( - j w x ) e x p ( - j w y )dx dy n  x  1  1  1  1  2.4  For a proof of equation 2.4 see appendix. The s p a t i a l frequencies w  x  and to are defined by r e l a -  t i o n 2.5: -2jtx,  -2%y  to  r  2.5  to  where \ i s the wavelength of the l i g h t used. We see that  i-  w i t h i n the l i m i t s -C, -D.  s  'the Fourier transform of U , l y i n g 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 immediately:  Besides being a t o o l f o r spectrum a n a l y s i s , f i l t e r i n g  i s e a s i l y accomplished by p l a c i n g 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 n a l , we need only a one dimensional system. -  sig-  The second dimension  can then be used.to accommodate a large number of independent channels f o r one dimensional s i g n a l s , thus not wasting the capaci t y of the system.  ^2  Fig. 3  Multichannel one-dimensional Fourier transformer  8  The lens system of Figure 3 focuses only i n one dimension, performing an imaging i n the other dimension, y  i s an inverted image of y^.  2  such that  The Fourier transform obtained  with t h i s system therefore becomes  r  +  U (x ,y ) 2  2  =  2  J  U (x ,y )exp(-j(o x ) dx 1  1  1  x  1  2.6 1  -C  Two or more F o u r i e r transforming systems may be cascaded to perform successive transforms.  The conventional F o u r i e r  transform theory requires the kernel f u n c t i o n exp(-jwt) f o r the transform from time to frequency domain, and the f u n c t i o n exp (j cot) for the inverse transform from frequency to time.  An o p t i c a l sys-  tem ( i . e . , a lens) always introduces the kernel f u n c t i o n exp  0  x  1  y  1  We can obtain the r i g h t s i g n f o r the ker-  nel f u n c t i o n of the inverse transform by merely l a b e l l i n g the co-ordinates a p p r o p r i a t e l y , as shown i n Figure 4 .  1  Fig. 2.2  Successive F o u r i e r transformers  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 a c t i o n on a s i g n a l  9 (plane T^,  i n the frequency plane o f an o p t i c a l system  Figure 4).  The r e s u l t i n g e f f e c t can be observed immediately i n t h e plane of the r e c o n s t r u c t i o n (P^, F i g u r e 4 ) . B a s i c a l l y t h e r e a r e two k i n d s of  filters  t h a t may be i n t r o d u c e d i n the frequency p l a n e :  tude f i l t e r s  and phase f i l t e r s .  plex f i l t e r f u n c t i o n .  ampli-  Together they can e f f e c t a com-  An a m p l i t u d e f i l t e r  the o p t i c a l d e n s i t y of a t r a n s p a r e n c y .  i s o b t a i n e d by v a r y i n g  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 t h e t h i c k n e s s , which i n t u r n v a r i e s t h e phase r e t a r d ation.  A s i m p l e form of an amplitude f i l t e r might be a s l i t ,  whic  corresponds t o a s p a t i a l bandpass f i l t e r ; a s t o p r e p r e s e n t s a r e j ection f i l t e r . Complex f i l t e r f u n c t i o n s appear t o be p o s s i b l e , a l t h o u g h more d i f f i c u l t  to realize 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 i n f o r m a t i o n o f 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 a r e t o be found main(6)  l y i n the f i e l d  of p a t t e r n r e c o g n i t i o n .  .  The o n e - d i m e n s i o n a l F o u r i e r t r a n s f o r m plane may be sampled by narrow s l i t s  ( i n f i n i t e l y narrow i n t h e l i m i t ) ,  spaced a t r e g -  u l a r i n t e r v a l s , t o produce a p e r f e c t r e c o n s t r u c t i o n .  T h i s i s the  • o p t i c a l a n a l o g of t h e frequency sampling theorem, which s t a t e s t h a a time l i m i t e d f u n c t i o n can be r e p r e s e n t e d by i t s u n i f o r m samples i n t h e frequency domain.^ ^ For each p o i n t i n a l i n e of a scanned a d i s t i n c t correspondence  p i c t u r e , time has  w i t h each p o i n t i n t h e x - d i r e c t i o n i n  plane P-^ of t h e o p t i c a l system  ( F i g u r e 3)-  The i n p u t s i g n a l  be a p i c t u r e of f i n i t e s i z e , p l a c e d i n t o t h i s p l a n e , thus l i n g t h e 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 .  will  fulfil-  Now we can proceed  to i n t r o d u c e some k i n d of a comb f i l t e r i n t h e F o u r i e r t r a n s f o r m or s p a t i a l f r e q u e n c y plane P . The e f f e c t , observed a t 2  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 g r a t i n g - l i k e a c t i o n of the comb f i l t e r , producing a string of d i f f r a c t e d output p i c t u r e s .  A coarse f i l t e r produces overlapping  output images; the spacing of the g r a t i n g l i n e s has to be made f i n e 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 l e a s t one p i c t u r e width o f f the o p t i c a l axis (see chapter 3 ) -  11 3. 3•1  DESIGN OP THE OPTICAL SYSTEM  Basic considerations In the o p t i c a l system described here Ronchi r u l i n g s were  used as a comb f i l t e r to v e r i f y the frequency sampling theorem. These r u l i n g s are o p t i c a l l y f l a t glass pieces with engraved,, meta l - f i l l e d l i n e s of high p r e c i s i o n , g i v i n g a 50/50 opaque/transparent g r a t i n g .  They are r e a d i l y a v a i l a b l e only with 500 l i n e s  per inch, which imposes some l i m i t s on . the p h y s i c a l s i z e of the whole system, because of the quite l a r g e d i f f r a c t i o n length needed to get the d i f f r a c t e d output p i c t u r e s separated i n a_ one to one imaging system (see chapter 3-2.).  One to one imaging was found  to be d e s i r a b l e i n order to allow easy observation of the output. A system using long f o c a l length lenses i s a l s o b e t t e r with r e s pect to lens aberrations, because the " t h i n l e n s " concept i s more closely realized. Further l i m i t a t i o n s of the p h y s i c a l dimensions are given by the width of the l a s e r beam a v a i l a b l e , which provides the <-.oherent l i g h t .  Here a commercially a v a i l a b l e beam expander was  used, g i v i n g a beam of 50 m i l l i m e t e r s diameter, with gaussian phase d i s t r i b u t i o n over the aperture.  Standard 35 m i l l i m e t e r s l i d e s ,  which could be i l l u m i n a t e d quite uniformly with the expanded beam, were used i n the input plane. The l a s e r beam can be made p a r a l l e l or converging by ad1  j u s t i n g 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 the " v a r i a b l e s c a l e " F o u r i e r transform system.  as  The input plane P-^  may be moved a x i a l l y without d i s t u r b i n g the exact F o u r i e r t r a n s form r e l a t i o n between plane P-^ and P ; only the scale of the 2  transform i s v a r i e d .  This system has a l s o the advantage of being  space i n v a r i a n t 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  V a r i a b l e scale F o u r i e r transformer  A s p h e r i c a l l e n s , placed r i g h t behind the F o u r i e r t r a n s form plane, can be used to perform a second transform, g i v i n g an approximate one to one imaging onto the output plane.  Two c y l i n -  d r i c a l lenses, i n s e r t e d at the appropriate places make the system one-dimensional.  The basic setup i s shown i n Figure 6.  13  p.  Pig. 6 3.2  Basic o p t i c a l system  Calculations The computations of the p h y s i c a l dimensions of the sys-  tem according to Figure 6 w i l l be based on the few d e s i r a b l e prope r t i e s and given dimensions discussed above, such as s i z e of i n put p i c t u r e , beam width, imaging c o n d i t i o n s , s i z e 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 p i c t u r e s w e l l separated.  The 500 l i n e s per inch  Ronchi r u l i n g s w i l l be used to perform the s p a t i a l frequency samp l i 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 f o r the i n t e n s i t y d i s t r i b u t i o n at a point behind a g r a t (8) ing according to Figure 7 i s given by equation 3-1 • kNdp  =  KP)  where  sinG - sin9  o  X  sin- 2 .  kdp  3-1  3-2  14  d  N slits  Fig.  7  Diffraction grating  L i s the length of a s l i t ,  k = 0, 1, 2 . . .  The i n t e 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 g r a t i n g , represented by the f i r s t bracket i n equation 3.1.  P  These maxima w i l l occur at m \ d  (m  =  0,-1,-2  3-3  )  m i s the order of i n t e r f e r e n c e , i t represents the path length d i f f e r e n c e i n wavelengths  i n the d i r e 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-  , lmum occurs at p = ^X .  In our case we have 9  = 0 , which means that the l i g h t o i s normally incident on the g r a t i n g . to  p  l  -  s  i  n  e  i  3.4  = d  ©]_ j s the angle of the f i r s t order d i f f r a c t e d p i c t u r e with respect to the zero order p i c t u r e on the o p t i c a l a x i s .  We may replace  s i n 9 ^ by the l a t e r a l separation b of the f i r s t order p i c t u r e , 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" 632.8  X  =  m m  10~ mm  1  6  =  2.8 m  I f 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  a c t u a l system. The 35 mm p i c t u r e i n input and output plane corresponds to a t e l e v i s i o n p i c t u r e scanned by an e l e c t r o n beam, to give an e l e c t r o n i c s i g n a l of a c e r t a i n bandwidth.  The standard t e l e v i s -  i o n system used here has 525 l i n e s , of which 21 are used f o r f i e l d blanking; t h i s leaves 504 a c t i v e l i n e s .  The time f o r one  l i n e scan i s 63-5 us, of which 10.8 us are l i n e blanking time, l e a v i n g 52.7 us f o r one a c t i v e l i n e . . Introducing a K e l l . f a c t o r of 0.73, the v e r t i c a l r e s o l u t i o n of the system i s 368 l i n e s per screen height.  A 4 to 3 aspect  r a t i o r e s u l t s i n 490 l i n e s h o r i z o n t a l r e s o l u t i o n .  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 r e s o l u t i o n 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 52.7x10'  m a x  =  4.65  MHz  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 p i c t u r e correspond to a frequency of 4.65 MHz of the video s i g nal.  In the o p t 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 chosen p i c t u r e s i z e . We r e c a l l equation 2.4, which r e l a t e s the scale of the s p a t i a l frequency plane with the p h y s i c a l dimensions of the o p t i c a l processing system.  x =  w  2TCX  *  ~W  OJ  i n radians per  / \ 0 A  u n i t length  To convert i n t o the s p a t i a l frequency f , we d i v i d e 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 i n s i d e an area i n the Fourier transform plane given by the s i z e of the Ronchi r u l i n g s .  500 l i n e r u l i n g s are made i n a s i z e 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,  f o r 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 l e s s than one inch can be allowed.  From Figure 6 and the 1 to 1 imaging condi-  t i o n we f i n d that the d i f f r a c t i o n length of the output s e c t i o n i s also the f o c a l 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 a c t u a l bandwidth of a video s i g n a l , 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 m i l l i m e t e r .  17  x,  =.  1  1 2rc\f  = — =  17.5 mm  2it  3-8  x-^ i s therefore w e l l within the l i m i t of one inch or 25.4 mm given by the s i z e of the Ronchi r u l i n g . Prom 3-8 we now f i n d that 1 m i l l i m e t e r i n the s p a t i a l 7  frequency plane corresponds to  ^  =  0.4 l i n e s per mm.  i s equivalent t o an a c t u a l s i g n a l frequency f ^ f f, =• = 266 kHz l 1  This  3-9  x  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 t o a sampling i n t e r v a l Af i n a c t u a l s i g n a l space. Af  =  d  f  ±  =  13.5 kHz  3-10  Taking the approach from the d i f f r a c t i o n theory, we can c a l c u l a t e the spacing of some g r a t i n g l i n e s , which would correspond to separated output p i c t u r e s 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  1  =  -r-kdmax  d  max  =  K  1  3.11  b  With 1 = 4 m, b = 35 mm, X = 632.8 10~ m, we get d 9  = 0.072 mm.  niQ,x  Converting i n t o frequency, t h i s corresponds to a sampling i n t e r v a l Af max Af  = max  f, d 1 max  =19  kHz  3.12  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 l i m i t e d s i g n a l . The time duration T f o r one l i n e scan • ^ m i n the a c t u a l t e l e v i s i o n system i s 52.7 us.  The necessary sam-  p l i n g i n t e r v a l therefore becomes f max  =  7K  Tm  =  19 kHz  3-13  This i s the same r e s u l t as obtained from d i f f r a c t i o n theory. The 500 l i n e per inch Ronchi r u l i n g s used here, having a spacing equivalent to 13-5 kHz i n the 4 m long system, some- • what oversample the spatial frequency plane. deliberately  by t a k i n g 4m  This was  introduced  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 d i a 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 F o u r i e r transform plane ?2.  The cause of t h i s noise i s i n t e r f e r e n c e due to the uneven  f i l m surface, which acts i n the coherent i l l u m i n a t i o n as a phase modulator. This undesired e f f e c t can be g r e a t l y 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 g l a s s .  The  l i q u i d has to be of the same r e f r a c t i v e index as the f i l m m a t e r i a l , which i s around 1.5, so that a change i n r e f 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 f o r the l i q u i d , with pure turpentine g i v i n g the best results.  A demonstration of the e f f e c t i v e n e s s of the l i q u i d c e l l 4.3-  i s given i n s e c t i o n  T i l II III n  film  1  coherent light  l i q u i d , r e f r a c t i v e index equal to f i l m m a t e r i a l  1  111  o p t i c a l l y f l a t glass  I) I '  4  n 11 J  Pig. 8 3.4  transparency  Liquid  cell  Frequency sampling arrangement To sample the s p a t i a l frequency plane at regular i n t e r -  v a l s , 2 Ronchi r u l i n g s were used, providing a v a r i a b l e s l i t of 50/50 black/ transparent to 100$ black.  One r u l i n g was  width fixed-  mounted, while the other one was l a t e r a l l y movable by a f i n e adj u s t i n g 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 e a s i l y on each other.  Figure 9 shows the  arrangement of the sampling r u l i n g schematically.  20  mounts  f i x e d mounted grating  spring adjustable grating  V  m e t a l f i l l e d , engraved r u l i n g , ( g r e a t l y exaggerated)  oil  Fig. 9 3•5  adjusting  film  screw  A d j u s t a b l e sampling g r a t i n g  D e s c r i p t i o n of the system In the a c t u a l system of F i g u r e 10 a two meter f o c a l  l e n g t h l e n s i s used as the second F o u r i e r t r a n s f o r m i n g l e n s , and i t i s p l a c e d r i g h t behind t h e ' s p a t i a l f r e q u e n c y plane P , 2  from the input plane and 4 meters from the output p l a n e . arrangement g i v e s a 1 t o 1 imaging.  4 meters This  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 l e n s e s L  2  and 1^.  The f o c a l l e n g t h of these two l e n s e s i s not  critical  as l o n g as L^, t h e . s p h e r i c a l l e n s , i s p l a c e d r i g h t behind the F o u r i e r t r a n s f o r m p l a n e , thus b e i n g of almost n e g l i g i b l e  effect  on the imaging c o n d i t i o n between F o u r i e r t r a n s f o r m plane and output plane.  The s t a n d a r d e q u a t i o n 3•14,  r e l a t i n g the imaging d i s -  tance B and the o b j e c t d i s t a n c e G w i t h the f o c a l l e n g t h F of a l e n s , may  be a p p l i e d t o c a l c u l a t e the dimensions r e l a t e d w i t h the  c y l i n d r i c a l l e n s e s L„ and  L..  21 1 F  1 1 = B  •? 1 A +  G  J  '  1 A  T h e i r f o c a l l e n g t h s have t o be s h o r t e r than one meter, t o 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 e n g t h of 0.8  meters was  chosen f o r both l e n s e s  and  ,  g i v i n g a p p r o x i m a t e l y 3 t o 1 imaging between the y - d i r e c t i o n of i n p u t and F o u r i e r t r a n s f o r m p l a n e , and 1 t o 3 e n l a r g i n g from F o u r i e r t r a n s f o r m t o output p l a n e .  The.one-dimensional  Fourier  t r a n s f o r m i s t h e r e f o r e 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 i n c h v e r t i c a l space l i m i t g i v e n by the Ronchi  ruling. S l i g h t o f f s e t of the l e n s  between i n p u t and output plane may  from the exact h a l f d i s t a n c e be compensated by a s y m m e t r i c a l  arrangement of the c y l i n d r i c a l l e n s e s , but o n l y 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 g e n e r a l a s y m m e t r i c a l case  (8) the e q u a t i o n 3-15  f o r a two.lens system s h o u l d be used f o r the  output s e c t i o n . —  F  F  and F  2  =  —  P  +  F  — 2  _  F F 1  H  : 5 , 1 5  _  2  are the f o c a l l e n g t h s of the two l e n s e s , H i s t h e i r  separation.  For l e n s e s i n c o n t a c t , (H = 0 ) , t h i s e q u a t i o n r e -  duces t o a s i m p l e a d d i t i o n of the powers of the l e n s e s . In p r a c t i c e , the s y m m e t r i c a l system was  found t o be eas-  i e s t t o handle, because alignment procedures soon get v e r y d i f f i c u l t w i t h an a s y m m e t r i c a l setup, due t o the l a r g e number of v a r i a b l e s • i n v o l v e d and the p h y s i c a l dimensions of the system. F i g u r e 10 shows s c h e m a t i c a l l y the f i n a l  system.  L 1  Laser  Beam expander  Liquid cell  Ronchi r u l i n g 1.1m «33  4m  'Fourier transforming  F i g . 10 L^: '• L^: L.:  section  1.1m  4m  Reconstructing  section  The f i n a l o p t i c a l system  Beam expander telescope, adjusted to F - 4m, 50mm diam. C y l i n d r i c a l l e n s , F = 0.8m, 55mm diameter Spherical l e n s , F = 2m, 55mm diameter Same as L„  A l l l e n s e s had t o be of e x c e l l e n t ' q u a l i t y , ground t o w i t h i n the o r d e r of a wavelength.  Any k i n d of s u r f a c e d i s t o r -  t i o n was r e a d i l y o b s e r v a b l e i n the output p l a n e .  The c y l i n d r i -  c a l l e n s e s were mounted i n r o t a t a b l e rings t o p r o v i d e easy a d j u s t ment of the o p t i c a l a x i s . The s c a l e of the s p a t i a l frequency plane  i n this  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 f r e q u e n c y plane corresponds t o 0.4 l i n e s per mm i n t h e i n p u t p l a n e , or t o 266 kHz of an a c t u a l v i d e o s i g n a l .  24 4. 4.1  FOURIER TRANSFORMS AND SPATIAL FILTERING  Two-dimensional F o u r i e r  transforms  The f i r s t s e c t i o n o f the o p t i c a l system a c c o r d i n g t o F i g u r e 10 i s converted  i n t o a two-dimensional F o u r i e r t r a n s -  f o r m i n g arrangement by removing the c y l i n d r i c a l l e n s L^. 11 and 12 show the ROWI t e s t c h a r t and the c o r r e s p o n d i n g mensional F o u r i e r t r a n s f o r m as observed i n plane P,~,. p a r t , r e p r e s e n t i n g t h e dc and low frequency  content  Figures two-di-  The center-  o f the t r a n s -  formed p i c t u r e , had t o be somewhat overexposed, t o show t h e weaker p a r t s o f the l i g h t Plane P  2  distribution. may be l a b e l l e d i n s p a t i a l frequency  by a p o l a r  c o - o r d i n a t e system w (r,<p), w i t h o r i g i n i n t h e c e n t r a l dc p o i n t .  P The c o n c e n t r i c f r i n g e p a t t e r n r e p r e s e n t s t h e t r a n s f o r m of t h e r i n g s i n the o r i g i n a l , w i t h s t r o n g harmonics a t t h e s p a t i a l  frequencies  corresponding  The r e p e t -  t o the w i d t h and s p a c i n g of the r i n g s .  i t i v e dot p a t t e r n s a r e due t o 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 directions.  F i g u r e s 13 and 14 show an o f f c e n t e r d e t a i l o f t h e  same c h a r t and i t s t r a n s f o r m .  Note here e s p e c i a l l y t h e s t r o n g ,  widely-spaced  harmonics i n t h e h o r i z o n t a l and v e r t i c a l  directions,  corresponding  t o o v a l c l u s t e r s o f f i n e v e r t i c a l and h o r i z o n t a l  lines. Although  these t r a n s f o r m s  a r e n o t o f primary  interest  f o r i n v e s t i g a t i o n s o f a one-dimensional t e l e v i s i o n s i g n a l ,  they  show some b a s i c c h a r a c t e r i s t i c s . o f the performance o f an o p t i c a l system.  F o r example, they show c l e a r l y t h a t o n l y a s m a l l p a r t o f  the t o t a l a r e a o f the frequency  plane i s r e a l l y occupied by t h e  l i g h t d i s t r i b u t i o n , a t 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.  F i g . 11  F i g . 12  ROWI t e s t chart  Two-dimensional Fourier transform of F i g . 11 (Center part overexposed)  26  P i g . 14  Two-dimensional Fourier transform of F i g . 13  27 Furthermore, the analogy "between the F o u r i e r transform plane i n the o p 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 F o u r i e r transform we get a hologram of the input p i c t u r e , 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 c f i n t e r f e r e n c e , because photographic only responds to i n t e n s i t y and not to phase.  emulsion  A hologram then i s  able to f u l f i l l the c o n d i t i o n that the phase information a l s o has to be retained i n the Fourier•transform plane i f f u r t h e r process i n g of the s i g n a l , e.g., a second Fourier transform producing a (7) r e c o n s t r u c t i o n 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 techniques may be introduced i n the F o u r i e r transform plane to achieve complex f i l t e r i n g , as has been done i n some pattern r e c o g n i t i o n +. (6) experiments. 4.2  One-dimensional Fourier transforms I n s e r t i n g the c y l i n d r i c a l lens  at the appropriate  place i n t o the system of Figure 10, we obtain a multichannel F o u r i e r transform arrangement.  one-dimensional,  Now an imaging^ con-  d i t i o n r e l a t e s the y-axis of the planes P^ and P^, while the xaxis i s unchanged- and s t i l l governed by the Fourier transform relation. Figure 15 shows the one-dimensional transform of the cent r a l part of the ROWI t e s t chart; Figures 16 and 17 show the Marconi r e s o l u t i o n chart No. 1 and i t s Fourier transform.  Here  i t i s easy t o 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 F o u r i e r t r a n s f o r m t o 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 e q u a t i o n 3 » 3 , the s e p a r a t i o n of the secondary maxima of a d i f f r a c t i o n pattern i s inversely  p r o p o r t i o n a l t o the s p a c i n g  of the g r a t i n g ; the same r e l a t i o n may a l s o be d e r i v e d from the d e f i n i t i o n of the s p a t i a l frequency ( e q u a t i o n 2.4).  We are thus  a b l e t o c a l i b r a t e F i g u r e 17 v e r y e a s i l y i n a s p a t i a l frequency s c a l e , w i t h r e s p e c t t o the o r i g i n a l t e s t c h a r t . maxima, f o r the d i f f e r e n t per  The i n t e n s i t y  l i n e s p a c i n g s from 100 up t o 600 l i n e s  p i c t u r e w i d t h 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 c o r r e s p o n d i n g t o the f a n n i n g - o u t l i n e s i n the c e n t e r p a r t of the o r i g i n a l .  1  i  f  F i g . 15  I  I  0  250  I  500 ( l i n e s per p i c t u r e width)  One-dimensional F o u r i e r t r a n s f o r m of ROWI t e s t c h a r t ( c e n t e r p a r t )  ^  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.  I  0  I  I  200  400  1  L  600  ( l i n e s / p i c t u r e width) F i g . 17  One-dimensional Fourier transform of Marconi chart (centre part)  f x  30 4.3  R e l a t i o n to v i d e o 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 s c a n n i n g a p i c t u r e , (3)  l i n e by l i n e , a t a c e r t a i n r a t e .  As i t i s well.known,  l e a d s t o a c o n c e n t r a t i o n of the power i n the frequency at  the harmonics of the l i n e r e p e t i t i o n frequency.  this spectrum  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 e q u i v a l e n t t o  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 t r a n s f o r m 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  t i m e , and the p i c t u r e w i d t h then determines  the time f o r one  line  scan, which, i n the F o u r i e r t r a n s f o r m p l a n e , w i l l g i v e r i s e t o power c o n c e n t r a t i o n s a t the harmonics of the s p a t i a l  frequency  c o r r e s p o n d i n g t o the p i c t u r e w i d t h . The a p e r t u r e g i v e n by an empty frame as the i n p u t p i c t u r e produces a F o u r i e r t r a n s f o r m as shown i n the F i g u r e s 18 19. at  T h i s i s the w e l l known p a t t e r n of a F r a u n h o f e r (8) an. a p e r t u r e i n o p t i c s .  Here the secondary  and  diffraction  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 c o r r e s p o n d i n g t o the i n v e r s e l i n e duration. The e f f e c t of the l i q u i d c e l l d e s c r i b e d i n s e c t i o n 3-3 i s demonstrated by the F i g u r e s 20 and 21, both showing the F o u r i e r t r a n s f o r m of an a p e r t u r e w i t h an empty t r a n s p a r e n c y clear f i l m material introduced.  of  The s e v e r e l y d i s t u r b e d l i n e p a t -  t e r n of F i g u r e 20 i s r e s t o r e d i n F i g u r e 21, which was the same t r a n s p a r e n c y , immersed i n the l i q u i d  cell.  taken with,  0  18  190  kHz actual video signal  One-dimensional Fourier transform of an aperture (Center part overexposed)  .9  Part of the same transform as i n F i g . 18, only showing higher s p a t i a l frequencies. Line spacing equivalent 19 kHz a c t u a l video signal.  (Fringe pattern due to lens used  f o r enlargement i n photographic  process)  F i g . 20  Fourier transform of aperture with empty transparency  F i g . 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 p i c t u r e s produced by the frequency sampling i s shown i n Figure 22.  The input p i c t u r e was  a 35 mm frame c o n t a i n i n g the center part of the ROWI test chart. As c a l c u l a t e d i n s e c t i o n 3-2, the r u l i n g s are able to sample a 50 mm p i c t u r e without ambiguity, i . e . , without producing overlapping outputs. Figure 23 shows the output of the system without the sampling r u l i n g .  The rounded o f f edges are due to the small size  lens used f o r enlargement i n the photographic process. Figure 24 shows the same image of the output plane, but with the r u l i n g s i n s e r t e d 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  e f f e c t on the output p i c t u r e i s merely a decrease i n o v e r a l l i n t e n s i t y (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 F o u r i e r t r a n s form plane with the sampling g r a t i n g , adjusted to the same s l i t width as used f o r 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  F i g . 22  S t r i n g of output pictures a f t e r frequency sampling  F i g . 23  Single output p i c t u r e without sampling  F i g . 24  Central  (zero order) output  . a f t e r frequency  F i g . 25  picture  sampling  Enlarged part of sampled s p a t i a l frequency plane. to  (Apparent i r r e g u l a r sample width due  overexposure)  36 .4-5  Coarse  filtering  For t h e f o l l o w i n g experiments,  f o r ease of o b s e r v a t i o n ,  the output plane was viewed by a camera of a c l o s e d c i r c u i t e v i s i o n system and d i s p l a y e d on a monitor.  The p i c t u r e on the  m o n i t o r was n a t u r a l l y somewhat degraded, but much more to  observe.  tel-  convenient  F i g u r e 26 i s a photograph of the output p i c t u r e of  F i g u r e 24, d i s p l a y e d on the monitor. Some b a s i c p r o p e r t i e s of the o p t i c a l system may be shown by v e r y s i m p l e , 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 p a r t s of the F o u r i e r t r a n s f o r m p l a n e . r e a l i z e d by a 10 mm wide s l i t  The e f f e c t of a low pass f i l t e r ,  i n the F o u r i e r t r a n s f o r m p l a n e , pas-  s i n g o n l y the c e n t r a l dc and low frequency by F i g u r e 27.  r e g i o n , i s demonstrated  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 h o r -  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 n o t a f f e c t e d  by t h i s f i l t e r i n t h e one-dimensional  transform.  A h i g h pass f i l t e r i s r e a l i z e d by a stop i n the dc r e g ion.  The e f f e c t of a 5 mm wide stop i s demonstrated by F i g u r e 28.  H o r i z o n t a l l i n e s a r e c o m p l e t e l y l o s t because of the m i s s i n g low frequency  components. As i t can be seen from F i g u r e 15, the frequency  spectrum  of the ROWI t e s t c h a r t c o n t a i n s many empty and low i n t e n s i t y  spots.  A v e r y crude f i l t e r , p a s s i n g o n l y some of the b r i g h t e s t p a r t s of the F o u r i e r t r a n s f o r m plane  ( F i g u r e 2 9 ) , g i v e s a f a i r l y good r e c o n -  s t r u c t i o n , shown i n F i g u r e 30.  Note here, f o r i n s t a n c e , the p e r -  f e c t r e c o n s t r u c t i o n of t h e f i n e checkerboard p a t t e r n , which i s c o n t a i n e d i n the string of harmonics a t the t o p of F i g u r e 29.  The  r e d u c t i o n i n bandwidth f o r t h i s p a r t of the p i c t u r e i s approxima t e l y 6 t o 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 p i c t u r e displayed on closed c i r c u i t t e l e v i s i o n monitor  F i g . 27  E f f e c t of low pass f i l t e r  Fig.  28  E f f e c t of high  pass  filter  ( l i n e s / p i c t u r e width) F i g . 29  Mask f i l t e r i n Fourier transform plane of F i g . 13 (Broken l i n e s mark high intensityregions i n spectrum)  39  Pig.  30  Output from mask f i l t e r of F i g . 29  produced much better than the top h a l f .  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 e s s e n t i a l f o r the reconstruction of the r i n g 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 .  ( I t 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 s i g n a l 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 t r e a t a continuous tone p i c t u r e i n the same way.  The spectrum of such a p i c t u r e (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 i n f e r r e d 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 a c t u a l shape of the Fourier  transform  F i g . 31  Fourier transform of a continuous tone p i c t u r e ("Face" Figure 38)  for t h i s class of p i c t u r e s .  41 5. 5 .1  SPATIAL FREQUENCY FLICKER EXPERIMENTS  B a s i c '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 t h a t 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., t h a t a frame r e p -  e t i t i o n as h i g h as 30 per second i s unnecessary f o r most t e l e v i s i o n r e p r o d u c t i o n s , even of f a s t moving scenes (9)  Some sav-  i n g s of t r a n s m i s s i o n bandwidth c o u l d be a c h i e v e d 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 t o our approach of i n v e s t i g a t i n g the s p a t i a l f r e q u e n c y domain i s the v a r i a t i o n i n response of the human eye t o d i f f e r e n t s p a t i a l frequencies.  Measurements of t h i s  r e l a t i o n s h i p have been made by s e v e r a l workers u l t s found by Lowry and de P a l m a ^ ^ 1  t h i s time. ( F i g u r e  .  "static" ; the r e s -  seem most w i d e l y a c c e p t e d at  32)  N o r m a l i z e d response  1  (lines/mm on r e t i n a ) F i g . 32  Sine wave response of the human eye  42 With r e s p e c t t o 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 q u e s t i o n seems of s p e c i a l i n t e r e s t t o us:  How i s the response  of the human eye t o s p a t i a l f r e q u e n c i e s a f f e c t e d by the f a c t t h a t the p i c t u r e i s presented uously?  o n l y p a r t of the time r a t h e r than c o n t i n -  Or, i n o t h e r words, what i s t h e c r i t i c a l f l i c k e r  quency as a f u n c t i o n of s p a t i a l frequency?  fre-  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 h i g h s p a t i a l f r e q u e n c i e s as t h e " s t a t i c " one, then i t c o u l d be taken advantage of by p r e s e n t i n g the h i g h  spatial  f r e q u e n c i e s of a t e l e v i s i o n d i s p l a y a t a lower r a t e than the a c 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  investi-  ng)  gations  seem t o j u s t i f y a c l o s e r l o o k i n t o t h a t q u e s t i o n . The o p t i c a l s i g n a l p r o c e s s i n g system may be used q u i t e  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 f r e q u e n c i e s are  r e a d i l y a c c e s s i b l e i n t h e F o u r i e r transform plane.  A s i m p l e chop-  p i n g d i s c may be used t o step out a l l s p a t i a l f r e q u e n c i e s above a c e r t a i n 3.imit temporarily,  a t a v a r i a b l e r e p e t i t i o n r a t e , thus  " f l i c k e r i n g " the h i g h e r 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 s i m u l t a n e o u s l y by t h e r e c o n s t r u c t i o n i n t h e output 5.2  plane.  Test arrangement To get some g e n e r a l and r e p r o d u c i b l e 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 b a r p a t t e 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 . t e s t s i s shown i n F i g u r e 33-  The setup f o r these  flicker  A chopping wheel i s r o t a t e d by a  s m a l l dc motor, p r o d u c i n g a v a r i a b l e f l i c k e r r a t e of 50/50 on/ o f f time r a t i o f o r a p a r t of the F o u r i e r t r a n s f o r m p l a n e .  The  s i d e band s t o p b l o c k s out one h a l f of the spectrum, p a s s i n g o n l y a "dc p l u s one sideband" s i g n a l , which i s s u f f i c i e n t t o r e c o n struct  the l i n e s of t h e t e s t p i c t u r e .  The t o t a l i n f o r m a t i o n i s  c o n t a i n e d i n e i t h e r s i d e of the s y m m e t r i c a l F o u r i e r t r a n s f o r m , as f o r the normal a m p l i t u d e m o d u l a t i o n spectrum.  Only one s i d e -  band was used i n t h e f l i c k e r experiment h e r e , t o a v o i d t h e nece s s i t y of two synchronous chopping wheels f o r t h e h i g h s p a t i a l f r e q u e n c i e s of both s i d e s of t h e spectrum. Compensating Chopping disc  input  TV-Camera L 'J  output plane (ground g l a s s )  sideband s t o p  TV-monitor subject  A^Y"  3  •  F i g . 33  viewing distance • •  -«ss  Flicker test  1.5m •  arrangement  The output p l a n e was viewed by means of the t e l e v i s i o n camera and m o n i t o r , so t h a t b r i g h t n e s s and c o n s t r a s t r a d i o c o u l d be e a s i l y a d j u s t e d .  The secondary f l i c k e r i n t r o d u c e d by t h i s  v i e w i n g arrangement i s n e g l i g i b l e  i f the set i s w e l l  w i t h r e g a r d t o s t o r a g e time of v i d i c o n  adjusted  and m o n i t o r , and i f t h e  f l i c k e r i n t r o d u c e d by the chopping wheel i s not i n t h e 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 f r e q u e n c y e f f e c t s - As i t t u r n e d out, the  crit-  i c a l s p a t i a l f r e q u e n c y f l i c k e r was always below 30 per second, and no s t r o b o s c o p i c 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 p r o v i d e d by a Z e i s s  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 a p p r o p r i a t e time.  I t was found t o be n e c e s s a r y t o i l l u m i n a t e the output  plane d u r i n g the time when'the s p a t i a l f r e q u e n c y plane was tially  par-  obscured. The e x p l a n a t i o n f o r t h i s seems t o 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 r e q u e n c i e s , the i m p r e s s i o n of a grey s u r f a c e 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 t o become more and more dominant i n the p e r c e i v e d image.  C u t t i n g out p a r t  of the F o u r i e r t r a n s f o r m plane n a t u r a l l y reduces the t o t a l 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.  inten-  This i s per-  c e i v e d as a change i n the o v e r a l l b r i g h t n e s s of the p i c t u r e , i . e . , a flicker.  U s i n g B i e r n s o n ' 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 e x p l a i n e d by the f a s t  response of the s p a t i a l average feedback, which a l s o  produces  the grey i m p r e s s i o n . The a u x i l i a r y , compensating  l i g h t , superposed d u r i n g the  chopping t i m e , e l i m i n a t e d t h i s e f f e c t , and the eye seemed t o conc e n t r a t e on the l i n e s t r u c t u r e a g a i n , 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 a d j u s t e d  e a s i l y t o the n e c e s s a r y 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 U s i n g the arrangement of F i g u r e 33, a s e r i e s of s u b j e c -  45 t i v e t e s t s was c a r r i e d o u t , w i t h 4 s u b j e c t s , 3 male and 1 f e male; t h e i r ages ranged from 20 t o 28 y e a r s .  The t e s t  persons  were asked t o judge the image c o n s i s t i n g of a v e r t i c a l b a r p a t t e r n (50/50 b l a c k / w h i t e r a t i o ) as "good" and " a c c e p t a b l e " , w h i l e the f l i c k e r r a t e of the e s s e n t i a l f i r s t harmonic f r e q u e n c y plane was v a r i e d .  i n the s p a t i a l  The r e s u l t s of these t e s t s a r e sum-  marized i n the F i g u r e s 34 and 35. The t e s t s were r u n 3 t i m e s , t o check the c o n s i s t e n c y of the judgement.  I t was found t h a t 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 o n l y s l i g h t l y , m o s t l y by no more than -1 c y c l e of flicker  rate.  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 w i t h o u t b r i g h t n e s s  compensation)  4-6 f  c  (Hz  A: B:  Contrast r a t i o Contrast r a t i o  2 :1 2^:1 7  16  -J  F i g . 35  .  .  100  200  50  100  !  C r i t i c a l f l i c k e r frequency of s p a t i a l frequency  (lines/picture 300  width) f  -tar-  150  X  as a f u n c t i o n  f o r judgement "accep-  table" The  c o n t r a s t r a t i o of the l i n e p a t t e r n was  the l i g h t i n t e n s i t i e s  f o r peak w h i t e and peak b l a c k d i r e c t l y  the s c r e e n w i t h a l i g h t meter. r a t i o on the r e s u l t s  a d j u s t e d by measuring  The  on  i n f l u e n c e of the c o n t r a s t  i s made c l e a r by the curves of F i g u r e  36,  which are based on "good" judgements l i k e the curves of F i g u r e ^  A  34  ( H Z )  16  f  f  = v  1  0  = 125  0  lines/mm on r e t i n a  8 Contrast Fig.  36  C r i t i c a l f l i c k e r frequency contrast r a t i o .  vs  ratio  47 The c r i t i c a l f l i c k e r frequency appears t o be a l o g a r i t h m i c f u n c t i o n of the c o n t r a s t r a t i o . frequencies  spatial  a t low c o n t r a s t r a t i o s i s t h e r e 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 b e h a v i o u r . ing  Only f o r h i g h  grey i m p r e s s i o n  This may be due t o t h e dominat-  r e c e i v e d 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 h e l d a t a reduced l e v e l of a p p r o x i m a t e l y 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 t o 700 l u x were t e s t e d , but found t o be of n e g l i g i b l e i n fluence.  A b r i g h t background i n c r e a s e d the c r i t i c a l  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 The i n f l u e n c e of the average b r i g h t n e s s  flicker frequencies.  of the p i c t u r e  was checked over a 9 t o 1 luminance range, from a p p r o x i m a t e l y 40 to 350 cd/m . brightness  The e f f e c t of the c o n t r a s t r a t i o dominates the  e f f e c t by f a r , but i t seems t h a t the c r i t i c a l  flicker  frequency i n c r e a s e s v e r y s l i g h t l y w i t h i n c r e a s i n g b r i g h t n e s s . 2 average s c r e e n luminance of 200 cd/m  An  was used f o r t h e experiments  o f . F i g u r e s 3^ t o 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 a r e a i s shown i n F i g u r e 37; i t i s v e r y small a l s o , and l i e s almost w i t h i n the u n c e r t a i n t y of about -1 Hz b a s i c a l l y i n h e r e n t trend to increased is  c r i t i c a l f l i c k e r frequency  i n the t e s t s .  A  with l a r g e r area  noticeable. A much l a r g e r mumber of t e s t s has t o be c a r r i e d out t o  get more exact r e s u l t s , but t h i s was beyond the scope of t h i s thesis.  Generally,  area, brightness  i t may be s a i d t h a t the e f f e c t s of p i c t u r e  and background a r e only s m a l l and seem t o be  c o n s i s t e n t w i t h r e s u l t s f o r t o t a l r a t h e r than p a r t i a l  flickering  (17) found by F o l e y  , which show b a s i c a l l y l o g a r i t h m i c b e h a v i o u r .  48 f  G  | (Hz)  24  A B C  20 16 12 8  A B C  P i c t u r e a r e a 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 P i g . 37  C r i t i c a l f l i c k e r frequency  (.lines/mm on r e t i n a )  with  p i c t u r e a r e a 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 w i t h the p i c t u r e s of F i g u r e s 38 and quencies.  Here i t was  39,  f l i c k e r i n g the h i g h e r s p a t i a l  not n e c e s s a r y  to r e s t o r e the average b r i g h t -  ness d u r i n g the chopping p e r i o d ; the power of the h i g h frequency ness was  fre-  spatial  components i s v e r y low, and no change i n average b r i g h t observed. The r e s u l t s of these t e s t s are summed up i n F i g u r e  40.  They show, f o r example, t h a t the s e v e r e l y b a n d l i m i t e d p i c t u r e of F i g u r e 41, which r e s o l v e s o n l y 50 l i n e s per p i c t u r e w i d t h , be presented  a l t e r n a t i v e l y w i t h the o r i g i n a l p i c t u r e ( F i g u r e  at a r a t e of 19 Hz, t o g i v e a s u b j e c t i v e l y p e r f e c t image. l e s s b a n d l i m i t a t i o n , the r a t e may  38)  For  be decreased below t h a t v a l u e .  I t can be seen immediately  t h a t t h i s f a c t may  be used  t o save t r a n s m i s s i o n bandwidth i n a t e l e v i s i o n system. however, an obvious l i m i t to the compression t h a t can be t h i s way.  may  There i s , achieved  I t i s g i v e n by the r a t i o of the t o t a l a r e a of F i g u r e  t o the area under the c u r v e s , which comes out to be  40  approximately  F i g . .38  "Pace"  (viewed on TV-monitor)  50  ; H Z )  \  A; B:  241  "Face" ( f i g u r e 38) "Group" ( f i g u r e 39 ( R a t i n g "good")  16*  8h  l i n e s per picture width) 100 50  Fig.  40  300  200 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 picture  (Resolution  l i n e s per p i c t u r e width)  50  51  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  ures 34, 35, and  40 by a m a t h e m a t i c a l e x p r e s s i o n  them i n t o the form of a b a s i c law.  Fig-  i n order to put  I t seems t h a t some k i n d of  an e x p o n e n t i a l f u n c t i o n would d e s c r i b e the b e h a v i o u r of these curves q u i t e w e l l . of e q u a t i o n  t h e r e f o r e t r y an e x p r e s s i o n  =  f o exp(-kf x )  5.1  1  denotes the c r i t i c a l f l i c k e r f r e q u e n c y , f  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 . a t e d , merely t h e o r e t i c a l v a l u e f o r f equal to z e r o . for  the s p a t i a l f  fre-  i s an e x t r a p o l -  at a s p a t i a l f r e q u e n c y  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  v e r y low s p a t i a l f r e q u e n c i e s we  " t o t a l a r e a " f l i c k e r , and difficult  of the form  5.1 fc  f  We may  approach the case of normal  judgements of q u a l i t y are a l s o v e r y  t o make i n t h i s r e g i o n .  The  i n f l u e n c e of some p a r a -  meters changes as w e l l , the c o n t r a s t r a t i o f o r example becomes a measure f o r the average b r i g h t n e s s  too.  I t can be seen, from e x t r a p o l a t i o n of our c u r v e s , f  that  w i l l depend on the c o n t r a s t r a t i o and n a t u r a l l y on the k i n d of  judgement we are w o r k i n g w i t h ("good", " a c c e p t a b l e " ) .  The  factor  k i n the exponent w i l l a l s o be a parameter'depending on the periment.  ex-  I t i s , f o r example, apparent t h a t k w i l l be d i f f e r e n t  for  the l i n e p a t t e r n experiments and  and  i t may  a l s o depend on the c o n t r a s t  The ween 24 and  f o r the p i c t u r e experiments,  a c t u a l experimental 34 Hz.  The  ratio.  values f o r f  factor k lies  g e n e r a l l y l i e bet-  q u i t e c o n s t a n t l y around  0.012  f o r a l l l i n e p a t t e r n experiments,  pictures,  and at 0.02  f o r the  k g e n e r a l l y seems t o i n c r e a s e v e r y s l i g h t l y f o r i n -  creasing contrast r a t i o . For curve A of F i g u r e 35 we get the mathematical p r e s s s i o n of e q u a t i o n f  c  5.2 30 exp(-0.012 f )  Curve B of F i g u r e 40 obeys a law a c c o r d i n g t o e q u a t i o n f  c  ex-  28 exp(-.0.02 f )  5.2  5.3  5.3  F i g s . 42 and  43  View of t e s t apparatus f o r the present work  used  54 6.  CONCLUSIONS AND FUTURE WORK  An o p t i c a l s i g n a l p r o c e s s i n g 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 t h e s p a t i a l frequency domain of an image s i g n a l .  T h i s has been the o b j e c t of the p r e s e n t work,  w i t h s p e c i a l emphasis on image compression  research.  I t i s not  p o s s i b l e a t t h e p r e s e n t time t o i n c o r p o r a t e an o p t i c a l . s y s t e m d i r e c t l y i n a bandwidth compression  scheme; but t h e r e s u l t s of  o p t i c a l s i g n a l p r o c e s s i n g r e s e a r c h can be very u s e f u l f o r study and d e s i g n 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 compress i o n a r e apparent  f o r c e r t a i n t e s t c h a r t s which contain, v e r y d e f -  i n i t e s p a t i a l f r e q u e n c i e s ; t h e l a r g e empty r e g i o n s i n t h e i r tra  spec-  can be o m i t t e d t o a c h i e v e s u b s t a n t i a l s a v i n g s i n bandwidth.  The coarse f i l t e r i n g experiment  i n chapter 4 showed q u i t e 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 r a n g i n g from 2 : 1 t o  8 : 1 depending on t h e p i c t u r e c o m p l e x i t y . The s p e c t r a of continuous tone p i c t u r e s c o u l d not be observed  a c c u r a t e l y enough, because of n o i s e e f f e c t s ; n o t h i n g can  be s a i d about p o s s i b i l i t i e s of bandwidth compression  u s i n g 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' t h e human eye. The o p t i c a l system has been shown t o be a v e r y 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 question, c o n c e r n i n g the v i s u a l p e r c e p t i o n of t h e eye. The r e s u l t s of these experiments,  r e p o r t e d i n chapter 5, a r e v e r y  w i t h r e s p e c t t o compression  possibilities.  promising  The decrease  in crit-  i c a l f l i c k e r f r e q u e n c y ' f o r h i g h s p a t i a l f r e q u e n c i e s 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 p r e s e n t i n g the h i g h  . s p a t i a l frequency content at a reduced t i o n of p i c t u r e s  rate.  55  Some d e t e r i o r a -  of f a s t moving scenes w i l l p r o b a b l y occur, sim-  i l a r t o the e f f e c t s r e p o r t e d f o r a frame r e p e t i t i o n and r e p l e n ishment s y s t e m ^ " ' .  Here these e f f e c t s w i l l be l e s s s e v e r e ,  because the i m p o r t a n t low frequency content i s presented a t 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 p r o c e s s i n g t o the field  of image compression  ting results.  r e s e a r c h has produced  some i n t e r e s -  A number of q u e s t i o n s and problems,  remain and have t o be l e f t f o r f u t u r e work.  however,  still  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 t o 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 t o a n a l y s e s p e c t r a of " c o n t i n u o u s " tone p i c t u r e s , i n which the grey shades are p r o duced by a r e g u l a r l y spaced r a s t e r , thus c o n c e n t r a t i n g the s p a t i a l frequency content a t 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)  F u r t h e r 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  flicker  have t o be c a r r i e d out, u s i n g v a r i a b l e chopping (instead influence  of 50/50 o n / o f f t i m e ) . of such parameters  frequency, intervals  A more d e t a i l e d study of the  as c o n t r a s t ,  p i c t u r e area, b r i g h t -  ness, e t c . i s suggested as w e l l . c)  There are many ways i n which, a compression  system may  be  des-  igned u s i n g v a r i a b l e p r e s e n t a t i o n r a t e 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 . iment, a v e r y s i m p l e system may ferent r e p e t i t i o n rates:  Two  be b u i l t ,  As a f i r s t  exper-  u s i n g o n l y two  dif-  s c a n n i n g s p o t s , 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 c o r r e s p o n d i n g t o  56  a 1 MHz b a n d l i m i t e d  t r a n s m i s s i o n a t normal r e p e t i t i o n r a t e ( 3 0  frames per second),  and one c o n t a i n i n g the s p a t i a l  from 1 t o 5 MHz, but a t h a l f the r e p e t i t i o n r a t e . i t i o n o f the two s i g n a l s a t the r e c e i v i n g  frequencies The superpos-  end c o u l d be a c h i e v e d  o p t i c a l l y by a s u i t a b l e v i e w i n g arrangement.  The compression  r a t i o would o n l y be 1 . 6 7 w i t h t h i s system; h i g h e r r a t i o s a r e obviously possible,  u s i n g more channels,  frame r e p e t i t i o n r a t e s . l i m i t of a p p r o x i m a t e l y plexity.  w i t h more d i f f e r e n t i a t e d  C l o s e r r e a l i z a t i o n of the t h e o r e t i c a l 3 t o 1 i s merely a q u e s t i o n of system com-  57  REFERENCES 1.  P r a t t , W.K., "A B i b l i o g r a p h y on T e l e v i s i o n Bandwidth R e d u c t i o n S t u d i e s " , IEEE Trans, on I n f . Theory,' v o l . IT-13, 1, January 1967.  2.  S c h r e i b e r , W. F., " P i c t u r e Coding", P r o c . IEEE, v o l . 55 3, March 1967.  3.  M e r t z , P., and Gray, F., "A Theory of Scanning and i t s R e l a t i o n to the C h a r a c t e r i s t i c s of the T r a n s m i t t e d S i g n a l i n Telephotography and T e l e v i s i o n " , BSTJ v o l . 13, J u l y 1934.  4.  J a v i d , M., and Brenner, E., "Analysis, Transmission F i l t e r i n g of S i g n a l s " , McGraw H i l l 1963."  5.  Cutrona, L. J . , et a l . , " O p t i c a l Data P r o c e s s i n g and F i l t e r i n g Systems", IRE Trans, on I n f . Theory, v o l IT-6, June I 9 6 0 .  6.  Vander Lugt, A., " S i g n a l d e t e c t i o n by Complex S p a t i a l F i l t e r i n g " , IEEE Trans, on I n f . Theory, v o l . IT-10,  and  1964.  7.  Vand_er Lugt, A. " O p e r a t i o n a l N o t a t i o n f o r the A n a l y s i s And S y n t h e s i s of O p t i c a l Data P r o c e s s i n g Systems". P r o c . IEEE, v o l . 54, 1, Aug. 1966.  8.  Born, M., and Wolf, E., " P r i n c i p l e s of O p t i c s " , Pergamon P r e s s , 2nd e d i t i o n , M a c m i l l a n N.Y. 1964-  9.  Anner, G. E., H a l l , N.Y.  10.  S e i l e r , A. J . , " P r o b a b i l i t y D i s t r i b u t i o n of T e l e v i s i o n Frame D i f f e r e n c e s " , P r o c . TREE A u s t r a l i a , Nov. 1965.  11.  B r a i n a r d , R. C., et a l • , " S u b j e c t i v e 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., " D i r e c t 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 G r a i n i n e s s and G r a n u l a r i t y f o r B l a c k and White Samples w i t h 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.  "Elements of T e l e v i s i o n Systems", P r e n t i c e 1951.  58 15.  B u d r i k i s , Z. L., Seyler, A. L., " D e t a i l P e r c e p t i o n A f t e r Scene Changes i n T e l e v i s i o n Image P r e s e n t a t i o n s " , IEEE Trans, on I n f . Theory, v o l . IT-11, Jan.1965-  16.  B i e r n s c n , G., "A F e e d b a c k - c o n t r o l Model of Human V i s i o n " , Proc. IEEE, v o l . 54, 6, June 1966.  59 APPENDIX F o u r i e r t r a n s f o r m re I at i oil of a coherent  optical  Coherent l i g h t can be t r e a t e d as an wave and  d e s c r i b e d by g i v i n g i t s amplitude  system  electromagnetic  and phase as a f u n c -  t i o n of the t h r e e space v a r i a b l e s . U  x ,y,z  =  I(x,y,z)cos[~cot + 0 ( x , y , z ) ]  A.l  For the f i e l d i n a plane p e r p e n d i c u l a r to the z - a x i s i n an o p t i c a l system, we U  Q  =  can w r i t e  l ( x , y ) c o s [ w t + 0(x,y)]  As a c o n v e n t i o n , t h i s may U  o  =  A.2  a l s o be w r i t t e n i n the form  I(x,y)exp[j0(x,yj] -  A.3  T h i s 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 i n v a r i a n c e of a l l the s i g n i f i c a n t f e a t u r e s of the o p t i c a l system, where CJ (the temporal  r a d i a n frequency  carrier  frequency. Let us now  c o n s i d e r F i g u r e 2 a g a i n (from c h a p t e r  which I s repeated here f o r  Fig. A.l  of the l i g h t ) a c t s i n a sense l i k e a  convenience.  Two-dimensional F o u r i e r t r a n s f o r m e r  2.1),  60 In plane P^ a t r a n s p a r e n c y of the complex t r a n s m i s s i o n f u n c t i o n S(x,y) i s i n t r o d u c e d i n the "beam of coherent monochromatic light. S(x,y) Emerging  =  t(x,y)exp ha(x,y)l  A.4  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 w i t h S(x,y) t\ 1  =  S U  A. 5 o  T h i s wave now i s summed up over P^ onto P^ by focussinglens  .  Calculation  of Uv, r e q u i r e s f i n d i n g the o p t i c a l p a t h  l e n g t h from x^Y-^ "to x^,y^.  Up then i s the i n t e g r a l over P^  of U^, p r o p e r l y d e l a y e d i n phase a c c o r d i n g t o the d i s t a n c e r . .2%T -D-T-  dx^dy^  A. 6  X  =  wavelength of l i g h t  d  =  a m p l i t u d e 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 d i s t a n c e between P-^ and P .  1 -f^cosQ r  =  _  obliquity  d i s t a n c e between  factor x  -j_5 ]_ v  "to X p , y p .  In our system, —• can be dropped  because a b s o l u t e phase  and amplitude a r e 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 0- i s always s u f f i c i e n t l y s m a l l , so t h a t cosO  because  We then get  61  JJ  U^exp  -3—  r(x ,y 1  l f  dx dy  x ,y . 2  1  2  A.7  1  To c a l c u l a t e the d i s t a n c e r , c o n s i d e r F i g u r e A.2  X,  x1 0 x  1  9<  -BH-SJ  P ^  -r-  P' l F i g . A.2  Geometrical r e l a t i o n s  A plane wave emerging from plane P-^ a t an a n g l e 9 t o the o p t i c a l a x i s i s brought t o f o c u s a t x ,' where x 2  i m p l i e s t h a t the o p t i c a l d i s t a n c e between x  = f sin9.  2  This  and any p o i n t on P^  2  i s a c o n s t a n t c. c  =  r-^ +. r  c = g + f  2  =  2  l|g  2  - X COS Q  , 2 \ x 1 + — f 2f 0  29  +  1/2 |f.  2  +  x  A.8  2  f o r s m a l l 9 and x x 2 taking o g  fi  +  A.9  0  The d i s t a n c e from the plane P-^ t o x  2  i s o b t a i n e d by adding  the term X  ] 2 X  A.10  -x^sin.9 = —j— The t o t a l d i s t a n c e from x-^ to x  2  i s then  In two dimensions, the same approach l e a d s t o \ x +y 2  r U j , y , x ,y / = .const. I 1 - ^ 1  2  For the wave IL-, a t P  U exp(-j 1  x  y  n  2  y y. i l l 'f n  A.12  we then get  2  x )exp)-j y _) 1  x x  2  2f  2  ]  d x  d 1  3^  1  exp j (3 ( o ,  OJ  ) A. 13  1  where 2JI;X  x  2rty, oo = - , J y \±  2  '~\f~ '  A.14  and  P = 1  \ 2 2 &\ 2 2 f 2f X  +  y  A.15  For the system of F i g u r e A . l g i s equal t o f , so t h a t (3 = 0.  E q u a t i o n 2.4 i n c h a p t e r 2.1 f o l l o w s immediately.  The  c o n d i t i o n f = g i s n e c e s s a r y t o o b t a i n an exact F o u r i e r t r a n s f o r m between P^ and P  2  i n this  system.  

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