UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Optical signal processing and television bandwidth compression Chu, Thien-Ke 1970

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1970_A7 C48.pdf [ 5.13MB ]
Metadata
JSON: 831-1.0102183.json
JSON-LD: 831-1.0102183-ld.json
RDF/XML (Pretty): 831-1.0102183-rdf.xml
RDF/JSON: 831-1.0102183-rdf.json
Turtle: 831-1.0102183-turtle.txt
N-Triples: 831-1.0102183-rdf-ntriples.txt
Original Record: 831-1.0102183-source.json
Full Text
831-1.0102183-fulltext.txt
Citation
831-1.0102183.ris

Full Text

OPTICAL SIGNAL PROCESSING AND TELEVISION BANDWIDTH COMPRESSION by THIEN-KE CHU B.A.Sc, Univ e r s i t e de Montreal, 1968 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 standard Research Supervisor Members of Committee Acting Head of Department Members of the Department of E l e c t r i c a l Engineering THE UNIVERSITY OF BRITISH COLUMBIA September, .1970 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced d e g r e e at t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by the Head o f my Depar tment o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Depa r tment The U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r 8 , Canada ABSTRACT A t e l e v i s i o n band compression scheme which depends p r i m a r i l y on matching i n one sense the eye's s e n s i t i v i t y to f l i c k e r has been proposed. For a s t a t i c p i c t u r e as the source ma t e r i a l , i t i s found that the compression r a t i o i s not d i r e c t l y l i m i t e d by the f l i c k e r e f f e c t , but the p i c t u r e q u a l i t y assessed s u b j e c t i v e l y , f a l l s quite f a s t as the compression r a t i o i s increased. A compression r a t i o of 1.5:1 i s accompanied by a very small drop i n sub-j e c t i v e q u a l i t y . Using a "high frequency boost" c i r c u i t the compression r a t i o can be increased to 3:1 under conditions of s a t i s f a c t o r y p i c t u r e q u a l i t y . Experiments were performed using as source a movie p i c t u r e , and higher compression r a t i o s than those for the s t a t i c p i c t u r e were i n d i c a t e d . A l l the experiments were performed using a simulated t e l e v i s i o n transmission system. The system was based on a l a s e r source, and i t i s an improvement on a system designed by Otto Meier i n 1968. ( i i ) TABLE OF CONTENTS Page ABSTRACT i i TABLE OF CONTENTS i i i LIST OF ILLUSTRATIONS i v ACKNOWLEDGEMENT v I. INTRODUCTION • 1 I I . BASIC OPTICAL SYSTEM AND CALCULATION 3 2.1 Basic O p t i c a l Elements 3 2.1.1 S p a t i a l Fourier Transform 3 2.1.2 Approximation and Operational Notation of Some Basic Elements 3 2.2 Design of the O p t i c a l System 6 2.3 Frequency and Image-Position Relation 9 I I I . STATIC PICTURE TESTS 10 3.1 Basic Idea 10 3.2 Test Arrangement 11 3.3 Test Results ' 15 3.3.1 Test r e s u l t s 15 3.3.2 Discussion 15 3.4 L i m i t a t i o n of the Experimental System- 19 3.4.1 Noise due to coherent l i g h t source 19 3.4.2 L i m i t a t i o n of fx i n Low Frequency range 22 3.5 Bandwidth Compression Ratio C a l c u l a t i o n s . 24 3.6 P i c t u r e Quality Studies 25 3.6.1 P o t e n t i a l Compression r a t i o 25 3.6.2 Test r e s u l t s showing degradation vs. C 26 3.6.3 Discussion 26 3.7 High Frequency Boost 27 IV. MOTION PICTURE TESTS 34 4.1 Analysis of Motion Picture Projector Mechanism 34 4.2 Test Results and Discussion '35 V. CONCLUSIONS 38 REFERENCES.. 40 APPENDIX A - l 41 APPENDIX A-2 • 42 LIST OF ILLUSTRATIONS Figure Page 2-.1 (a) Lines test pattern; (b) Two-dimensional Fourier transform of (a); (c) One-dimensional Fourier Trans-form of (a) 4 2.2 (a) Half-tone p i c t u r e ; (b) One-dimensional Fourier Transform of (a) 4 2.3 L i g h t wave and f i l m ; (a) O p t i c a l system; (b) Block diagram 3 2.4 Spherical lens; (a) O p t i c a l system; (b) Block d i a -gram 5 2.5 Free Space; (a) O p t i c a l system; (b) Block diagram... 6 2.6 The O p t i c a l System Experimented 7 2.7 Image-Position Relation i n Fourier Transform Plane; (a) Enlarged photo of a test pattern; (b) one-dimen-s i o n a l F.T. of (a) shows a l i n e a r dependence of fx with respect to x 9 3.1 Test arrangement 13 3.2 Test apparatus 14 3.3 O p t i c a l System set up 14 3.4 Test pattern No. 1 16 3.5 C r i t i c a l frequency as a function of l i m i t fx of t e s t pattern No. 1 16 3.6 Test pattern No. 2 . 17 3.7 C r i t i c a l frequency as a function of l i m i t fx of t e s t pattern No. 2 17 3.8 Test pattern No. 3 . 18 3.9 C r i t i c a l frequency as a function of l i m i t fx of test pattern No . 3 18 (iv) Figure Page 3.10 (a) T h e o r e t i c a l i n t e n s i t y d i s t r i b u t i o n i n the coherent and incoherent image of a bar test ( a f t e r Skinner [10]) (b) Photograph from T.V. monitor 21 3.11 "Contour noise" e f f e c t s on a half-tone picture due to coherent i l l u m i n a t i o n 21 3.12 (a) Output of a bar test pattern from T.V. monitor fx = fm; (b) S p a t i a l one-dimensional Fourier transform of (a); (c) Fringes due to l i m i t a t i o n of bandwidth fx < 20 lines/p.w 23 3.13 Results of p i c t u r e - q u a l i t y - t e s t s 27 3.14 P i c t u r e q u a l i t y vs. compression r a t i o 28 3.15 O r i g i n a l p i c t u r e 29 3.16 Output p i c t u r e corresponds to double-sideband trans-mission; fx = fm 29 3.17 Output p i c t u r e corresponds to single-sideband trans-mission fx = fm 29 3.18 Same as 3.16 except fx = 1/2 fm... 29 3.19 Results of "the high frequency boost" 31 3.20 Curves p i c t u r e - q u a l i t y vs. compression r a t i o showing ef f e c t s of the "high frequency boost" 31 3.21 E f f e c t of the "high frequency boost"; (a) Normal s i n g l e sideband p i c t u r e ; (b), ( c ) , (d) Compressed p i c t u r e s , R= 4, without high frequency boost; (e), ( f ) , (g) Compres-sed pictui'es, R=4 , with high frequency boost 32 4.1 Moving-object f i l m p r o j e c t i o n ; (a) f i l m ; (b) sequence of f i l m presentation vs. time 34 4.2 Sequence of a s t i l l - o b j e c t - f i l m presentation 35 4.3 Set up for motion-picture projector simulation 36 4.4 C r i t i c a l f l i c k e r i n g frequency as a function of upper l i m i t s p a t i a l frequency fx, for test pattern No. 1, F i g . 3.4, using the apparatus i l l u s t r a t e d i n F i g . 4.3 36 Figure Page A.2.1 One-dimensional Fourier transform System; (a) Opt-i c a l system; (b) Block diagram 42 Table 1 8 (vi) ACKNOWLEDGEMENT I am deeply indebted to my supervisor, Dr. M.P. Beddoes for more than j u s t h i s advice and encouragement. I am g r a t e f u l to Dr. B.P. Hildebrand for reading the manuscript. I am thankful to Dr. E.V. Bohn f o r g i v i n g the very accurate motor; Mr. W. Walters and Mr. Chris S h e f f i e l d f o r t h e i r help i n s e l e c t i n g the accessories; Mr. C.G. Chubb and Derek Daines f o r b u i l d i n g the equip-ment; Mr. Herb Black f o r valuable photographic work. I express my sincere appreciation to Miss Veronica Komczynski for typing the manuscript; Mr. G.J. F i t z p a t r i c k and Mr. J . Bennett for proofreading. F i n a l l y I also wish to express my thanks to the National Research Council of Canada f o r f i n a n c i a l assistance. ( v i i ) 1 I. INTRODUCTION Numerous pub l i c a t i o n s and references [1] - [5], [11] deal with the t e l e v i s i o n bandwidth compression problem. The need f o r v i s u a l com-munication i s increased every day and a plethora of devices have been proposed i n this f i e l d . An example i s the v i s u a l telephone. I t i s said [4] that the sending of banking messages and the exchanging of t e c h n i c a l drawing messages w i l l only be possible i f a new t e l e v i s i o n system using r e l a t i v e l y narrow bandwidth can be made a v a i l a b l e . Compression techniques have been c l a s s i f i e d [5] into three d i f -ferent categories: pure s t a t i s t i c a l , psychophysical and a combination of the two. An example of the pure s t a t i s t i c a l approach i s the work done by C o l i n Cherry et a l . [4]. They pioneered a run-length-coding method and compression r a t i o s of up to 3.5:1 for a h a l f tone p i c t u r e have been obtained. Very elaborate work has been done by Schreiber's group [3] i n which the combination approach has been used. They took advantage of the fac t that the eye i s very s e n s i t i v e to the detection of edges and they proposed a system c a l l e d "Synthetic Highs". Experiments were c a r r i e d out by computer-simulation and e f f i c i e n t coding and quantizing methods were inves t i g a t e d . The re s u l t s were good, as shown by high compression r a t i o s of 5 or 6 to 1 for a h a l f tone p i c t u r e [5]. In comparison with b u i l d i n g e l e c t r o n i c equipment, computer-simulation has many advantages. However, computer simulation cannot be used for r e a l time studies because i t takes many seconds to generate a s i n g l e p i c t u r e frame, and i t i s v i r t u a l l y impossible to study the r e a l t e l e v i s i o n s i t u a t i o n which involves motion p i c t u r e s . An experimental system based on a coherent l i g h t source for processing v i s u a l signals has the remarkable property that i t i s very f a s t . 2 Real time studies can be undertaken and these can include the motion p i c t u r e problem. This analog system has noise problems but these can be tolerated by the eye and f i l t e r i n g i s easy to r e a l i z e . In p a r t i c u l a r we have used such an o p t i c a l system to perform the Fourier and the inverse transform; we could therefore study bandwidth compression under conditions which approach the p r a c t i c a l case very c l o s e l y . A s t a r t to the work reported here was made i n 1968 by Otto Meier [1], [2]. In h i s work a s e r i e s of high q u a l i t y and low q u a l i t y versions of the same pi c t u r e were presented a l t e r n a t e l y f o r equal i n t e r v a l s of time, T, on a t e l e v i s i o n monitor and a viewer was asked to state i f he could see any f l i c k e r i n g i n the display. Meier showed that the eye i s s e n s i t i v e to f l i c k e r frequency by very d i f f e r e n t amounts according to the highest s p a t i a l frequency present i n the pi c t u r e . With a view to obtaining reduction i n channel bandwidth, i t seemed natural to suggest that the t e l e v i s i o n p i c t u r e source encoder could be designed to match more c l o s e l y the f l i c k e r s e n s i t i v i t y of the eye. Although one can p r e d i c t that up to 2:1 compression should be possible from Meier's r e s u l t s , he did not explore higher p o t e n t i a l compression r a t i o s . In the present work the apparatus used by Meier has been improved, so that higher q u a l i t y r e s o l u t i o n was obtained. This enables us to explore furth e r the proposed compression scheme. The absence of f l i c k e r i s only one c r i t e r i o n that the compression scheme must meet. One might ask how much the subjective impression of p i c t u r e q u a l i t y f a l l s as the compression r a t i o , C, i s increased. A further series of tests were made using a se r i e s of graded photographs i n which a subject was asked to p a i r p i c t u r e s having s i m i l a r subjective p i c t u r e q u a l i t y . Using t h i s technique, i t was found that the p i c t u r e q u a l i t y f a l l s quite fast as C i s increased, but a "high frequency boost" c i r c u i t o f f s e t s to a c e r t a i n degree this decline. 3 I I . BASIC OPTICAL SYSTEM AND CALCULATION Meier's o p t i c a l processing system used a l a s e r , three lenses and a closed c i r c u i t t e l e v i s i o n camera-monitor dis p l a y . A s o l u t i o n to the problem of plac i n g the lenses was ar r i v e d at using t r i a l and error techniques. An adequate theory to give the po s i t i o n s of the lenses and the stop s i z e s was not a v a i l a b l e . This d e f i c i e n c y i s supplied by. the theory part given i n this chapter which i s based on Vander Lugt's notation [6]. 2.1 Basic O p t i c a l Elements 2.1.1 S p a t i a l Fourier Transform A s p a t i a l Fourier transform of a pattern i s an array of points whose p o s i t i o n corresponds to frequency, and brightness corresponds to amplitude. F i g . 2.1 shows a simple t e s t pattern and i t s one- and two-dimensional Fourier transform. F i g . 2.2 shows a half-tone p i c t u r e and i t s Fourier transform. 2.1.2 Approximation and Operational Notation of Some Basic Elements (a) l i g h t wave and f i l m l i g h t wave: A(x,y) = |A(x,y) |exp[j(j)(x,y) ] f i l m : f(x,y) = |f(x,y)|exp[j£(x,y)] A(x,y) f(x,y) (a) f(x,y) A(x,y) f(x,y) A(x,y) A(x,y) f(x,y) (b) F i g . 2.3 Light Wave and Film (a) O p t i c a l System • (b) Block Diagram Illlllllll (a) F i g . 2.1 (a) L i n e s test pattern (b) Two-dimensional Fourier transform of (a) I I I t t ' l (c) ( c ) One-dimensional F o u r i e r transform of (a) n i i 1 (a) F i g . 2.2 (a) Half-tone p i c t u r e (b) One-dimensional Fourier transform of (a) 5 follows: w i l l be: (b) Spherical lens 1 I f F = Focal length; f =—;- and a function I/J i s defined as r ijj(x,y;f) = exp [j — (x + y ) ] Then the approximation and notation of a s p h e r i c a l lens if<x,y;f) = e x P [ - j ^ ^ + y 2 ) 1 i ( x,y;f) f(x,y) exp [ ] f(x,y) f ( x , y ) ^ ( x , y ; f ) f ( x , y ) 2 2 exp[-j ^ r ( x + y ) ] (b) (a) F i g . 2.4 Spherical Lens (a) O p t i c a l System (b) Block diagram (c) C y l i n d r i c a l lens t|i(x;f) - exp[-j -^T x ] k 2 ^ ( y ; f ) - exp[-j j^- y ] (d) free space D = distance between two planes 1 d = D approximation of free space w i l l be: ! T e x p [J 2D = 1 k 2 2 d -ijj(x,y;d) - — exp [j — (x + y )] 6 f(x,y) g(u,v) di^(x,y ;d) f(x,y) g(u,v) (a) (b) F i g . 2.5 Free space (a) O p t i c a l System (b) Block Diagram 2.2 Design of the O p t i c a l System The system using o p t i c a l f i l t e r i n g techniques f o r th i s work con-s i s t s of three parts (Figure 2.6). The f i r s t part displays a Fourier transform F(u,v) of a s p a t i a l pattern f ( x , y ) , i n plane P^- The second part i s a f i l t e r H(u,v)-a side band stop and a chopping wheel-in plane P^-The l a s t part gives the inverse Fourier transform of the product F(u,v)• H(u,v). Such a system i s described by Vander Lugt [6] as a Variable-Scale C o r r e l a t o r . i n s e r t e d i n t h e i r appropriate places to obtain a "one-dimensional" Fourier transform and reconstruction. To s i m p l i f y the c a l c u l a t i o n , we assume that L., = 0; L. = 0. i 4 Such an approximation i s very reasonable because of two reasons: 1. A l l lenses are weak, that means: F 1,F„,F ,L ,L_,L C,L >>> , L 1 2 j z j 5 6 1 2. The lenses are not perfect; a f t e r some accurate c a l c u l a t i o n f i n e adjustment by t r i a l and error should be made. The set up i n t h i s lab. i s a 1:1 symmetrical system. The sym-met r i c a l system i s simpler than one with a scale change. Meier [2] remarks that i t i s p r a c t i c a l l y impossible to a l i g n the asymmetrical system. The necessary modification i s made, two c y l i n d r i c a l lenses are 7 Fourier Transform Section Inverse Transform Section S p a t i a l F i l t e r F i g . 2.6 The O p t i c a l System Experimented F^: Laser beam expander F^: C y L i n d r i c a l lens F^: Spherical lens : Input plane Fourier Transform plane P : Output plane To a t t a i n the one to one symmetrical set up the separations i n F i g . 2.6 should s a t i s f y the following e q u a l i t i e s . L 3 = L 5 (2.1) L 2 + L 3 = L 5 + L 6 = 2F 3 (2.2) If a two dimensional s p a t i a l coordinate test pattern function f(x,y) i s placed i n plane P^, the l i g h t d i s t r i b u t i o n i n plane P 2 then w i l l be given by equation 2.3. F(u,v) = C - ^ ( u , v ; l 3 ) / / f ( x > y ) ^ ( x , y ; l 2 - f 1 ) P l 1 I 2 . [x + —— u; 1 2 ' 1 2 + 1 3 h i 2 • [y + J " v ; 1 ] dxdy 2 1, + l ^ - f 9 (2.3) 8 To obtain the Fourier transform along the h o r i z o n t a l axis and image along the v e r t i c a l axis i n the plane P^, the conditions f o r setting lenses are as follows: Imaging condition on v e r t i c a l axis X2 — - (2.4) 1 + 1 - f 2 3 2 or ( 2 - 5 > \ L3 2 Fourier transform condition 17 ~ f-r - = 0 (2.6) 1 + 1 2 3 or ^ - 4 + 1.3 (2.7) The proof of equations 2.3, 2.5, and 2.7 w i l l be found i n Appendix A-2. The lenses used here have the following characters. Laser beam expander F^ = 4 meters Spherical lens F^ = 2 meters C y l i n d r i c a l lenses F^ = 0.8 meter In s o l v i n g equations 2.5, 2.7, 2.1 and 2.2 the a x i a l p o s i t i o n s of lenses are obtained as i n Table 1. TABLE 1 Th e o r e t i c a l Experimental Err o r L 2 2.895m 2.90 0.2% L6 2.895m 2.91 0.5% L 3 1.105m 1.1 0.5% L 5 1.105m 1.09 1.4% The close correspondence between experimental and th e o r e t i c a l values i n Table 1 indicates that the f i r s t order theory used i n this the-o r e t i c a l treatment i s quite adequate. 2.3 Frequency and Image-Position Relation In t his one to one system a 16 mm width picture i n the input plane w i l l correspond to a 16 mm width p i c t u r e i n the output plane which i s received by a v i d i c o n . The f i n e s t r e s o l u t i o n can be resolved by the vi d i c o n i s 250 l i n e s / p i c t u r e width, i n this case 250 lines/16 mm. To r e l a t e the p o s i t i o n of image points i n the F.T plane to frequency, f^, i n lines/p.w. i n the input and the output planes a simple test pattern was used. The distance from the f i r s t to second maxima was measured and i t i s proportional to the number of lines/p.w. i n the input and the output p i c t u r e s . The c a l i b r a t i o n i s shown i n F i g . 2.7 and i t demonstrates that f »x - a l i n e a r dependence -. x (a) (b) 1/4" :50 1/p.w. 3/16":37.5 1/p.w. 1/8" :25 1/p.w. 1/16":12.5 1/p.w. Fig. 2.7 Image-Position Relation in Fourier Transform Plane (a) enlarged photo of a test pattern (b) one dimensional F.T of (a) shows a l i n e a r dependence of fx with respect'to x 10 I I I . STATIC PICTURE TESTS In t h i s chapter a b r i e f d e s c r i p t i o n of test procedure, apparatus and r e s u l t s are given. I t contains r e s u l t s of f l i c k e r experiments i n which the high q u a l i t y p i c t u r e i s presented f o r a period T and the low q u a l i t y p i c t u r e for T and i t i s shown that the sensation of f l i c k e r i s T L l a r g e l y independent of . This suggests that large compression r a t i o s T H might be p o s s i b l e . The subjective evaluation of compressed pictures was also measured and r e l a t e d to band-reduced but otherwise normal t e l e v i s i o n p i c t u r e s . I t i s shown that p i c t u r e q u a l i t y f a l l s r a p i d l y as the compression r a t i o i s increased but i t i s also shown that a high frequency boost c i r c u i t arrests to a c e r t a i n l i m i t t his d e t e r i o r a t i o n . 3.1 Basic Idea The compression scheme considered here presents a s e r i e s of high q u a l i t y and low q u a l i t y versions of the same p i c t u r e . The high q u a l i t y p i c t u r e contains dc up to a highest s p a t i a l frequency fm. The low q u a l i t y p i c t u r e contains dc up to a s p a t i a l frequency fx. The d i f f e r e n c e between the two sets of p i c t u r e s i s due to the s p a t i a l frequency components l y i n g between fx and fm and i t w i l l be shown that the eye needs to have these components replenished at a low rate. Thus the basic idea i s to produce such pic t u r e s by a two-velocity-scanning system and t h i s w i l l r e s u l t i n a reduction i n the channel bandwidth. The experiments reported were performed using the analog apparatus described i n the next s e c t i o n . Define: T : period i n which low q u a l i t y video s i g n a l i s sent T : period i n which high q u a l i t y video s i g n a l i s sent 11 fm: highest s p a t i a l frequency i n high q u a l i t y p i c t u r e ( l i n e s / p i c t u r e width) fx: highest s p a t i a l frequency i n low q u a l i t y p i c t u r e ( l i n e s / p i c t u r e width) f: frame r e p e t i t i o n frequency F: . the bandwidth needed to pass the high q u a l i t y p i c t u r e ( i n Hz) F^: the bandwidth of the compressed system S: dimension proportional constant (lines/p.w. and Hz) I f i _ _ P (3-D H F = S • 60•fm v = s-f.f R f x + £ m ] R 1 + R F^ = F- J L . [ 1 + R ' £ x / f m ] (3.2) R 60 1 + R The experiments obtained the l i m i t fc<_f/(l+R) f o r which the f l i c k e r e f f e c t i s j u s t not noticeable under a number of conditions. f<? = f(R, fx, Contrast, Brightness) (3.3) 1 1 f G = f + T = T (1+R) (3.4) H L H V ^ For a fixed value T , f c = F(R) = F(fx) H or R = F(fx) = F(fc) (3.5) Thus (3.5) and(3.2) can be solved to obtain the compressed bandwidth. 3.2 Test Arrangement D i f f e r e n t pictures were put i n the plane of F i g . 2.6 as test patterns, A mask i s placed at the Fourier transform plane P^ to remove a 12 h a l f of the s p a t i a l frequencies of a symmetrical spectrum. The t o t a l information to be reconstructed now corresponds to a s i n g l e sideband of a t e l e v i s i o n transmission system. A chopping wheel with v a r i a b l e OFF:ON r a t i o , R, was used to cut a l l s p a t i a l frequencies above a c e r t a i n l i m i t fx temporarily at a v a r i a b l e r e p e t i t i o n rate f . The high q u a l i t y p i c t u r e corresponds to the "ON" part; P the low q u a l i t y p i c t u r e corresponds to the "OFF" part. The output p i c t u r e at the plane P^ was received d i r e c t l y by a v i d i c o n (T.V. camera without lenses) and appeared on a T.V. monitor. An experiment was started by s e t t i n g fx to a chosen value and ro t a t i n g the wheel, Figure 3.1. At f i r s t when the chopping wheel rotated slowly the f l i c k e r e f f e c t x^ as very pronounced and e a s i l y observed by a subject who was at 1.5 m from the monitor. The wheel v e l o c i t y was then increased to a point where the subject f e l t that no f l i c k e r i n g e f f e c t appeared. The value of r e p e t i t i o n rate at this point was recorded as fc ( c r i t i c a l f l i c k e r i n g frequency). Constrast r a t i o and brightness can be adjusted e a s i l y on the monitor to give a pleasing p i c t u r e and "maximum d e t a i l s " . F i g . 3.2 and 3.3 show the apparatus set up. P 3 2 40 Laser and Pin-hole Beam expander Test pattern A WJ Spherical lens 0 c y l i n d r i c a l lens . . Sideband chopping T.V. camera c y l i n d r i c a l without lenses lens wheel s top 1.1m l . l r 4m tm -4L viewing distance 1.5m T.V. monitor F i g . 3.1 Test arrangement Beam expander telescope adjusted to F=4m Input plane; Test pattern: 16 mm width s l i d e C y l i n d r i c a l lenses; F=0.8m Fourier transform plane; chopping wheel and sideband stop Spherical lens; F=2m Output plane; T.V. camera without lenses r-U F i g . 3.2 Test Apparatus (a) Laser and beam expander (b) Test p a t t e r n (c) O p t i c a l System (d) Monitor F i g . 3 . 3 O p t i c a l System Set up (a)-(e) C y l i n d r i c a l lenses F2 (b) Chopping wheel (c) Sideband stop (d) S p h e r i c a l lens 15 3.3 Test Results 3.3.1 Test Results Using d i f f e r e n t test patterns and d i f f e r e n t OFF:ON r a t i o R = 1, 2, 3, r e s u l t s were obtained and they are reported on the following pages. To check the consistency of the r e s u l t s , three sets of tests were c a r r i e d out at d i f f e r e n t times at l e a s t one day apart. It i s shown that the experimental points varied s l i g h t l y f o r one subject but more noticeably from one subject to another. Only the upper bound or the worse cases are presented and used f o r compression r a t i o c a l c u l a t i o n s . 3.3.2 Discussion The r e s u l t s of these tests show that fc i s l a r g e l y independent of 0FF:0N r a t i o R. The only changing f a c t o r when R i s changed, i s the q u a l i t y of the output p i c t u r e ; this point w i l l be considered more c a r e f u l l y l a t e r . The experimental points v a r i e d widely from one test p i c t u r e to the other; that means fc i s strongly dependent upon p i c t u r e content. Contrast r a t i o and brightness, as reported i n Meier's thesis [2], have l i t t l e i n fluence on f c . The mask used to suppress one sideband produced deleterious e f f e c t s which are i l l u s t r a t e d i n the next s e c t i o n . I t must be pointed out that with normal t e l e v i s i o n transmission the f i l t e r s which eliminate one side-band are designed to alternate at 6 db/oct on the s k i r t s . The e f f e c t s of overshoot which we experienced are much exaggerated because we used a " b r i c k w a l l " f i l t e r . The problem was mitigated by placing the stop s l i g h t l y o f f center. Computations of fx take this into account. F i g . 3.4 T e s t P a t t e r n No. 1 F i g . 3.5 C r i t i c a l f r e q u e n c y as a f u n c t i o n o f l i m i t f x o f t e s t p a t t e r n No. 1 17 Fig. 3.7 C r i t i c a l frequency as a function of l i m i t fx of test pattern No. 2 F i g . 3.8 Test Pattern No. 3 0 50 100 150 200 250 F i g . 3-9 C r i t i c a l frequency as a f u n c t i o n of l i m i t fx of t e s t p a t t e r n No. 3 19 "Over a l l " f l i c k e r i n g always occurred when fx was lower than 25 lines/p.w. The value of fc at fx = 0 i s j u s t a mathematical extrapol-at i o n . The o v e r a l l f l i c k e r i n g e f f e c t i s due to d i f f r a c t i o n phenomena and w i l l be ref e r r e d to when we discuss the l i m i t a t i o n s of the system. The expression f c = fo exp [-kfx] used to approximate the Meier's r e s u l t s i s once again found to f i t the experimental points. Values of fo i n the actual tests varied from 35 to 40 Hz. The fa c t o r k l i e s between 0.005 to 0.01; f c i s i n Hertz ..;and fx i s i n l i n e s / p i c t u r e width. For the test pattern i n F i g . 3.4, f c - 35 exp (-0.0056 f x ) ; i n F i g . 3.6, f c = 35 exp (-0.0055 f x ) ; i n F i g . 3.8, f c = 40 exp (-0.0095 f x ) . 3.4 L i m i t a t i o n of the Experimental System 3.4.1 Noise due to coherent l i g h t source [10] Let g(x,t) be the complex amplitude of an o p t i c a l f i e l d . The instantaneous i n t e n s i t y I(x,t) i s given by: I(x,t) = g(x,t)- g*(x,t) (3.6) where g*(x,t) denotes the complex conjugate. As an image i s a combination of weighted and displaced d e l t a functions, we f i r s t examine the r e s u l t s of a two-point-source a d d i t i o n . If g(x,t) = g x ( x , t ) + g 2(x,t) (3.7) Then I(x,t) = g(x,t)•g*(x,t) g 1 ( x , t ) ^ g 1 * ( x , t ) + g 2(x,t)«g 2*(x,t) ,(x, (3.8) + g ( x , t ) . g 2 * ( x , t ) + g * ( x , t ) . g 2 , t ) The time average i s : ,. . . l i m 1 r^ I(x) = J I ( x , t ) d t (3.9) T -*- <*> 2T Incoherent a d d i t i o n In the incoherent case g^(x,t) and g 2(x,t) both vary randomly with time and also vary randomly with respect to each other. li m 1 r T , . ., . ,^  lim 1 fT . . . . . , _ J g (x,t)-g * ( x , t ) d t = J g * ( x , t ) - g (x,t)dt=0 X _ * o = 2T -T T —«> 2T ~ T (3.10) I(x) = I 1 ( x ) + I 2 ( x ) (3.11) i n general for n points n I (x) = E I.(x) (3.12) n i = 1 i Coherent a d d i t i o n For coherent l i g h t : g(x,t) = g l ( x , t ) + g 2(x,t) = § 1 ( x ) £ j 2 7 f V t + g 2 ( x ) e j 2 7 T V t (3.13) where Then or g i ( x ) - A l ( x ) e ^ l ^ g 2(x) = A 2(x)e j (f'2( x) ( 3. 1 5) I(x) = |A 1(x)I 2 + |A 2(x)I 2 4- A 1 ( x ) . A 2 ( x ) { e J [ ^ ( x ) - ( J , 2 ( - ) 3 + J[<|>2(x)-<|>1(x)] , (3.16) I(x) = | g l ( x ) + g 2 ( x ) | 2 (3.17) In general: I (x) = | I g . ( x ) I 2 (3.18) n i = l 1 21 (a) (b) Fig. 3.10 (a) Theoretical intensity d i s t r i b u t i o n i n the coherent and incoherent image of a bar test (after Skinner [10]) (b) Photograph from T.V. monitor Fig. 3.11 "Contour noise" effects on a half-tone picture due to coherent illumination 22 The e f f e c t of these c r o s s - c o r r e l a t i o n terms i n case of a bar test pattern i s shown t h e o r e t i c a l l y and experimentally i n F i g . 3.10. F i g . 3.11 shows th i s e f f e c t on a h a l f tone p i c t u r e . The fringes due to coherent i l l u m i n a t i o n are the main contributors to. the f l i c k e r i n g . e f f e c t for high values of fx. F l i c k e r was perceived by the v a r i a t i o n i n i n t e n s i t y of f r i n g e l i n e s rather than the v a r i a t i o n of edges i n the p i c t u r e . 3.4.2 L i m i t a t i o n of fx i n low frequency range As mentioned e a r l i e r , when the chopping wheel went too close to the sideband stop, (fx <25 lines/p.w.) the f l i c k e r i n g of the t o t a l area occurred. This f a c t can be explained by examining the Fourier trans-form of a bar test pattern. F i g . 3.12(b) shows the i n t e n s i t y d i s t r i b u t i o n i n Fourier transform plane of a bar t e s t pattern. The width L of the 0 ^ order d i f f r a c t i o n pattern varies depending upon the s i z e W of the bar t e s t . In F i g . 3.12 L — 30. l i n e s when W — 1/18 of p i c t u r e width. If the wheel i s i n the p o s i t i o n shown i n F i g . 3.12(b) then the output l i g h t from plane P ( F i g . 2.6) w i l l act l i k e a s i n g l e s l i t l i g h t source. Reconstruction lenses w i l l produce a s e r i e s of fringes i n output plane Pg. These fringes are the cause of o v e r a l l f l i c k e r i n g and are shown i n F i g . 3.12(c). (c) Fig. 3.12 (a) Output of a bar test pattern from T . V . monitor fx = fm (b) Spatial one-dimensional Fourier transform of (a) (c) Fringes due to limitation of bandwidth fx<20 lines/p.w., output from T . V . monitor ro U> 24 3.5 Bandwidth Compression Ratio Calculations For r e a l i z i n g the t e l e v i s i o n system we propose a method using two scanning v e l o c i t i e s , a slow one for high q u a l i t y pictures and a f a s t one for band l i m i t e d p i c t u r e s . Equation 3.2 can be used to c a l c u l a t e the compression r a t i o C, f o r such a system. F = F — [ 1 + R f x / f m ] R 60 1 + R C - f - -f°-[ 1 + R ] (3.19) R 1 + Rfx/fm In the l i m i t case f = (1 + R)fc <_ 60 • 60 1 C = — [ ] (3.20) fc If we f i x I = second H 60 1 + Rfx/fm then f c - - ^ _ (3.21) 1 + R for each value of R, f c can be calcu l a t e d , arid the corresponding l i m i t f can be found i n the curves f c vs. l i m i t fx. Example: c a l c u l a t i n g the maximum compression r a t i o for te s t pattern No. 2, F i g . 3.6. 1. R = 1 60 f c = = 30 1 + R f i g . 3.7 gives fx — 30 lines/p.w. x 25 2. R = 4 60 fc = — = 12 1 + R f i g . 3.7 gives fx — 180 lines/p.w. 12 1 1 + 4 x 180/250J I t i s i n t e r e s t i n g to note that the compression r a t i o i n t h i s case goes down when the 0FF:0N •ratio i s increased. The upper l i m i t of 1.8 f o r compression i s disappointing but this i s predicated on the method of keeping T equal to a whole frame period. This w i l l not allow us to compress by a large amount. Other questions are: What i s the r e s u l t i n g p i c t u r e i f we send only one part of the high q u a l i t y p i c t u r e instead of a whole frame? How does the degradation change with respect to the compression ratio? The work following provides answers to these questions. 3.6 P i c t u r e Quality Studies 3.6.1 P o t e n t i a l compression r a t i o High q u a l i t y p i c t u r e period i n t h i s case i s : 1 TH = d + R ) f c * 6 0 The compressed bandwidth then i s : 60 F R = s--o+l)fT- f c [ R f x + f m ] F = S ' 6 ° • [Rfx.+ fm] (3.22) R (1+R) The compression r a t i o w i l l be: F S•60•fm C FR S.60 (1+R) [Rfx + fm] C = - 1 + R (3.23) 1 + Rfx/fm 26 C tends to (1 + R) when fx goes to zero. The r e l a t i o n between- compression r a t i o and q u a l i t y of the r e s u l t i n g p i c t u r e w i l l be found i n the next s e c t i o n . 3.6.2 Test r e s u l t s showing degradation vs. C In order to gain high compression r a t i o s we must take advantage of the eye, by sending f c sets of f r a c t i o n - of -picture-frames instead of fc sets of whole frames. However f o r C large the d i f f e r e n c e i n q u a l i t y i s pronounced and noticeable. In this section the r e l a t i o n between compression r a t i o and p i c t u r e q u a l i t y i s reported. To perform the test two s e r i e s of pictures were taken. One of them i s a s e r i e s of bandlimited but otherwise normal p i c t u r e s ; the others are p i c t u r e s obtained by varying 0FF:0N r a t i o R and f c . The assumption i s made that the p i c t u r e seen by the camera and by the eye are the same. In order to check the assumption, a long exposure time was set, and a p r i n t e d p i c t u r e obtained; t h i s was compared with respect to c e r t a i n c r i t i c a l d e t a i l , with the same p i c t u r e at a back of an unloaded camera. A close s i m i l a r i t y was established. The subjects were asked to match the compressed pictures to band-l i m i t e d p i c t u r e s . The q u a l i t y of the p i c t u r e was divided according to the • highest frequency contained i n the bandlimited p i c t u r e s . Two c r i t e r i a were used to judge the p i c t u r e q u a l i t y i n this t e s t . (1) D e t a i l s of the p i c t u r e ; this i s r e l a t e d to high frequency range. (2) O v e r a l l pleasantness of the p i c t u r e ; this seems to be r e l a t e d to low frequencies range and the noise. The r e s u l t s are summarized i n F i g . 3.13. 27 50 100 150 200 250 F i g . 3.13 Results of p i c t u r e - q u a l i t y - t e s t s A. Band l i m i t e d pictures B. Compressed p i c t u r e s ; R=l C. Compressed pictures; R= 4 Applying equation 3.23 to the experimental points of F i g . 3.13 we obtain the compression r a t i o s for d i f f e r e n t r e s u l t i n g output p i c t u r e s . The r e s u l t s are presented i n F i g . 3.14; picture q u a l i t y vs. compression ratio.. 3.6.3 Discussion Before discussing the r e s u l t s of t h i s t e s t , a few things r e l a t e d to the p i c t u r e q u a l i t y should be.mentioned. From F i g . 3.15' to 3.18 we see that the q u a l i t y of the p i c t u r e s decreases•noticeably. F i g . 3.16, 3.17 and 3.18 have the same bandwidth but d i f f e r e n t output fronv the Fourier transform plane. F i g . 3.16 corresponds to a double sideband modulation i n plan P with fx = fm; the q u a l i t y of 28 F i g . 3.14 P i c t u r e q u a l i t y vs. compression r a t i o A. band l i m i t e d pictures B. compressed pictures R=l C. compressed pictures R=4 Fig. 3.15 Original picture Fig. 3.17 Output picture corresponds to single sideband trans-mission fx = fm Output picture corresponds to double-sideband transmission; fx = fm Same as 3.16 except fx • 1/2 fm 30 t h i s - p i c t u r e i s obviously superior to the remaining two. F i g . 3.17 cor-responds to a s i n g l e sideband modulation. F i g . 3.18 i s the same as F i g . 3.16 except that fx fin/2. Although figures 3.17 and 3.18 correspond to the same bandwidth i n plane T ^  but F i g . 3.18 looks more pleasing than 3.17 i n s p i t e of the fac t that 3.17 contains higher frequencies and more d e t a i l s can be observed. The noise i n F i g . 3.17 due to the b r i c k w a l l stop, mentioned i n se c t i o n 3.3.2, i s another f a c t o r c o n t r i b u t i n g to low q u a l i However, s i n g l e sideband simulation should be used to avoid the complexity of two synchronous chopping wheels for. stopping the high s p a t i a l frequencies of both sides of the spectrum. I t also corresponds to the p r a c t i c a l case. From F i g . 3.14 we see that for a compression r a t i o smaller than 1.6 the system with 0FF:0N r a t i o R=l gives a higher output p i c t u r e q u a l i t y . With the same compression r a t i o , say C = 1.5, F i g . 3.14 shows that f o r R = 1 the degradation of the p i c t u r e i s about 10%, f o r R = 4 about 13%, whichmeans with this system we gain about 25% equivalent p i c t u r e q u a l i t y over the bandlimited p i c t u r e with the same bandwidth. For a higher compres-sion r a t i o , a higher value of R i s necessary but the q u a l i t y of the pi c t u r e decreases f a s t e r as fx i s lowered and the advantage over the bandlimited system i s very small. This point leads us to the suggestion of attempting to restore the q u a l i t y of the pi c t u r e by boosting the high frequencies. 3.7 High Frequency Boost We can boost the high frequencies to increase the q u a l i t y of the pi c t u r e . The high frequency boost i s a high pass f i l t e r which cuts, down one part of the low frequency range up to about .75 MHz. The r e s u l t s using the high frequency boost are shown i n F i g . 3.19, 3.20 and 3.21. i>2 C •H >^ 4-1 •H rH CO (U U 3 4-) u •rl 100% 31 A. Band l i m i t e d p i c t u r e s Compressed p i c t u r e s ; R=l C. Compressed p i c t u r e s ; R=4 D. Compressed p i c t u r e s ; R=4 using high frequency boost F i g . 3.19 Results of "the high frequency boost" c •H r^ 4-) •H rH crj CT 0) 4-> O •H 100% 80 60 = 40 -20 A. Band l i m i t e d p i c t u r e s B. Compressed p i c t u r e s ; R=l C. Compressed p i c t u r e s ; R=4 D. Compressed p i c t u r e s ; R<=4 using high frequency boost compression r a t i o 1 1.5 2.5 3. F i g . 3.20 Curves p i c t u r e - q u a l i t y vs. compression r a t i o showing e f f e c t s of the "high frequency boost" 3.21 E f f e c t o f t h e " h i g h - f r e q u e n c y b o o s t " (a) n o r m a l s i n g l e s i d e b a n d p i c t u r e (b) , ( c ) , ( d ) c o m p r e s s e d p i c t u r e s , R=4, w i t h o u t h i g h f r e q u e n c y b o o s t ( e ) , ( f ) , ( g ) c o m p r e s s e d p i c t u r e s , R=4, w i t h h i g h f r e q u e n c y b o o s t 33 For C > 2 F i g . 3.20 shows that the p i c t u r e q u a l i t y increases about 20% when using the high frequency boost with respect to the ordinary compressed p i c t u r e . Better r e s u l t s s t i l l can be expected because of the l i m i t a t i o n i n t h i s experiment that the h.f. boost i s an R.C f i l t e r whereas a b r i c k w a l l f i l t e r has been used to l i m i t the q u a l i t y of the low q u a l i t y p i c t u r e s . The two f i l t e r s should, i d e a l l y , have s i m i l a r slopes on t h e i r attenuation s k i r t s . 34 IV. MOTION PICTURE TEST I t i s p l a u s i b l e to expect that motion picture reproduction w i l l enhance some defect i n a compression scheme. The purpose of t h i s chapter i s to describe experiments used to i n v e s t i g a t e this problem. I t i s shown, perhaps s u r p r i s i n g l y , that a moving p i c t u r e can be compressed by a larger amount than a s t a t i c one before d e t e r i o r a t i o n becomes noticeable. In place of a test pattern, a p r o j e c t o r with 16 mm f i l m i s used. The projector speed i s adjusted to match the T.V. camera i n the sense of avoiding stroboscopic e f f e c t s . D i f f e r e n t types of f i l m were used for t e s t i n g the f l i c k e r i n g e f f e c t . I t i s found that: (1) No f l i c k e r i n g could be perceived when fx > 125 lines/p.w. and the f l i c k e r e f f e c t was very weak. (2) The q u a l i t y of the p i c t u r e i n the f i l m i s generally low because of a long exposure time that i s employed i n the movie camera. (3) The most noticeable f l i c k e r was produced using a f i l m of a s t i l l object and t h i s case w i l l be discussed l a t e r . 4.1 Analysis of Motion P i c t u r e Projector Mechanism In order to convey the i l l u s i o n of motion a number of frames, 16 to 24, are projected per second. To eliminate the "smear" e f f e c t between two frames a chopping wheel i s used to cut-of f the l i g h t source when frame changes occur. The sequence of f i l m presentation i s i l l u s t r a t e d schematically i n F i g . 4.1 (a) (b) 1 2 3 4 5 6 7 1 m 1 m 2 2 J L T T, T„ T 0 T. T c 1' T_ Time o 1 .2 3 4 5 6 7 F i g . 4.1 Moving-object f i l m p r o j e c t i o n (a) f i l m ^ }-\ ^ o o n 11 o -n r- <ti r\ -f- f i 1 m -r\t-eio*r»T-iT-'3f--i/-v •n i to f- t m ^ 35 From T to the wheel covers the l i g h t source and the frame o 1 changing occurs. From to the p i c t u r e i s displayed, and so on. If a s t i l l object was filmed the projected image vs. time follows the sequence i l l u s t r a t e d i n F i g . 4 .2 t I • L To T l T 2 T 3 T 4 T 5 T 6 T 7 F i g . 4 .2 Sequence of a s t i l l - o b j e c t - f i l m presentation Thus a s t a t i c p i c t u r e test and a second chopping wheel i n plane P^  w i l l simulate the moving-picture version of a s t i l l object. The arrangement of apparatus to perform t h i s test i s shown i n F i g . 4 . 3 . The speed of the motor d r i v i n g the chopping wheel can be adjusted to minimize the stroboscopic e f f e c t . 4.2 Test Results and Discussion The same test pattern as F i g . 3.4 was used and the r e s u l t s are presented i n F i g . 4 . 4 . The experimental evidence given i n the graph of F i g . 4 .4 for a simulated moving p i c t u r e should be compared with the graph for the same s t a t i c p i c t u r e . Contrary to expectation, the s t a t i c p i c t u r e presentation i s more c r i t i c a l than the moving p i c t u r e presentation. The action of the p i c t u r e chopping wheel ( F i g . 4 .3) seems to make the eye le s s s e n s i t i v e to f l i c k e r from the chopping wheel i n the Fourier transform plane. Thus we 36 Fig. 4.3 Set up for motion-picture projector simulation 40 r 0 50 100 150 200 250 Fig. 4.4 Critical flickering frequency as a function of upper limit spatial frequency fx, for test pat-tern No. 1, Fig. 3.4, using the apparatus i l lus-trated in Fig. 4.3 37 can expect more bandwidth compression using a "moving p i c t u r e " than a s t a t i c p i c t u r e . Small scratches and the s l i g h t side way movement i n the projector give tremendous changes of the spectrum i n Fourier transform plane, and the reconstruction s u f f e r s i n consequence from pronounced "noise" e f f e c t s . The same f i l m used with an incandescent i l l u m i n a t o r and a normal p r o j e c t o r produced only s l i g h t noise e f f e c t s . Good r e s u l t s were obtained using the la s e r source only with nearly new f i l m . 38 V. CONCLUSIONS A scheme for T.V. band compression i s described. I t i s based on . the eye's s e n s i t i v i t y to f l i c k e r i n a sense which i s explored i n the t h e s i s . The method i s supported by psychophysical experiments using a simulated version of the t e l e v i s i o n system. In Chapter I I , an adequate theory has been used to check the design of the simulated t e l e v i s i o n system. In t h i s s e c t i o n the " l i n e a r i t y " of frequency with p o s i t i o n i n the Fourier transform plane i s established. The major findings of the thesis are contained i n Chapter I I I . There i t i s shown that the s e n s i t i v i t y of the eye to f l i c k e r , f c , i s i n -dependent of the OFF to ON r a t i o and t h i s rather s u r p r i s i n g r e s u l t would lead one to expect unlimited compression r a t i o i f the c r i t e r i a were based s o l e l y on the absence of f l i c k e r . Experimentally the maximum compression r a t i o investigated was 2.75:1; at this r a t i o , however, the reduction of " p i c t u r e q u a l i t y " was c l e a r l y marked. A high frequency boost was proposed and i t i s shown that this i s e f f e c t i v e to a considerable degree i n a r r e s t i n g the f a l l o f f i n q u a l i t y with increase of C. In order to measure pi c t u r e q u a l i t y , a comparison technique was proposed i n which a- compressed p i c t u r e was "matched" to a normally scanned band-limited p i c t u r e . The r e s u l t s using this technique are contained i n the important graphs, F i g . 3.20. It i s shown i n Chapter IV that the motion-picture case i s le s s c r i t i c a l than the s t a t i c p i c t ure case and that one can expect more bandwidth reduction for the moving pi c t u r e transmission than for the s t a t i c p i c t u r e one. Some disadvantages remain i n the simulation system: (1) Noise due to coherent l i g h t source. "Contour noise" makes the c r i t i c a l f l i c k e r frequency higher than i t should be. 39 (2) The b r i c k wall f i l t e r used i n the Fourier transform plane did not match the R-C high frequency-boost c i r c u i t . Some improvement might be expected i f such a match was made. The band compression scheme proposed here depends upon the prop-e r t i e s of the eye. I t seems reasonable to suggest, for further work, that i t be used along with a purely s t a t i s t i c a l encoder such as the run-length encoder of Cherry et a l . AO REFERENCES 1. M. P. Beddoes and Otto Meier, " F l i c k e r E f f e c t and T e l e v i s i o n Compression", IEEE Transactions on Information Theory, volume IT16, No. 2, pp. 214-218, March, 1970. 2. Otto Meier, -"Television P i c t u r e Transmission and O p t i c a l Signal Processing", M.A.Sc. Thesis, Dept. of E l e c t r i c a l Engineering, U.B.C., July,' 1968. 3. T. S. Huang and 0. J. Tretia k , "Research i n P i c t u r e Processing", O p t i c a l and E l e c t r o - O p t i c a l Information, MIT press, 1965; pp. 45-57. 4. C o l i n Cherry et a l . , "An Experimental Study of the Possible Bandwidth Compression of V i s u a l Image Signals", Proceedings of the IEEE, v o l . 51, No. 11; pp. 1506-1517, November, 1963. 5. W. F. Schreiber, "Picture Coding", Proceedings of the IEEE, v o l . 55, No. 3, pp. 320-330, March, 1967. 6. A. Vander Lugt, "Operational Notation f o r the Analysis and Synthesis of O p t i c a l Data-Processing Systems", Proceedings of the IEEE, v o l . 54, No. 8, pp. 1055-1063, August, 1966. 7 . J. W. Goodman, "Introduction to Fourier Optics", McGraw-Hill, 1968. 8. Anthanasios Papoulis, "System and Transforms with Applications i n Optics", McGraw-Hill, 1968. 9. M. Abramowitz and I. A. Stegun, "Handbook of Mathematical Functions", New York:Dover, 1964; p. 304. 10. Brian J. Thompson and John B. Develis, "Introduction to Coherent Optics and Holography", Paper 680012 presented at SAE Automotive Engineering Congress, Detr o i t , January 1968. 11. P r a t t , W. K., "A Bibliography on T e l e v i s i o n Bandwidth Reduction Studies", IEEE Transactions on Information Theory, v o l . IT-13,- No. 1, pp. 114-115, January, 1967. 41 APPENDIX A - l Properties of Function \p For the convenience of the reader some properties of i|i functions from Vander Lugt's paper [6] are given here. D e f i n i t i o n of function . kf 2 2 ifi(x,y;f) = exp[j — — (x + y )] The properties of function: P-i K x , y ; f ) = Mx,y;-f) P - i i ^(-x,-y;f) = ij;(x,y;f) . P - i i i ^ ( x , y ; f 1 ) ip ( x , y ; f 2 ) = t ( x , y ; ^.4- f ) P-iv i^(x,y;f ) f ( x , y ; f 2 ) = ijj(x,y;f 1 - f 2 ) ijj (x,y; f 2 - f ) 2 P-v ^(cx,cy;f) = if)(x,y; c f) P-vi ^ ( x ; f 1 ) ^ ( x , y ; f 2 ) = Tj>(y ;f 2> ^ ( x ; ^ + f 2 ) P - v i i ^ ( y ; f x ) ^ (x,y ; f 2 ) = ^ ( x ; f 2 ) K y ; ^ + f 2> P - v i i i ip(x-u,y-v; f) = i|j(x,y;f) IJJ (u,v;f) exp[-jkf(ux I- vy)] p-ix if<(x,y;f) = K x . f ) * (y;f) P-x l i m ij>(x,y;d) = 1 d — - 0 P-xi lim diKx,y;d) = 6(x,y) d — 0 0 42 A-2 Proof of Equations 2.3, 2.5, 2.7 The o p t i c a l system and block diagram to obtain Fourier transform i n plane P^ i s shown i n F i g . A.2.1. f ( x , y ) i> ( x , y ; f i ) ( s ; f 2 ) 1 2 ^ C^,y ; 1 2 ) | — — p . F(u,v) (a) l 3 ^ ( r , s ; 1 3 ) 'F(u.v) (b) F i g . A.2.1 One-dimensional Fourier Transform O p t i c a l Sys tem (a) O p t i c a l System (b) Block diagram From the block diagram we get F(u,v) = 1 2 1 3 // If ^ ( x , y ; f 1 ) f ( x , y ) ^ ( x , y ; l 2 ) ^ ( r , s ; l 2 ) P P 1 1 e x p [ - j k l 2 ( r x + sy) ] \p (s ; f 2)\p ( r , s ; 1 ) I K U . V ; ! ) e x p [ - j k l (ur + vs)] dxdy drds (A.2.1) Af t e r using P - i i i F(u,v) becomes F(u,v) l 2 l 3 ^ ( u , v ; l 3 ) // ff ^ ( x , y ; l 2 - f 1 ) f ( . x , y ) ^ ( r , s ; l 2 + l 3 ) P l P l i K s ; f 2 ) e x p [ - j k l 2 ( r x + sy) ] e x p [ - j k l 3 ( u r + vs)] dxdy drds (A.2.2) 43 Using P-vi f(u,v) = l„l^(u,v;l. // // * ( x , y ; l - f ) f (x,yH (r; 1 + 1 ) 2 3 3 p, p , 2 i 2 3 1 1 i K s ; l 2 + l 3 - f 2 > e x P [ " J k l 2 r ( x + — u) ] 12 X 3 ex p [ - j k l s(y + v)] dxdy drds \ From Handbook of Mathematical Functions, M. Abramowitz and I. A. Stegun [9], we have the r e l a t i o n (A.2.4) CO Q JJ ij;(x,y;f 1) exp [-jkf 2 (rx + sy) ] dxdy = — $ (r, s ; f 2 / f ±) (A.2.4) Using r e l a t i o n A.2.4 to carry out r,s i n t e g r a t i o n - h A F(u,v) = C-<Ku,v;l.) // ^ ( x , y ; l - f ) f(x,y)i^[x + — - u; ] P z 1 x2 1 + 1 1 ? 2 3 1 1 >My +~r v ; — ] dxdy (A.2.5) ? 1 +1 - f 2.3 2 This i s equation 2.3. i n Chapter I I . Imaging condition To perform the imaging system we use property P-xi to get the p o s i t i o n of lenses. By property P-xi, 2 2 1 _ 1 1 1 2 .<Hy+ — v; ] = <5(y +—2-v) (A.2.6) 1 2 + 1 3 " f 2 H 1 2 + 1 3 - f 2 h A.2.6 w i l l be s a t i s f i e d when ,2 12 -* co or 1 2 + 1 = f 2 V V f 2 1 . 1 1 (A.2.7) L 2 L 3 F This i s equation 5 i n Chapter II. 44 Fourier transform condition Applied equation A.2.6 i n A.2.5 and using the s i f t i n g property of the 6 function, we have: F(u,v) = C - K u , v ; l 3 ) . i K - p - v ; W * ( x ' 1 2 ~ f l ) f ( x ) ~ i v ) •2 ^2 - h Z I | J [ X + - r — u ; -j T — i — ^ d x 2 2 3 Using property P - v i i i and c o l l e c t i n g terms, we have: F(u,v) = C- ( u ; l 3 ) [ ( v ; l 3 + ( 1 ^ ) - i - ] / f ( x , - - — - v ) [ x ; l - f l- ] 1 + 1 2 3 exp[-jk( ^ - L - ) x v ] dx (A. 2. 9) 1 2 + 1 3 A.2.9 has almost a Fourier transform form. We w i l l use P-x to make the \p function i n s i d e the i n t e g r a l be equal to unity. Thus by P-x 2 1 - f — = 0 (A.2.10) 1+1 2 3 or L 2 + L 3 = F x (A.2.11) This i s equation 2.7 i n Chapter II and F(u,v) now i s : X3 X 3 V 3 F(u,v) = C - i K u , l 3 H [ v ; l 3 + ( 1 2 - f 1 ) ~f~ 1 / f ( x , - - I i - v ) e x p [ - j k ( T ~ | - ) x v ] dx (A.2.12) This equation shows that i n plane P 2 we obtain a one-dimensional Fourier transform F(u,v) of f ( x , y ) . 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0102183/manifest

Comment

Related Items