Mach Zehnder

- . .. .. - - 2005 3 ....................................................................................................... 5 ........................................................................................................ 6 ........................................................................ 7 1. ............................... 7 1.1. . ........................... 7 1.2. ................................................ 10 1.3. .. 10 2. -...................................................... 12 2.1. ......................... 12 2.2. ............................................................................................ 15 2.3. .......................................................................... 19 2.4. ................. 22 2.5. .................................................................. 24 2.6. ........................... 26 ......................................................... 27 3. ................................................................................................................... 27 3.1. ......................................................................... 27 3.2. ...................................................... 27 3.3. - ................................ 28 3.4. ................................................................ 30 3.5. ................................. 30 3.6. ........................................................ 32 ................................................... 34 .................................................................................................. 35 4 5 1988 (1940-1996)25. ..- , : ,, -, ,. ,, , ., -, ,, ,,- -, . ,, - - , . ,,. . .., .. ... ..-.., .. 6 . ,, . ,-, , , ., , ,,. . . , , ,, . . -- , . . . 7 1. 1.1. . . . .- () . , (.1) 9x xj = ( ) t r E ,2 [1]. .1. 1E 2E : ; ; , . 8 , 1E 2E . . , , : ( ) ( )2 2 2 1 1 1exp ; exp i a E i a E = = ,(1) a 1 , 2 -. ( ) ( )2 2 1 1 2 1exp exp i a i a E E E + = + = . (2) | | | | { } ) ( exp ) ( exp1 2 1 2 2 12221* + + + = = i i a a a a E E I ,(3) * . X 1E 2E , ) ( cos 2 ) cos( 2 ) (2 1 2 1 1 2 2 1 2 1y I I I I a a I I y I A + + = + + = . (4) 2 1 2 1 max2 I I I I I + + = ,.... 4 , 2 , 0 t t = A(5) 2 1 2 1 min2 I I I I I + = ,.... 5 , 3 , t t t = A (6) m, t2A= m(7) . ,... 2 , 1 , 0 = m , - ,.... , 2 5 , 2 3 , 2 1 = m, 0 2 1I I I = = ,(4) ( ) 2 / cos 4 ) cos 1 ( 220 0 A = A + = I I I 0min = I 0 max4I I = .V.00 = A . o sin y = A ,(8) o - 2E Y X,(. .1). ott sin2 2) ( y y = A = A , (9) 9 -., ,o sin m ym = . A, osin= A. (10) , (.1), .A . . Z ( 0 = o ), A= ,const I = .,A=const, . . V min maxmin maxI II IV+= . (11) , 0 2 1I I I = = ,1 = V . | |((

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\|A+ = A + = y V I y V I y It2cos 1 2 ) ( cos 1 2 ) (0 0, (12) 2 1 02 I I I + =( ) A = A y y t 2 . (. .1) ) , (2) , ( y x y x A = At ,) , ( y x A - , . (12) :((

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\|A A+ = ) , (2cos 1 2 ) , (0y xyV I y x I t.(13) 10 (14), , m y xyt t 2 ) , ( 2 = A A . (14) (14), m,, , . 1.2. , . [1]. (,, , ..). - ( , -, .). ., ,,-, . 1.3. A . ,,. A cos (4), , 2 1I I I + = ., ,, . 11 , v v A . 1 ~ Avt , t -,.., . cl ,, t , vtA=A~ =2cc lc c,(15) v A A- ,- . , , cl < A . . 310 2 ~ A ,20 ~cl , . D -[1]. , ,. , , . . ~310-3. 2 ~aD f 63 . 0 ~ 5 . 1 ~ D . 40 > O. -. . 12 c , . , c . -, () . 2. - 2.1. -(.2). . . . , . .2. -: ; ; 1 2 ; 1 2 ; 1 2 ; W, W1 W2 ; ( ). , , (2.2). 13 W. 1, 2 . 1,21,2 ,W1W2 . , . , 1, 2 o , o . W1, W2, o . ,(10),o sin = A . .,6 . 0 ~ , , , 6 ~ A, o, 310~ A ~ o . . - , , 02 (. 2). -. ,02 . | , 2O . ,, 2,-,, .. ( ) y x, A , , 14 ( ) z y x n , , .( ) y x, A , . .3 , , . ,( ) y x, A , ( )((

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\|+ = A2 20exp , by ax y x ,(16) b a, ,0- . .3. (, ) (, ) : , ; , . ,, ( ) y x, A , .( ) y x, A . 15 ( ) y x, A , , ( ) z y x n , , . 2.2. (13) ( ) ( ) ( ) | | { } y x y V I y x I , cos 1 2 ,0 A + A + = . ( ) y x I , , , . ( ) y x, A ,( ). 0(y) const A = A = , 0 A.( ) y A 0 A , ( ) A + A = A y y t 20,A - , (10). ( ) y x, A, 0 A ., . (14)( ) m y x t 2 ,0 = A + A ,m . , ( ) y x, A .t 2 (.4). , . , t 2 , t . , 1/10 (, )., 5 t ( ) y x, A .10 . 16 10 . xxy2tA +A(0x,y)A0 .4. ( ) y x, A () . ,0 = A 00 = A . mm A , . ( ) y , x A (14), : ( ) ( ) m m y x A + t = A 2 ,.(17) ( ) y x, A ,(13) cos . , ( ) y A . 1, . , ( ) y x, A , (. .5). 17 .5. , , , ( ) y x, A . ( ) y x, A . | Y , ( ) ( ) o = | sin tg , ( ) ( ) o t = A sin 2y y(.6). .6. ( ) y x, A . 18 ( ) y x, A , .( ) y A ,. , ( ) ( ) y y x A + A , t 2 .X - ,( ) y x, A . m m A ( ) y x, A (17), . 7 , ( ) y x, A . .7. : ; ( ) x A , . .7x , ( ) x A .x ,( ) x A . ,( ) 0 = A x . ,,( ) t = A x . ( ) t 2 = A x , -( ) t 5 . 2 ~ A x . , . , 9 , . , ( ) 0 = A x ,10( ) x A . 19 ( ) y x, A , . 2.3. .. . . , , , . ( .) . ,, . . . . . . : )]} , ( cos[ 1 ){ , ( 2 ) , (0 1y x V y x I y x I A + = , (18) )]} , ( ) , ( cos[ 1 ){ , ( 2 ) , (0 2y x y x V y x I y x I A + A + = ,(19) ( ) y x, A , . 20 ( ) y x I , A : | | )2sin( )2sin( 2 2 ) cos( ) cos( ) , ( 2 ) , (0 0 A A+ A = A + A A = A V I V y x I y x I . (20) ( ) y x I , A . , .|.|

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\| A+ A = A2sin2sin 4 ) , (0 V I y x I. (21) ,( ) y x, Ay x, ( ) y x, A . 2 o 1 A ,( ) y x, A . ,( ) 2 sin A + A (21)( ) 2 sin A . ,, ,. (20) S , ( ) y x, A 2,( ) y x, A . )2sin( 2 ) , (0 A>~ A < V I y x I,(22) S dxdyS}}>= < ... ... . , . . , , : tmy x=A2) , ( (23) , 21 ( )21 22) , ( t + =Amy x (24) . (14) ( ) y x, A , ,0 = o . ..8 , . . , . .8 . (, , ) (, ) :, ; , , . . . . 22 ( ) - (CCD-). 2.4. (),,2(..2). W2, W1. ( ) y x, A . , ( ) y x, A | |dz n z y x n y xzz} ~ A210) , , (2) , (t ,(25) ) , , ( z y x n -(x,y,z); 0n ; 1z 2z . (25), . (25) ) , , ( z y x n , , ) , , ( z y x n . , z. -: zy xn y x nAA+ =t 2) , () , (0,(26) z A . ..9 const y = . y ,z . cR -const y = ,x ,r , y=const. .9 , zdz xdx rdr z x r + = + = ,2 2 2. 23 .9. const y = . 0 ~ dx , 2 2x rrdrdz= . dz(25) , | |2 20) , ( 22) , (x rrdrn r y n y xcRx = A} t.(27) n(y,r)(27), y=const . . (27) | |2 20) ( 22) (x rrdrn r n xRx = A} t ,(28) R . (28) [2]. [4], , (28) , () }A= ARxmmmxd nx) (2 2) () ( 4) ( t ,(29) R; m - m- . . 24 2.5. ( ) y x, A (.2.2,.7), (.2.3,23,24)., ,(27) ( ) z y x n , , ( ) ( ) y r n z y x n , , , = .(27) const y = ( ) y r n , .( ) r n (27) (28) .(28), (.10)( ) r n ,, ., ( ) const r n = . (28). ( ). .10. (a) y=const. () ( ) x A , . const y = , , 10 , R- (.10)., 25 ( ) ( ) const n r n r n = = A0.,( ) 0 = > A R r n( ) 0 = > A R r . , , ) ( ) () ( 2 2 2 212 2 2 21 1|.|

\| A =A ~A+} }+ +j m j m mRRjmRRjx R x R R nx rrdrR nx rrdr r nmmmm (30) (28) 10 ( )j jn R n A = A : ...,4) (,4) (,4) (2728 727282729 8282927210 9 72829 8282928210 9 829210 9 9((

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A = AR R n R R R R n R R R R n RR R n R R R R n RR R n Rttt(31) 9n A , 8n A , 7n A , .. (27) (28) , A ,, , . 00 = = x xj 10.- jx ( ) j 10 . 9x xj = 10- (.10).10 R R = A ,R m RmA = ,( ) R m RmA + =+11,R j RjA = (31) ( ) R j m j m n Rj mm jA ((

+ A = A=2 2 2 2101 22) (t . (32) : 26 | |( ) | |( ) ( ) | |., 7 8 7 8 7 9 7 9 7 104) (, 8 9 8 9 8 104) (, 9 104) (2 272 2 2 282 2 2 29 72 282 2 2 29 82 29 9 A + A + A A = A A + A A = A A A = An n n R Rn n R Rn R Rttt (33) , ( ) x A (33), 10( )jR n .2.6. n [5]: TT00 = , (34) 0 -K T0. : constn=1, (35) n K T . (35) (34), ( )TnTn 1 =AA,(36) , .( ) T n A ( ) r T ( ) r n :( ) ( ) r nnTT T r T A= = A0001,(37) 0T 0n- . .11 , . 27 .11. , : I - ; II - ; III - ; IV - 2 ; V- ;VI - . 3. 3.1. ,( ) y x, A , . ( ) z y x n , , , . ( ) z y x T , , . 3.2. -.12. . 28 .12. : 1 - -75 ; 2 ; 3 4 3 4; 5 5 ; 6 6 ; 7 ; 8 ; 9 ( ); 10 - . -12, , 3 4, .550% . , , 6 6, 5. 7 ( ) 9. 109 . 8 - , 8 9. . , .3.3. - , .,, 29 , . . , , . . . 2(.13). .12 1 2 . , , 1 2 . . ,, . . 13. -.1 2 ; 2 ; ; . . . . 30 3.4. . . (.12).8' 9., ., , . ( ) y x, A , , . ,2.22.3, ( ) x A . 3.5. :1 ( ) y x, A - ;2( ) y x, A . (AdobePhotoshop,CorelPhotoPaint), . .Adobe Photoshop., ,, ,. , darken. ,. (.14). ( 31 View/Show/Grid).. Navigator/Info (. 14 ). . 14. () (). .Layers/Channels/PathsAdobePhotoshop . , ., , , , . (.14 ). , (MatLab,MathCad)., .,. , ,, .. , MatLab , MatLab .MathCad 32 ,. . MatLab : % % A=im2double(imread('DSCN1311.JPG'));B=im2double(imread('DSCN1312.JPG')); % % C=abs(A-B); % imwrite(C,'muar.jpg'); % figure; imshow(C); ( ) const y x = A , ,x ,. MatLab,Mathematica,Origin.Origin 9- (AnalysisFit PolinomialOrder9 Ok). Results Log.Rm=mAR,m=1,2,3,,10, ( )mx A . Anm (32)-(33). 3.6. 1.220-75"" . 24 . 2.( ). 3.(.12)7, . 4.. 7 9. 33 5. , , 9.6.: - ; - , ; - . , USB-. 7.:1 ;2- . 8.( ) y x, A . 9. ( ) z y x n , , . r ( ) r n . T ( ) r T . .11. 10. ( ) x A ,( ) r n ( ) r T . 34 1. , n . 2. . 3. . 4., d n ? 5.- . 6. , ?7. . ? 8.,, ? ? 9., ? . 10. ,, . 11. ? 12. ?, -. 35 1. ., . . - .: . 1970. 720 . 2. . . .. , ., ... - .: . 1957. 484 . 3. ..,..,.. . - .: . 1980. 207 . 4. ..,.. .//. 1988, - .64. - .1. - .159-164. 5. .. . - : - -. 1962. 83 . 6. ..,..,,.-.:. 1959. 333 .7. ../...-.: , 1985 - 400 .

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Mach Zehnder