Abstract

Over the years extensive studies have been carried out to apply coherent optics methods in real-time communications and image transmission. This is especially true when a large amount of information needs to be processed, e.g., in high-resolution imaging. The recent progress in data-processing networks and communication systems has considerably increased the capacity of information exchange. However, the transmitted data can be intercepted by nonauthorized people. This explains why considerable effort is being devoted at the current time to data encryption and secure transmission. In addition, only a small part of the overall information is really useful for many applications. Consequently, applications can tolerate information compression that requires important processing when the transmission bit rate is taken into account. To enable efficient and secure information exchange, it is often necessary to reduce the amount of transmitted information. In this context, much work has been undertaken using the principle of coherent optics filtering for selecting relevant information and encrypting it. Compression and encryption operations are often carried out separately, although they are strongly related and can influence each other. Optical processing methodologies, based on filtering, are described that are applicable to transmission and/or data storage. Finally, the advantages and limitations of a set of optical compression and encryption methods are discussed.

© 2009 Optical Society of America

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A. Alkholidi, A. Cottour, A. Alfalou, H. Hamam, and G. Keryer, “Real-time optical 2D wavelet transform based on the JPEG2000 standards,” Eur. Phys. J. Appl. Phys. 44, 261–272 (2008).
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D. Amaya, M. Tebaldi, R. Torroba, and N. Bolognini, “Digital color encryption using a multi-wavelength approach and a joint transform correlator,” J. Opt. A Pure Appl. Opt. 10, 104031–104035 (2008).
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M. Joshi, Chandrashakher K. Singh, “Color image encryption and decryption for twin images in fractional Fourier domain,” Opt. Commun. 281, 5713–5720 (2008).
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M. Nazrul Islam and M. S. Alam, “Optical security system employing shifted phase-encoded joint transform correlation,” Opt. Commun. 281, 248–254 (2008).
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A. Loussert, A. Alfalou, R. El Sawda, and A. Alkholidi, “Enhanced system for image’s compression and encryption by addition of biometric characteristics,” Int. J. Software Eng. Its Appl. 2, 111–118 (2008).

2007 (19)

E. Darakis, T. J. Naughton, and J. J. Soraghan, “Compression defects in different reconstructions from phase-shifting digital holographic data,” Appl. Opt. 46, 4579–4586 (2007).
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R. Tao, Y. Xin, and Y. Yang, “Double image encryption based on random phase encoding in the fractional Fourier domain,” Opt. Express 15, 16067–16079 (2007).
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D. S. Monaghan, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Key-space analysis of double random phase encryption technique,” Appl. Opt. 46, 6641–6647 (2007).
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S. Yuan, X. Zhou, D.-H. Li, and D.-F. Zhou, “Simultaneous transmission for an encrypted image and a double random-phase encryption key,” Appl. Opt. 46, 3747–3753 (2007).
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X. Wang and Y. Chen, “Securing information using digital optics,” J. Opt. A Pure Appl. Opt. 9, 152–155 (2007).
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M. Ragulskis, A. Aleksa, and L. Saunoriene, “Improved algorithm for image encryption based on stochastic geometric moiré and its application,” Opt. Commun. 273, 370–378 (2007).
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J. F. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiple-encoding retrieval for optical security,” Opt. Commun. 276, 231–236 (2007).
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M. Joshia, Chandrashakherb K. Singh, “Color image encryption and decryption using fractional Fourier transform,” Opt. Commun. 279, 34–42 (2007).

Z. Liu and S. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275, 324–329 (2007).
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A. Alfalou and A. Mansour, “All-optical video-image encryption with enforced security level using independent component analysis,” J. Opt. A Pure Appl. Opt. 9, 787–796 (2007).
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Y. Frauel, A. Castro, T. J. Naughton, and B. Javidi, “Resistance of the double random phase encryption against various attacks,” Opt. Express 15, 10253–10265 (2007).
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Z. Liu and S. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275, 324–329 (2007).
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A. Alkholidi, A. Alfalou, and H. Hamam, “A new approach for optical colored image compression using the JPEG standards,” Signal Process. 87, 569–583 (2007).
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B. Tavakoli, M. Daneshpanah, B. Javidi, and E. Watson, “Performance of 3D integral imaging with position uncertainty,” Opt. Express 15, 11889–11902 (2007).
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S. Soualmi, A. Alfalou, and H. Hamam, “Optical image compression based on segmentation of the Fourier plane: new approaches and critical analysis,” J. Opt. A Pure Appl. Opt. 9, 73–80 (2007).
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M. Kessels, M. El Bouz-Alfalou, R. Pagan, and K. Heggarty, “Versatile stepper based maskless microlithography using a liquid crystal display for direct-write of binary and multi-level microstructures,” J. Micro/Nanolith. MEMS MOEMS 6 (2007).
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M. Madec, W. Uhring, J. B Fasquel, P. Joffre, and Y. Hervé, “Compatibility of temporal multiplexed spatial light modulator with optical image processing,” Opt. Commun. 275, 27–37 (2007).
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E. Darakis and J. J. Soraghan, “Reconstruction domain compression of phase-shifting digital holograms,” Appl. Opt. 46, 351–356 (2007).
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2006 (17)

E. Darakis and J. J. Soraghan, “Compression of interference patterns with application to phase-shifting digital holography,” Appl. Opt. 45, 2437–2443 (2006).
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A. E. Shortt, T. J. Naughton, and B. Javidi, “Compression of digital holograms of three-dimensional objects using wavelets,” Opt. Express 14, 2625–2630 (2006).
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E. Darakis and J. J. Soraghan, “Compression of phase-shifting digital holography interference patterns,” Proc. SPIE 6187, 61870Y (2006).
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B. Culshaw, A. G. Mignani, H. Bartelt, and L. R. Jaroszewicz, “Implementation of high-speed imaging polarimeter using a liquid crystal ferroelectric modulator,” Proc. SPIE 6189, 618912 (2006).
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J. F. Barrera, R. Henao, M. Tebaldi, N. Bolognini, and R. Torroba, “Multiplexing encrypted data by using polarized light,” Opt. Commun. 260, 109–112 (2006).
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J. F. Barrera, R. Henao, M. Tebaldi, N. Bolognini, and R. Torroba, “Multiple image encryption using an aperture-modulated optical system,” Opt. Commun. 261, 29–33 (2006).
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L. Chen and D. Zhao, “Optical color image encryption by wavelength multiplexing and lensless Fresnel transform holograms,” Opt. Express 14, 8552–8560 (2006).
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J. F. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiplexing encrypted data by using polarized light,” Opt. Commun. 260, 109–112 (2006).
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U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Polarization encoding and multiplexing of two-dimensional signals: application to image encryption,” Appl. Opt. 45, 5693–5700 (2006).
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U. Gopinathan, D. S. Monaghan, T. J. Naughton, and J. T. Sheridan, “A known-plaintext heuristic attack on the Fourier plane encryption algorithm,” Opt. Express 14, 3181–3186 (2006).
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2005 (13)

G. A. Mills and I. Yamaguchi, “Effects of quantization in phase-shifting digital holography,” Appl. Opt. 44, 1216–1225 (2005).
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D. Abookasis, O. Montal, O. Abramson, and J. Rosen, “Watermarks encrypted in a concealogram and deciphered by a modified joint-transform correlator,” Appl. Opt. 44, 3019–3023 (2005).
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H. T. Chang and C. L. Tsan, “Image watermarking by use of digital holography embedded in the discrete-cosine-transform domain,” Appl. Opt. 44, 6211–6219 (2005).
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M. R. Haider, M. Nazrul Islam, M. S. Alam, and J. F. Khan, “Shifted phase-encoded fringe-adjusted joint transform correlation for multiple target detection,” Opt. Commun. 248, 69–88 (2005).
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A. Carnicer, M. Montes-Usategui, S. Arcos, and I. Juvells, “Vulnerability to chosen-cyphertext attacks of optical encryption schemes based on double random phase keys,” Opt. Lett. 30, 1644–1646 (2005).
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M. Z. He, L. Z. Cai, Q. Liu, X. C. Wang, and X. F. Meng, “Multiple image encryption and watermarking by random phase matching,” Opt. Commun. 247, 29–37 (2005).
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X. F. Meng, L. Z. Cai, M. Z. He, G. Y. Dong, and X. X. Shen, “Cross-talk-free double-image encryption and watermarking with amplitude-phase separate modulations,” J. Opt. A Pure Appl. Opt. 7, 624–631 (2005).
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S. L. Wijaya, M. Savvides, and B. V. K. Vijaya Kumar, “Illumination-tolerant face verification of low-bit-rate JPEG2000 wavelet images with advanced correlation filters for handheld devices,” Appl. Opt. 44, 655–665 (2005).
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A. Alfalou and A. Alkholidi, “Implementation of an all-optical image compression architecture based on Fourier transform which will be the core principle in the realisation of DCT,” Proc. SPIE 5823, 183–190 (2005).
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A. Alfalou, M. Elbouz, and H. Hamam, “Segmented phase-only filter binarized with a new error diffusion approach,” J. Opt. A Pure Appl. Opt. 7, 183–191 (2005).
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J. C. Dagher, M. W. Marcellin, and M. A. Neifeld, “Efficient storage and transmission of ladar imagery,” Appl. Opt. 42, 7023–7035 (2003).
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T. J. Naughton, J. B. McDonald, and B. Javidi, “Efficient compression of Fresnel fields for Internet transmission of three-dimensional images,” Appl. Opt. 42, 4758–4764 (2003).
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T. Nomura, S. Mikan, Y. Morimoto, and B. Javidi, “Secure optical data storage with random phase key codes by use of a configuration of a joint transform correlator,” Appl. Opt. 42, 1508–1514 (2003).
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B. M. Hennelly and J. T. Sheridan, “Image encryption techniques based on fractional Fourier transform,” Proc. SPIE 5202, 76–87 (2003).
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A. R. Alsamman and M. S. Alam, “Face recognition through pose estimation and fringe-adjusted joint transform correlation,” Opt. Eng. 42, 560–567 (2003).
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B. Hennelly and J. T. Sheridan, “Optical image encryption by random shifting in fractional Fourier domains,” Opt. Lett. 28, 269–271 (2003).
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L. Ding, Y. Yan, Q. Xue, and G. Jin, “Wavelet packet compression for volume holographic image recognition,” Opt. Commun. 216, 105–113 (2003).
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T. J. Naughton, John B. McDonald, and B. Javidi, “Efficient compression of Fresnel fields for Internet transmission of three-dimensional images,” Appl. Opt. 42, 4758–4764 (2003).
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D. Abookasis, O. Arazi, J. Rosen, and B. Javidi, “Security optical systems based on a joint transform correlator with significant output images,” Opt. Eng. 40, 1584–1589 (2001).
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Y. Frauel, E. Tajahuerce, M. A. Castro, and B. Javidi, “Distortion-tolerant three-dimensional object recognition with digital holography,” Appl. Opt. 40, 3887–3893 (2001).
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S. Coomber, C. Cameron, J. Hughes, D. Sheerin, C. Slinger, M. A. G. Smith, and M. Stanley, “Optically addressed spatial light modulators for replaying computer-generated holograms,” Proc. SPIE 4457, 9–19 (2001).
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G. Unnikrishnan and K. Singh, “Optical encryption using quadratic phase systems,” Opt. Commun. 193, 51–67 (2001).
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Y. Guo, Q. Huang, J. Du, and Y. Zhang, “Decomposition storage of information based on computer-generated hologram interference and its application in optical image encryption,” Appl. Opt. 40, 2860–2863 (2001).
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B. Javidi and N. Takanori, “Securing information by use of digital holography,” Opt. Lett. 25, 28–30 (2000).
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E. Tajahuerce and B. Javidi, “Encrypting three-dimensional information with digital holography,” Appl. Opt. 39, 6595–6601 (2000).
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G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption. by double-random phase encoding in the fractional Fourier domain,” Opt. Lett. 25, 887–889 (2000).
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J. M. Kilpatrick, A. J. Moore, J. S. Barton, J. D. C. Jones, M. Reeves, and C. Buckberry, “Measurement of complex surface deformation by high-speed dynamic phase-stepped digital speckle pattern interferometry,” Opt. Lett. 25, 1068–1070 (2000).
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T. E. Carlsson and A. Wei, “Phase evaluation of speckle patterns during continuous deformation by use of phase-shifting speckle interferometry,” Appl. Opt. 39, 2628–2637 (2000).
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B. Javidi and E. Tajahuerce, “Three-dimensional object recognition by use of digital holography,” Opt. Lett. 25, 610–612 (2000).
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T. Nomura and B. Javidi, “Optical encryption using a joint transform correlator architecture,” Opt. Eng. 39, 2031–2035 (2000).
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A. Bilgin, G. Zweig, and M. W. Marcellin, “Three-dimensional image compression with integer wavelet transforms,” Appl. Opt. 39, 1799–1814 (2000).
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Y. Li, K. Kreske, and J. Rosen, “Security and encryption optical systems based on a correlator with significant output images,” Appl. Opt. 39, 5295–5301 (2000).
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Figures (24)

Fig. 1
Fig. 1

Principle of the all-optical filtering 4 f setup. The 4 f setup is an optical system composed of two convergent lenses. The 2D object O is illuminated by a monochromatic wave. A first lens performs the Fourier transform FT of the input object O in its image focal plane, S O . In this focal plane, a specific filter H is positioned. Next, a second convergent lens performs the inverse Fourier transform ( FT 1 ) in the output plane of the system to get the filtered image O .

Fig. 2
Fig. 2

Setup for digital recording of the PSI hologram [31].

Fig. 3
Fig. 3

Synoptic diagrams [39]: (a) 3D object recording in compressed hologram form (transmitter), (b) decompression and reconstructing the 3D object (receiver). PSI, image capture and interferometry stage; DP, digital propagation (reconstruction) stage; ⊗, normalized cross-correlation operation.

Fig. 4
Fig. 4

Nonlinear JTC principle setup: (a) synoptic diagram, (b) write-in setup, (c) read-out setup.

Fig. 5
Fig. 5

Synoptic diagram of VLC.

Fig. 6
Fig. 6

Synoptic diagram of the network-independent multiple system proposed by Naughton et al. in [49].

Fig. 7
Fig. 7

Principle of decomposition of the 3D object into several multiple-view images: elemental images.

Fig. 8
Fig. 8

Left, schematic of image reconstruction in II proces; right, arrangement of elemental images as in Tavakoli et al. [50].

Fig. 9
Fig. 9

Three different scanning topologies for converting an II into a sequence of elemental images: (a) parallel scanning, (b) perpendicular scanning, (c) spiral scanning. [51]

Fig. 10
Fig. 10

Synoptic diagram of the proposed step implementing the DCT optically.

Fig. 11
Fig. 11

Synoptic diagram of optical JPEG decompression.

Fig. 12
Fig. 12

Optical part of optoelectronic JPEG2000 compression setup.

Fig. 13
Fig. 13

Diagram of optical compression with multiplexing from a spectral fusion schema: (a) multiplexing, (b) demultiplexing.

Fig. 14
Fig. 14

Diagram showing how to optimally gather information from different images.

Fig. 15
Fig. 15

Synoptic diagram of the double random phase encrypted system.

Fig. 16
Fig. 16

Undercover encryption diagram.

Fig. 17
Fig. 17

JTC encryption architecture: (a) write-in setup and (b) read-out setup; g ( x ) is the input object, r ( x ) and h ( x ) are the encoding phase masks; F stands for FT [93].

Fig. 18
Fig. 18

Block diagram of the SPJTC architecture: (a) encryption process, and (b) decryption process [111]. IFT is synonymous with the FT 1 .

Fig. 19
Fig. 19

Synoptic diagram of the image encryption method based on the fractional FT [118].

Fig. 20
Fig. 20

Flow chart of the iterative phase retrieval algorithm used in the image encryption scheme of Liu and Liu [118]. Two images are assigned to two complex functions A 1 exp ( i φ 1 ) and A 2 exp ( i φ 2 ) as the magnitudes, while one complex function is a fractional FT of another. F r denotes the fractional FT at order r, A 1 and A 2 are the two original target images, A is the encrypted image, and φ i is the phase function associated with each target image ( i = 1 , 2 ) .

Fig. 21
Fig. 21

Enforced encryption–decryption system using the ICA technique.

Fig. 22
Fig. 22

All-optical video-image encryption with enforced security level.

Fig. 23
Fig. 23

Regrouping and selection of information with a DCT: (a) image with several levels of gray ( 256 , 256 )  pixels , (b) its transformation into DCT, (c) low-pass filter, (d) the filtered spectrum containing the desired information.

Fig. 24
Fig. 24

Optical image compression and encryption

Equations (24)

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U 0 = U z 0 ( x , y ) exp ( i k 2 z 0 [ ( x x ) 2 + ( y y ) 2 ] ) d x d y ,
U z 0 = A z 0 ( x , y ) exp { i ϕ z 0 ( x , y ) } ,
I ( x , y ; ϕ ) = | U R ( x , y ; ϕ ) + U 0 ( x , y ) | 2
U ( x , y ) = 1 4 A R [ ( I ( x , y ; 0 ) I ( x , y ; π ) ) + i ( I ( x , y ; π 2 ) I ( x , y ; 3 π 2 ) ) ] .
NRMS = i = 1 N x j = 1 N y { I ( ( i , j ) ) 2 I ( ( i , j ) ) 2 } 2 i = 1 N x j = 1 N y { I ( ( i , j ) ) 2 } 2 ,
H ( x , y ) = round [ H ( x , y ) σ 1 β ] ,
s = t ¯ u ( v + t ¯ c + d ¯ ) ,
I ( x , y , z 0 ) = k = 1 K l = 1 L I k l ( x , y , z 0 ) R 2 ( x , y ) ,
R 2 ( x , y ) = ( z 0 , g ) + [ ( M x S x k ) 2 + ( M y S y l ) 2 ] ( 1 M + 1 ) .
PSNR ( A , B ) = 10 log 10 ( P 2 1 N x N y i = 1 N x j = 1 N y | A ( i , j ) B ( i , j ) | 2 ) ,
t ( x , y , k ) = 1 2 s ( x , y ) exp [ i ( ϕ ( x , y ) + Δ ( x , y , k ) + ψ ( x , y , k ) ) ] .
i ( x , y , k ) = r ( x , y ) + t ( x , y , k ) + t * ( x , y , k ) .
Δ ( x , y , k ) + ψ ( x , y , k ) = tan 1 ( Im ( t ( x , y , k ) ) Re ( t ( x , y , k ) ) ) Δ ( x , y , 0 ) .
λ ϕ ( p ) = f ( r ) δ ( p n r ) d 2 r ,
F ( ν ) = f ( r ) exp ( 2 π i ν n r ) d 2 r .
0 C ϕ | | ν | F ( ρ ) ρ = ν n | d ν = ( 0 | | ν | F ( ρ ) ρ = ν n | d ν max ( 0 | | ν | F ( ρ ) ρ = ν n | d ν ) ) T 0 | | ν | F ( ρ ) ρ = ν n | d ν .
E i ( k , l ) m = 0 N n = 0 N E i ( m , n ) = Max ( E j ( k , l ) m = 0 N n = 0 N E j ( m , n ) ) i j .
I c ( x , y ) = ( I ( x , y ) exp ( i 2 π n ( x , y ) ) ) h ( x , y ) ,
FT ( M ) E 1 * = FT ( O 1 RP 1 ) RP 2 ( E 1 ) * + FT ( O 2 RP 1 ) E 1 E 1 * .
JPS ( ν ) = | FT [ r ( x a ) g ( x a ) + h ( x b ) ] | 2 .
JPS ( x ) = [ r ( x ) g ( x ) ] [ r ( x ) g ( x ) ] + δ ( x ) + h ( x ) [ r ( x ) g ( x ) ] δ ( x b + a ) + [ r ( x ) g ( x ) ] h ( x ) δ ( x a + b ) ,
o ( x ) = h ( x ) [ r ( x ) g ( x ) ] [ r ( x ) g ( x ) ] δ ( x b ) + h ( x ) δ ( x b ) + h ( x ) h ( x ) [ r ( x ) g ( x ) ] δ ( x 2 b + a ) + r ( x ) g ( x ) δ ( x a ) .
s ( x , y ) = 2 [ t ( x , y y t ) c * ( x , y y c ) φ * ( x , y ) + t * ( x , y y t ) c ( x , y y c ) φ ( x , y ) ] .
F α ( A 1 exp ( i φ 1 ) ) = F β ( A 2 exp ( i φ 2 ) ) .

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