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, 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, 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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A. Loussert, A. Alfalou, R. El Sawda, 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, 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, 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, J. T. Sheridan, “Key-space analysis of double random phase encryption technique,” Appl. Opt. 46, 6641–6647 (2007).
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X. Wang, 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, 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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B. Tavakoli, M. Daneshpanah, B. Javidi, E. Watson, “Performance of 3D integral imaging with position uncertainty,” Opt. Express 15, 11889–11902 (2007).
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J. F. Barrera, R. Henao, M. Tebaldi, N. Bolognini, R. Torroba, “Multiple image encryption using an aperture-modulated optical system,” Opt. Commun. 261, 29–33 (2006).
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U. Gopinathan, T. J. Naughton, 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, J. T. Sheridan, “A known-plaintext heuristic attack on the Fourier plane encryption algorithm,” Opt. Express 14, 3181–3186 (2006).
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D. Abookasis, O. Montal, O. Abramson, 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, 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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A. E. Shortt, T. J. Naughton, B. Javidi, “Nonuniform quantization compression techniques for digital holograms of three-dimensional objects,” Proc. SPIE 5557, 30–41 (2004).
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L. Cai, M. He, Q. Liu, X. Yang, “Digital image encryption and watermarking by phase-shifting interferometry,” Appl. Opt. 43, 3078–3084 (2004).
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A. Zlotnik, Z. Zalevsky, E. Marom, “Optical encryption by using a synthesized mutual intensity function,” Appl. Opt. 43, 3456–3465 (2004).
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N. K. Nishchal, J. Joseph, K. Singh, “Securing information using fractional Fourier transform in digital holography,” Opt. Commun. 235, 253–259 (2004).
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J. C. Dagher, M. W. Marcellin, 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, B. Javidi, “Efficient compression of Fresnel fields for Internet transmission of three-dimensional images,” Appl. Opt. 42, 4758–4764 (2003).
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B. M. Hennelly, J. T. Sheridan, “Image encryption techniques based on fractional Fourier transform,” Proc. SPIE 5202, 76–87 (2003).
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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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