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Optical color image encryption by wavelength multiplexing and lensless Fresnel transform holograms

Linfei Chen and Daomu Zhao

Open Access Open Access

Abstract

We propose what we believe is a new method for color image encryption by use of wavelength multiplexing based on lensless Fresnel transform holograms. An image is separated into three channels: red, green, and blue, and each channel is independently encrypted. The system parameters of Fresnel transforms and random phase masks in each channel are keys in image encryption and decryption. An optical color image coding configuration with multichannel implementation and an optoelectronic color image encryption architecture with single-channel implementation are presented. The keys can be added by iteratively employing the Fresnel transforms. Computer simulations are given to prove the possibility of the proposed idea.

©2006 Optical Society of America

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Figures (8)
Fig. 1.
Fig. 1. Image encryption and decryption by single wavelength illumination. (a) Original image with 256×256 pixels; (b) encrypted image with red wavelength; (c) and (d) correct and incorrect decryption images with red wavelength; (e) and (f) correct and incorrect decoding images with green wavelength; (g) and (h) right and wrong decryption results with blue wavelength.

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Fig. 2.
Fig. 2. Color image decomposition. R: Red; G: Green; B: Blue.

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Fig. 3.
Fig. 3. Schematic of optical color image encoding implementation. Ms: dichroic mirrors; I: Input plane; P and Ks: random phase masks; H: hologram halide.

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Fig. 4.
Fig. 4. Optoelectronic color image encryption architecture. SLM: Spatial Light Modulator; CCD: Charge-Coupled Device.

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Fig. 5.
Fig. 5. Optical color image decoding realization. O: Output plane.

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Fig. 6.
Fig. 6. Optoelectronic color image decryption configuration.

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Fig. 7.
Fig. 7. Color image coding and decoding results. (a) Original image with 512×512 pixels; (b) encrypted result; (c)–(e) incorrect decryption image; (f) correct decryption image.

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Fig. 8.
Fig. 8. Partial color image encryption and decryption results. (a) Original image with 500×362 pixels; (b) encryption image (c) result with red component incorrectly decrypted; (d) result with green component incorrectly decrypted; (e) result with blue component incorrectly decrypted; (f) only red component correctly decrypted; (g) only green component correctly decrypted; (h) only blue component correctly decrypted; (i) correct decryption.

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Equations (14)

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g ( x 2 , y 2 ) = FsT { FsT [ f ( x , y ) P ( x , y ) ; z 1 ] × K ( x 1 , y 1 ) ; z 2 } ,
f ' ( x , y ) = FsT { FsT [ g * ( x 2 , y 2 ) ; z 2 ] × K ( x 1 , y 1 ) ; z 1 } ,
FsT [ f ( x , y ) ; z ] = exp ( i 2 π z ⁄ λ ) i λ z ∬ f ( x , y ) exp { i π λ z [ ( x 1 − x ) 2 + ( y 1 − y ) 2 ] } d x d y ,
P ( x , y ) = exp [ 2 π i p ( x , y ) ] , K ( x , y ) = exp [ 2 π i k ( x , y ) ] .
u ( x ' , y ' ) = ∣ 1 + g ( x 2 , y 2 ) ∣ 2
= 1 + ∣ g ( x 2 , y 2 ) ∣ 2 + g * ( x 2 , y 2 ) + g ( x 2 , y 2 ) .
g ( x n , y n ) = ∬ ∬ … ∬ f ( x , y ) P ( x , y ) h ( x 1 , x ; y 1 , y ; z 1 )
× K 1 ( x 1 , y 1 ) h ( x 2 , x 1 ; y 2 , y 1 ; z 2 ) K 2 ( x 2 , y 2 ) … …
× K n − 1 ( x n − 1 , y n − 1 ) h ( x n , x n − 1 ; y n , y n − 1 ; z n ) d x d x 1 … d x n − 1 d y d y 1 … d y n − 1 ,
h ( x n , x n − 1 ; y n , y n − 1 ; z n ) = exp ( i 2 π z n ⁄ λ ) i λ z n exp { i π λ z n [ ( x n − x n − 1 ) 2 + ( y n − y n − 1 ) 2 ] } ,
f ' ( x , y ) = ∬ ∬ … ∬ g * ( x n , y n ) h ( x n − 1 , x n ; y n − 1 , y n ; z n )
× K n − 1 ( x n − 1 , y n − 1 ) ∬ … … ∬ h ( x 1 , x 2 ; y 1 , y 2 ; z 2 ) K 1 ( x 1 , y 1 ) ,
× h ( x , x 1 ; y , y 1 ; z 1 ) d x n d x n − 1 … d x 1 d y n d y n − 1 … d y 1
MSE = ∑ m = 1 M ∑ n = 1 N [ ∣ f ( m Δ x , n Δ y ) − f 0 ( m Δ x , n Δ y ) ∣ 2 ] ⁄ ∑ m = 1 M ∑ n = 1 N [ f ( m Δ x , n Δ y ) 2 ] ,
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