Abstract

In the past two decades, generation and encryption of holographic images have been identified as two important areas of investigation in digital holography. The integration of these two technologies has enabled images to be encrypted with more dimensions of freedom on top of simply employing the encryption keys. Despite the moderate success attained to date, and the rapid advancement of computing technology in recent years, the heavy computation load involved in these two processes remains a major bottleneck in the evolution of the digital holography technology. To alleviate this problem, we have proposed a fast and economical solution which is capable of generating, and at the same time encrypting, holograms with numerical means. In our method, the hologram formation mechanism is decomposed into a pair of one-dimensional (1D) processes. In the first stage, a given three-dimensional (3D) scene is partitioned into a stack of uniformed spaced horizontal planes and converted into a set of hologram sublines. Next, the sublines are expanded to a hologram by convolving it with a 1D reference signal. To encrypt the hologram, the reference signal is first convolved with a key function in the form of a maximum length sequence (also known as MLS, or M-sequence). The use of a MLS has two advantages. First, an MLS is spectrally flat so that it will not jeopardize the frequency spectrum of the hologram. Second, the autocorrelation function of an MLS is close to a train of Kronecker delta function. As a result, the encrypted hologram can be decoded by correlating it with the same key that is adopted in the encoding process. Experimental results reveal that the proposed method can be applied to generate and encrypt holograms with a small number of computations. In addition, the encrypted hologram can be decoded and reconstructed to the original 3D scene with good fidelity.

© 2010 Optical Society of America

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2010

M. Sharma and M. K. Kowar, “Image encryption techniques using chaotic schemes: a review,” Int. J. Eng. Sci. Tech 2, 2359–2362 (2010).

2009

2008

S. C. Kim and E. S. Kim, “Effective generation of digital holograms of three-dimensional objects using a novel look-up table method,” Appl. Opt. 47, D55–D62 (2008).
[CrossRef]

S. J. Li, C. Q. Li, G. R. Chen, and K. T. Lo, “Cryptanalysis of the RCES/RSES image encryption scheme,” J. Syst. Softw. 81, 1130–1143 (2008).

M. Ali, B. Younes, and A. Jantan, “Image encryption using block-based transformation algorithm,” IAENG Int. J. Comput. Sci. 35, 15–23 (2008).

2007

T. Yamaguchi, G. Okabe, and H. Yoshikawa, “Real-time image plane full-color and full-parallax holographic video display system,” Opt. Eng. (Bellingham, Wash.) 46, 125801 (2007).
[CrossRef]

2005

2004

I. Ozturk and I. Sogukpinar, “Analysis and comparison of image encryption,” Int. J. Inf. Technol. , 1, 108–111 (2004).

2003

2002

Y. Sakamoto and T. Nagao, “A fast computational method for computer-generated Fourier hologram using patch model,” Electron. Commun. Jpn., Part 2, Electron. 85, 16–24(2002).
[CrossRef]

2001

H. Yoshikawa, “Fast computation of fresnel holograms employing difference,” Opt. Rev. 8, 331–335 (2001).
[CrossRef]

2000

Akin, T.

Ali, M.

M. Ali, B. Younes, and A. Jantan, “Image encryption using block-based transformation algorithm,” IAENG Int. J. Comput. Sci. 35, 15–23 (2008).

Alvarez, G.

D. Arroyo, C. Q. Li, S. J. Li, G. Alvarez, and W. A. Halang, “Cryptanalysis of an image encryption scheme based on a new total shuffling algorithm,” Chaos Solitons Fractals 41, 2613–2616 (2009).
[CrossRef]

Arroyo, D.

D. Arroyo, C. Q. Li, S. J. Li, G. Alvarez, and W. A. Halang, “Cryptanalysis of an image encryption scheme based on a new total shuffling algorithm,” Chaos Solitons Fractals 41, 2613–2616 (2009).
[CrossRef]

Chau, P. M.

P. P. Dang and P. M. Chau, “Image encryption for secure internet multimedia applications,” IEEE Trans. Consum. Electron. 46, 395–403 (2000).
[CrossRef]

Chen, G. R.

S. J. Li, C. Q. Li, G. R. Chen, and K. T. Lo, “Cryptanalysis of the RCES/RSES image encryption scheme,” J. Syst. Softw. 81, 1130–1143 (2008).

Cheung, K. W. K.

Choi, H. J.

Y.-H. Seo, H. J. Choi, and D. W. Kim, “Digital hologram encryption using discrete wavelet packet transform,” Opt. Commun. 282, 367–377 (2009).
[CrossRef]

Chung, P. S.

Dang, P. P.

P. P. Dang and P. M. Chau, “Image encryption for secure internet multimedia applications,” IEEE Trans. Consum. Electron. 46, 395–403 (2000).
[CrossRef]

Dobson, K.

Doh, K. B.

K. B. Doh, K. Dobson, T.-C. Poon, and P. S. Chung, “Optical image coding with a circular Dammann grating,” Appl. Opt. 48, 134–139 (2009).
[CrossRef]

K. B. Doh, K. Kim, and T.-C. Poon, “Computer generated holographic image processing for information security,” Lect. Notes Comput. Sci. 3320, 313–322 (2005).

Golomb, S. W.

S. W. Golomb, Shift Register Sequences, revised ed. (Aegean Park Press, 1981).

Halang, W. A.

D. Arroyo, C. Q. Li, S. J. Li, G. Alvarez, and W. A. Halang, “Cryptanalysis of an image encryption scheme based on a new total shuffling algorithm,” Chaos Solitons Fractals 41, 2613–2616 (2009).
[CrossRef]

Indebetouw, G.

Jantan, A.

M. Ali, B. Younes, and A. Jantan, “Image encryption using block-based transformation algorithm,” IAENG Int. J. Comput. Sci. 35, 15–23 (2008).

Javidi, B.

Kim, D. W.

Y.-H. Seo, H. J. Choi, and D. W. Kim, “Digital hologram encryption using discrete wavelet packet transform,” Opt. Commun. 282, 367–377 (2009).
[CrossRef]

Kim, E. S.

Kim, K.

K. B. Doh, K. Kim, and T.-C. Poon, “Computer generated holographic image processing for information security,” Lect. Notes Comput. Sci. 3320, 313–322 (2005).

Kim, S. C.

Kim, T.

Kowar, M. K.

M. Sharma and M. K. Kowar, “Image encryption techniques using chaotic schemes: a review,” Int. J. Eng. Sci. Tech 2, 2359–2362 (2010).

Li, C. Q.

D. Arroyo, C. Q. Li, S. J. Li, G. Alvarez, and W. A. Halang, “Cryptanalysis of an image encryption scheme based on a new total shuffling algorithm,” Chaos Solitons Fractals 41, 2613–2616 (2009).
[CrossRef]

S. J. Li, C. Q. Li, G. R. Chen, and K. T. Lo, “Cryptanalysis of the RCES/RSES image encryption scheme,” J. Syst. Softw. 81, 1130–1143 (2008).

Li, S. J.

D. Arroyo, C. Q. Li, S. J. Li, G. Alvarez, and W. A. Halang, “Cryptanalysis of an image encryption scheme based on a new total shuffling algorithm,” Chaos Solitons Fractals 41, 2613–2616 (2009).
[CrossRef]

S. J. Li, C. Q. Li, G. R. Chen, and K. T. Lo, “Cryptanalysis of the RCES/RSES image encryption scheme,” J. Syst. Softw. 81, 1130–1143 (2008).

Liang, X. Y.

X. Y. Liang and X. L. Min, “An image encryption approach using a shuffling map,” Commun. Theor. Phys. 52, 876–880(2009).
[CrossRef]

Liu, J. P.

Lo, K. T.

S. J. Li, C. Q. Li, G. R. Chen, and K. T. Lo, “Cryptanalysis of the RCES/RSES image encryption scheme,” J. Syst. Softw. 81, 1130–1143 (2008).

Matsushima, K.

Min, X. L.

X. Y. Liang and X. L. Min, “An image encryption approach using a shuffling map,” Commun. Theor. Phys. 52, 876–880(2009).
[CrossRef]

Nagao, T.

Y. Sakamoto and T. Nagao, “A fast computational method for computer-generated Fourier hologram using patch model,” Electron. Commun. Jpn., Part 2, Electron. 85, 16–24(2002).
[CrossRef]

Nakahara, S.

Nomura, T.

Okabe, G.

T. Yamaguchi, G. Okabe, and H. Yoshikawa, “Real-time image plane full-color and full-parallax holographic video display system,” Opt. Eng. (Bellingham, Wash.) 46, 125801 (2007).
[CrossRef]

Ozturk, I.

I. Ozturk and I. Sogukpinar, “Analysis and comparison of image encryption,” Int. J. Inf. Technol. , 1, 108–111 (2004).

Poon, T.-C.

Sakamoto, Y.

H. Sakata and Y. Sakamoto, “A fast computation method for Fresnel hologram using three-dimensional affine transformations in real space,” Appl. Opt. 48, H212–H221 (2009).
[CrossRef]

Y. Sakamoto and T. Nagao, “A fast computational method for computer-generated Fourier hologram using patch model,” Electron. Commun. Jpn., Part 2, Electron. 85, 16–24(2002).
[CrossRef]

Sakata, H.

Schimmel, H.

Seo, Y.-H.

Y.-H. Seo, H. J. Choi, and D. W. Kim, “Digital hologram encryption using discrete wavelet packet transform,” Opt. Commun. 282, 367–377 (2009).
[CrossRef]

Sharma, M.

M. Sharma and M. K. Kowar, “Image encryption techniques using chaotic schemes: a review,” Int. J. Eng. Sci. Tech 2, 2359–2362 (2010).

Sogukpinar, I.

I. Ozturk and I. Sogukpinar, “Analysis and comparison of image encryption,” Int. J. Inf. Technol. , 1, 108–111 (2004).

Tajahuerce, E.

Tsang, P. W. M.

Wyrowski, F.

Yamaguchi, T.

T. Yamaguchi, G. Okabe, and H. Yoshikawa, “Real-time image plane full-color and full-parallax holographic video display system,” Opt. Eng. (Bellingham, Wash.) 46, 125801 (2007).
[CrossRef]

Yoshikawa, H.

T. Yamaguchi, G. Okabe, and H. Yoshikawa, “Real-time image plane full-color and full-parallax holographic video display system,” Opt. Eng. (Bellingham, Wash.) 46, 125801 (2007).
[CrossRef]

H. Yoshikawa, “Fast computation of fresnel holograms employing difference,” Opt. Rev. 8, 331–335 (2001).
[CrossRef]

H. Yoshikawa, “Computer-generated holograms for white light reconstruction,” in Digital Holography and Three-Dimensional Display: Principles and Applications, T.-C.Poon, ed. (Springer, 2006).

Younes, B.

M. Ali, B. Younes, and A. Jantan, “Image encryption using block-based transformation algorithm,” IAENG Int. J. Comput. Sci. 35, 15–23 (2008).

Appl. Opt.

Chaos Solitons Fractals

D. Arroyo, C. Q. Li, S. J. Li, G. Alvarez, and W. A. Halang, “Cryptanalysis of an image encryption scheme based on a new total shuffling algorithm,” Chaos Solitons Fractals 41, 2613–2616 (2009).
[CrossRef]

Commun. Theor. Phys.

X. Y. Liang and X. L. Min, “An image encryption approach using a shuffling map,” Commun. Theor. Phys. 52, 876–880(2009).
[CrossRef]

Electron. Commun. Jpn., Part 2, Electron.

Y. Sakamoto and T. Nagao, “A fast computational method for computer-generated Fourier hologram using patch model,” Electron. Commun. Jpn., Part 2, Electron. 85, 16–24(2002).
[CrossRef]

IAENG Int. J. Comput. Sci.

M. Ali, B. Younes, and A. Jantan, “Image encryption using block-based transformation algorithm,” IAENG Int. J. Comput. Sci. 35, 15–23 (2008).

IEEE Trans. Consum. Electron.

P. P. Dang and P. M. Chau, “Image encryption for secure internet multimedia applications,” IEEE Trans. Consum. Electron. 46, 395–403 (2000).
[CrossRef]

Int. J. Eng. Sci. Tech

M. Sharma and M. K. Kowar, “Image encryption techniques using chaotic schemes: a review,” Int. J. Eng. Sci. Tech 2, 2359–2362 (2010).

Int. J. Inf. Technol.

I. Ozturk and I. Sogukpinar, “Analysis and comparison of image encryption,” Int. J. Inf. Technol. , 1, 108–111 (2004).

J. Opt. Soc. Am. A

J. Syst. Softw.

S. J. Li, C. Q. Li, G. R. Chen, and K. T. Lo, “Cryptanalysis of the RCES/RSES image encryption scheme,” J. Syst. Softw. 81, 1130–1143 (2008).

Lect. Notes Comput. Sci.

K. B. Doh, K. Kim, and T.-C. Poon, “Computer generated holographic image processing for information security,” Lect. Notes Comput. Sci. 3320, 313–322 (2005).

Opt. Commun.

Y.-H. Seo, H. J. Choi, and D. W. Kim, “Digital hologram encryption using discrete wavelet packet transform,” Opt. Commun. 282, 367–377 (2009).
[CrossRef]

Opt. Eng. (Bellingham, Wash.)

T. Yamaguchi, G. Okabe, and H. Yoshikawa, “Real-time image plane full-color and full-parallax holographic video display system,” Opt. Eng. (Bellingham, Wash.) 46, 125801 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Rev.

H. Yoshikawa, “Fast computation of fresnel holograms employing difference,” Opt. Rev. 8, 331–335 (2001).
[CrossRef]

Other

T.-C.Poon, ed., Digital Holography and Three-Dimensional Display: Principles and Application (Springer, 2006).

H. Yoshikawa, “Computer-generated holograms for white light reconstruction,” in Digital Holography and Three-Dimensional Display: Principles and Applications, T.-C.Poon, ed. (Springer, 2006).

S. W. Golomb, Shift Register Sequences, revised ed. (Aegean Park Press, 1981).

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Figures (6)

Fig. 1
Fig. 1

Partitioning an object scene into a vertical stack (along y direction) of horizontal planes.

Fig. 2
Fig. 2

M-stage LFSR for the realization of M-sequence.

Fig. 3
Fig. 3

Test image Lenna positioned at 0.5 m from the hologram.

Fig. 4
Fig. 4

(a) Reconstructed image from a hologram generated from the test image in Fig. 3. (b) Reconstructed image from a hologram generated from the test image in Fig. 3 and encrypted with the M-sequence generated by S 1 ( y ) . PSNR = 13.1 dB . (c) Reconstructed image from a hologram generated from the test image in Fig. 1 and that has been encrypted and decrypted with the same encryption key, S 1 ( y ) . The MSE, as compared with the reconstructed image of the unencrypted hologram, is 0. (d) Reconstructed image from a hologram generated from the test image in Fig. 1 and that has been encrypted with the encryption key S 1 ( y ) and decrypted with the key S 2 ( y ) . PSNR = 16.3 dB . (e) Reconstructed image from a hologram generated from the test image in Fig. 3 and that has been encrypted and decrypted with the same encryption key, S 3 ( y ) . The key is derived from an eight-taps M-sequence. The MSE, as compared with the reconstructed image of the unencrypted hologram in Fig. 4a, is 0.

Fig. 5
Fig. 5

(a) Test image evenly divided into an upper and lower section, each locating at a different depth from the hologram as shown in Fig. 5b. (b) Depth of each section of the image in Fig. 5a to the hologram.

Fig. 6
Fig. 6

(a) Reconstructed image from a hologram generated from the test image in Fig. 5a at a depth of z = 0.502 m (i.e., z 1 ). The hologram is not encrypted. (b) Reconstructed image from a hologram generated from the test image in Fig. 5a at a depth of z = 0.498 m (i.e., z 2 ). The hologram is not encrypted. (c) Reconstructed image from a hologram that is generated and encrypted with the proposed method from the test image in Fig. 5a, at a depth of z = 0.502 m (i.e., z 1 ). The encrypted hologram is decrypted with the correct key S 3 ( y ) prior to reconstruction. The MSE, as compared with the reconstructed image of the unencrypted hologram in Fig. 6a, is 0. (d) Reconstructed image from a hologram that is generated and encrypted with the proposed method from the test image in Fig. 5a at a depth of z = 0.498 m (i.e., z 2 ). The encrypted hologram is decrypted with the correct key S 3 ( y ) prior to reconstruction. The MSE, as compared with the reconstructed image of the unencrypted hologram in Fig. 6b, is 0. (e) Reconstructed image from a hologram generated from the test image in Fig. 5a at a depth of z = 0.51 m (i.e., z 1 ). The hologram is not encrypted. (f) Reconstructed image from a hologram generated from the test image in Fig. 5a at a depth of z = 0.49 m (i.e., z 2 ). The hologram is not encrypted. (g) Reconstructed image from a hologram that is generated and encrypted with the proposed method from the test image in Fig. 5a, at a depth of z = 0.51 m (i.e., z 1 ). The encrypted hologram is decrypted with the correct key S 3 ( y ) prior to reconstruction. The MSE, as compared with the reconstructed image of the unencrypted hologram in Fig. 6e, is 0. (h) Reconstructed image from a hologram that is generated and encrypted with the proposed method from the test image in Fig. 5a at a depth of z = 0.49 m (i.e., z 2 ). The encrypted hologram is decrypted with the correct key S 3 ( y ) prior to reconstruction. The MSE, as compared with the reconstructed image of the unencrypted hologram in Fig. 6f, is 0.

Tables (2)

Tables Icon

Table 1 Breakdown of Number of Complex Multiplications for Each Step in Eq. (10)

Tables Icon

Table 2 Optical Setting for Generating the Hologram

Equations (17)

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D ( x , y ) = i = 0 N 1 a i r i exp ( j k r i ) = i = 0 N 1 [ a i r i cos ( k r i ) + j a i r i sin ( k r i ) ] ,
2 × N × X × Y .
D ( x , y ) τ i = 0 N ( τ ) a i r i exp ( j k ( x x i ) 2 2 z i ) exp ( j k ( y τ ) 2 2 z o ) = exp ( j k ( y τ ) 2 2 z o ) i = 0 N ( τ ) a i r i exp ( j k ( x x i ) 2 2 z i ) = R ( y τ ) O ( x , τ ) .
D ( x , y ) = τ D ( x , y ) τ = τ O ( x , τ ) R ( y τ ) .
D ( x , y ) = O ( x , y ) * R ( y ) .
S ( y ) = 1 + g 1 y 1 + g 2 y 2 + + g M y M ,
g i = { 1 ( i = 5 , 6 ) 0 otherwise ,
g i = { 1 ( i = 1 , 6 ) 0 otherwise ,
D E ( x , y ) = O ( x , y ) * R ( y ) * Ψ M ( y ) .
D ˜ E ( x , e j ω ) = O ˜ ( x , e j ω ) R ˜ ( e j ω ) Ψ ˜ M ( e j ω ) = O ˜ ( x , e j ω ) E ˜ ( e j ω ) ,
D E ( x , y ) = FT 1 { D ˜ E ( x , e j ω ) } .
( X × Y log 2 Y ) + ( X × Y ) + ( X × Y log 2 Y ) = ( X × Y ) ( 1 + 2 Y log 2 Y ) .
4 ( X × Y ) ( 1 + 2 Y log 2 Y ) .
CA = 2 × N × X × Y 4 × X × Y [ 1 + 2 log 2 Y ] = N 2 [ 1 + 2 log 2 Y ] .
CA = X Y 2 [ 1 + 2 log 2 Y ] .
D ( x , y ) = FT 1 { D ˜ E ( x , e j ω ) E ˜ ( e j ω ) } .
S 2 ( y ) = 1 + y 1 + y 6 ,

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