Abstract

Past research has demonstrated that, by downsampling the source object scene in multiple directions, a binary Fresnel hologram can be generated to preserve favorable quality on the reconstructed image. In this paper, we will show that a binary hologram generated with such an approach is also insensitive to noise contamination. On this basis, we propose a method to embed an intensity image into the binary hologram. To prevent the embedded information from being tampered or retrieved with unauthorized means, scrambling is applied to relocate each pixel to a unique position in the binary hologram according to a random assignment that is only known with the availability of a descrambling key. Experimental results demonstrate that our proposed method is capable of embedding an intensity image that is one quarter the size of the binary hologram without causing observable degradation on the reconstructed image. In addition, the embedded image can be retrieved with acceptable quality even if the binary hologram is damaged and contaminated with noise.

© 2013 Optical Society of America

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References

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  1. T.-C. Poon, ed., Digital Holography and Three-Dimensional Display: Principles and Applications (Springer, 2006).
  2. L. C. Ferri, “Visualization of 3D information with digital holography using laser printers,” Comput. Graph. 25, 309–321 (2001).
    [CrossRef]
  3. H. Yoshikawa and M. Tachinami, “Development of direct fringe printer for computer-generated holograms,” Proc. SPIE 5742, 259–266 (2005).
    [CrossRef]
  4. A. W. Lohmann and D. P. Paris, “Binary Fraunhofer holograms, generated by computer,” Appl. Opt. 6, 1739–1748 (1967).
    [CrossRef]
  5. B. R. Brown and A. W. Lohmann, “Computer-generated binary holograms,” IBM J. Res. Devel. 13, 160–168 (1969).
    [CrossRef]
  6. M. P. Chang and O. K. Ersoy, “Iterative interlacing error diffusion for synthesis of computer-generated holograms,” Appl. Opt. 32, 3122–3129 (1993).
    [CrossRef]
  7. E. Zhang, S. Noehte, C. H. Dietrich, and R. Männer, “Gradual and random binarization of gray-scale holograms,” Appl. Opt. 34, 5987–5995 (1995).
    [CrossRef]
  8. B. B. Chhetri, S. Yang, and T. Shimomura, “Iterative stepwise binarization of digital amplitude holograms with added energy to the signal window,” Opt. Eng. 40, 2718–2725 (2001).
    [CrossRef]
  9. R. W. Floyd and L. Steinberg, “An adaptive algorithm for spatial grey scale,” Proc. Soc. Inf. Disp 17, 75–77 (1976).
  10. R. Eschbach, “Comparison of error diffusion methods for computer-generated holograms,” Appl. Opt. 30, 3702–3710 (1991).
    [CrossRef]
  11. R. Eschbach and Z. Fan, “Complex-valued error diffusion for off-axis computer-generated holograms,” Appl. Opt. 32, 3130–3136 (1993).
    [CrossRef]
  12. R. L. Easton, R. Eschbach, and R. Nagarajan, “Error diffusion in cell-oriented Fourier-transform computer-generated holograms to compensate for printing constraints,” J. Mod. Opt. 43, 1219–1236 (1996).
    [CrossRef]
  13. F. Fetthauer, S. Weissbach, and O. Bryngdahl, “Computer-generated Fresnel holograms: quantization with the error diffusion algorithm,” Opt. Commun. 114, 230–234 (1995).
    [CrossRef]
  14. P. Tsang, T.-C. Poon, W.-K. Cheung, and J.-P. Liu, “Computer generation of binary Fresnel holography,” Appl. Opt. 50, B88–B95 (2011).
    [CrossRef]
  15. W. K. Cheung, P. Tsang, T.-C. Poon, and C.-H. Zhou, “Enhanced method for the generation of binary Fresnel holograms based on grid-cross downsampling,” Chinese Opt. Lett. 9, 120005 (2011).
    [CrossRef]
  16. C. Martinez, O. Lemonnier, F. Laulagnet, A. Fargeix, F. Tissot, and M. Armand, “Complementary computer generated holography for aesthetic watermarking,” Opt. Express 20, 5547–5556 (2012).
    [CrossRef]
  17. K. Tanaka, “Embedding of computer-generated hologram in a dithered image,” Appl. Opt. 50, H315–H326 (2011).
    [CrossRef]
  18. X. Zhou, L. Chen, and J. Shao, “Investigation of digital hologram watermarking with double binary phase encoding,” Proc. SPIE 5636, 220–228 (2005).
    [CrossRef]
  19. A. Yoshinao, “Watermarking technique using computer generated holograms,” Electron. Commun. Jpn. III 84, 21–31 (2001).
  20. X. Shi and D. Zhao, “Image hiding in Fourier domain by use of joint transform correlator architecture and holographic technique,” Appl. Opt. 50, 766–772 (2011).
    [CrossRef]
  21. N. K. Nishchal, T. Pitkaaho, and T. J. Naughton, “Digital Fresnel hologram watermarking,” in Proceedings of the 9th Euro-American Workshop on Information Optics (WIO) (IEEE, 2010), pp. 1–3.
  22. S. Deng, L. Liu, H. Lang, W. Pan, and D. Zhao, “Hiding an image in cascaded Fresnel digital holograms,” Chin. Opt. Lett. 4, 268–271 (2006).
  23. P. Tsang, W.-K. Cheung, T.-C. Poon, and J.-P. Liu, “An enhanced method for generation of binary Fresnel hologram based on adaptive and uniform grid-cross down-sampling,” Opt. Commun. 285, 4027–4032 (2012).
    [CrossRef]

2012 (2)

C. Martinez, O. Lemonnier, F. Laulagnet, A. Fargeix, F. Tissot, and M. Armand, “Complementary computer generated holography for aesthetic watermarking,” Opt. Express 20, 5547–5556 (2012).
[CrossRef]

P. Tsang, W.-K. Cheung, T.-C. Poon, and J.-P. Liu, “An enhanced method for generation of binary Fresnel hologram based on adaptive and uniform grid-cross down-sampling,” Opt. Commun. 285, 4027–4032 (2012).
[CrossRef]

2011 (4)

2006 (1)

2005 (2)

X. Zhou, L. Chen, and J. Shao, “Investigation of digital hologram watermarking with double binary phase encoding,” Proc. SPIE 5636, 220–228 (2005).
[CrossRef]

H. Yoshikawa and M. Tachinami, “Development of direct fringe printer for computer-generated holograms,” Proc. SPIE 5742, 259–266 (2005).
[CrossRef]

2001 (3)

L. C. Ferri, “Visualization of 3D information with digital holography using laser printers,” Comput. Graph. 25, 309–321 (2001).
[CrossRef]

B. B. Chhetri, S. Yang, and T. Shimomura, “Iterative stepwise binarization of digital amplitude holograms with added energy to the signal window,” Opt. Eng. 40, 2718–2725 (2001).
[CrossRef]

A. Yoshinao, “Watermarking technique using computer generated holograms,” Electron. Commun. Jpn. III 84, 21–31 (2001).

1996 (1)

R. L. Easton, R. Eschbach, and R. Nagarajan, “Error diffusion in cell-oriented Fourier-transform computer-generated holograms to compensate for printing constraints,” J. Mod. Opt. 43, 1219–1236 (1996).
[CrossRef]

1995 (2)

F. Fetthauer, S. Weissbach, and O. Bryngdahl, “Computer-generated Fresnel holograms: quantization with the error diffusion algorithm,” Opt. Commun. 114, 230–234 (1995).
[CrossRef]

E. Zhang, S. Noehte, C. H. Dietrich, and R. Männer, “Gradual and random binarization of gray-scale holograms,” Appl. Opt. 34, 5987–5995 (1995).
[CrossRef]

1993 (2)

1991 (1)

1976 (1)

R. W. Floyd and L. Steinberg, “An adaptive algorithm for spatial grey scale,” Proc. Soc. Inf. Disp 17, 75–77 (1976).

1969 (1)

B. R. Brown and A. W. Lohmann, “Computer-generated binary holograms,” IBM J. Res. Devel. 13, 160–168 (1969).
[CrossRef]

1967 (1)

Armand, M.

Brown, B. R.

B. R. Brown and A. W. Lohmann, “Computer-generated binary holograms,” IBM J. Res. Devel. 13, 160–168 (1969).
[CrossRef]

Bryngdahl, O.

F. Fetthauer, S. Weissbach, and O. Bryngdahl, “Computer-generated Fresnel holograms: quantization with the error diffusion algorithm,” Opt. Commun. 114, 230–234 (1995).
[CrossRef]

Chang, M. P.

Chen, L.

X. Zhou, L. Chen, and J. Shao, “Investigation of digital hologram watermarking with double binary phase encoding,” Proc. SPIE 5636, 220–228 (2005).
[CrossRef]

Cheung, W. K.

W. K. Cheung, P. Tsang, T.-C. Poon, and C.-H. Zhou, “Enhanced method for the generation of binary Fresnel holograms based on grid-cross downsampling,” Chinese Opt. Lett. 9, 120005 (2011).
[CrossRef]

Cheung, W.-K.

P. Tsang, W.-K. Cheung, T.-C. Poon, and J.-P. Liu, “An enhanced method for generation of binary Fresnel hologram based on adaptive and uniform grid-cross down-sampling,” Opt. Commun. 285, 4027–4032 (2012).
[CrossRef]

P. Tsang, T.-C. Poon, W.-K. Cheung, and J.-P. Liu, “Computer generation of binary Fresnel holography,” Appl. Opt. 50, B88–B95 (2011).
[CrossRef]

Chhetri, B. B.

B. B. Chhetri, S. Yang, and T. Shimomura, “Iterative stepwise binarization of digital amplitude holograms with added energy to the signal window,” Opt. Eng. 40, 2718–2725 (2001).
[CrossRef]

Deng, S.

Dietrich, C. H.

Easton, R. L.

R. L. Easton, R. Eschbach, and R. Nagarajan, “Error diffusion in cell-oriented Fourier-transform computer-generated holograms to compensate for printing constraints,” J. Mod. Opt. 43, 1219–1236 (1996).
[CrossRef]

Ersoy, O. K.

Eschbach, R.

R. L. Easton, R. Eschbach, and R. Nagarajan, “Error diffusion in cell-oriented Fourier-transform computer-generated holograms to compensate for printing constraints,” J. Mod. Opt. 43, 1219–1236 (1996).
[CrossRef]

R. Eschbach and Z. Fan, “Complex-valued error diffusion for off-axis computer-generated holograms,” Appl. Opt. 32, 3130–3136 (1993).
[CrossRef]

R. Eschbach, “Comparison of error diffusion methods for computer-generated holograms,” Appl. Opt. 30, 3702–3710 (1991).
[CrossRef]

Fan, Z.

Fargeix, A.

Ferri, L. C.

L. C. Ferri, “Visualization of 3D information with digital holography using laser printers,” Comput. Graph. 25, 309–321 (2001).
[CrossRef]

Fetthauer, F.

F. Fetthauer, S. Weissbach, and O. Bryngdahl, “Computer-generated Fresnel holograms: quantization with the error diffusion algorithm,” Opt. Commun. 114, 230–234 (1995).
[CrossRef]

Floyd, R. W.

R. W. Floyd and L. Steinberg, “An adaptive algorithm for spatial grey scale,” Proc. Soc. Inf. Disp 17, 75–77 (1976).

Lang, H.

Laulagnet, F.

Lemonnier, O.

Liu, J.-P.

P. Tsang, W.-K. Cheung, T.-C. Poon, and J.-P. Liu, “An enhanced method for generation of binary Fresnel hologram based on adaptive and uniform grid-cross down-sampling,” Opt. Commun. 285, 4027–4032 (2012).
[CrossRef]

P. Tsang, T.-C. Poon, W.-K. Cheung, and J.-P. Liu, “Computer generation of binary Fresnel holography,” Appl. Opt. 50, B88–B95 (2011).
[CrossRef]

Liu, L.

Lohmann, A. W.

B. R. Brown and A. W. Lohmann, “Computer-generated binary holograms,” IBM J. Res. Devel. 13, 160–168 (1969).
[CrossRef]

A. W. Lohmann and D. P. Paris, “Binary Fraunhofer holograms, generated by computer,” Appl. Opt. 6, 1739–1748 (1967).
[CrossRef]

Männer, R.

Martinez, C.

Nagarajan, R.

R. L. Easton, R. Eschbach, and R. Nagarajan, “Error diffusion in cell-oriented Fourier-transform computer-generated holograms to compensate for printing constraints,” J. Mod. Opt. 43, 1219–1236 (1996).
[CrossRef]

Naughton, T. J.

N. K. Nishchal, T. Pitkaaho, and T. J. Naughton, “Digital Fresnel hologram watermarking,” in Proceedings of the 9th Euro-American Workshop on Information Optics (WIO) (IEEE, 2010), pp. 1–3.

Nishchal, N. K.

N. K. Nishchal, T. Pitkaaho, and T. J. Naughton, “Digital Fresnel hologram watermarking,” in Proceedings of the 9th Euro-American Workshop on Information Optics (WIO) (IEEE, 2010), pp. 1–3.

Noehte, S.

Pan, W.

Paris, D. P.

Pitkaaho, T.

N. K. Nishchal, T. Pitkaaho, and T. J. Naughton, “Digital Fresnel hologram watermarking,” in Proceedings of the 9th Euro-American Workshop on Information Optics (WIO) (IEEE, 2010), pp. 1–3.

Poon, T.-C.

P. Tsang, W.-K. Cheung, T.-C. Poon, and J.-P. Liu, “An enhanced method for generation of binary Fresnel hologram based on adaptive and uniform grid-cross down-sampling,” Opt. Commun. 285, 4027–4032 (2012).
[CrossRef]

W. K. Cheung, P. Tsang, T.-C. Poon, and C.-H. Zhou, “Enhanced method for the generation of binary Fresnel holograms based on grid-cross downsampling,” Chinese Opt. Lett. 9, 120005 (2011).
[CrossRef]

P. Tsang, T.-C. Poon, W.-K. Cheung, and J.-P. Liu, “Computer generation of binary Fresnel holography,” Appl. Opt. 50, B88–B95 (2011).
[CrossRef]

Shao, J.

X. Zhou, L. Chen, and J. Shao, “Investigation of digital hologram watermarking with double binary phase encoding,” Proc. SPIE 5636, 220–228 (2005).
[CrossRef]

Shi, X.

Shimomura, T.

B. B. Chhetri, S. Yang, and T. Shimomura, “Iterative stepwise binarization of digital amplitude holograms with added energy to the signal window,” Opt. Eng. 40, 2718–2725 (2001).
[CrossRef]

Steinberg, L.

R. W. Floyd and L. Steinberg, “An adaptive algorithm for spatial grey scale,” Proc. Soc. Inf. Disp 17, 75–77 (1976).

Tachinami, M.

H. Yoshikawa and M. Tachinami, “Development of direct fringe printer for computer-generated holograms,” Proc. SPIE 5742, 259–266 (2005).
[CrossRef]

Tanaka, K.

Tissot, F.

Tsang, P.

P. Tsang, W.-K. Cheung, T.-C. Poon, and J.-P. Liu, “An enhanced method for generation of binary Fresnel hologram based on adaptive and uniform grid-cross down-sampling,” Opt. Commun. 285, 4027–4032 (2012).
[CrossRef]

W. K. Cheung, P. Tsang, T.-C. Poon, and C.-H. Zhou, “Enhanced method for the generation of binary Fresnel holograms based on grid-cross downsampling,” Chinese Opt. Lett. 9, 120005 (2011).
[CrossRef]

P. Tsang, T.-C. Poon, W.-K. Cheung, and J.-P. Liu, “Computer generation of binary Fresnel holography,” Appl. Opt. 50, B88–B95 (2011).
[CrossRef]

Weissbach, S.

F. Fetthauer, S. Weissbach, and O. Bryngdahl, “Computer-generated Fresnel holograms: quantization with the error diffusion algorithm,” Opt. Commun. 114, 230–234 (1995).
[CrossRef]

Yang, S.

B. B. Chhetri, S. Yang, and T. Shimomura, “Iterative stepwise binarization of digital amplitude holograms with added energy to the signal window,” Opt. Eng. 40, 2718–2725 (2001).
[CrossRef]

Yoshikawa, H.

H. Yoshikawa and M. Tachinami, “Development of direct fringe printer for computer-generated holograms,” Proc. SPIE 5742, 259–266 (2005).
[CrossRef]

Yoshinao, A.

A. Yoshinao, “Watermarking technique using computer generated holograms,” Electron. Commun. Jpn. III 84, 21–31 (2001).

Zhang, E.

Zhao, D.

Zhou, C.-H.

W. K. Cheung, P. Tsang, T.-C. Poon, and C.-H. Zhou, “Enhanced method for the generation of binary Fresnel holograms based on grid-cross downsampling,” Chinese Opt. Lett. 9, 120005 (2011).
[CrossRef]

Zhou, X.

X. Zhou, L. Chen, and J. Shao, “Investigation of digital hologram watermarking with double binary phase encoding,” Proc. SPIE 5636, 220–228 (2005).
[CrossRef]

Appl. Opt. (8)

Chin. Opt. Lett. (1)

Chinese Opt. Lett. (1)

W. K. Cheung, P. Tsang, T.-C. Poon, and C.-H. Zhou, “Enhanced method for the generation of binary Fresnel holograms based on grid-cross downsampling,” Chinese Opt. Lett. 9, 120005 (2011).
[CrossRef]

Comput. Graph. (1)

L. C. Ferri, “Visualization of 3D information with digital holography using laser printers,” Comput. Graph. 25, 309–321 (2001).
[CrossRef]

Electron. Commun. Jpn. III (1)

A. Yoshinao, “Watermarking technique using computer generated holograms,” Electron. Commun. Jpn. III 84, 21–31 (2001).

IBM J. Res. Devel. (1)

B. R. Brown and A. W. Lohmann, “Computer-generated binary holograms,” IBM J. Res. Devel. 13, 160–168 (1969).
[CrossRef]

J. Mod. Opt. (1)

R. L. Easton, R. Eschbach, and R. Nagarajan, “Error diffusion in cell-oriented Fourier-transform computer-generated holograms to compensate for printing constraints,” J. Mod. Opt. 43, 1219–1236 (1996).
[CrossRef]

Opt. Commun. (2)

F. Fetthauer, S. Weissbach, and O. Bryngdahl, “Computer-generated Fresnel holograms: quantization with the error diffusion algorithm,” Opt. Commun. 114, 230–234 (1995).
[CrossRef]

P. Tsang, W.-K. Cheung, T.-C. Poon, and J.-P. Liu, “An enhanced method for generation of binary Fresnel hologram based on adaptive and uniform grid-cross down-sampling,” Opt. Commun. 285, 4027–4032 (2012).
[CrossRef]

Opt. Eng. (1)

B. B. Chhetri, S. Yang, and T. Shimomura, “Iterative stepwise binarization of digital amplitude holograms with added energy to the signal window,” Opt. Eng. 40, 2718–2725 (2001).
[CrossRef]

Opt. Express (1)

Proc. Soc. Inf. Disp (1)

R. W. Floyd and L. Steinberg, “An adaptive algorithm for spatial grey scale,” Proc. Soc. Inf. Disp 17, 75–77 (1976).

Proc. SPIE (2)

H. Yoshikawa and M. Tachinami, “Development of direct fringe printer for computer-generated holograms,” Proc. SPIE 5742, 259–266 (2005).
[CrossRef]

X. Zhou, L. Chen, and J. Shao, “Investigation of digital hologram watermarking with double binary phase encoding,” Proc. SPIE 5636, 220–228 (2005).
[CrossRef]

Other (2)

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

N. K. Nishchal, T. Pitkaaho, and T. J. Naughton, “Digital Fresnel hologram watermarking,” in Proceedings of the 9th Euro-American Workshop on Information Optics (WIO) (IEEE, 2010), pp. 1–3.

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Figures (8)

Fig. 1.
Fig. 1.

Hologram illuminated with an inclined planar reference beam.

Fig. 2.
Fig. 2.

a. Planar image positioned at 0.5 m from the hologram. b. Numerical reconstructed image of the binary hologram representing the image in a. The binary hologram is generated with the method in [15]. c. Numerical reconstructed image of the binary hologram representing the image in a. The binary hologram is generated with the method in [15] and contaminated with 20% of random noise. d. Numerical reconstructed image of the binary hologram representing the image in a. The binary hologram is generated with the method in [15] and contaminated with 30% of random noise.

Fig. 3.
Fig. 3.

Proposed intensity image-embedded binary hologram method.

Fig. 4.
Fig. 4.

a. Double depth image evenly divided into left and right sections, located at 0.5 and 0.55 m from the hologram, respectively. b. Numerical reconstructed image of the off-axis binary hologram at 0.5 m representing the double depth image in a. c. Numerical reconstructed image of the off-axis binary hologram at 0.55 m representing the double image in a.

Fig. 5.
Fig. 5.

a. Image to be embedded into the off-axis binary hologram representing the double depth image in Fig. 4a. b. Binarization of the image in Fig. 4a with error diffusion.

Fig. 6.
Fig. 6.

a. Numerical reconstructed image of the off-axis binary hologram at 0.5 m representing the double depth image in Fig. 4a. The image in Fig. 5b is embedded into the binary hologram based on the proposed method. b. Numerical reconstructed image of the off-axis binary hologram at 0.55 m representing the double image in Fig. 4a. The image in Fig. 5b is embedded into the binary hologram based on the proposed method. c. Extracted image from the binary hologram (that has been embedded with the image in Fig. 5b with our proposed method and a seed value SD = 0 ), based on a different seed value SD = 1 .

Fig. 7.
Fig. 7.

a. Blanking a rectangular region in the off-axis binary hologram representing the double depth image in Fig. 4a, and which has been embedded with the binary image in Fig. 5b. b. Numerical reconstructed image of the damaged and noise-contaminated off-axis binary hologram in a., at 0.5 m representing the double image in Fig. 4a. The image in Fig. 5a is embedded into the binary hologram based on the proposed method. c. Numerical reconstructed image of the damaged and noise-contaminated off-axis binary hologram in a., at 0.55 m representing the double image in Fig. 4a. The image in Fig. 5a is embedded into the binary hologram based on the proposed method.

Fig. 8.
Fig. 8.

Extracted embedded image from the damaged and noise-contaminated binary hologram in Fig. 7a.

Tables (1)

Tables Icon

Table 1. Optical Setting Adopted in the Hologram Generation Process

Equations (10)

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I D ( u , v ) = I 1 ( u , v ) I 2 ( u , v ) I 3 ( u , v ) I 4 ( u , v ) .
I 1 ( u , v ) = { I ( u , v ) u = τ M 0 otherwise ,
I 2 ( u , v ) = { I ( u , v ) v = τ M 0 otherwise .
I 3 ( u , v ) = { I ( u , v ) ( u mod M ) = ( v mod M ) 0 otherwise ,
I 4 ( u , v ) = { I ( u , v ) ( u mod M ) = [ ( M 1 ) ( v mod M ) ] 0 otherwise ,
O ( x , y ) | 0 x < X 0 y < Y = u = 0 X 1 v = 0 Y 1 I D ( u , v ) exp ( i 2 π r u ; v ; x ; y / λ ) r u ; v ; x ; y ,
H ( x , y ) = Re [ O ( x , y ) R ( y ) ] ,
H B ( x , y ) = { 1 if H ( x , y ) 0 0 otherwise .
H ( s j , t j ) = i j .
i j = H ( s j , t j ) .

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