Abstract

An optical security system based on a correlation between two separate binary computer-generated holograms has been developed and experimentally tested. The two holograms are designed using two different iterative algorithms: the projection- onto constrained sets algorithm and the direct binary search (DBS) algorithm. By placing the ready-to-use holograms on a modified joint transform correlator input plane, an output image is constructed as a result of a spatial correlation between the two functions coded by the holograms. Both simulation and experimental results are presented to demonstrate the system's performance. While we concentrate mainly on the DBS algorithm, we also compare the performance of both algorithms.

© 2006 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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  7. M. A. Seldowitz, J. P. Allebach, and D. W. Sweeney, "Synthesis of digital holograms by direct binary search," Appl. Opt. 26, 2788-2798 (1987).
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    [CrossRef]
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2005 (1)

2003 (2)

A. Sinha, and K. Singh, "A technique for image encryption using digital signature," Opt. Commun. 218, 229-234 (2003).
[CrossRef]

D. Abookasis and J. Rosen, "Digital correlation holograms implemented on a joint transform correlator," Opt. Commun. 225, 31-37 (2003).
[CrossRef]

2002 (2)

2001 (1)

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).
[CrossRef]

2000 (1)

1997 (1)

B. Javidi, "Securing information with optical technologies," Phys. Today 50(3), 27-32 (1997).
[CrossRef]

1994 (1)

J-Y. Zhuang and O. K. Ersoy, "Fast decimation-in-frequency direct binary search algorithms for synthesis of computer-generated holograms," J. Opt. Soc. A 11, 135-143 (1994).
[CrossRef]

1991 (1)

B. K. Jennison, J. P. Allebach, and D. W. Sweeney, "Efficient design of direct-binary-search computer generated holograms," J. Opt. Soc. A 8, 652-660 (1991).
[CrossRef]

1987 (1)

1967 (1)

J. J. Burch, "A computer algorithm for the synthesis of spatial frequency filter," Proc. IEEE 55, 599-601 (1967).
[CrossRef]

Abookasis, D.

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).
[CrossRef] [PubMed]

D. Abookasis and J. Rosen, "Digital correlation holograms implemented on a joint transform correlator," Opt. Commun. 225, 31-37 (2003).
[CrossRef]

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).
[CrossRef]

Abramson, O.

Allebach, J. P.

B. K. Jennison, J. P. Allebach, and D. W. Sweeney, "Efficient design of direct-binary-search computer generated holograms," J. Opt. Soc. A 8, 652-660 (1991).
[CrossRef]

M. A. Seldowitz, J. P. Allebach, and D. W. Sweeney, "Synthesis of digital holograms by direct binary search," Appl. Opt. 26, 2788-2798 (1987).
[CrossRef] [PubMed]

Arazi, O.

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).
[CrossRef]

Burch, J. J.

J. J. Burch, "A computer algorithm for the synthesis of spatial frequency filter," Proc. IEEE 55, 599-601 (1967).
[CrossRef]

Chang, H. T.

Chhetri, B. B.

Ersoy, O. K.

J-Y. Zhuang and O. K. Ersoy, "Fast decimation-in-frequency direct binary search algorithms for synthesis of computer-generated holograms," J. Opt. Soc. A 11, 135-143 (1994).
[CrossRef]

Fujimoto, A.

Javidi, B.

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).
[CrossRef]

B. Javidi, "Securing information with optical technologies," Phys. Today 50(3), 27-32 (1997).
[CrossRef]

Jennison, B. K.

B. K. Jennison, J. P. Allebach, and D. W. Sweeney, "Efficient design of direct-binary-search computer generated holograms," J. Opt. Soc. A 8, 652-660 (1991).
[CrossRef]

Kuo, C. J.

Lu, W. C.

Montal, O.

Ohtsubo, J.

Rosen, J.

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).
[CrossRef] [PubMed]

D. Abookasis and J. Rosen, "Digital correlation holograms implemented on a joint transform correlator," Opt. Commun. 225, 31-37 (2003).
[CrossRef]

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).
[CrossRef]

Seldowitz, M. A.

Shimomura, T.

Singh, K.

A. Sinha, and K. Singh, "A technique for image encryption using digital signature," Opt. Commun. 218, 229-234 (2003).
[CrossRef]

Sinha, A.

A. Sinha, and K. Singh, "A technique for image encryption using digital signature," Opt. Commun. 218, 229-234 (2003).
[CrossRef]

Sweeney, D. W.

B. K. Jennison, J. P. Allebach, and D. W. Sweeney, "Efficient design of direct-binary-search computer generated holograms," J. Opt. Soc. A 8, 652-660 (1991).
[CrossRef]

M. A. Seldowitz, J. P. Allebach, and D. W. Sweeney, "Synthesis of digital holograms by direct binary search," Appl. Opt. 26, 2788-2798 (1987).
[CrossRef] [PubMed]

Yang, S.

Zhuang, J-Y.

J-Y. Zhuang and O. K. Ersoy, "Fast decimation-in-frequency direct binary search algorithms for synthesis of computer-generated holograms," J. Opt. Soc. A 11, 135-143 (1994).
[CrossRef]

Appl. Opt. (5)

J. Opt. Soc. A (2)

B. K. Jennison, J. P. Allebach, and D. W. Sweeney, "Efficient design of direct-binary-search computer generated holograms," J. Opt. Soc. A 8, 652-660 (1991).
[CrossRef]

J-Y. Zhuang and O. K. Ersoy, "Fast decimation-in-frequency direct binary search algorithms for synthesis of computer-generated holograms," J. Opt. Soc. A 11, 135-143 (1994).
[CrossRef]

Opt. Commun. (2)

A. Sinha, and K. Singh, "A technique for image encryption using digital signature," Opt. Commun. 218, 229-234 (2003).
[CrossRef]

D. Abookasis and J. Rosen, "Digital correlation holograms implemented on a joint transform correlator," Opt. Commun. 225, 31-37 (2003).
[CrossRef]

Opt. Eng. (1)

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).
[CrossRef]

Phys. Today (1)

B. Javidi, "Securing information with optical technologies," Phys. Today 50(3), 27-32 (1997).
[CrossRef]

Proc. IEEE (1)

J. J. Burch, "A computer algorithm for the synthesis of spatial frequency filter," Proc. IEEE 55, 599-601 (1967).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Schematics of a modified JTC used for both the computer simulation and the optical experiments.

Fig. 2
Fig. 2

Enlarged portion (550 × 550 pixels out of 1344 × 960 pixels) of the DCH transparency generated by the DBS algorithm.

Fig. 3
Fig. 3

Enlarged portion (550 × 550 pixels out of 1344 × 960 pixels) of the DCH transparency generated by the POCS algorithm.

Fig. 4
Fig. 4

MSE versus the number of iterations of the (a) DBS and (b) POCS algorithms.

Fig. 5
Fig. 5

Hologram pixel changes versus number of iterations during the DBS algorithm.

Fig. 6
Fig. 6

Digital reconstitution of the distribution of the three diffraction orders on the power spectrum plane obtained from (a) the hologram shown in Fig. 2 and (b) the hologram shown in Fig. 3.

Fig. 7
Fig. 7

Digital image reconstruction of the modified JTC output plane from Fig. 6; (a) DBS and (b) binary POCS.

Fig. 8
Fig. 8

DBS optical results of the (a) three diffraction orders on the power spectrum plane and (b) image construction on the correlation plane.

Fig. 9
Fig. 9

Binary POCS optical results of the (a) three diffraction orders on the power spectrum plane and (b) image construction on the correlation plane.

Tables (1)

Tables Icon

Table 1 Comparison Performance for DBS and Binary POCS Algorithms

Equations (5)

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k b ( x , y ) = B ( x , y ) r e c t ( x A , y B ) δ ( x a , y b ) ,
l b ( x , y ) = Bin { cos [ 2 π ( α x + β y ) + ϕ r ( x , y ) ] } ×   rect ( x A , y B ) δ ( x + a , y + b ) ,
H ( f x , f y ) = 2D { k b ( x , y ) + l b ( x , y ) } rect ( f x α A ˜ , f y β B ˜ ) = K ( f x α , f y β ) exp [ i 2 π { ( f x α ) a + ( f y β ) b } ] + L ( f x α , f y β ) × exp [ i 2 π { ( f x α ) a + ( f y β ) b } ] ,
I ( f ˜ x , f ˜ y ) = | exp [ i 2 π ( a f ˜ x + b f ˜ y ) ] K ( f ˜ x , f ˜ y ) + exp [ i 2 π ( a f ˜ x + b f ˜ y ) ] L ( f ˜ x , f ˜ y ) | 2 = | K ( f ˜ x , f ˜ y ) | 2 + | L ( f ˜ x , f ˜ y ) | 2 + exp [ i 4 π ( a f ˜ x + b f ˜ y ) ] K ( f ˜ x , f ˜ y ) L ( f ˜ x , f ˜ y ) + exp [ i 4 π ( a f ˜ x + b f ˜ y ) ] K ( f ˜ x , f ˜ y ) L ( f ˜ x , f ˜ y ) ,
c ( x o , y o ) = k ( x o , y o ) k ( x o , y o ) + l ( x o , y o ) l ( x o , y o ) + [ k ( x o , y o ) l ( x o , y o ) ] δ ( x o 2 a , y o 2 b ) + [ l ( x o , y o ) k ( x o , y o ) ] δ ×   ( x o + 2 a , y o + 2 b ) ,

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