Abstract

Conventionally a holographic data storage system uses binary digital data as the input pages. We propose and demonstrate the use of a holographic data storage system for the purpose of invariant pattern recognition of gray-scale images. To improve the correlation accuracy for gray-scale images, we present a coding technique, phase Fourier transform (phase-FT) coding, to code a gray-scale image into a random and balanced digital binary image. In addition to the fact that a digital data page is obtained for incorporation into a holographic data storage system, this phase-FT coded image produces dc-free homogenized Fourier spectrum. This coded image can also be treated as an image for further processing, such as synthesis of distortion-invariant filters for invariant pattern recognition. A space-domain synthetic discriminant function (SDF) filter has been synthesized using these phase-FT coded images for rotation-invariant pattern recognition. Both simulation and experimental results are presented. The results show good correlation accuracy in comparison to correlation results obtained for SDF filter synthesized using the original gray-scale images themselves.

© 2010 Optical Society of America

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2009 (2)

2008 (1)

E. Watanabe, Y. Ichikawa, R. Akiyama, and K. Kodate, “Ultrahigh-speed optical correlation system using holographic disc,” Jpn. J. Appl. Phy. 47, 5964-5967 (2008).

2007 (1)

2006 (1)

2005 (2)

R. John, J. Joseph, and K. Singh, “An input-data page modulation scheme for content-addressable holographic digital data storage,” Opt. Commun. 249, 387-395 (2005).
[CrossRef]

R. John, J. Joseph, and K. Singh, “Holographic digital data storage using phase-modulated pixels,” Opt. Lasers Eng. 43, 183-194 (2005).

2004 (1)

R. John, J. Joseph, and K. Singh, “Phase-image based content-addressable holographic data storage,” Opt. Commun. 232, 99-106 (2004).
[CrossRef]

2003 (4)

T. Alieva and M. L. Calvo, “Importance of the phase and amplitude in the fractional Fourier transform,” J. Opt. Soc. Am. A 20, 533-541 (2003).
[CrossRef]

G. W. Burr, “Holography for information storage and processing,” Proc. SPIE 5181, 70-84 (2003).

W. Tan, Q. Xue, Y. Yan, and G. Jin, “Rotation invariant pattern recognition with a volume holographic wavelet correlation processor,” Chin. Opt. Lett. 1, 74-77 (2003).

L. Ding, Y. Yan, Q. Xue, and G. Jin, “Wavelet packet compression for volume holographic image recognition,” Opt. Commun. 216, 105-113 (2003).
[CrossRef]

2002 (1)

L. Domjan, P. Koppa, G. Szarvas, and J. Remenyi, “Ternary phase-amplitude modulation with twisted nematic liquid crystal displays for Fourier-plane homogenization in holographic data storage,” Optik (Jena) 113, 382-390 (2002).
[CrossRef]

2001 (1)

2000 (2)

W. Feng, Y. Yan, G. Jin, M. Wu, and Q. He, “Invariant performance of a volume holographic wavelet correlation processor,” Opt. Commun. 177, 141-148 (2000).
[CrossRef]

F. Grawert, G. W. Burr, S. Kobras, H. Hanssen, M. Riedel, C. M. Jefferson, M. Jurich, and H. Coufal, “Content-addressable holographic databases,” Proc. SPIE 4109, 177-188 (2000).

1999 (1)

1998 (1)

1997 (2)

1992 (1)

1988 (1)

1986 (2)

P. H. Gardenier, B. C. McCallum, and R. H. T. Bates, “Fourier transform magnitudes are unique pattern recognition templates,” Biol. Cybern. 54, 385-391 (1986).
[CrossRef]

D. Casasent and W. T. Chang, “Correlation synthetic discriminant functions,” Appl. Opt. 25, 2343-2350 (1986).
[CrossRef]

1984 (1)

R. H. T. Bates, “Uniqueness of solutions to two-dimensional Fourier phase problems for localized and positive images,” Comput. Vis. Graph. Image Process. 25, 205-217 (1984).

1982 (1)

M. H. Hayes, “The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform,” IEEE Trans. Acoust. Speech Signal Process. 30, 140-154(1982).
[CrossRef]

1981 (1)

A. V. Oppenheim and J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529-541 (1981).
[CrossRef]

1972 (1)

1971 (1)

G. Goldmann, “Recording of digital data masks in quasi Fourier holograms,” Optik (Jena) 34, 254-267 (1971).

1970 (1)

1964 (1)

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory 10, 139-145 (1964).
[CrossRef]

Akiyama, R.

E. Watanabe, Y. Ichikawa, R. Akiyama, and K. Kodate, “Ultrahigh-speed optical correlation system using holographic disc,” Jpn. J. Appl. Phy. 47, 5964-5967 (2008).

E. Watanabe, A. Naito, R. Akiyama, and K. Kodate, “Ultra-high-speed holographic optical correlation system using a new coding method for various images,” presented at the International Workshop on Holographic Memories, Irago, Aichi, Japan, 20-23 October 2008, p. 104.

Alieva, T.

Bahri, Z.

Bates, R. H. T.

P. H. Gardenier, B. C. McCallum, and R. H. T. Bates, “Fourier transform magnitudes are unique pattern recognition templates,” Biol. Cybern. 54, 385-391 (1986).
[CrossRef]

R. H. T. Bates, “Uniqueness of solutions to two-dimensional Fourier phase problems for localized and positive images,” Comput. Vis. Graph. Image Process. 25, 205-217 (1984).

Bernal, M. P.

Bernal Artajona, M. P.

R. K. Kostuk, M. P. Bernal Artajona, and Q. Gao, “Beam conditioning techniques for holographic recording systems,” in Holographic Data Storage, H. J. Coufal, D. Psaltis, and G. T. Sincerbox, eds. (Springer, 2000), pp. 259-269.

Burckhardt, C. B.

Burr, G. W.

Calvo, M. L.

Cao, L.

Cao, L.-C.

Casasent, D.

Chang, W. T.

Collings, N.

Coufal, H.

Dandliker, R.

Das, B.

Ding, L.

L. Ding, Y. Yan, Q. Xue, and G. Jin, “Wavelet packet compression for volume holographic image recognition,” Opt. Commun. 216, 105-113 (2003).
[CrossRef]

Domjan, L.

L. Domjan, P. Koppa, G. Szarvas, and J. Remenyi, “Ternary phase-amplitude modulation with twisted nematic liquid crystal displays for Fourier-plane homogenization in holographic data storage,” Optik (Jena) 113, 382-390 (2002).
[CrossRef]

Duelli, M.

Feng, W.

W. Feng, Y. Yan, G. Jin, M. Wu, and Q. He, “Invariant performance of a volume holographic wavelet correlation processor,” Opt. Commun. 177, 141-148 (2000).
[CrossRef]

Gao, Q.

R. K. Kostuk, M. P. Bernal Artajona, and Q. Gao, “Beam conditioning techniques for holographic recording systems,” in Holographic Data Storage, H. J. Coufal, D. Psaltis, and G. T. Sincerbox, eds. (Springer, 2000), pp. 259-269.

Gardenier, P. H.

P. H. Gardenier, B. C. McCallum, and R. H. T. Bates, “Fourier transform magnitudes are unique pattern recognition templates,” Biol. Cybern. 54, 385-391 (1986).
[CrossRef]

Goldmann, G.

G. Goldmann, “Recording of digital data masks in quasi Fourier holograms,” Optik (Jena) 34, 254-267 (1971).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Grawert, F.

F. Grawert, G. W. Burr, S. Kobras, H. Hanssen, M. Riedel, C. M. Jefferson, M. Jurich, and H. Coufal, “Content-addressable holographic databases,” Proc. SPIE 4109, 177-188 (2000).

Hanssen, H.

F. Grawert, G. W. Burr, S. Kobras, H. Hanssen, M. Riedel, C. M. Jefferson, M. Jurich, and H. Coufal, “Content-addressable holographic databases,” Proc. SPIE 4109, 177-188 (2000).

G. W. Burr, S. Kobras, H. Hanssen, and H. Coufal, “Content-addressable data storage by use of volume holograms,” Appl. Opt. 38, 6779-6784 (1999).
[CrossRef]

Hayes, M. H.

M. H. Hayes, “The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform,” IEEE Trans. Acoust. Speech Signal Process. 30, 140-154(1982).
[CrossRef]

He, Q.

K. Ni, Z. Qu, L. Cao, P. Su, Q. He, and G. Jin, “Improving accuracy of multichannel volume holographic correlators by using a two-dimensional interleaving method,” Opt. Lett. 32, 2972-2974 (2007).
[CrossRef]

W. Feng, Y. Yan, G. Jin, M. Wu, and Q. He, “Invariant performance of a volume holographic wavelet correlation processor,” Opt. Commun. 177, 141-148 (2000).
[CrossRef]

He, Q.-S.

Hoffnagle, J. A.

Ichikawa, Y.

E. Watanabe, Y. Ichikawa, R. Akiyama, and K. Kodate, “Ultrahigh-speed optical correlation system using holographic disc,” Jpn. J. Appl. Phy. 47, 5964-5967 (2008).

Jang, J.-S.

Jefferson, C. M.

Jin, G.

K. Ni, Z. Qu, L. Cao, P. Su, Q. He, and G. Jin, “Improving accuracy of multichannel volume holographic correlators by using a two-dimensional interleaving method,” Opt. Lett. 32, 2972-2974 (2007).
[CrossRef]

L. Ding, Y. Yan, Q. Xue, and G. Jin, “Wavelet packet compression for volume holographic image recognition,” Opt. Commun. 216, 105-113 (2003).
[CrossRef]

W. Tan, Q. Xue, Y. Yan, and G. Jin, “Rotation invariant pattern recognition with a volume holographic wavelet correlation processor,” Chin. Opt. Lett. 1, 74-77 (2003).

W. Feng, Y. Yan, G. Jin, M. Wu, and Q. He, “Invariant performance of a volume holographic wavelet correlation processor,” Opt. Commun. 177, 141-148 (2000).
[CrossRef]

Jin, G.-F.

John, R.

R. John, J. Joseph, and K. Singh, “An input-data page modulation scheme for content-addressable holographic digital data storage,” Opt. Commun. 249, 387-395 (2005).
[CrossRef]

R. John, J. Joseph, and K. Singh, “Holographic digital data storage using phase-modulated pixels,” Opt. Lasers Eng. 43, 183-194 (2005).

R. John, J. Joseph, and K. Singh, “Phase-image based content-addressable holographic data storage,” Opt. Commun. 232, 99-106 (2004).
[CrossRef]

Joseph, J.

B. Das, J. Joseph, and K. Singh, “Improved data search by zero-order (dc) peak filtering in a defocused volume holographic content-addressable memory,” Appl. Opt. 48, 55-63(2009).
[CrossRef]

J. Joseph and D. A. Waldman, “Homogenized Fourier transform holographic data storage using phase spatial light modulators and methods for recovery of data from the phase image,” Appl. Opt. 45, 6374-6380 (2006).
[CrossRef]

R. John, J. Joseph, and K. Singh, “An input-data page modulation scheme for content-addressable holographic digital data storage,” Opt. Commun. 249, 387-395 (2005).
[CrossRef]

R. John, J. Joseph, and K. Singh, “Holographic digital data storage using phase-modulated pixels,” Opt. Lasers Eng. 43, 183-194 (2005).

R. John, J. Joseph, and K. Singh, “Phase-image based content-addressable holographic data storage,” Opt. Commun. 232, 99-106 (2004).
[CrossRef]

Juday, R.

B. V. K. Vijaya Kumar, A. Mahalanobis, and R. Juday, Correlation Pattern Recognition (Cambridge Univ. Press, 2005).

Jurich, M.

F. Grawert, G. W. Burr, S. Kobras, H. Hanssen, M. Riedel, C. M. Jefferson, M. Jurich, and H. Coufal, “Content-addressable holographic databases,” Proc. SPIE 4109, 177-188 (2000).

Kobras, S.

F. Grawert, G. W. Burr, S. Kobras, H. Hanssen, M. Riedel, C. M. Jefferson, M. Jurich, and H. Coufal, “Content-addressable holographic databases,” Proc. SPIE 4109, 177-188 (2000).

G. W. Burr, S. Kobras, H. Hanssen, and H. Coufal, “Content-addressable data storage by use of volume holograms,” Appl. Opt. 38, 6779-6784 (1999).
[CrossRef]

Kodate, K.

E. Watanabe, Y. Ichikawa, R. Akiyama, and K. Kodate, “Ultrahigh-speed optical correlation system using holographic disc,” Jpn. J. Appl. Phy. 47, 5964-5967 (2008).

E. Watanabe, A. Naito, R. Akiyama, and K. Kodate, “Ultra-high-speed holographic optical correlation system using a new coding method for various images,” presented at the International Workshop on Holographic Memories, Irago, Aichi, Japan, 20-23 October 2008, p. 104.

Koppa, P.

L. Domjan, P. Koppa, G. Szarvas, and J. Remenyi, “Ternary phase-amplitude modulation with twisted nematic liquid crystal displays for Fourier-plane homogenization in holographic data storage,” Optik (Jena) 113, 382-390 (2002).
[CrossRef]

Kostuk, R. K.

R. K. Kostuk, M. P. Bernal Artajona, and Q. Gao, “Beam conditioning techniques for holographic recording systems,” in Holographic Data Storage, H. J. Coufal, D. Psaltis, and G. T. Sincerbox, eds. (Springer, 2000), pp. 259-269.

Lim, J. S.

A. V. Oppenheim and J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529-541 (1981).
[CrossRef]

Lohmann, A. W.

Ma, Q.

Macfarlane, R. M.

Mahalanobis, A.

B. V. K. Vijaya Kumar, A. Mahalanobis, and R. Juday, Correlation Pattern Recognition (Cambridge Univ. Press, 2005).

McCallum, B. C.

P. H. Gardenier, B. C. McCallum, and R. H. T. Bates, “Fourier transform magnitudes are unique pattern recognition templates,” Biol. Cybern. 54, 385-391 (1986).
[CrossRef]

Mendlovic, D.

Miyamura, Y.

Naito, A.

E. Watanabe, A. Naito, R. Akiyama, and K. Kodate, “Ultra-high-speed holographic optical correlation system using a new coding method for various images,” presented at the International Workshop on Holographic Memories, Irago, Aichi, Japan, 20-23 October 2008, p. 104.

Ni, K.

Oppenheim, A. V.

A. V. Oppenheim and J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529-541 (1981).
[CrossRef]

Oshida, Y.

Pourzand, A. R.

Qu, Z.

Quintanilla, M.

Remenyi, J.

L. Domjan, P. Koppa, G. Szarvas, and J. Remenyi, “Ternary phase-amplitude modulation with twisted nematic liquid crystal displays for Fourier-plane homogenization in holographic data storage,” Optik (Jena) 113, 382-390 (2002).
[CrossRef]

Riedel, M.

F. Grawert, G. W. Burr, S. Kobras, H. Hanssen, M. Riedel, C. M. Jefferson, M. Jurich, and H. Coufal, “Content-addressable holographic databases,” Proc. SPIE 4109, 177-188 (2000).

Shabtay, G.

Shelby, R. M.

Shin, D.-H.

Singh, K.

B. Das, J. Joseph, and K. Singh, “Improved data search by zero-order (dc) peak filtering in a defocused volume holographic content-addressable memory,” Appl. Opt. 48, 55-63(2009).
[CrossRef]

R. John, J. Joseph, and K. Singh, “An input-data page modulation scheme for content-addressable holographic digital data storage,” Opt. Commun. 249, 387-395 (2005).
[CrossRef]

R. John, J. Joseph, and K. Singh, “Holographic digital data storage using phase-modulated pixels,” Opt. Lasers Eng. 43, 183-194 (2005).

R. John, J. Joseph, and K. Singh, “Phase-image based content-addressable holographic data storage,” Opt. Commun. 232, 99-106 (2004).
[CrossRef]

Su, P.

Szarvas, G.

L. Domjan, P. Koppa, G. Szarvas, and J. Remenyi, “Ternary phase-amplitude modulation with twisted nematic liquid crystal displays for Fourier-plane homogenization in holographic data storage,” Optik (Jena) 113, 382-390 (2002).
[CrossRef]

Takeda, Y.

Tan, W.

VanderLugt, A.

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory 10, 139-145 (1964).
[CrossRef]

Vijaya Kumar, B. V. K.

Waldman, D. A.

Watanabe, E.

E. Watanabe, Y. Ichikawa, R. Akiyama, and K. Kodate, “Ultrahigh-speed optical correlation system using holographic disc,” Jpn. J. Appl. Phy. 47, 5964-5967 (2008).

E. Watanabe, A. Naito, R. Akiyama, and K. Kodate, “Ultra-high-speed holographic optical correlation system using a new coding method for various images,” presented at the International Workshop on Holographic Memories, Irago, Aichi, Japan, 20-23 October 2008, p. 104.

Wu, M.

W. Feng, Y. Yan, G. Jin, M. Wu, and Q. He, “Invariant performance of a volume holographic wavelet correlation processor,” Opt. Commun. 177, 141-148 (2000).
[CrossRef]

Xue, Q.

W. Tan, Q. Xue, Y. Yan, and G. Jin, “Rotation invariant pattern recognition with a volume holographic wavelet correlation processor,” Chin. Opt. Lett. 1, 74-77 (2003).

L. Ding, Y. Yan, Q. Xue, and G. Jin, “Wavelet packet compression for volume holographic image recognition,” Opt. Commun. 216, 105-113 (2003).
[CrossRef]

Yan, Y.

W. Tan, Q. Xue, Y. Yan, and G. Jin, “Rotation invariant pattern recognition with a volume holographic wavelet correlation processor,” Chin. Opt. Lett. 1, 74-77 (2003).

L. Ding, Y. Yan, Q. Xue, and G. Jin, “Wavelet packet compression for volume holographic image recognition,” Opt. Commun. 216, 105-113 (2003).
[CrossRef]

W. Feng, Y. Yan, G. Jin, M. Wu, and Q. He, “Invariant performance of a volume holographic wavelet correlation processor,” Opt. Commun. 177, 141-148 (2000).
[CrossRef]

Appl. Opt. (8)

Biol. Cybern. (1)

P. H. Gardenier, B. C. McCallum, and R. H. T. Bates, “Fourier transform magnitudes are unique pattern recognition templates,” Biol. Cybern. 54, 385-391 (1986).
[CrossRef]

Chin. Opt. Lett. (1)

Comput. Vis. Graph. Image Process. (1)

R. H. T. Bates, “Uniqueness of solutions to two-dimensional Fourier phase problems for localized and positive images,” Comput. Vis. Graph. Image Process. 25, 205-217 (1984).

IEEE Trans. Acoust. Speech Signal Process. (1)

M. H. Hayes, “The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform,” IEEE Trans. Acoust. Speech Signal Process. 30, 140-154(1982).
[CrossRef]

IEEE Trans. Inf. Theory (1)

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory 10, 139-145 (1964).
[CrossRef]

J. Opt. Soc. Am. A (3)

Jpn. J. Appl. Phy. (1)

E. Watanabe, Y. Ichikawa, R. Akiyama, and K. Kodate, “Ultrahigh-speed optical correlation system using holographic disc,” Jpn. J. Appl. Phy. 47, 5964-5967 (2008).

Opt. Commun. (4)

R. John, J. Joseph, and K. Singh, “An input-data page modulation scheme for content-addressable holographic digital data storage,” Opt. Commun. 249, 387-395 (2005).
[CrossRef]

W. Feng, Y. Yan, G. Jin, M. Wu, and Q. He, “Invariant performance of a volume holographic wavelet correlation processor,” Opt. Commun. 177, 141-148 (2000).
[CrossRef]

L. Ding, Y. Yan, Q. Xue, and G. Jin, “Wavelet packet compression for volume holographic image recognition,” Opt. Commun. 216, 105-113 (2003).
[CrossRef]

R. John, J. Joseph, and K. Singh, “Phase-image based content-addressable holographic data storage,” Opt. Commun. 232, 99-106 (2004).
[CrossRef]

Opt. Express (1)

Opt. Lasers Eng. (1)

R. John, J. Joseph, and K. Singh, “Holographic digital data storage using phase-modulated pixels,” Opt. Lasers Eng. 43, 183-194 (2005).

Opt. Lett. (3)

Optik (Jena) (2)

G. Goldmann, “Recording of digital data masks in quasi Fourier holograms,” Optik (Jena) 34, 254-267 (1971).

L. Domjan, P. Koppa, G. Szarvas, and J. Remenyi, “Ternary phase-amplitude modulation with twisted nematic liquid crystal displays for Fourier-plane homogenization in holographic data storage,” Optik (Jena) 113, 382-390 (2002).
[CrossRef]

Proc. IEEE (1)

A. V. Oppenheim and J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529-541 (1981).
[CrossRef]

Proc. SPIE (2)

F. Grawert, G. W. Burr, S. Kobras, H. Hanssen, M. Riedel, C. M. Jefferson, M. Jurich, and H. Coufal, “Content-addressable holographic databases,” Proc. SPIE 4109, 177-188 (2000).

G. W. Burr, “Holography for information storage and processing,” Proc. SPIE 5181, 70-84 (2003).

Other (7)

H. J. Coufal, D. Psaltis, and G. T. Sincerbox, eds., Holographic Data Storage (Springer-Verlag, 2000).

F. T. S. Yu and S. Jutamulia, eds., Optical Pattern Recognition (Cambridge Univ. Press, 1998).

B. Javidi, ed., Image Recognition and Classification; Algorithms, Systems, and Applications (Marcel Dekker, 2002).

R. K. Kostuk, M. P. Bernal Artajona, and Q. Gao, “Beam conditioning techniques for holographic recording systems,” in Holographic Data Storage, H. J. Coufal, D. Psaltis, and G. T. Sincerbox, eds. (Springer, 2000), pp. 259-269.

B. V. K. Vijaya Kumar, A. Mahalanobis, and R. Juday, Correlation Pattern Recognition (Cambridge Univ. Press, 2005).

E. Watanabe, A. Naito, R. Akiyama, and K. Kodate, “Ultra-high-speed holographic optical correlation system using a new coding method for various images,” presented at the International Workshop on Holographic Memories, Irago, Aichi, Japan, 20-23 October 2008, p. 104.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

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Figures (12)

Fig. 1
Fig. 1

(a) Gray-scale image of Tank 1, (b) Fourier spectrum of the image of Tank 1.

Fig. 2
Fig. 2

(a) Image obtained on binarizing the phase of the FT of the gray-scale image of Tank 1; (b) Fourier spectrum of (a); (c) phase-FT coded image of Tank 1 obtained through interleaving of (a); (d) Fourier spectrum of (c), showing dc-free homogenized spectrum at the Fourier plane.

Fig. 3
Fig. 3

False class gray-scale images: (a) Tank 2, (b) Tank 3, (c) Tank 4, and (d) Tank 5.

Fig. 4
Fig. 4

Synthesized rotation-invariant spatial-domain SDF filter for phase-FT coded images of Tank 1.

Fig. 5
Fig. 5

Simulation and experimental results for true class phase-FT coded images of Tank 1: (a)  15 ° rotated trained image, (b) simulated correlation output for (a), (c) experimental correlation output for (a), (d)  26 ° rotated untrained image, (e) simulated correlation output for (d), and (f) experimental correlation output for (d).

Fig. 6
Fig. 6

Simulation and experimental results for the false class phase-FT coded image of Tank 2: (a) simulated correlation output, (b) experimental correlation output.

Fig. 7
Fig. 7

Synthesized rotation-invariant spatial-domain SDF filter for gray-scale images of Tank 1.

Fig. 8
Fig. 8

Simulation and experimental results for true-class gray-scale images of Tank 1: (a)  15 ° rotated trained image, (b) simulated correlation output for (a), (c) experimental correlation output for (a), (d)  26 ° rotated untrained image, (e) simulated correlation output for (d), and (f) experimental correlation output for (d).

Fig. 9
Fig. 9

Simulation and experimental results for false-class gray scale images: (a)  21 ° rotated image of Tank 2, (b) simulated correlation output for (a), (c) experimental correlation output for (a), (d)  21 ° rotated image of Tank 3, (e) simulated correlation output for (d); (f) experimental correlation output for (d), (g)  21 ° rotated image of Tank 4, (h) simulated correlation output for (g);,(i) experimental correlation output for (g), (j)  21 ° rotated image of Tank 5, (k) simulated correlation output for (j), (l) experimental correlation output for (j).

Fig. 10
Fig. 10

Plot of correlation peak height versus angle of rotation ( 40 ° to + 40 ° ) for phase-FT coded images of true class (Tank 1) and false class (Tank 2, Tank 3, Tank 4, and Tank 5).

Fig. 11
Fig. 11

Plot of correlation peak height versus angle of rotation ( 40 ° to + 40 ° ) for gray-scale images of true class (Tank 1) and false class (Tank 2, Tank 3, Tank 4, and Tank 5).

Fig. 12
Fig. 12

Experimental setup for content-addressable holographic data storage system: S, shutter; PBS, polarizing beam splitter; SFBE, spatial filter-beam expander assembly; SLM, spatial light modulator; HWP, half-wave plate; QWP, quarter-wave plate; POL, polarizer; PRC, photorefractive crystal; L, lenses; M, mirrors; M rot , mirror mounted on precision rotation stage; CCD, charge-coupled device.

Equations (4)

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h ( k , l ) = n = 1 N a n x n ( k , l ) ,
u i = n = 1 N a n p in .
P a = u ,
a = P 1 u .

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