Abstract

The use of photorefractive materials such as Bi12SiO20 as dynamic holographic media is becoming an interesting alternative to that of the current liquid-crystal-based modulators in real-time optical image processing. We present an experimental realization of optical correlation for pattern recognition by means of a photorefractive joint transform correlator. The correlator operates with a liquid-crystal television as the input and a photorefractive crystal at the recording plane. We consider two possible ways of registering the Fourier plane information: conventional detection of the joint power spectrum, and utilization of only phase information at the Fourier plane by suitable preprocessing of the scene and the reference at the object plane. We compare the latter case with the performance of a binary joint transform correlator. Analysis, simulations, and experimental results are presented.

[Optical Society of America ]

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References

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  1. A. VanderLugt , Signal detection by complex spatial filtering , IEEE Trans. Inf. Theory IETTAW IT-10 , 139 145 ( 1964
  2. C. S. Weaver and J. W. Goodman , A technique for optically convolving two functions , Appl. Opt. APOPAI 5 , 1248 1249 ( 1966
    [CrossRef] [PubMed]
  3. S. Yu and X. J. Lu , A real-time programmable joint transform correlator , Opt. Commun. OPCOB8 52 , 10 16 ( 1984
    [CrossRef]
  4. H-K. Liu , J. A. Davis , and R. A. Lilly , Optical-data-processing properties of a liquid-crystal television spatial light modulator , Opt. Lett. OPLEDP 10 , 635 637 ( 1985
    [CrossRef] [PubMed]
  5. C. Kirsch , D. A. Gregory , M. W. Thie , and B. K. Jones , Modulation characteristics of the Epson liquid crystal television , Opt. Eng. OPEGAR 31 , 963 969 ( 1992
    [CrossRef]
  6. L. Pichon and J. P. Huignard , Dynamic joint-Fourier transform correlator by Bragg diffraction in photorefractive Bi 12 SiO 20 crystals , Opt. Commun. OPCOB8 36 , 277 280 ( 1981
    [CrossRef]
  7. C. Soutar , Z. Q. Wang , C. M. Cartwright , and W. A. Gillespie , Real-time optical intensity correlator using photorefractive BSO and liquid crystal television , J. Mod. Opt. JMOPEW 39 , 761 769 ( 1992
    [CrossRef]
  8. B. Javidi , Nonlinear correlation joint transform correlation , Appl. Opt. APOPAI 28 , 2358 2367 ( 1989
    [CrossRef] [PubMed]
  9. S. Vallmitjana , A. Carnicer , E. Mart n-Badosa , and I. Juvells , Nonlinear filtering in object and Fourier space in a joint transform optical correlator: comparison and experimental realization , Appl. Opt. APOPAI 34 , 3942 3949 ( 1995
    [CrossRef] [PubMed]
  10. F. T. S. Yu , S. Jutamulia , T. W. Lin , and D. A. Gregory , Adaptive real-time pattern recognition using a liquid crystal TV based joint transform correlator , Appl. Opt. APOPAI 26 , 1370 1372 ( 1987
    [CrossRef] [PubMed]
  11. B. Javidi , J. Wang , and Q. Tang , Multiple-object binary joint transform correlation using multiple level threshold crossing , Appl. Opt. APOPAI 30 , 4234 4244 ( 1991
    [CrossRef] [PubMed]
  12. Q. Zhan and T. Minemoto , Successful pattern matching with a large number of reference patterns using a joint Fourier-transform correlator , Jpn. J. Appl. Phys. JAPNDE 32 , 3471 3476 ( 1993
    [CrossRef]
  13. Y. Osugi , Q. Zhan , and T. Minemoto , Hybrid binary subtracted joint transform correlator for a large number of reference patterns using a Bi 12 SiO 20 (BSO) spatial light modulator and a laser scanner , Opt. Rev. OPREFN 1 , 159 162 ( 1994
    [CrossRef]
  14. K. Chalasinska-Macukow and C. Gorecki , Optoelectronic implementation of a quasi-phase correlator , Opt. Commun. OPCOB8 93 , 11 18 ( 1992
    [CrossRef]
  15. A. Carnicer , E. Mart n-Badosa , I. Juvells , and S. Vallmitjana , Spatial envelope-free nonlinear joint transform correlator , Opt. Commun. OPCOB8 114 , 336 343 ( 1995
    [CrossRef]
  16. D. Feng , H. Zhao , and S. Xia , Amplitude modulated joint transform correlator for improving correlation discrimination , Opt. Commun. OPCOB8 86 , 260 264 ( 1991
    [CrossRef]
  17. F. Cheng , F. T. S. Yu , and D. A. Gregory , Multitarget detection using spatial synthesis joint transform correlator , Appl. Opt. APOPAI 32 , 6521 6526 ( 1993
    [CrossRef] [PubMed]
  18. T. J. Hall , R. Jaura , L. M. Connors , and P. D. Foote , The photorefractive effect. A review , Prog. Quantum Electron. PQUEAH 10 , 77 146 ( 1985
    [CrossRef]
  19. M. G. Moharam , T. K. Gaylord , R. Magusson , and L. Young , Holographic grating formation in photorefractive crystals with arbitrary electron transport lengths , J. Appl. Phys. JAPIAU 50 , 5642 5651 ( 1979
    [CrossRef]
  20. E. Ochoa , F. Vachss , and L. Hesselink , Higher order analysis of the photorefractive effect for large modulation depths , J. Opt. Soc. Am. A JOAOD6 3 , 181 187 ( 1986
    [CrossRef]
  21. Y. Osugi , H. Mizukawa , and T. Minemoto , Quantization and truncation conditions of Fourier power spectrum for good performance in a binary subtracted joint transform correlator , Opt. Rev. OPREFN 3 , 161 170 ( 1996
    [CrossRef]
  22. B. Javidi , J. Ruiz , and C. Ruiz , Performance of the binary nonlinear joint transform correlators in the presence of the Fourier plane quantization , Opt. Commun. OPCOB8 80 , 275 284 ( 1991
    [CrossRef]
  23. W. H. Lee , Sampled Fourier transform hologram generated by computer , Appl. Opt. APOPAI 9 , 639 643 ( 1970
    [CrossRef] [PubMed]
  24. B. V. K. Vijaya Kumar and L. Hassebrook , Performance measures for correlation filters , Appl. Opt. APOPAI 29 , 2997 3006 ( 1990
    [CrossRef]
  25. C. Soutar , W. A. Gillespie , and C. M. Cartwright , The effect of optical bias on grating formation dynamics in photorefractive BSO , Opt. Commun. OPCOB8 90 , 329 334 ( 1992
    [CrossRef]

Cartwright, C. M

C. Soutar , Z. Q. Wang , C. M. Cartwright , and W. A. Gillespie , Real-time optical intensity correlator using photorefractive BSO and liquid crystal television , J. Mod. Opt. JMOPEW 39 , 761 769 ( 1992
[CrossRef]

Gillespie, W. A

C. Soutar , Z. Q. Wang , C. M. Cartwright , and W. A. Gillespie , Real-time optical intensity correlator using photorefractive BSO and liquid crystal television , J. Mod. Opt. JMOPEW 39 , 761 769 ( 1992
[CrossRef]

Jones, B. K

C. Kirsch , D. A. Gregory , M. W. Thie , and B. K. Jones , Modulation characteristics of the Epson liquid crystal television , Opt. Eng. OPEGAR 31 , 963 969 ( 1992
[CrossRef]

Kirsch, C

C. Kirsch , D. A. Gregory , M. W. Thie , and B. K. Jones , Modulation characteristics of the Epson liquid crystal television , Opt. Eng. OPEGAR 31 , 963 969 ( 1992
[CrossRef]

Lin, T. W

F. T. S. Yu , S. Jutamulia , T. W. Lin , and D. A. Gregory , Adaptive real-time pattern recognition using a liquid crystal TV based joint transform correlator , Appl. Opt. APOPAI 26 , 1370 1372 ( 1987
[CrossRef] [PubMed]

Liu, H-K

Magusson, R

M. G. Moharam , T. K. Gaylord , R. Magusson , and L. Young , Holographic grating formation in photorefractive crystals with arbitrary electron transport lengths , J. Appl. Phys. JAPIAU 50 , 5642 5651 ( 1979
[CrossRef]

Martn-Badosa, E

Mizukawa, H

Y. Osugi , H. Mizukawa , and T. Minemoto , Quantization and truncation conditions of Fourier power spectrum for good performance in a binary subtracted joint transform correlator , Opt. Rev. OPREFN 3 , 161 170 ( 1996
[CrossRef]

Osugi, Y

Y. Osugi , Q. Zhan , and T. Minemoto , Hybrid binary subtracted joint transform correlator for a large number of reference patterns using a Bi 12 SiO 20 (BSO) spatial light modulator and a laser scanner , Opt. Rev. OPREFN 1 , 159 162 ( 1994
[CrossRef]

Ruiz, C

B. Javidi , J. Ruiz , and C. Ruiz , Performance of the binary nonlinear joint transform correlators in the presence of the Fourier plane quantization , Opt. Commun. OPCOB8 80 , 275 284 ( 1991
[CrossRef]

Thie, M. W

C. Kirsch , D. A. Gregory , M. W. Thie , and B. K. Jones , Modulation characteristics of the Epson liquid crystal television , Opt. Eng. OPEGAR 31 , 963 969 ( 1992
[CrossRef]

Wang, Z. Q

C. Soutar , Z. Q. Wang , C. M. Cartwright , and W. A. Gillespie , Real-time optical intensity correlator using photorefractive BSO and liquid crystal television , J. Mod. Opt. JMOPEW 39 , 761 769 ( 1992
[CrossRef]

Xia, S

D. Feng , H. Zhao , and S. Xia , Amplitude modulated joint transform correlator for improving correlation discrimination , Opt. Commun. OPCOB8 86 , 260 264 ( 1991
[CrossRef]

Zhan, Q

Q. Zhan and T. Minemoto , Successful pattern matching with a large number of reference patterns using a joint Fourier-transform correlator , Jpn. J. Appl. Phys. JAPNDE 32 , 3471 3476 ( 1993
[CrossRef]

Other (25)

A. VanderLugt , Signal detection by complex spatial filtering , IEEE Trans. Inf. Theory IETTAW IT-10 , 139 145 ( 1964

C. S. Weaver and J. W. Goodman , A technique for optically convolving two functions , Appl. Opt. APOPAI 5 , 1248 1249 ( 1966
[CrossRef] [PubMed]

S. Yu and X. J. Lu , A real-time programmable joint transform correlator , Opt. Commun. OPCOB8 52 , 10 16 ( 1984
[CrossRef]

C. Kirsch , D. A. Gregory , M. W. Thie , and B. K. Jones , Modulation characteristics of the Epson liquid crystal television , Opt. Eng. OPEGAR 31 , 963 969 ( 1992
[CrossRef]

L. Pichon and J. P. Huignard , Dynamic joint-Fourier transform correlator by Bragg diffraction in photorefractive Bi 12 SiO 20 crystals , Opt. Commun. OPCOB8 36 , 277 280 ( 1981
[CrossRef]

C. Soutar , Z. Q. Wang , C. M. Cartwright , and W. A. Gillespie , Real-time optical intensity correlator using photorefractive BSO and liquid crystal television , J. Mod. Opt. JMOPEW 39 , 761 769 ( 1992
[CrossRef]

Q. Zhan and T. Minemoto , Successful pattern matching with a large number of reference patterns using a joint Fourier-transform correlator , Jpn. J. Appl. Phys. JAPNDE 32 , 3471 3476 ( 1993
[CrossRef]

Y. Osugi , Q. Zhan , and T. Minemoto , Hybrid binary subtracted joint transform correlator for a large number of reference patterns using a Bi 12 SiO 20 (BSO) spatial light modulator and a laser scanner , Opt. Rev. OPREFN 1 , 159 162 ( 1994
[CrossRef]

K. Chalasinska-Macukow and C. Gorecki , Optoelectronic implementation of a quasi-phase correlator , Opt. Commun. OPCOB8 93 , 11 18 ( 1992
[CrossRef]

A. Carnicer , E. Mart n-Badosa , I. Juvells , and S. Vallmitjana , Spatial envelope-free nonlinear joint transform correlator , Opt. Commun. OPCOB8 114 , 336 343 ( 1995
[CrossRef]

D. Feng , H. Zhao , and S. Xia , Amplitude modulated joint transform correlator for improving correlation discrimination , Opt. Commun. OPCOB8 86 , 260 264 ( 1991
[CrossRef]

F. T. S. Yu , S. Jutamulia , T. W. Lin , and D. A. Gregory , Adaptive real-time pattern recognition using a liquid crystal TV based joint transform correlator , Appl. Opt. APOPAI 26 , 1370 1372 ( 1987
[CrossRef] [PubMed]

T. J. Hall , R. Jaura , L. M. Connors , and P. D. Foote , The photorefractive effect. A review , Prog. Quantum Electron. PQUEAH 10 , 77 146 ( 1985
[CrossRef]

M. G. Moharam , T. K. Gaylord , R. Magusson , and L. Young , Holographic grating formation in photorefractive crystals with arbitrary electron transport lengths , J. Appl. Phys. JAPIAU 50 , 5642 5651 ( 1979
[CrossRef]

Y. Osugi , H. Mizukawa , and T. Minemoto , Quantization and truncation conditions of Fourier power spectrum for good performance in a binary subtracted joint transform correlator , Opt. Rev. OPREFN 3 , 161 170 ( 1996
[CrossRef]

B. Javidi , J. Ruiz , and C. Ruiz , Performance of the binary nonlinear joint transform correlators in the presence of the Fourier plane quantization , Opt. Commun. OPCOB8 80 , 275 284 ( 1991
[CrossRef]

W. H. Lee , Sampled Fourier transform hologram generated by computer , Appl. Opt. APOPAI 9 , 639 643 ( 1970
[CrossRef] [PubMed]

C. Soutar , W. A. Gillespie , and C. M. Cartwright , The effect of optical bias on grating formation dynamics in photorefractive BSO , Opt. Commun. OPCOB8 90 , 329 334 ( 1992
[CrossRef]

E. Ochoa , F. Vachss , and L. Hesselink , Higher order analysis of the photorefractive effect for large modulation depths , J. Opt. Soc. Am. A JOAOD6 3 , 181 187 ( 1986
[CrossRef]

H-K. Liu , J. A. Davis , and R. A. Lilly , Optical-data-processing properties of a liquid-crystal television spatial light modulator , Opt. Lett. OPLEDP 10 , 635 637 ( 1985
[CrossRef] [PubMed]

B. Javidi , Nonlinear correlation joint transform correlation , Appl. Opt. APOPAI 28 , 2358 2367 ( 1989
[CrossRef] [PubMed]

B. V. K. Vijaya Kumar and L. Hassebrook , Performance measures for correlation filters , Appl. Opt. APOPAI 29 , 2997 3006 ( 1990
[CrossRef]

B. Javidi , J. Wang , and Q. Tang , Multiple-object binary joint transform correlation using multiple level threshold crossing , Appl. Opt. APOPAI 30 , 4234 4244 ( 1991
[CrossRef] [PubMed]

F. Cheng , F. T. S. Yu , and D. A. Gregory , Multitarget detection using spatial synthesis joint transform correlator , Appl. Opt. APOPAI 32 , 6521 6526 ( 1993
[CrossRef] [PubMed]

S. Vallmitjana , A. Carnicer , E. Mart n-Badosa , and I. Juvells , Nonlinear filtering in object and Fourier space in a joint transform optical correlator: comparison and experimental realization , Appl. Opt. APOPAI 34 , 3942 3949 ( 1995
[CrossRef] [PubMed]

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Figures (9)

Fig. 1
Fig. 1

Standard JTC experimental setup: L1, L2, lenses.

Fig. 2
Fig. 2

Variation of the square modulus of the space-charge field (proportional to the refractive index) with intensity modulation for a range of acceptor concentrations.

Fig. 3
Fig. 3

Matched joint scene with zero-mean Gaussian additive noise of standard deviation σ=70.

Fig. 4
Fig. 4

Simulated PTE results for the POPJTC and the PJTC with increasing noise.

Fig. 5
Fig. 5

BSO JTC experimental setup: P’s, polarizers; A, analyzer; other abbreviations as defined in text.

Fig. 6
Fig. 6

Experimental correlation of conventional input with a noisy scene (σ=70).

Fig. 7
Fig. 7

Experimental correlation of the encoded phase-only input with a noisy scene (σ=70).

Fig. 8
Fig. 8

Experimental PTE results for the POPJTC and the PJTC.

Fig. 9
Fig. 9

Measure of signal degradation owing to increasing noise.

Equations (26)

Equations on this page are rendered with MathJax. Learn more.

I(u, v)=|FR(u, v)|2+|FS(u, v)|2+2|FR(u, v)||FS(u, v)|cos[x0u+y0v+ϕS(u, v)-ϕR(u, v)],
Ib(u, v)=1I(u, v)IT(u, v)-1I(u, v)<IT(u, v),
Ib(u, v)=n=1An[u, v; IT(u, v)]cos{n[x0u+y0v+ϕS(u, v)-ϕR(u, v)]}.
IT(u, v)=|FR(u, v)|2+|FS(u, v)|2.
Ib(u, v)=n=0 12n+1 cos{(2n+1)[x0u+y0v+ϕS(u, v)-ϕR(u, v)]}=cos[x0u+y0v+ϕS(u, v)-ϕR(u, v)]+,
c(x, y)=δ(x-x0, y-y0)+δ(x+x0, y+y0).
m(u, v)=2[IS(u, v)IR(u, v)]1/2IS(u, v)+IR(u, v),
I(u, v)=[IR(u, v)+IS(u, v)]{1+m(u, v)×cos[x0u+y0v+ϕS(u, v)-ϕR(u, v)]}.
|Δn|=(n3r|E|)/2,
η=sin2πΔndλ2 cos θ2πΔndλ2 cos θ22,
|E|2 cos[x0u+y0v+ϕS(u, v)-ϕR(u, v)].
E=(1-m2)1/2-1m(Ea2+Ed2)1/2,
|E|2=(1-m2)1/2-1m2(Ea2+Ed2)+EdEq 2(1-m2)1/2-1m2(Ea2-Ed2)+2(1-m2)1/2-1(1-m2)1/2(Ea2+Ed2),
m=m1+(Ed/Eq)m.
fPO(x, y)=FT-1F(u, v)|F(u, v)|=FT-1FT[f(x, y)]|FT[f(x, y)]|,
h+(x, y)=h(x, y)h(x, y)00h(x, y)<0,
h-(x, y)=h(x, y)h(x, y)00h(x, y)>0.
r+(x, y)=1+nrn sin2πnxp,
r-(x, y)=1-nrn sin2πnxp.
hc(x, y)=h+(x, y)r+(x, y)+h-(x, y)r-(x, y)=[h+(x, y)+h-(x, y)]+[h+(x, y)-h-(x, y)]nrn sin2πnxp.
Hc(x, y)=[H+(u, v)+H-(u, v)]+[H+(u, v)-H-(u, v)]nrnδu-np=[H+(u, v)+H-(u, v)]+H(u, v)nrnδu-np.
flops=5N2(log2 N-2)+32N.
5N2(log2 N-2)+32N+5N2+5N2(log2 N-2)+32 N
=5N2(2 log2 N-3)+64N.
PTE=(fg)(0, 0)R2(fg)(x, y)dxdy.
SNR=correlationpeakmaximumvarianceofintensities<(max/2)

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