Abstract

Synthesis of gray-level computer-generated holograms allows for an increase of the information storage capability that is usually achieved with conventional binary filters. This is mainly because more degrees of freedom are available. We propose to profit from this feature by synthesizing complex filters formed by many superimposed holograms, each with a different carrier frequency. We apply these gray-level filters to perform multichannel correlation and in this way enhance the capability of optical correlators to process the information in parallel and simultaneously. First, we analyze the behavior of some performance criteria on the impulse response and on the correlation as a function of the number of holograms that are multiplexed. Then we show the results of two experiments: In the first a composed phase-only filter is used in a multiple-object recognition process. In the second a composed synthetic discriminant function filter is used to implement an object classification by means of a binary code.

© 2000 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 IT-1, 139–145 (1964).
  2. F. T. S. Yu, Q. Zhou, C. Zhang, “Multiple channel optical correlator via rotating grating on LCTV,” Appl. Opt. 27, 3770–3772 (1988).
    [CrossRef] [PubMed]
  3. Y. Sheng, T. Lu, D. Roberge, H. Caulfield, “Optical N4 implementation of a two dimensional wavelet transform,” Opt. Eng. 31, 1859–1864 (1992).
    [CrossRef]
  4. D. Mendlovic, I. Ouzieli, I. Kiryuschev, E. Marom, “Two-dimensional wavelet transform achieved by computer-generated multireference matched filter and Damman grating,” Appl. Opt. 34, 8213–8219 (1995).
    [CrossRef] [PubMed]
  5. A. Vargas, J. Campos, M. J. Yzuel, C. Iemmi, S. Ledesma, “One-step multichannel pattern recognition based on the pixelated structure of a spatial light modulator,” Appl. Opt. 37, 2063–2066 (1998).
    [CrossRef]
  6. D. Casasent, “Unified synthetic discriminant function computational formulation,” Appl. Opt. 23, 1620–1627 (1984).
    [CrossRef] [PubMed]
  7. D. Casasent, W. T. Chang, “Correlation synthetic discriminant functions,” Appl. Opt. 25, 2343–2350 (1986).
    [CrossRef] [PubMed]
  8. B. V. K. Vijaya Kumar, “Tutorial survey of composite filter designs for optical correlators,” Appl. Opt. 31, 4773–4801 (1992).
    [CrossRef]
  9. M. Montes-Usategui, J. Campos, I. Juvells, “Computation of arbitrarily constrained synthetic discriminant functions,” Appl. Opt. 34, 3904–3914 (1995).
    [CrossRef] [PubMed]
  10. S. M. Arnold, “Electron beam fabrication of computer generated holograms,” Opt. Eng. 24, 803–807 (1985).
    [CrossRef]
  11. N. Emerton, R. W. Smith, R. G. Cañas, “Blazed surface relief diffractive optical elements,” in Holographic Systems Components and Applications, IERE Conf. Proc. 76 (Cambridge University, Cambridge, UK, 1987), pp. 99–103.
  12. K. S. Urquhart, R. Stein, S. H. Lee, “Computer generated holograms fabricated by direct write of positive electron beam resist,” Opt. Lett. 18, 308–310 (1993).
    [CrossRef]
  13. B. R. Brown, A. W. Lohmann, “Complex spatial filtering with binary masks,” Appl. Opt. 5, 967–969 (1966).
    [CrossRef] [PubMed]
  14. W. H. Lee, “Sampled Fourier transform hologram generated by computer,” Appl. Opt. 9, 639–643 (1970).
    [CrossRef] [PubMed]
  15. W. H. Lee, “Binary synthetic holograms,” Appl. Opt. 13, 1677–1682 (1974).
    [CrossRef] [PubMed]
  16. A. J. Lee, P. Casasent, “Computer generated hologram recording using a laser printer,” Appl. Opt. 26, 136–138 (1987).
    [CrossRef] [PubMed]
  17. D. C. O’Shea, J. W. Beletic, M. Poutus, “Binary-mask generation for diffractive optical elements using microcomputers,” Appl. Opt. 32, 2566–2572 (1993).
    [CrossRef] [PubMed]
  18. U. Karckhard, J. Schwider, M. Schrader, N. Streibl, “Synthetic holograms written by a laser pattern generator,” Opt. Eng. 32, 781–785 (1993).
    [CrossRef]
  19. I. Moreno, C. Gorecki, J. Campos, M. J. Yzuel, “Comparison of computer generated holograms produced by laser printers and lithography: application to pattern recognition,” Opt. Eng. 34, 3520–3525 (1995).
    [CrossRef]
  20. J. J. Burch, “A computer algorithm for the synthesis of spatial frequency filters,” Proc. IEEE 55, 599–600 (1967).
    [CrossRef]
  21. J. L. Horner, P. D. Gianino, “Phase-only matched filtering,” Appl. Opt. 23, 812–816 (1984).
    [CrossRef] [PubMed]
  22. M. Bernhardt, F. Wyrowski, O. Bryngdahl, “Iterative techniques to integrate different optical functions in a diffractive phase element,” Appl. Opt. 30, 4629–4635 (1991).
    [CrossRef] [PubMed]

1998 (1)

1995 (3)

1993 (3)

1992 (2)

Y. Sheng, T. Lu, D. Roberge, H. Caulfield, “Optical N4 implementation of a two dimensional wavelet transform,” Opt. Eng. 31, 1859–1864 (1992).
[CrossRef]

B. V. K. Vijaya Kumar, “Tutorial survey of composite filter designs for optical correlators,” Appl. Opt. 31, 4773–4801 (1992).
[CrossRef]

1991 (1)

1988 (1)

1987 (1)

1986 (1)

1985 (1)

S. M. Arnold, “Electron beam fabrication of computer generated holograms,” Opt. Eng. 24, 803–807 (1985).
[CrossRef]

1984 (2)

1974 (1)

1970 (1)

1967 (1)

J. J. Burch, “A computer algorithm for the synthesis of spatial frequency filters,” Proc. IEEE 55, 599–600 (1967).
[CrossRef]

1966 (1)

1964 (1)

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-1, 139–145 (1964).

Arnold, S. M.

S. M. Arnold, “Electron beam fabrication of computer generated holograms,” Opt. Eng. 24, 803–807 (1985).
[CrossRef]

Beletic, J. W.

Bernhardt, M.

Brown, B. R.

Bryngdahl, O.

Burch, J. J.

J. J. Burch, “A computer algorithm for the synthesis of spatial frequency filters,” Proc. IEEE 55, 599–600 (1967).
[CrossRef]

Campos, J.

Cañas, R. G.

N. Emerton, R. W. Smith, R. G. Cañas, “Blazed surface relief diffractive optical elements,” in Holographic Systems Components and Applications, IERE Conf. Proc. 76 (Cambridge University, Cambridge, UK, 1987), pp. 99–103.

Casasent, D.

Casasent, P.

Caulfield, H.

Y. Sheng, T. Lu, D. Roberge, H. Caulfield, “Optical N4 implementation of a two dimensional wavelet transform,” Opt. Eng. 31, 1859–1864 (1992).
[CrossRef]

Chang, W. T.

Emerton, N.

N. Emerton, R. W. Smith, R. G. Cañas, “Blazed surface relief diffractive optical elements,” in Holographic Systems Components and Applications, IERE Conf. Proc. 76 (Cambridge University, Cambridge, UK, 1987), pp. 99–103.

Gianino, P. D.

Gorecki, C.

I. Moreno, C. Gorecki, J. Campos, M. J. Yzuel, “Comparison of computer generated holograms produced by laser printers and lithography: application to pattern recognition,” Opt. Eng. 34, 3520–3525 (1995).
[CrossRef]

Horner, J. L.

Iemmi, C.

Juvells, I.

Karckhard, U.

U. Karckhard, J. Schwider, M. Schrader, N. Streibl, “Synthetic holograms written by a laser pattern generator,” Opt. Eng. 32, 781–785 (1993).
[CrossRef]

Kiryuschev, I.

Ledesma, S.

Lee, A. J.

Lee, S. H.

Lee, W. H.

Lohmann, A. W.

Lu, T.

Y. Sheng, T. Lu, D. Roberge, H. Caulfield, “Optical N4 implementation of a two dimensional wavelet transform,” Opt. Eng. 31, 1859–1864 (1992).
[CrossRef]

Marom, E.

Mendlovic, D.

Montes-Usategui, M.

Moreno, I.

I. Moreno, C. Gorecki, J. Campos, M. J. Yzuel, “Comparison of computer generated holograms produced by laser printers and lithography: application to pattern recognition,” Opt. Eng. 34, 3520–3525 (1995).
[CrossRef]

O’Shea, D. C.

Ouzieli, I.

Poutus, M.

Roberge, D.

Y. Sheng, T. Lu, D. Roberge, H. Caulfield, “Optical N4 implementation of a two dimensional wavelet transform,” Opt. Eng. 31, 1859–1864 (1992).
[CrossRef]

Schrader, M.

U. Karckhard, J. Schwider, M. Schrader, N. Streibl, “Synthetic holograms written by a laser pattern generator,” Opt. Eng. 32, 781–785 (1993).
[CrossRef]

Schwider, J.

U. Karckhard, J. Schwider, M. Schrader, N. Streibl, “Synthetic holograms written by a laser pattern generator,” Opt. Eng. 32, 781–785 (1993).
[CrossRef]

Sheng, Y.

Y. Sheng, T. Lu, D. Roberge, H. Caulfield, “Optical N4 implementation of a two dimensional wavelet transform,” Opt. Eng. 31, 1859–1864 (1992).
[CrossRef]

Smith, R. W.

N. Emerton, R. W. Smith, R. G. Cañas, “Blazed surface relief diffractive optical elements,” in Holographic Systems Components and Applications, IERE Conf. Proc. 76 (Cambridge University, Cambridge, UK, 1987), pp. 99–103.

Stein, R.

Streibl, N.

U. Karckhard, J. Schwider, M. Schrader, N. Streibl, “Synthetic holograms written by a laser pattern generator,” Opt. Eng. 32, 781–785 (1993).
[CrossRef]

Urquhart, K. S.

VanderLugt, A.

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-1, 139–145 (1964).

Vargas, A.

Vijaya Kumar, B. V. K.

Wyrowski, F.

Yu, F. T. S.

Yzuel, M. J.

A. Vargas, J. Campos, M. J. Yzuel, C. Iemmi, S. Ledesma, “One-step multichannel pattern recognition based on the pixelated structure of a spatial light modulator,” Appl. Opt. 37, 2063–2066 (1998).
[CrossRef]

I. Moreno, C. Gorecki, J. Campos, M. J. Yzuel, “Comparison of computer generated holograms produced by laser printers and lithography: application to pattern recognition,” Opt. Eng. 34, 3520–3525 (1995).
[CrossRef]

Zhang, C.

Zhou, Q.

Appl. Opt. (14)

B. R. Brown, A. W. Lohmann, “Complex spatial filtering with binary masks,” Appl. Opt. 5, 967–969 (1966).
[CrossRef] [PubMed]

W. H. Lee, “Binary synthetic holograms,” Appl. Opt. 13, 1677–1682 (1974).
[CrossRef] [PubMed]

J. L. Horner, P. D. Gianino, “Phase-only matched filtering,” Appl. Opt. 23, 812–816 (1984).
[CrossRef] [PubMed]

D. Casasent, “Unified synthetic discriminant function computational formulation,” Appl. Opt. 23, 1620–1627 (1984).
[CrossRef] [PubMed]

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

A. J. Lee, P. Casasent, “Computer generated hologram recording using a laser printer,” Appl. Opt. 26, 136–138 (1987).
[CrossRef] [PubMed]

F. T. S. Yu, Q. Zhou, C. Zhang, “Multiple channel optical correlator via rotating grating on LCTV,” Appl. Opt. 27, 3770–3772 (1988).
[CrossRef] [PubMed]

M. Bernhardt, F. Wyrowski, O. Bryngdahl, “Iterative techniques to integrate different optical functions in a diffractive phase element,” Appl. Opt. 30, 4629–4635 (1991).
[CrossRef] [PubMed]

B. V. K. Vijaya Kumar, “Tutorial survey of composite filter designs for optical correlators,” Appl. Opt. 31, 4773–4801 (1992).
[CrossRef]

D. C. O’Shea, J. W. Beletic, M. Poutus, “Binary-mask generation for diffractive optical elements using microcomputers,” Appl. Opt. 32, 2566–2572 (1993).
[CrossRef] [PubMed]

M. Montes-Usategui, J. Campos, I. Juvells, “Computation of arbitrarily constrained synthetic discriminant functions,” Appl. Opt. 34, 3904–3914 (1995).
[CrossRef] [PubMed]

D. Mendlovic, I. Ouzieli, I. Kiryuschev, E. Marom, “Two-dimensional wavelet transform achieved by computer-generated multireference matched filter and Damman grating,” Appl. Opt. 34, 8213–8219 (1995).
[CrossRef] [PubMed]

A. Vargas, J. Campos, M. J. Yzuel, C. Iemmi, S. Ledesma, “One-step multichannel pattern recognition based on the pixelated structure of a spatial light modulator,” Appl. Opt. 37, 2063–2066 (1998).
[CrossRef]

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

IEEE Trans. Inf. Theory (1)

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-1, 139–145 (1964).

Opt. Eng. (4)

Y. Sheng, T. Lu, D. Roberge, H. Caulfield, “Optical N4 implementation of a two dimensional wavelet transform,” Opt. Eng. 31, 1859–1864 (1992).
[CrossRef]

S. M. Arnold, “Electron beam fabrication of computer generated holograms,” Opt. Eng. 24, 803–807 (1985).
[CrossRef]

U. Karckhard, J. Schwider, M. Schrader, N. Streibl, “Synthetic holograms written by a laser pattern generator,” Opt. Eng. 32, 781–785 (1993).
[CrossRef]

I. Moreno, C. Gorecki, J. Campos, M. J. Yzuel, “Comparison of computer generated holograms produced by laser printers and lithography: application to pattern recognition,” Opt. Eng. 34, 3520–3525 (1995).
[CrossRef]

Opt. Lett. (1)

Proc. IEEE (1)

J. J. Burch, “A computer algorithm for the synthesis of spatial frequency filters,” Proc. IEEE 55, 599–600 (1967).
[CrossRef]

Other (1)

N. Emerton, R. W. Smith, R. G. Cañas, “Blazed surface relief diffractive optical elements,” in Holographic Systems Components and Applications, IERE Conf. Proc. 76 (Cambridge University, Cambridge, UK, 1987), pp. 99–103.

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Figures (8)

Fig. 1
Fig. 1

Training set is formed by all the dinosaur bodies and heads. Moreover, groups (a) and (b) are the scenes used in the different situations.

Fig. 2
Fig. 2

Enlarged portion of the holograms: (a) computed following the binary Lee codification and with a horizontal carrier frequency used just to completely separate the different diffracted orders. (b) As in (a) but with doubling of the carrier frequency. (c), (d) Generated following the gray-level method; the holograms have the same carrier frequency as (a) and (b), respectively.

Fig. 3
Fig. 3

(a), (b), (c) and (d) Numerically simulated impulse responses of the filters shown in Figs. 2(a), (b), (c), and (d), respectively.

Fig. 4
Fig. 4

Impulse response of three multiplexed filters. (a) Four objects are encoded with different linear phases. (b) As in (a) but with an additional quadratic phase. In this case only the diffraction order of 1 is focalized. (c) Eight objects are encoded with linear and quadratic phases.

Fig. 5
Fig. 5

Different performance criteria as a function of the number of objects encoded in the filter: (a) light efficiency, (b) SNR ratio in the reconstruction plane, (c) value of the correlation peak, (d) peak-to-correlation energy (CE), (e) discrimination capability (DC). Solid curve, results obtained without linear phase; dashed curve, those with quadratic phase. Dotted curve, intensity signals; dotted–dashed curve, complex signals, both for the case in which a quadratic phase is applied.

Fig. 6
Fig. 6

Scheme of the convergent correlator employed in the different situations. O is a transparency with the input scene; L1 and L2 are lenses; s and s′ are the distances from the source to L1 and from L1 to the image of the source, respectively; F is the composed filter, f is the focal length of L2, and Π is the correlation plane.

Fig. 7
Fig. 7

(a) Impulse response of the composed POF. A different dinosaur head is reconstructed in each channel. (b) Correlation signals obtained in the output plane of the optical correlator when the scene shown in Fig. 1(b) is used as input. The correlation regions corresponding to the different channels are indicated with dashed lines.

Fig. 8
Fig. 8

Images of the final plane in which the different channels are marked with dashed lines. We can see that the correlation signals obtained when the scenes are conformed by (a) the dinosaur bodies and (b) the dinosaur heads are processed by the optical system.

Tables (1)

Tables Icon

Table 1 Binary Code in the Output Plane

Equations (8)

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

Hiu, v=Aiu, vexpjϕiu, v.
tiu, v=12Aiu, vexpjϕiu, v+expjϕLiu, v=1+Aiu, vcosϕiu, v+ϕLiu, v,
Tu, v=i=1N tiu, v=i=1N1+Aiu, v×cosϕiu, v-ϕLiu, v.
Tu, v=i=1N tiu, v=i=1N1+Aiu, v×cosϕiu, v-ϕLiu, v+ϕqu, v,
ϕqu, v=π/λfu2+v2,
λf2nΔx2.
η=|gx|2xF|gx|2xD,
SNR=c2|fx-xf|2xF|gx|-c|fx-xf|2xF, c=|gx||fx-xf|xF|fx-xf|2xF,

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