Abstract

Correlation is considered to be a fundamental operation in the field of signal processing. The fact that this operation can be implemented optically in a relatively simple manner is an important advantage of utilizing optical systems for signal processing. The VanderLugt 4-f system and the joint transform correlator (JTC) are the two most popular configurations for performing a spatial correlation operation optically. So far the JTC architecture has been used for performing correlation between two images, which are illuminated by a quasi-monochromatic light source. We propose a generalization of the JTC that performs a correlation between two temporal optical signals.

© 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-10, 139–143 (1964).
  2. A. W. Lohnmann, H. W. Werlich, “Incoherent matched filter with Fourier holograms,” Appl. Opt. 7, 561–563 (1968).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  8. W. T. Rhodes, “Acousto-optic signal processing: convolution and correlation,” Proc. IEEE 69, 65–79 (1981).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  15. M. Weiner, J. P. Heritage, “Picosecond and femtosecond Fourier pulse shape synthesis,” Rev. Phys. Appl. 22, 1619–1628 (1987).
    [CrossRef]
  16. F. Salin, J. Squier, G. Mourou, “Large temporal stretching of ultrashort pulses,” Appl. Opt. 31, 1225–1228 (1992).
    [CrossRef] [PubMed]
  17. P. C. Sun, Y. T. Mazurenko, W. S. C. Chang, P. K. L. Yu, Y. Fainman, “All optical parallel-to-serial conversion by holographic spatial-to-temporal frequency encoding,” Opt. Lett. 20, 1–3 (1995).
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    [CrossRef]

1996 (1)

1995 (1)

1994 (3)

1992 (2)

1989 (1)

1988 (1)

A. M. Weiner, J. P. Heritage, E. M. Kirschner, “High-resolution femtosecond pulse shaping,” J. Opt. Soc. Am. B. 5, 1563–1572 (1988).
[CrossRef]

1987 (1)

M. Weiner, J. P. Heritage, “Picosecond and femtosecond Fourier pulse shape synthesis,” Rev. Phys. Appl. 22, 1619–1628 (1987).
[CrossRef]

1982 (1)

D. Grischkowsky, A. C. Balant, “Optical pulse compression based on enhanced frequency chirping,” Appl. Phys. Lett. 41, 1–3 (1982).
[CrossRef]

1981 (1)

W. T. Rhodes, “Acousto-optic signal processing: convolution and correlation,” Proc. IEEE 69, 65–79 (1981).
[CrossRef]

1975 (1)

C. A. Sprague, C. L. Koliopoulos, “Time integrating acousto-optic correlator (A),” J. Opt. Soc. Am. 65, 1178 (1975).

1968 (1)

1966 (2)

1964 (1)

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–143 (1964).

Aguilar, M.

Agullo-Lopez, F.

Balant, A. C.

D. Grischkowsky, A. C. Balant, “Optical pulse compression based on enhanced frequency chirping,” Appl. Phys. Lett. 41, 1–3 (1982).
[CrossRef]

Carrascosa, M.

Chang, W. S. C.

Chiu, T. H.

Colombeau, B.

C. Froehly, B. Colombeau, M. Vampouille, “Shaping and analysis of picosecond light pulses,” in Progress in Optics XX, E. Wolf, ed. (Elsevier, Amsterdam, 1983), pp. 63–153.
[CrossRef]

Fainman, Y.

Froehly, C.

C. Froehly, B. Colombeau, M. Vampouille, “Shaping and analysis of picosecond light pulses,” in Progress in Optics XX, E. Wolf, ed. (Elsevier, Amsterdam, 1983), pp. 63–153.
[CrossRef]

Goodman, J. W.

Grischkowsky, D.

D. Grischkowsky, A. C. Balant, “Optical pulse compression based on enhanced frequency chirping,” Appl. Phys. Lett. 41, 1–3 (1982).
[CrossRef]

Heritage, J. P.

A. M. Weiner, J. P. Heritage, E. M. Kirschner, “High-resolution femtosecond pulse shaping,” J. Opt. Soc. Am. B. 5, 1563–1572 (1988).
[CrossRef]

M. Weiner, J. P. Heritage, “Picosecond and femtosecond Fourier pulse shape synthesis,” Rev. Phys. Appl. 22, 1619–1628 (1987).
[CrossRef]

Kirschner, E. M.

A. M. Weiner, J. P. Heritage, E. M. Kirschner, “High-resolution femtosecond pulse shaping,” J. Opt. Soc. Am. B. 5, 1563–1572 (1988).
[CrossRef]

Koliopoulos, C. L.

C. A. Sprague, C. L. Koliopoulos, “Time integrating acousto-optic correlator (A),” J. Opt. Soc. Am. 65, 1178 (1975).

Kolner, W.

Li, M.

Lohmann, A. W.

Lohnmann, A. W.

Magana, L. F.

Mazurenko, T.

T. Mazurenko, “Time-domain Fourier transform holography and possible applications in signal processing,” Opt. Eng. 31, 739–749 (1994).
[CrossRef]

Mazurenko, Y. T.

Mendlovic, D.

Mourou, G.

Nazarathy, M.

Nuss, M. C.

Partovi, A.

Rau, J. E.

Rhodes, W. T.

W. T. Rhodes, “Acousto-optic signal processing: convolution and correlation,” Proc. IEEE 69, 65–79 (1981).
[CrossRef]

Riza, N. A.

Salin, F.

Solymar, L.

Sprague, C. A.

C. A. Sprague, C. L. Koliopoulos, “Time integrating acousto-optic correlator (A),” J. Opt. Soc. Am. 65, 1178 (1975).

Squier, J.

Sun, P. C.

Vampouille, M.

C. Froehly, B. Colombeau, M. Vampouille, “Shaping and analysis of picosecond light pulses,” in Progress in Optics XX, E. Wolf, ed. (Elsevier, Amsterdam, 1983), pp. 63–153.
[CrossRef]

VanderLugt, A.

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–143 (1964).

Weaver, C. S.

Weiner, A. M.

M. C. Nuss, M. Li, T. H. Chiu, A. M. Weiner, A. Partovi, “Time-to-space mapping of femtosecond pulses,” Opt. Lett. 19, 664–666 (1994).
[CrossRef] [PubMed]

A. M. Weiner, J. P. Heritage, E. M. Kirschner, “High-resolution femtosecond pulse shaping,” J. Opt. Soc. Am. B. 5, 1563–1572 (1988).
[CrossRef]

Weiner, M.

M. Weiner, J. P. Heritage, “Picosecond and femtosecond Fourier pulse shape synthesis,” Rev. Phys. Appl. 22, 1619–1628 (1987).
[CrossRef]

Werlich, H. W.

Yu, P. K. L.

Appl. Opt. (5)

Appl. Phys. Lett. (1)

D. Grischkowsky, A. C. Balant, “Optical pulse compression based on enhanced frequency chirping,” Appl. Phys. Lett. 41, 1–3 (1982).
[CrossRef]

IEEE Trans. Inf. Theory (1)

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–143 (1964).

J. Opt. Soc. Am. (2)

C. A. Sprague, C. L. Koliopoulos, “Time integrating acousto-optic correlator (A),” J. Opt. Soc. Am. 65, 1178 (1975).

J. E. Rau, “Detection of differences in real distributions,” J. Opt. Soc. Am. 56, 1490–1494 (1966).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Opt. Soc. Am. B. (1)

A. M. Weiner, J. P. Heritage, E. M. Kirschner, “High-resolution femtosecond pulse shaping,” J. Opt. Soc. Am. B. 5, 1563–1572 (1988).
[CrossRef]

Opt. Eng. (1)

T. Mazurenko, “Time-domain Fourier transform holography and possible applications in signal processing,” Opt. Eng. 31, 739–749 (1994).
[CrossRef]

Opt. Lett. (3)

Proc. IEEE (1)

W. T. Rhodes, “Acousto-optic signal processing: convolution and correlation,” Proc. IEEE 69, 65–79 (1981).
[CrossRef]

Rev. Phys. Appl. (1)

M. Weiner, J. P. Heritage, “Picosecond and femtosecond Fourier pulse shape synthesis,” Rev. Phys. Appl. 22, 1619–1628 (1987).
[CrossRef]

Other (1)

C. Froehly, B. Colombeau, M. Vampouille, “Shaping and analysis of picosecond light pulses,” in Progress in Optics XX, E. Wolf, ed. (Elsevier, Amsterdam, 1983), pp. 63–153.
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Conventional JTC scheme. SLM, spatial light modulator; F.T., Fourier transform; J.T., joint transform.

Fig. 2
Fig. 2

Quasi-monochromatic spatial Fourier transformer.

Fig. 3
Fig. 3

Temporal Fourier transformer.

Fig. 4
Fig. 4

Preprocessing step for joining two point sources with a time delay.

Fig. 5
Fig. 5

Second stage of the temporal JTC.

Equations (13)

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ux, t=expi2πν0texp-i2π ν0c 2fi cν0 f× uinx¯exp-i2π ν0cf x¯xdx¯,
ũx, ν=1i cν0 f  ũinx¯, νexp-i2π νc 2f×exp-i2π νcf xx¯dx¯.
ux, t=1i cν0 f  ũinx¯, νexp-i2π νc 2f×exp-i2π νcf xx¯expi2πνtdx¯dν=1i cν0 f  uinx¯, t¯exp-i2π νc 2f×exp-i2π νcf xx¯expi2πνt×exp-i2πt¯νdt¯dνdx¯.
 exp-i2πνt¯-t+xx¯cf+2fcdν=δt¯-t+xx¯cf+2fc,
ux, t=1i cν0 f  uinx¯, t¯δt¯-t+xx¯cf+2fcdt¯dx¯=1i cν0 f  uinx¯, t-xx¯cf-2fcdx¯.
ux, t= uinx¯, t-x¯xcfdx¯.
u1x, t=uintexpi2παx.
uoutx, t= uint-xx¯cfexpi2παx¯dx¯=cfxexpi2π αcfx t  uint¯exp-i2π αcfx t¯×dt¯=cfxexpi2π αcfx tũinαcfx.
uintδx=u1t+u2t-t0δx.
uinx, t=u1tδx+u2tδx-x0.
out1x=expi2π αcfx tũ1αcfx+ũ2αcfxexp-i2π αcfx t02=ũ1αcfx+ũ2αcfxexp-i2π αcfx t02,
u3x, t=expi2π αcfx tũ1αcfx+ũ2αcfxexp-i2π αcfx t02.
outx, t=u1t * u1t+u2t * u2t+u1t* u2t-t0+u2t * u1t+t0δx.

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