Abstract

Fourier- and Hartley-related transforms are realized in a family of interferometers. The implementation of these interferometers as image correlators is investigated theoretically and experimentally with both coherent and spatially incoherent illumination. Several correlators that can be used for pattern recognition are studied and demonstrated experimentally as special cases.

© 1992 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  4. E. Ribak, C. Roddier, F. Roddier, J. B. Breckinridge, “Signal-to-noise limitations in white light holography,” Appl. Opt. 27, 1183–1186 (1988).
    [CrossRef] [PubMed]
  5. J. B. Breckinridge, E. Ribak, C. Roddier, F. Roddier, C. Habecker, “Real time optical correlation using white light Fourier transforms,” final report of the technical work (Jet Propulsion Laboratory, California Institute of Technology, Pasadena, Calif., 1988).
  6. R. N. Bracewell, H. Bartelt, A. W. Lohmann, N. Streibl, “Optical synthesis of the Hartley transform,” Appl. Opt. 24, 1401–1402 (1985).
    [CrossRef] [PubMed]
  7. J. Villasenor, R. N. Bracewell, “Optical phase obtained by analogue Hartley transformation,” Nature (London) 330, 735–737 (1987).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  18. J. Rosen, T. Kotzer, J. Shamir, “Optical implementation of phase extraction pattern recognition,” Opt. Commun. 83, 10–14 (1991).
    [CrossRef]
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1992

1991

J. Rosen, T. Kotzer, J. Shamir, “Optical implementation of phase extraction pattern recognition,” Opt. Commun. 83, 10–14 (1991).
[CrossRef]

U. Mahlab, J. Rosen, J. Shamir, “Iterative generation of complex reference functions in joint transform correlator,” Opt. Lett. 16, 330–332 (1991).
[CrossRef] [PubMed]

1990

1988

1987

J. Villasenor, R. N. Bracewell, “Optical phase obtained by analogue Hartley transformation,” Nature (London) 330, 735–737 (1987).
[CrossRef]

1985

S. Wang, N. George, “Fresnel zone transforms in spatially incoherent illumination,” Appl. Opt. 24, 84–850 (1985).
[CrossRef]

R. N. Bracewell, H. Bartelt, A. W. Lohmann, N. Streibl, “Optical synthesis of the Hartley transform,” Appl. Opt. 24, 1401–1402 (1985).
[CrossRef] [PubMed]

1984

1983

1982

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Passive (self pump) phase conjugate mirror: theoretical and experimental investigation,” Appl. Phys. Lett. 41, 689–691 (1982).
[CrossRef]

1981

1979

1967

K. V. Konjaev, “Interference method of two-dimensional Fourier transform with spatially incoherent illumination,” Phys. Lett. A 24, 490–491 (1967).
[CrossRef]

1966

Bartelt, H.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

Bracewell, R. N.

Breckinridge, J. B.

E. Ribak, C. Roddier, F. Roddier, J. B. Breckinridge, “Signal-to-noise limitations in white light holography,” Appl. Opt. 27, 1183–1186 (1988).
[CrossRef] [PubMed]

J. B. Breckinridge, E. Ribak, C. Roddier, F. Roddier, C. Habecker, “Real time optical correlation using white light Fourier transforms,” final report of the technical work (Jet Propulsion Laboratory, California Institute of Technology, Pasadena, Calif., 1988).

Cronin-Golomb, M.

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Passive (self pump) phase conjugate mirror: theoretical and experimental investigation,” Appl. Phys. Lett. 41, 689–691 (1982).
[CrossRef]

Fainman, Y.

Fischer, B.

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Passive (self pump) phase conjugate mirror: theoretical and experimental investigation,” Appl. Phys. Lett. 41, 689–691 (1982).
[CrossRef]

George, N.

S. Wang, N. George, “Fresnel zone transforms in spatially incoherent illumination,” Appl. Opt. 24, 84–850 (1985).
[CrossRef]

Gianino, P. D.

Goodman, J. W.

Habecker, C.

J. B. Breckinridge, E. Ribak, C. Roddier, F. Roddier, C. Habecker, “Real time optical correlation using white light Fourier transforms,” final report of the technical work (Jet Propulsion Laboratory, California Institute of Technology, Pasadena, Calif., 1988).

Horner, J. L.

Ichioka, Y.

Itoh, K.

Konforti, N.

Konjaev, K. V.

K. V. Konjaev, “Interference method of two-dimensional Fourier transform with spatially incoherent illumination,” Phys. Lett. A 24, 490–491 (1967).
[CrossRef]

Kotzer, T.

J. Rosen, T. Kotzer, J. Shamir, “Optical implementation of phase extraction pattern recognition,” Opt. Commun. 83, 10–14 (1991).
[CrossRef]

Lenz, E.

Lohmann, A. W.

Mahlab, U.

Marom, E.

Mendlovic, D.

Mertz, L.

L. Mertz, Transformations in Optics (Wiley, New York, 1965).

Nomura, T.

Potaturkin, O. I.

Ribak, E.

E. Ribak, C. Roddier, F. Roddier, J. B. Breckinridge, “Signal-to-noise limitations in white light holography,” Appl. Opt. 27, 1183–1186 (1988).
[CrossRef] [PubMed]

J. B. Breckinridge, E. Ribak, C. Roddier, F. Roddier, C. Habecker, “Real time optical correlation using white light Fourier transforms,” final report of the technical work (Jet Propulsion Laboratory, California Institute of Technology, Pasadena, Calif., 1988).

Roddier, C.

E. Ribak, C. Roddier, F. Roddier, J. B. Breckinridge, “Signal-to-noise limitations in white light holography,” Appl. Opt. 27, 1183–1186 (1988).
[CrossRef] [PubMed]

J. B. Breckinridge, E. Ribak, C. Roddier, F. Roddier, C. Habecker, “Real time optical correlation using white light Fourier transforms,” final report of the technical work (Jet Propulsion Laboratory, California Institute of Technology, Pasadena, Calif., 1988).

Roddier, F.

E. Ribak, C. Roddier, F. Roddier, J. B. Breckinridge, “Signal-to-noise limitations in white light holography,” Appl. Opt. 27, 1183–1186 (1988).
[CrossRef] [PubMed]

J. B. Breckinridge, E. Ribak, C. Roddier, F. Roddier, C. Habecker, “Real time optical correlation using white light Fourier transforms,” final report of the technical work (Jet Propulsion Laboratory, California Institute of Technology, Pasadena, Calif., 1988).

Rosen, J.

U. Mahlab, J. Rosen, J. Shamir, “Iterative generation of complex reference functions in joint transform correlator,” Opt. Lett. 16, 330–332 (1991).
[CrossRef] [PubMed]

J. Rosen, T. Kotzer, J. Shamir, “Optical implementation of phase extraction pattern recognition,” Opt. Commun. 83, 10–14 (1991).
[CrossRef]

Segev, M.

Shamir, J.

Streibl, N.

Villasenor, J.

J. Villasenor, R. N. Bracewell, “Optical phase obtained by analogue Hartley transformation,” Nature (London) 330, 735–737 (1987).
[CrossRef]

Wang, S.

S. Wang, N. George, “Fresnel zone transforms in spatially incoherent illumination,” Appl. Opt. 24, 84–850 (1985).
[CrossRef]

Weaver, C. S.

White, J. O.

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Passive (self pump) phase conjugate mirror: theoretical and experimental investigation,” Appl. Phys. Lett. 41, 689–691 (1982).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

Yariv, A.

M. Segev, A. Yariv, “Optical interferometry between image-bearing beams and their redirected phase conjugates,” Opt. Lett. 17, 145–147 (1992).
[CrossRef] [PubMed]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Passive (self pump) phase conjugate mirror: theoretical and experimental investigation,” Appl. Phys. Lett. 41, 689–691 (1982).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Passive (self pump) phase conjugate mirror: theoretical and experimental investigation,” Appl. Phys. Lett. 41, 689–691 (1982).
[CrossRef]

J. Opt. Soc. Am.

Nature (London)

J. Villasenor, R. N. Bracewell, “Optical phase obtained by analogue Hartley transformation,” Nature (London) 330, 735–737 (1987).
[CrossRef]

Opt. Commun.

J. Rosen, T. Kotzer, J. Shamir, “Optical implementation of phase extraction pattern recognition,” Opt. Commun. 83, 10–14 (1991).
[CrossRef]

Opt. Lett.

Phys. Lett. A

K. V. Konjaev, “Interference method of two-dimensional Fourier transform with spatially incoherent illumination,” Phys. Lett. A 24, 490–491 (1967).
[CrossRef]

Other

L. Mertz, Transformations in Optics (Wiley, New York, 1965).

J. B. Breckinridge, E. Ribak, C. Roddier, F. Roddier, C. Habecker, “Real time optical correlation using white light Fourier transforms,” final report of the technical work (Jet Propulsion Laboratory, California Institute of Technology, Pasadena, Calif., 1988).

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

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