Abstract

Interference techniques can be used to measure both the amplitude and phase of optically generated Fourier transforms. Because phase information is recovered by observing an interference pattern, source coherence can significantly influence phase accuracy. System performance is analyzed using simple test functions and the phase error is estimated in terms of the source transverse coherence length and space-bandwidth product of the input function.

© 1978 Optical Society of America

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References

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  1. W. Kock, "Optical computing, an example of change," Proc. IEEE 75, 6 (1977).
  2. A. Vander Lugt, "Coherent optical processing," Proc. IEEE 62, 1300–1319 (1974).
  3. G. Lendaris and G. Stanley, "An opticalogical self-organizing recognition system," in Optical and Electro-Optical Information Processing, edited by J. Tippett et al. (MIT, Cambridge, Mass., 1965).
  4. K.Preston, Jr., Coherent Optical Computers McGraw-Hill, New York, 1972), p. 268.
  5. B. Thompson, "Hybrid processing systems—an assessment," Proc. IEEE 65, 62–76 (1977).
  6. J. Goodman, "Operations achievable with coherent optical information processing systems," Proc. IEEE 65, 29–38 (1977).
  7. Y. Ichioka and M. Inuiya, "Direct Phase detecting system," Appl. Opt. 11, 1507 (1972).
  8. R. Gonsalves, "Phase retrieval from modulus data," J. Opt. Soc. Am. 66, 961–964 (1976).
  9. R. Gershberg and W. Saxton, "Phase determination from image and diffraction plane pictures in the electron microscope," Optik (Stuttg.) 34, 275–283 (1971).
  10. W. Dallas, "Digital computation of image complex amplitude from image and diffraction intensity: An alternative to holography," Optik (Stuttg.) 41, 45–59 (1975).
  11. The actual focal spot size will probably be determined by lens aberrations.
  12. M. Janossy, L. Csillag, and K. Kantor, "The spatial coherence of a He-Ne laser operating at 1.15 µm measured with a Mach-Zehnder interferometer," Phys. Lett. 18, 124–125 (1965).
  13. R. Chwalki, S. Stepinski, and H. Hammer, "Coherence measurement of gas laser output," Acta Phys. Pol. 19, 753–757 (1966).

1976 (1)

1975 (1)

W. Dallas, "Digital computation of image complex amplitude from image and diffraction intensity: An alternative to holography," Optik (Stuttg.) 41, 45–59 (1975).

1972 (1)

1971 (1)

R. Gershberg and W. Saxton, "Phase determination from image and diffraction plane pictures in the electron microscope," Optik (Stuttg.) 34, 275–283 (1971).

1966 (1)

R. Chwalki, S. Stepinski, and H. Hammer, "Coherence measurement of gas laser output," Acta Phys. Pol. 19, 753–757 (1966).

1965 (1)

M. Janossy, L. Csillag, and K. Kantor, "The spatial coherence of a He-Ne laser operating at 1.15 µm measured with a Mach-Zehnder interferometer," Phys. Lett. 18, 124–125 (1965).

Chwalki, R.

R. Chwalki, S. Stepinski, and H. Hammer, "Coherence measurement of gas laser output," Acta Phys. Pol. 19, 753–757 (1966).

Csillag, L.

M. Janossy, L. Csillag, and K. Kantor, "The spatial coherence of a He-Ne laser operating at 1.15 µm measured with a Mach-Zehnder interferometer," Phys. Lett. 18, 124–125 (1965).

Dallas, W.

W. Dallas, "Digital computation of image complex amplitude from image and diffraction intensity: An alternative to holography," Optik (Stuttg.) 41, 45–59 (1975).

Gershberg, R.

R. Gershberg and W. Saxton, "Phase determination from image and diffraction plane pictures in the electron microscope," Optik (Stuttg.) 34, 275–283 (1971).

Gonsalves, R.

Goodman, J.

J. Goodman, "Operations achievable with coherent optical information processing systems," Proc. IEEE 65, 29–38 (1977).

Hammer, H.

R. Chwalki, S. Stepinski, and H. Hammer, "Coherence measurement of gas laser output," Acta Phys. Pol. 19, 753–757 (1966).

Ichioka, Y.

Inuiya, M.

Janossy, M.

M. Janossy, L. Csillag, and K. Kantor, "The spatial coherence of a He-Ne laser operating at 1.15 µm measured with a Mach-Zehnder interferometer," Phys. Lett. 18, 124–125 (1965).

Kantor, K.

M. Janossy, L. Csillag, and K. Kantor, "The spatial coherence of a He-Ne laser operating at 1.15 µm measured with a Mach-Zehnder interferometer," Phys. Lett. 18, 124–125 (1965).

Kock, W.

W. Kock, "Optical computing, an example of change," Proc. IEEE 75, 6 (1977).

Lendaris, G.

G. Lendaris and G. Stanley, "An opticalogical self-organizing recognition system," in Optical and Electro-Optical Information Processing, edited by J. Tippett et al. (MIT, Cambridge, Mass., 1965).

Lugt, A. Vander

A. Vander Lugt, "Coherent optical processing," Proc. IEEE 62, 1300–1319 (1974).

Preston, Jr., K

K.Preston, Jr., Coherent Optical Computers McGraw-Hill, New York, 1972), p. 268.

Saxton, W.

R. Gershberg and W. Saxton, "Phase determination from image and diffraction plane pictures in the electron microscope," Optik (Stuttg.) 34, 275–283 (1971).

Stanley, G.

G. Lendaris and G. Stanley, "An opticalogical self-organizing recognition system," in Optical and Electro-Optical Information Processing, edited by J. Tippett et al. (MIT, Cambridge, Mass., 1965).

Stepinski, S.

R. Chwalki, S. Stepinski, and H. Hammer, "Coherence measurement of gas laser output," Acta Phys. Pol. 19, 753–757 (1966).

Thompson, B.

B. Thompson, "Hybrid processing systems—an assessment," Proc. IEEE 65, 62–76 (1977).

Acta Phys. Pol. (1)

R. Chwalki, S. Stepinski, and H. Hammer, "Coherence measurement of gas laser output," Acta Phys. Pol. 19, 753–757 (1966).

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

Optik (2)

R. Gershberg and W. Saxton, "Phase determination from image and diffraction plane pictures in the electron microscope," Optik (Stuttg.) 34, 275–283 (1971).

W. Dallas, "Digital computation of image complex amplitude from image and diffraction intensity: An alternative to holography," Optik (Stuttg.) 41, 45–59 (1975).

Phys. Lett. (1)

M. Janossy, L. Csillag, and K. Kantor, "The spatial coherence of a He-Ne laser operating at 1.15 µm measured with a Mach-Zehnder interferometer," Phys. Lett. 18, 124–125 (1965).

Other (7)

The actual focal spot size will probably be determined by lens aberrations.

W. Kock, "Optical computing, an example of change," Proc. IEEE 75, 6 (1977).

A. Vander Lugt, "Coherent optical processing," Proc. IEEE 62, 1300–1319 (1974).

G. Lendaris and G. Stanley, "An opticalogical self-organizing recognition system," in Optical and Electro-Optical Information Processing, edited by J. Tippett et al. (MIT, Cambridge, Mass., 1965).

K.Preston, Jr., Coherent Optical Computers McGraw-Hill, New York, 1972), p. 268.

B. Thompson, "Hybrid processing systems—an assessment," Proc. IEEE 65, 62–76 (1977).

J. Goodman, "Operations achievable with coherent optical information processing systems," Proc. IEEE 65, 29–38 (1977).

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