Abstract

We consider the relations between bandlimited one-dimensional object-plane fields which yield the same intensity distribution in the Fraunhofer (Fourier transform) plane. In the case in which the Fraunhofer-plane fields differ by the conjugation of a single zero, a simple relation results which appears useful in phase-retrieval algorithms.

© 1980 Optical Society of America

PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. A. Ferwerda, "The phase reconstruction problem for wave amplitudes and coherence functions," in Inverse Source Problems in Optics, edited by H. P. Baltes (Springer-Verlag, Berlin, 1978), Chap. 2.
  2. R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik 35, 237–246 (1972).
  3. R. E. Burge et al., "The phase problem" Proc. R. Soc. London Ser. A 350, 191–212 (1976).
  4. A. H. Greenaway, "Proposal for phase recovery from a single intensity distribution," Opt. Lett. 1, 10–12 (1977).
  5. M. S. Fiddy and G. Ross, "Analytic Fourier optics: the encoding of information by complex zeros," Opt. Acta 26, 1139–1146 (1979).
  6. A. Walther, "The question of phase retrieval in optics," Opt. Acta 10, 41–49 (1963).
  7. R. Bracewell, The Fourier Transform and Its Application (McGraw-Hill, New York, 1975).
  8. A. V. Oppenheim and R. W. Schafer, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975), Ch. 7.
  9. A. N. J. Huiser, A. J. J. Drenth, and H. A. Ferwerda, "On phase retrieval in electron microscopy form image and diffraction pattern," Optik 45, 303–316 (1976).
  10. R. W. Gerchberg and W. O. Saxton, "Wave phase from image and diffraction plane pictures," in Image Processing and Computer-aided Design in Electron Optics, edited by P. W. Hawkes (Academic, London, 1973)
  11. R. A. Gonsalves, "Phase retrieval from modulus data," J. Opt. Soc. Am. 66, 961–964 (1976).
  12. A. M. J. Huiser et al., "On the problem of phase retrieval in electron microscopy from image and diffraction pattern, III," Optik 47, 1–8 (1977).
  13. P. van Toorn and H. A. Ferwerda, "On the problem of phase retrieval in electron microscopy from image and diffraction pattern, IV," Optik 47, 123–134 (1977).
  14. J. R. Fienup, "Reconstruction of an object from the modulus of its Fourier transform" Opt. Lett. 3, 27–29 (1978).

1979 (1)

M. S. Fiddy and G. Ross, "Analytic Fourier optics: the encoding of information by complex zeros," Opt. Acta 26, 1139–1146 (1979).

1978 (2)

H. A. Ferwerda, "The phase reconstruction problem for wave amplitudes and coherence functions," in Inverse Source Problems in Optics, edited by H. P. Baltes (Springer-Verlag, Berlin, 1978), Chap. 2.

J. R. Fienup, "Reconstruction of an object from the modulus of its Fourier transform" Opt. Lett. 3, 27–29 (1978).

1977 (3)

A. M. J. Huiser et al., "On the problem of phase retrieval in electron microscopy from image and diffraction pattern, III," Optik 47, 1–8 (1977).

P. van Toorn and H. A. Ferwerda, "On the problem of phase retrieval in electron microscopy from image and diffraction pattern, IV," Optik 47, 123–134 (1977).

A. H. Greenaway, "Proposal for phase recovery from a single intensity distribution," Opt. Lett. 1, 10–12 (1977).

1976 (3)

R. E. Burge et al., "The phase problem" Proc. R. Soc. London Ser. A 350, 191–212 (1976).

A. N. J. Huiser, A. J. J. Drenth, and H. A. Ferwerda, "On phase retrieval in electron microscopy form image and diffraction pattern," Optik 45, 303–316 (1976).

R. A. Gonsalves, "Phase retrieval from modulus data," J. Opt. Soc. Am. 66, 961–964 (1976).

1973 (1)

R. W. Gerchberg and W. O. Saxton, "Wave phase from image and diffraction plane pictures," in Image Processing and Computer-aided Design in Electron Optics, edited by P. W. Hawkes (Academic, London, 1973)

1972 (1)

R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik 35, 237–246 (1972).

1963 (1)

A. Walther, "The question of phase retrieval in optics," Opt. Acta 10, 41–49 (1963).

Bracewell, R.

R. Bracewell, The Fourier Transform and Its Application (McGraw-Hill, New York, 1975).

Burge, R. E.

R. E. Burge et al., "The phase problem" Proc. R. Soc. London Ser. A 350, 191–212 (1976).

Drenth, A. J. J.

A. N. J. Huiser, A. J. J. Drenth, and H. A. Ferwerda, "On phase retrieval in electron microscopy form image and diffraction pattern," Optik 45, 303–316 (1976).

Ferwerda, H. A.

H. A. Ferwerda, "The phase reconstruction problem for wave amplitudes and coherence functions," in Inverse Source Problems in Optics, edited by H. P. Baltes (Springer-Verlag, Berlin, 1978), Chap. 2.

P. van Toorn and H. A. Ferwerda, "On the problem of phase retrieval in electron microscopy from image and diffraction pattern, IV," Optik 47, 123–134 (1977).

A. N. J. Huiser, A. J. J. Drenth, and H. A. Ferwerda, "On phase retrieval in electron microscopy form image and diffraction pattern," Optik 45, 303–316 (1976).

Fiddy, M. S.

M. S. Fiddy and G. Ross, "Analytic Fourier optics: the encoding of information by complex zeros," Opt. Acta 26, 1139–1146 (1979).

Fienup, J. R.

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, "Wave phase from image and diffraction plane pictures," in Image Processing and Computer-aided Design in Electron Optics, edited by P. W. Hawkes (Academic, London, 1973)

R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik 35, 237–246 (1972).

Gonsalves, R. A.

Greenaway, A. H.

Huiser, A. M. J.

A. M. J. Huiser et al., "On the problem of phase retrieval in electron microscopy from image and diffraction pattern, III," Optik 47, 1–8 (1977).

Huiser, A. N. J.

A. N. J. Huiser, A. J. J. Drenth, and H. A. Ferwerda, "On phase retrieval in electron microscopy form image and diffraction pattern," Optik 45, 303–316 (1976).

Oppenheim, A. V.

A. V. Oppenheim and R. W. Schafer, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975), Ch. 7.

Ross, G.

M. S. Fiddy and G. Ross, "Analytic Fourier optics: the encoding of information by complex zeros," Opt. Acta 26, 1139–1146 (1979).

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, "Wave phase from image and diffraction plane pictures," in Image Processing and Computer-aided Design in Electron Optics, edited by P. W. Hawkes (Academic, London, 1973)

R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik 35, 237–246 (1972).

Schafer, R. W.

A. V. Oppenheim and R. W. Schafer, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975), Ch. 7.

van Toorn, P.

P. van Toorn and H. A. Ferwerda, "On the problem of phase retrieval in electron microscopy from image and diffraction pattern, IV," Optik 47, 123–134 (1977).

Walther, A.

A. Walther, "The question of phase retrieval in optics," Opt. Acta 10, 41–49 (1963).

J. Opt. Soc. Am. (1)

Opt. Acta (2)

M. S. Fiddy and G. Ross, "Analytic Fourier optics: the encoding of information by complex zeros," Opt. Acta 26, 1139–1146 (1979).

A. Walther, "The question of phase retrieval in optics," Opt. Acta 10, 41–49 (1963).

Opt. Lett. (2)

Optik (4)

A. M. J. Huiser et al., "On the problem of phase retrieval in electron microscopy from image and diffraction pattern, III," Optik 47, 1–8 (1977).

P. van Toorn and H. A. Ferwerda, "On the problem of phase retrieval in electron microscopy from image and diffraction pattern, IV," Optik 47, 123–134 (1977).

A. N. J. Huiser, A. J. J. Drenth, and H. A. Ferwerda, "On phase retrieval in electron microscopy form image and diffraction pattern," Optik 45, 303–316 (1976).

R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik 35, 237–246 (1972).

Proc. R. Soc. London Ser. A (1)

R. E. Burge et al., "The phase problem" Proc. R. Soc. London Ser. A 350, 191–212 (1976).

Other (4)

H. A. Ferwerda, "The phase reconstruction problem for wave amplitudes and coherence functions," in Inverse Source Problems in Optics, edited by H. P. Baltes (Springer-Verlag, Berlin, 1978), Chap. 2.

R. Bracewell, The Fourier Transform and Its Application (McGraw-Hill, New York, 1975).

A. V. Oppenheim and R. W. Schafer, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975), Ch. 7.

R. W. Gerchberg and W. O. Saxton, "Wave phase from image and diffraction plane pictures," in Image Processing and Computer-aided Design in Electron Optics, edited by P. W. Hawkes (Academic, London, 1973)

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.