Abstract

In the generation of computer-generated holograms the phase is in many applications a free parameter that can be manipulated to achieve a high diffraction efficiency, a small space–bandwidth product, and a speckle-free reconstruction. An iterative algorithm to determine such phase distributions is described. Experimental verifications are given.

© 1988 Optical Society of America

PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W.-H. Lee, “Computer-generated holograms: techniques and applications,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1978), Vol. 16, pp. 119–232.
  2. E. N. Leith, J. Upatnieks, “Wavefront reconstruction with diffused illumination and three-dimensional objects,”J. Opt. Soc. Am. 54, 1295–1301 (1964).
    [CrossRef]
  3. R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), pp. 194–203.
  4. L. B. Lesem, P. M. Hirsch, J. A. Jordan, “Computer synthesis of holograms for 3-D display,” Commun. ACM 11, 661–674 (1968).
    [CrossRef]
  5. W. J. Dallas, “Computer-generated holograms,” in The Computer in Optical Research, B. R. Frieden, ed. Vol. 41 of Topics in Applied Physics (Springer-Verlag, Berlin, 1980), pp. 291–366.
  6. H. J. Gerritsen, W. J. Hannan, E. G. Ramberg, “Elimination of speckle noise in holograms with redundancy,” Appl. Opt. 7, 2301–2311 (1968).
    [CrossRef] [PubMed]
  7. F. Wyrowski, R. Hauck, O. Bryngdahl, “Computer-generated holograms: hologram repetition and phase manipulations,” J. Opt. Soc. Am. A 4, 694–698 (1987).
    [CrossRef]
  8. N. C. Gallagher, B. Liu, “Method for computing kinoforms that reduces image reconstruction error,” Appl. Opt. 12, 2328–2335 (1973).
    [CrossRef] [PubMed]
  9. J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19, 297–305 (1980).
    [CrossRef]
  10. J. P. Allebach, B. Liu, “Minimax spectrum shaping with a bandwidth constraint,” Appl. Opt. 14, 3062–3072 (1975).
    [CrossRef] [PubMed]
  11. J. P. Allebach, N. C. Gallagher, B. Liu, “Aliasing error in digital holography,” Appl. Opt. 15, 2183–2188 (1976).
    [CrossRef] [PubMed]
  12. R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).
  13. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
    [CrossRef] [PubMed]
  14. M. S. Scivier, M. A. Fiddy, “Phase ambiguities and the zeros of multidimensional band-limited functions,” J. Opt. Soc. Am. A 2, 693–697 (1985).
    [CrossRef]
  15. A. Walther, “The question of phase retrieval in optics,” Opt. Acta 10, 41–49 (1963).
    [CrossRef]
  16. Y. M. Bruck, L. G. Sodin, “On the ambiguity of the image reconstruction problem,” Opt. Commun. 30, 304–308 (1979).
    [CrossRef]
  17. R. H. T. Bates, “Fourier phase problems are uniquely solvable in more than one dimension. I. Underlying theory,” Optik 61, 247–262 (1982).
  18. T. R. Crimmins, J. R. Fienup, “Uniqueness of phase retrieval for functions with sufficiently disconnected support,”J. Opt. Soc. Am. 73, 218–221 (1983).
    [CrossRef]
  19. H. V. Deighton, M. S. Scievier, M. A. Fiddy, “Solution of the two-dimensional phase-retrieval problem,” Opt. Lett. 10, 250–251 (1985).
    [CrossRef] [PubMed]
  20. H. A. Ferwerda, “Phase retrieval in imaging,” in Digest of Topical Meeting on Signal Recovery and Synthesis II (Optical Society of America, Washington, D.C., 1986), pp. 36–39.
  21. R. Barakat, G. Newsam, “Algorithm for reconstruction of partially known, band-limited Fourier-transform pairs from noisy data,” J. Opt. Soc. Am. A 2, 2027–2039 (1985).
    [CrossRef]
  22. J. R. Fienup, C. C. Wackerman, “Phase-retrieval stagnation problems and solutions,” J. Opt. Soc. Am. A 3, 1897–1907 (1986).
    [CrossRef]
  23. W. L. Root, “Ill-posedness and precision in object-field reconstruction problems,” J. Opt. Soc. Am. A 4, 171–179 (1987).
    [CrossRef]
  24. P. M. Hirsch, J. A. Jordan, L. B. Lesem, “Method of making an object-dependent diffuser,”U.S. Patent No.3,619,022 (November9, 1971).
  25. L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
    [CrossRef]

1987 (2)

1986 (1)

1985 (3)

1983 (1)

1982 (2)

J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
[CrossRef] [PubMed]

R. H. T. Bates, “Fourier phase problems are uniquely solvable in more than one dimension. I. Underlying theory,” Optik 61, 247–262 (1982).

1980 (1)

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19, 297–305 (1980).
[CrossRef]

1979 (1)

Y. M. Bruck, L. G. Sodin, “On the ambiguity of the image reconstruction problem,” Opt. Commun. 30, 304–308 (1979).
[CrossRef]

1976 (1)

1975 (1)

1973 (1)

1972 (1)

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

1969 (1)

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[CrossRef]

1968 (2)

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “Computer synthesis of holograms for 3-D display,” Commun. ACM 11, 661–674 (1968).
[CrossRef]

H. J. Gerritsen, W. J. Hannan, E. G. Ramberg, “Elimination of speckle noise in holograms with redundancy,” Appl. Opt. 7, 2301–2311 (1968).
[CrossRef] [PubMed]

1964 (1)

1963 (1)

A. Walther, “The question of phase retrieval in optics,” Opt. Acta 10, 41–49 (1963).
[CrossRef]

Allebach, J. P.

Barakat, R.

Bates, R. H. T.

R. H. T. Bates, “Fourier phase problems are uniquely solvable in more than one dimension. I. Underlying theory,” Optik 61, 247–262 (1982).

Bruck, Y. M.

Y. M. Bruck, L. G. Sodin, “On the ambiguity of the image reconstruction problem,” Opt. Commun. 30, 304–308 (1979).
[CrossRef]

Bryngdahl, O.

Burckhardt, C. B.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), pp. 194–203.

Collier, R. J.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), pp. 194–203.

Crimmins, T. R.

Dallas, W. J.

W. J. Dallas, “Computer-generated holograms,” in The Computer in Optical Research, B. R. Frieden, ed. Vol. 41 of Topics in Applied Physics (Springer-Verlag, Berlin, 1980), pp. 291–366.

Deighton, H. V.

Ferwerda, H. A.

H. A. Ferwerda, “Phase retrieval in imaging,” in Digest of Topical Meeting on Signal Recovery and Synthesis II (Optical Society of America, Washington, D.C., 1986), pp. 36–39.

Fiddy, M. A.

Fienup, J. R.

Gallagher, N. C.

Gerchberg, R. W.

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

Gerritsen, H. J.

Hannan, W. J.

Hauck, R.

Hirsch, P. M.

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[CrossRef]

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “Computer synthesis of holograms for 3-D display,” Commun. ACM 11, 661–674 (1968).
[CrossRef]

P. M. Hirsch, J. A. Jordan, L. B. Lesem, “Method of making an object-dependent diffuser,”U.S. Patent No.3,619,022 (November9, 1971).

Jordan, J. A.

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[CrossRef]

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “Computer synthesis of holograms for 3-D display,” Commun. ACM 11, 661–674 (1968).
[CrossRef]

P. M. Hirsch, J. A. Jordan, L. B. Lesem, “Method of making an object-dependent diffuser,”U.S. Patent No.3,619,022 (November9, 1971).

Lee, W.-H.

W.-H. Lee, “Computer-generated holograms: techniques and applications,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1978), Vol. 16, pp. 119–232.

Leith, E. N.

Lesem, L. B.

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[CrossRef]

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “Computer synthesis of holograms for 3-D display,” Commun. ACM 11, 661–674 (1968).
[CrossRef]

P. M. Hirsch, J. A. Jordan, L. B. Lesem, “Method of making an object-dependent diffuser,”U.S. Patent No.3,619,022 (November9, 1971).

Lin, L. H.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), pp. 194–203.

Liu, B.

Newsam, G.

Ramberg, E. G.

Root, W. L.

Saxton, W. O.

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

Scievier, M. S.

Scivier, M. S.

Sodin, L. G.

Y. M. Bruck, L. G. Sodin, “On the ambiguity of the image reconstruction problem,” Opt. Commun. 30, 304–308 (1979).
[CrossRef]

Upatnieks, J.

Wackerman, C. C.

Walther, A.

A. Walther, “The question of phase retrieval in optics,” Opt. Acta 10, 41–49 (1963).
[CrossRef]

Wyrowski, F.

Appl. Opt. (5)

Commun. ACM (1)

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “Computer synthesis of holograms for 3-D display,” Commun. ACM 11, 661–674 (1968).
[CrossRef]

IBM J. Res. Dev. (1)

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (5)

Opt. Acta (1)

A. Walther, “The question of phase retrieval in optics,” Opt. Acta 10, 41–49 (1963).
[CrossRef]

Opt. Commun. (1)

Y. M. Bruck, L. G. Sodin, “On the ambiguity of the image reconstruction problem,” Opt. Commun. 30, 304–308 (1979).
[CrossRef]

Opt. Eng. (1)

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19, 297–305 (1980).
[CrossRef]

Opt. Lett. (1)

Optik (2)

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

R. H. T. Bates, “Fourier phase problems are uniquely solvable in more than one dimension. I. Underlying theory,” Optik 61, 247–262 (1982).

Other (5)

H. A. Ferwerda, “Phase retrieval in imaging,” in Digest of Topical Meeting on Signal Recovery and Synthesis II (Optical Society of America, Washington, D.C., 1986), pp. 36–39.

P. M. Hirsch, J. A. Jordan, L. B. Lesem, “Method of making an object-dependent diffuser,”U.S. Patent No.3,619,022 (November9, 1971).

W. J. Dallas, “Computer-generated holograms,” in The Computer in Optical Research, B. R. Frieden, ed. Vol. 41 of Topics in Applied Physics (Springer-Verlag, Berlin, 1980), pp. 291–366.

W.-H. Lee, “Computer-generated holograms: techniques and applications,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1978), Vol. 16, pp. 119–232.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), pp. 194–203.

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.


Metrics