Abstract

The “circular plane-wave” expansion of a spherical wave is newly proposed, and the reconstructed images from volume holograms are studied analytically by applying this method to the expansion of the object wave. The analysis is performed on the weakly coupled amplitude holograms in the Fraunhofer approximation. Both the amplitude and phase of the reconstructed waves are modulated, except the case of exact reconstruction, and are determined by recording and reconstruction parameters and the hologram thickness. The amplitude modulation by the volume hologram of a semitransparent object causes the space-variant or the space-invariant bandpass filtering effect by the spherical-wave or the plane-wave illumination of the object, respectively. The phase modulation causes aberrations and becomes small for a hologram having the large thickness.

© 1976 Optical Society of America

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  1. D. Gabour, Nature (Lond.) 161, 777 (1948).
  2. E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962).
  3. Yu. N. Denisyuk, Opt. Spectrosc. 15, 279 (1963).
  4. E. N. Leith, A. Kozma, J. Upatnieks, J. Marks, and N. Massey, Appl. Opt. 5, 1303 (1966).
  5. C. B. Burckhardt, J. Opt. Soc. Am. 56, 1502 (1966).
  6. H. Kogelnic, Bell. Syst. Tech. J. 48, 2909 (1969).
  7. D. Kermisch, J. Opt. Soc. Am. 59, 1409 (1969).
  8. D. Gabour and G. W. Stroke, Proc. R. Soc. A 304, 275 (1968).
  9. C. B. Burckhardt, J. Opt. Soc. Am. 57, 601 (1967).
  10. N. George and J. W. Matthewa, Appl. Phys. Lett. 9, 212 (1966).
  11. A. A. Friesem and J. L. Walker, Appl. Opt. 9, 201 (1970).
  12. A. A. Friesem, Appl. Phys. Lett. 7, 102 (1965).
  13. M. J. Landry, Appl. Opt. 6, 1947 (1967).
  14. J. M. Moran and I. P. Kaminow, Appl. Opt. 12, 1964 (1973).
  15. M. R. B. Forshaw, Opt. Commun. 8, 201 (1973).
  16. R. Magnusson and T. K. Gaylord, Appl. Opt. 13, 1545 (1974).
  17. M. R. B. Forshaw, Appl. Opt. 13, 2 (1974).
  18. V. I. Sukhnov and Yu. N. Denisyuk, Opt. Spectrosc. 21, 62 (1969).
  19. E. Wolf, J. Opt. Soc. Am. 60, 18 (1970).
  20. E. Wolf, J. Math. Phys. 11, 2254 (1970).
  21. E. T. Whittaker and G. N. Watson, A Course of Modern Analysis (Cambridge U. P., Cambridge, England, 1927), p. 397.
  22. G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge U. P., Cambridge, England, 1922), p. 51.
  23. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1965), p. 585.
  24. H. Margenau and G. M. Murphy, The Mathematics of Physics and Chemistry (Van Nostrand, New York, 1943), pp. 119 and 236.
  25. See Ref. 23, p. 384.
  26. Y. Shono, T. Inuzuka, and T. Hoshino, Appl. Phys. Lett. 22, 299 (1973).
  27. Y. Shono and T. Inuzuka, Optik (Stuttg.) 41, 50 (1974).
  28. J. N. Latta, Appl. Opt. 10, 609 (1971).
  29. L. H. Lin and E. T. Doherty, Appl. Opt. 10, 1314 (1971).
  30. J. M. Moran, Appl. Opt. 10, 1909 (1971).
  31. N. Uchida, J. Opt. Soc. Am. 63, 280 (1973).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1965), p. 585.

Burckhardt, C. B.

C. B. Burckhardt, J. Opt. Soc. Am. 56, 1502 (1966).

C. B. Burckhardt, J. Opt. Soc. Am. 57, 601 (1967).

Denisyuk, Yu. N.

Yu. N. Denisyuk, Opt. Spectrosc. 15, 279 (1963).

V. I. Sukhnov and Yu. N. Denisyuk, Opt. Spectrosc. 21, 62 (1969).

Doherty, E. T.

L. H. Lin and E. T. Doherty, Appl. Opt. 10, 1314 (1971).

Forshaw, M. R. B.

M. R. B. Forshaw, Appl. Opt. 13, 2 (1974).

M. R. B. Forshaw, Opt. Commun. 8, 201 (1973).

Friesem, A. A.

A. A. Friesem and J. L. Walker, Appl. Opt. 9, 201 (1970).

A. A. Friesem, Appl. Phys. Lett. 7, 102 (1965).

Gabour, D.

D. Gabour, Nature (Lond.) 161, 777 (1948).

D. Gabour and G. W. Stroke, Proc. R. Soc. A 304, 275 (1968).

Gaylord, T. K.

R. Magnusson and T. K. Gaylord, Appl. Opt. 13, 1545 (1974).

George, N.

N. George and J. W. Matthewa, Appl. Phys. Lett. 9, 212 (1966).

Hoshino, T.

Y. Shono, T. Inuzuka, and T. Hoshino, Appl. Phys. Lett. 22, 299 (1973).

Inuzuka, T.

Y. Shono, T. Inuzuka, and T. Hoshino, Appl. Phys. Lett. 22, 299 (1973).

Y. Shono and T. Inuzuka, Optik (Stuttg.) 41, 50 (1974).

Kaminow, I. P.

J. M. Moran and I. P. Kaminow, Appl. Opt. 12, 1964 (1973).

Kermisch, D.

D. Kermisch, J. Opt. Soc. Am. 59, 1409 (1969).

Kogelnic, H.

H. Kogelnic, Bell. Syst. Tech. J. 48, 2909 (1969).

Kozma, A.

E. N. Leith, A. Kozma, J. Upatnieks, J. Marks, and N. Massey, Appl. Opt. 5, 1303 (1966).

Landry, M. J.

M. J. Landry, Appl. Opt. 6, 1947 (1967).

Latta, J. N.

J. N. Latta, Appl. Opt. 10, 609 (1971).

Leith, E. N.

E. N. Leith, A. Kozma, J. Upatnieks, J. Marks, and N. Massey, Appl. Opt. 5, 1303 (1966).

E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962).

Lin, L. H.

L. H. Lin and E. T. Doherty, Appl. Opt. 10, 1314 (1971).

Magnusson, R.

R. Magnusson and T. K. Gaylord, Appl. Opt. 13, 1545 (1974).

Margenau, H.

H. Margenau and G. M. Murphy, The Mathematics of Physics and Chemistry (Van Nostrand, New York, 1943), pp. 119 and 236.

Marks, J.

E. N. Leith, A. Kozma, J. Upatnieks, J. Marks, and N. Massey, Appl. Opt. 5, 1303 (1966).

Massey, N.

E. N. Leith, A. Kozma, J. Upatnieks, J. Marks, and N. Massey, Appl. Opt. 5, 1303 (1966).

Matthewa, J. W.

N. George and J. W. Matthewa, Appl. Phys. Lett. 9, 212 (1966).

Moran, J. M.

J. M. Moran and I. P. Kaminow, Appl. Opt. 12, 1964 (1973).

J. M. Moran, Appl. Opt. 10, 1909 (1971).

Murphy, G. M.

H. Margenau and G. M. Murphy, The Mathematics of Physics and Chemistry (Van Nostrand, New York, 1943), pp. 119 and 236.

Shono, Y.

Y. Shono and T. Inuzuka, Optik (Stuttg.) 41, 50 (1974).

Y. Shono, T. Inuzuka, and T. Hoshino, Appl. Phys. Lett. 22, 299 (1973).

Stroke, G. W.

D. Gabour and G. W. Stroke, Proc. R. Soc. A 304, 275 (1968).

Sukhnov, V. I.

V. I. Sukhnov and Yu. N. Denisyuk, Opt. Spectrosc. 21, 62 (1969).

Uchida, N.

N. Uchida, J. Opt. Soc. Am. 63, 280 (1973).

Upatnieks, J.

E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962).

E. N. Leith, A. Kozma, J. Upatnieks, J. Marks, and N. Massey, Appl. Opt. 5, 1303 (1966).

Walker, J. L.

A. A. Friesem and J. L. Walker, Appl. Opt. 9, 201 (1970).

Watson, G. N.

G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge U. P., Cambridge, England, 1922), p. 51.

E. T. Whittaker and G. N. Watson, A Course of Modern Analysis (Cambridge U. P., Cambridge, England, 1927), p. 397.

Whittaker, E. T.

E. T. Whittaker and G. N. Watson, A Course of Modern Analysis (Cambridge U. P., Cambridge, England, 1927), p. 397.

Wolf, E.

E. Wolf, J. Opt. Soc. Am. 60, 18 (1970).

E. Wolf, J. Math. Phys. 11, 2254 (1970).

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1965), p. 585.

Other (31)

D. Gabour, Nature (Lond.) 161, 777 (1948).

E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962).

Yu. N. Denisyuk, Opt. Spectrosc. 15, 279 (1963).

E. N. Leith, A. Kozma, J. Upatnieks, J. Marks, and N. Massey, Appl. Opt. 5, 1303 (1966).

C. B. Burckhardt, J. Opt. Soc. Am. 56, 1502 (1966).

H. Kogelnic, Bell. Syst. Tech. J. 48, 2909 (1969).

D. Kermisch, J. Opt. Soc. Am. 59, 1409 (1969).

D. Gabour and G. W. Stroke, Proc. R. Soc. A 304, 275 (1968).

C. B. Burckhardt, J. Opt. Soc. Am. 57, 601 (1967).

N. George and J. W. Matthewa, Appl. Phys. Lett. 9, 212 (1966).

A. A. Friesem and J. L. Walker, Appl. Opt. 9, 201 (1970).

A. A. Friesem, Appl. Phys. Lett. 7, 102 (1965).

M. J. Landry, Appl. Opt. 6, 1947 (1967).

J. M. Moran and I. P. Kaminow, Appl. Opt. 12, 1964 (1973).

M. R. B. Forshaw, Opt. Commun. 8, 201 (1973).

R. Magnusson and T. K. Gaylord, Appl. Opt. 13, 1545 (1974).

M. R. B. Forshaw, Appl. Opt. 13, 2 (1974).

V. I. Sukhnov and Yu. N. Denisyuk, Opt. Spectrosc. 21, 62 (1969).

E. Wolf, J. Opt. Soc. Am. 60, 18 (1970).

E. Wolf, J. Math. Phys. 11, 2254 (1970).

E. T. Whittaker and G. N. Watson, A Course of Modern Analysis (Cambridge U. P., Cambridge, England, 1927), p. 397.

G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge U. P., Cambridge, England, 1922), p. 51.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1965), p. 585.

H. Margenau and G. M. Murphy, The Mathematics of Physics and Chemistry (Van Nostrand, New York, 1943), pp. 119 and 236.

See Ref. 23, p. 384.

Y. Shono, T. Inuzuka, and T. Hoshino, Appl. Phys. Lett. 22, 299 (1973).

Y. Shono and T. Inuzuka, Optik (Stuttg.) 41, 50 (1974).

J. N. Latta, Appl. Opt. 10, 609 (1971).

L. H. Lin and E. T. Doherty, Appl. Opt. 10, 1314 (1971).

J. M. Moran, Appl. Opt. 10, 1909 (1971).

N. Uchida, J. Opt. Soc. Am. 63, 280 (1973).

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