Abstract

A statistical analysis of the effects of film nonlinearities on wavefront-reconstruction images of diffuse objects is presented. Regardless of the particular nature of the nonlinearity, the image distortions are shown to consist of additive irradiance contributions which may be found as multiple autoconvolutions of the ideal image irradiance distribution produced by a linear film. The predictions of the general nature of the image distortions are supported by experimental evidence.

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  1. D. Gabor, Nature 161, 777 (1948); Proc. Roy. Soc. (London) A197, 454 (1949); Proc. Phys. Soc. (London) B64, 449 (1951).
  2. E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962); 53, 1377 (1963); 54, 1295 (1964).
  3. E. N. Leith, J. Upatnieks, and K. A. Haines, J. Opt. Soc. Am. 55, 981 (1965).
  4. R. W. Meier, J. Opt. Soc. Am. 55, 987 (1965).
  5. R. F. van Ligten, J. Opt. Soc. Am. 56, 1009 (1966).
  6. J. W. Goodman, J. Opt. Soc. Am. 57, 493 (1967).
  7. A. Kozma, J. Opt. Soc. Am. 56, 428 (1966).
  8. A. A. Friesem and J. S. Zelenka, Appl. Opt. 6, 1755 (1967).
  9. G. W. Stroke, An Introduction to Coherent Optics and Holographzy (Academic Press Inc., New York, 1966), p. 116.
  10. G. R. Knight, Ph.D. dissertation, Stanford University, Stanford, California, 1967 (University Microfilms, Ann Arbor, Mich.). 1276
  11. M. Born and E. Wolf, Principles of Optics, 2nd (rev.) ed. (Pergamon Press, New York, 1964), p. 508.
  12. W. B. Davenport, Jr., and W. L. Root, Randomn Signals and Noise (McGraw-Hill Book Co., New York, 1958), p. 288.
  13. D. Middleton, Introduction to Statistical Communication Theory (McGraw-Hill Book Co., New York, 1960), Sec. 7.7.
  14. Reference 13, Sec. 9.1.
  15. Reference 12, P. 289.
  16. Here, as throughout this paper, we neglect the finite aperture of the hologram, concentrating our attention on nonlinear effects rather than on diffraction and its limitations of resolution.
  17. Reference 12, p. 281.
  18. J. W. Goodman and R. W. Lawrence, Appl. Phys. Letters 11, 77 (1967).
  19. J. H. Van Vleck and D. Middleton, Proc. IEEE 54, 2 (1967).
  20. Reference 12, p. 163.

Born, M.

M. Born and E. Wolf, Principles of Optics, 2nd (rev.) ed. (Pergamon Press, New York, 1964), p. 508.

Davenport, Jr., W. B.

W. B. Davenport, Jr., and W. L. Root, Randomn Signals and Noise (McGraw-Hill Book Co., New York, 1958), p. 288.

Friesem, A. A.

A. A. Friesem and J. S. Zelenka, Appl. Opt. 6, 1755 (1967).

Gabor, D.

D. Gabor, Nature 161, 777 (1948); Proc. Roy. Soc. (London) A197, 454 (1949); Proc. Phys. Soc. (London) B64, 449 (1951).

Goodman, J. W.

J. W. Goodman, J. Opt. Soc. Am. 57, 493 (1967).

J. W. Goodman and R. W. Lawrence, Appl. Phys. Letters 11, 77 (1967).

Haines, K. A.

E. N. Leith, J. Upatnieks, and K. A. Haines, J. Opt. Soc. Am. 55, 981 (1965).

Knight, G. R.

G. R. Knight, Ph.D. dissertation, Stanford University, Stanford, California, 1967 (University Microfilms, Ann Arbor, Mich.). 1276

Kozma, A.

A. Kozma, J. Opt. Soc. Am. 56, 428 (1966).

Lawrence, R. W.

J. W. Goodman and R. W. Lawrence, Appl. Phys. Letters 11, 77 (1967).

Leith, E. N.

E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962); 53, 1377 (1963); 54, 1295 (1964).

E. N. Leith, J. Upatnieks, and K. A. Haines, J. Opt. Soc. Am. 55, 981 (1965).

Meier, R. W.

R. W. Meier, J. Opt. Soc. Am. 55, 987 (1965).

Middleton, D.

D. Middleton, Introduction to Statistical Communication Theory (McGraw-Hill Book Co., New York, 1960), Sec. 7.7.

J. H. Van Vleck and D. Middleton, Proc. IEEE 54, 2 (1967).

Root, W. L.

W. B. Davenport, Jr., and W. L. Root, Randomn Signals and Noise (McGraw-Hill Book Co., New York, 1958), p. 288.

Stroke, G. W.

G. W. Stroke, An Introduction to Coherent Optics and Holographzy (Academic Press Inc., New York, 1966), p. 116.

Upatnieks, J.

E. N. Leith, J. Upatnieks, and K. A. Haines, J. Opt. Soc. Am. 55, 981 (1965).

E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962); 53, 1377 (1963); 54, 1295 (1964).

van Ligten, R. F.

R. F. van Ligten, J. Opt. Soc. Am. 56, 1009 (1966).

Van Vleck, J. H.

J. H. Van Vleck and D. Middleton, Proc. IEEE 54, 2 (1967).

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 2nd (rev.) ed. (Pergamon Press, New York, 1964), p. 508.

Zelenka, J. S.

A. A. Friesem and J. S. Zelenka, Appl. Opt. 6, 1755 (1967).

Other (20)

D. Gabor, Nature 161, 777 (1948); Proc. Roy. Soc. (London) A197, 454 (1949); Proc. Phys. Soc. (London) B64, 449 (1951).

E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962); 53, 1377 (1963); 54, 1295 (1964).

E. N. Leith, J. Upatnieks, and K. A. Haines, J. Opt. Soc. Am. 55, 981 (1965).

R. W. Meier, J. Opt. Soc. Am. 55, 987 (1965).

R. F. van Ligten, J. Opt. Soc. Am. 56, 1009 (1966).

J. W. Goodman, J. Opt. Soc. Am. 57, 493 (1967).

A. Kozma, J. Opt. Soc. Am. 56, 428 (1966).

A. A. Friesem and J. S. Zelenka, Appl. Opt. 6, 1755 (1967).

G. W. Stroke, An Introduction to Coherent Optics and Holographzy (Academic Press Inc., New York, 1966), p. 116.

G. R. Knight, Ph.D. dissertation, Stanford University, Stanford, California, 1967 (University Microfilms, Ann Arbor, Mich.). 1276

M. Born and E. Wolf, Principles of Optics, 2nd (rev.) ed. (Pergamon Press, New York, 1964), p. 508.

W. B. Davenport, Jr., and W. L. Root, Randomn Signals and Noise (McGraw-Hill Book Co., New York, 1958), p. 288.

D. Middleton, Introduction to Statistical Communication Theory (McGraw-Hill Book Co., New York, 1960), Sec. 7.7.

Reference 13, Sec. 9.1.

Reference 12, P. 289.

Here, as throughout this paper, we neglect the finite aperture of the hologram, concentrating our attention on nonlinear effects rather than on diffraction and its limitations of resolution.

Reference 12, p. 281.

J. W. Goodman and R. W. Lawrence, Appl. Phys. Letters 11, 77 (1967).

J. H. Van Vleck and D. Middleton, Proc. IEEE 54, 2 (1967).

Reference 12, p. 163.

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