Abstract

The use of weak phase-retarding diffusers in coherent imaging systems is analyzed. It is shown that ringing caused by diffraction from dust or blemishes can be significantly reduced by a diffuser that scatters light slightly beyond the first interference minimum of the diffraction pattern, provided that the specular transmission of the diffuser is small. Weak phase diffusers, whose phase standard deviations are a small part of a wavelength, accomplish this is an optimal manner. The characteristics of the speckle patterns that consititute their spatially filtered images are found to depend not only on the size of the aperture of the imaging system, but on the Wiener spectrum of the phase and the statistical law that the phase obeys. It is shown that random diffusers with normally distributed phase can easily be constructed that produce image speckle patterns whose Wiener spectra consist primarily of high spatial frequencies, if the size of the aperture of the imaging system is greater than a specified minimum.Speckle patterns are also found to exist near the image of a phase diffuser even when the aperture of the imaging system is large, and their Wiener spectra are functions of their distances from the image of the diffuser.

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  1. L. H. Enloe, Bell Syst. Tech. J. 46, 1479 (1967).
  2. H. J. Gerritsen, W. J. Hannan, and E. G. Ramberg, Appl. Opt. 7, 2301 (1968).
  3. J. Upatnieks and R. W. Lewis, Appl. Opt. 12, 2161 (1973).
  4. J. Upatnieks, Appl. Opt. 6, 1905 (1967).
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  6. E. D. Rainville, Special Functions (Macmillan, New York, 1960), p. 56.
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  9. J. C. Dainty and W. T. Welford, Opt. Commun. 3, 289 (1971).
  10. H. J. Caulfield, in Proceedings of the SPIE Seminar on Developments in Holography, Vol. 25 (Redondo Beach, Calif., 1971), p. 111.
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  14. J. C. Dainty, Opt. Acta 17, 761 (1970).
  15. J. C. Dainty, J. Opt. Soc. Am. 62, 595 (1972).
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  18. R. Barakat, Opt. Acta 20, 729 (1973).
  19. A. A. Scribot, Opt. Commun. 11, 348 (1974).
  20. C. N. Kurtz, J. Opt. Soc. Am. 62, 982 (1972).
  21. M. J. Beran and G. P. Parrent, Theory of Partial Coherence (Prentice-Hall, Englewood Cliffs, N.J., 1964), p. 118.
  22. P. S. Considine, J. Opt. Soc. Am. 56, 1001 (1966).
  23. S. Lowenthal and D. Joyeux, J. Opt. Soc. Am. 61, 847 (1971)

Barakat, R.

R. Barakat, Opt. Acta 20, 729 (1973).

Battin, R. H.

J. H. Laning, Jr and R. H. Battin, Random Processes in Automatic Control (McGraw-Hill, New York, 1956), p. 83.

Bendat, J. S.

J. S. Bendat and A. G. Piersol, Measurement and Analysis of Random Data (Wiley, New York, 1966), p. 79.

Beran, M. J.

M. J. Beran and G. P. Parrent, Theory of Partial Coherence (Prentice-Hall, Englewood Cliffs, N.J., 1964), p. 118.

Caulfield, H. J.

H. J. Caulfield, in Proceedings of the SPIE Seminar on Developments in Holography, Vol. 25 (Redondo Beach, Calif., 1971), p. 111.

Considine, P. S.

P. S. Considine, J. Opt. Soc. Am. 56, 1001 (1966).

Dainty, J. C.

J. C. Dainty, Opt. Acta 18, 327 (1971).

J. C. Dainty, Opt. Acta 17, 761 (1970).

J. C. Dainty, J. Opt. Soc. Am. 62, 595 (1972).

J. C. Dainty and W. T. Welford, Opt. Commun. 3, 289 (1971).

Enloe, L. H.

L. H. Enloe, Bell Syst. Tech. J. 46, 1479 (1967).

Gerritsen, H. J.

H. J. Gerritsen, W. J. Hannan, and E. G. Ramberg, Appl. Opt. 7, 2301 (1968).

Goldfischer, L. I.

L. I. Goldfischer, J. Opt. Soc. Am. 55, 247 (1965).

Goodman, J. W.

J. W. Goodman, Proc. IEEE 53, 1688 (1965).

Hannan, W. J.

H. J. Gerritsen, W. J. Hannan, and E. G. Ramberg, Appl. Opt. 7, 2301 (1968).

Hopkins, H. H.

H. H. Hopkins, Proc. R. Soc. (London) A 217, 408 (1953).

Joyeux, D.

S. Lowenthal and D. Joyeux, J. Opt. Soc. Am. 61, 847 (1971)

Knox, K. T.

R. C. Waag and K. T. Knox, J. Opt. Soc. Am. 62, 877 (1972).

Kurtz, C. N.

C. N. Kurtz, J. Opt. Soc. Am. 62, 982 (1972).

Laning, Jr, J. H.

J. H. Laning, Jr and R. H. Battin, Random Processes in Automatic Control (McGraw-Hill, New York, 1956), p. 83.

Lewis, R. W.

J. Upatnieks and R. W. Lewis, Appl. Opt. 12, 2161 (1973).

Lowenthal, S.

S. Lowenthal and D. Joyeux, J. Opt. Soc. Am. 61, 847 (1971)

O’Neill, E. L.

E. L. O'Neill, Introduction to Statistical Optics (Addison-Wesley, Reading, Mass., 1963), p. 101.

Parrent, G. P.

M. J. Beran and G. P. Parrent, Theory of Partial Coherence (Prentice-Hall, Englewood Cliffs, N.J., 1964), p. 118.

Piersol, A. G.

J. S. Bendat and A. G. Piersol, Measurement and Analysis of Random Data (Wiley, New York, 1966), p. 79.

Rainville, E. D.

E. D. Rainville, Special Functions (Macmillan, New York, 1960), p. 56.

Ramberg, E. G.

H. J. Gerritsen, W. J. Hannan, and E. G. Ramberg, Appl. Opt. 7, 2301 (1968).

Scribot, A. A.

A. A. Scribot, Opt. Commun. 11, 348 (1974).

Upatnieks, J.

J. Upatnieks and R. W. Lewis, Appl. Opt. 12, 2161 (1973).

J. Upatnieks, Appl. Opt. 6, 1905 (1967).

Waag, R. C.

R. C. Waag and K. T. Knox, J. Opt. Soc. Am. 62, 877 (1972).

Welford, W. T.

J. C. Dainty and W. T. Welford, Opt. Commun. 3, 289 (1971).

Other

L. H. Enloe, Bell Syst. Tech. J. 46, 1479 (1967).

H. J. Gerritsen, W. J. Hannan, and E. G. Ramberg, Appl. Opt. 7, 2301 (1968).

J. Upatnieks and R. W. Lewis, Appl. Opt. 12, 2161 (1973).

J. Upatnieks, Appl. Opt. 6, 1905 (1967).

J. S. Bendat and A. G. Piersol, Measurement and Analysis of Random Data (Wiley, New York, 1966), p. 79.

E. D. Rainville, Special Functions (Macmillan, New York, 1960), p. 56.

J. H. Laning, Jr and R. H. Battin, Random Processes in Automatic Control (McGraw-Hill, New York, 1956), p. 83.

E. L. O'Neill, Introduction to Statistical Optics (Addison-Wesley, Reading, Mass., 1963), p. 101.

J. C. Dainty and W. T. Welford, Opt. Commun. 3, 289 (1971).

H. J. Caulfield, in Proceedings of the SPIE Seminar on Developments in Holography, Vol. 25 (Redondo Beach, Calif., 1971), p. 111.

R. C. Waag and K. T. Knox, J. Opt. Soc. Am. 62, 877 (1972).

J. W. Goodman, Proc. IEEE 53, 1688 (1965).

L. I. Goldfischer, J. Opt. Soc. Am. 55, 247 (1965).

J. C. Dainty, Opt. Acta 17, 761 (1970).

J. C. Dainty, J. Opt. Soc. Am. 62, 595 (1972).

H. H. Hopkins, Proc. R. Soc. (London) A 217, 408 (1953).

J. C. Dainty, Opt. Acta 18, 327 (1971).

R. Barakat, Opt. Acta 20, 729 (1973).

A. A. Scribot, Opt. Commun. 11, 348 (1974).

C. N. Kurtz, J. Opt. Soc. Am. 62, 982 (1972).

M. J. Beran and G. P. Parrent, Theory of Partial Coherence (Prentice-Hall, Englewood Cliffs, N.J., 1964), p. 118.

P. S. Considine, J. Opt. Soc. Am. 56, 1001 (1966).

S. Lowenthal and D. Joyeux, J. Opt. Soc. Am. 61, 847 (1971)

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