Abstract

This paper considers diffusers characterized by random variations of optical path, such as ground-glass-surface diffusers. The theoretical limits on the light distributions realizable with random phase diffusers are derived, and the important parameters controlling these light distributions are identified. Methods for generating controlled random signals that, when converted to optical-path variations, have the correct parameters to synthesize diffusers with any desired, realizable light distribution are described. Some goniophotometric data taken from diffusers synthesized by this method are given in support of the theory. These results represent a basic solution of the random-phase-diffuser synthesis problem.

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  1. J. Upatneiks, Appl. Opt. 6, 1905 (1967).
  2. J. S. Chandler and J. J. DePalma, J. Soc. Motion Pict. Telev. Eng. 77, 1012 (1968).
  3. C. N. Kurtz, J. Opt. Soc. Am. 62, 982 (1972).
  4. H. J. Caulfield, in Proceedings of the SPIE Seminar on Developments in Holography, Vol. 25 (Society of Photo-Optical Instrumentation Engineers, Redondo Beach, Calif., 1971), p. 111.
  5. R. C. Waag and K. T. Knox, J. Opt. Soc. Am. 62, 877 (1972).
  6. F. Bestenreiner and W. Weiershausen, Optik 32, 446 (1971).
  7. H. F. Langworthy and J. J. DePalma, J. Opt. Soc. Am. 63, 488A (1973).
  8. D. O. Muhleman, Astron. J. 69, 34 (1964).
  9. D. E. Barrick, IEEE Trans. Antennas Propag. 16, 449 (1968).
  10. M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1965), p. 402.
  11. Reference 10, p. 752.
  12. W. B. Davenport and W. L. Root, Random Signals and Noise (McGraw-Hill, New York, 1958), pp. 32–35.
  13. Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun. Natl. Bur. Stand. (U.S.) Appl. Math. Ser. 55 (U. S. Government Printing Office, Washington, D. C., 1964; Dover, New York, 1965), p. 297.
  14. A. Papoulis, Probability, Random Signals and Stochastic Processes (McGraw-Hill, New York, 1965), p. 226.
  15. Reference 10, p. 513, Prob. No. 14–12.
  16. Y. W. Lee, Statistical Theory of Communication (Wiley, New York, 1960), p. 332.

Barrick, D. E.

D. E. Barrick, IEEE Trans. Antennas Propag. 16, 449 (1968).

Bestenreiner, F.

F. Bestenreiner and W. Weiershausen, Optik 32, 446 (1971).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1965), p. 402.

Caulfield, H. J.

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

Chandler, J. S.

J. S. Chandler and J. J. DePalma, J. Soc. Motion Pict. Telev. Eng. 77, 1012 (1968).

Davenport, W. B.

W. B. Davenport and W. L. Root, Random Signals and Noise (McGraw-Hill, New York, 1958), pp. 32–35.

DePalma, J. J.

H. F. Langworthy and J. J. DePalma, J. Opt. Soc. Am. 63, 488A (1973).

J. S. Chandler and J. J. DePalma, J. Soc. Motion Pict. Telev. Eng. 77, 1012 (1968).

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).

Langworthy, H. F.

H. F. Langworthy and J. J. DePalma, J. Opt. Soc. Am. 63, 488A (1973).

Lee, Y. W.

Y. W. Lee, Statistical Theory of Communication (Wiley, New York, 1960), p. 332.

Muhleman, D. O.

D. O. Muhleman, Astron. J. 69, 34 (1964).

Papoulis, A.

A. Papoulis, Probability, Random Signals and Stochastic Processes (McGraw-Hill, New York, 1965), p. 226.

Root, W. L.

W. B. Davenport and W. L. Root, Random Signals and Noise (McGraw-Hill, New York, 1958), pp. 32–35.

Upatneiks, J.

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

Waag, R. C.

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

Weiershausen, W.

F. Bestenreiner and W. Weiershausen, Optik 32, 446 (1971).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1965), p. 402.

Other (16)

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

J. S. Chandler and J. J. DePalma, J. Soc. Motion Pict. Telev. Eng. 77, 1012 (1968).

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

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

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

F. Bestenreiner and W. Weiershausen, Optik 32, 446 (1971).

H. F. Langworthy and J. J. DePalma, J. Opt. Soc. Am. 63, 488A (1973).

D. O. Muhleman, Astron. J. 69, 34 (1964).

D. E. Barrick, IEEE Trans. Antennas Propag. 16, 449 (1968).

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1965), p. 402.

Reference 10, p. 752.

W. B. Davenport and W. L. Root, Random Signals and Noise (McGraw-Hill, New York, 1958), pp. 32–35.

Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun. Natl. Bur. Stand. (U.S.) Appl. Math. Ser. 55 (U. S. Government Printing Office, Washington, D. C., 1964; Dover, New York, 1965), p. 297.

A. Papoulis, Probability, Random Signals and Stochastic Processes (McGraw-Hill, New York, 1965), p. 226.

Reference 10, p. 513, Prob. No. 14–12.

Y. W. Lee, Statistical Theory of Communication (Wiley, New York, 1960), p. 332.

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