Abstract

The properties of the amplitude and illuminance of the images of coherently illuminated diffuse objects are studied. Uniform and nonuniform objects are considered. The image illuminance is considered to result from a linear transformation of a nonstationary gaussian stochastic process followed by a square-law detection. Expressions are obtained for the mean, autocorrelation, variance, and spatial power spectral density of the amplitude and of the illuminance. Interpretation of the results led to conclusions concerning he speckle size, the noise power in the image, and the transfer function of an optical system when the object diffuses coherent light. When the autocorrelation width of the random fluctuations of the object amplitude is small compared to the impulse response of the system, the mean illuminance in the image plane is that which would be given by an incoherent object having the same luminance as the object considered; the average speckle size is equal to that of the impulse response of the system; the average transfer function of the system is the incoherent transfer function; and the distribution of the noise spatial frequencies does not depend upon the form of the signal, but only upon its total energy. Other results concerning the image statistics have also been obtained.

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  1. P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).
  2. J. W. Goodman, Proc. IEEE 53, 1688 (1965).
  3. J. D. Rigden and E. I. Gordon, Proc. IRE 50, 2367 (1962).
  4. B. M. Oliver, Proc. IEEE 51, 220 (1963).
  5. L. Allen and D. G. C. Jones, Phys. Letters 7, 321 (1963).
  6. T. J. Skinner, J. Opt. Soc. Am. 53, 1351A (1963).
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  9. P. Dumontet, Publ. Sci. Univ. Alger, Série B, 203 (1956).
  10. S. Lowenthal, Opt. Acta 12, 261 (1965).
  11. A. W. Lohmann and D. P. Paris, J. Opt. Soc. Am. 55, 1007 (1965).
  12. A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1965).
  13. A. Blanc-Lapierre and Robert Fortet, Théorie des Fonctions Aléatoires (Masson, Paris, 1953).
  14. A. Blanc-Lapierre and B. Picinbono, Propriétés Statistiques du Bruit de Fond (Masson, Paris, 1961).
  15. B. Picinbono, Rev. Cethedec 11, 1 (1967).
  16. W. B. Davenport and W. L. Root, Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958).
  17. A. Maréchal and M. Françon, Diffraction: Structure des Images (Ed. Rev. d'Optique, Paris, 1960).
  18. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1965).

Allen, L.

L. Allen and D. G. C. Jones, Phys. Letters 7, 321 (1963).

Beckmann, P.

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).

Blanc-Lapierre, A.

A. Blanc-Lapierre and Robert Fortet, Théorie des Fonctions Aléatoires (Masson, Paris, 1953).

A. Blanc-Lapierre and B. Picinbono, Propriétés Statistiques du Bruit de Fond (Masson, Paris, 1961).

Born, M.

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

Davenport, W. B.

W. B. Davenport and W. L. Root, Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958).

Dumontet, P.

P. Dumontet, Publ. Sci. Univ. Alger, Série B, 203 (1956).

Enloe, L. H.

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

Fortet, Robert

A. Blanc-Lapierre and Robert Fortet, Théorie des Fonctions Aléatoires (Masson, Paris, 1953).

Françon, M.

A. Maréchal and M. Françon, Diffraction: Structure des Images (Ed. Rev. d'Optique, Paris, 1960).

Goldfischer, L. I.

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

Goodman, J. W.

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

Gordon, E. I.

J. D. Rigden and E. I. Gordon, Proc. IRE 50, 2367 (1962).

Jones, D. G. C.

L. Allen and D. G. C. Jones, Phys. Letters 7, 321 (1963).

Lohmann, A. W.

A. W. Lohmann and D. P. Paris, J. Opt. Soc. Am. 55, 1007 (1965).

Lowenthal, S.

S. Lowenthal, Opt. Acta 12, 261 (1965).

Maréchal, A.

A. Maréchal and M. Françon, Diffraction: Structure des Images (Ed. Rev. d'Optique, Paris, 1960).

Oliver, B. M.

B. M. Oliver, Proc. IEEE 51, 220 (1963).

Papoulis, A.

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

Paris, D. P.

A. W. Lohmann and D. P. Paris, J. Opt. Soc. Am. 55, 1007 (1965).

Picinbono, B.

B. Picinbono, Rev. Cethedec 11, 1 (1967).

A. Blanc-Lapierre and B. Picinbono, Propriétés Statistiques du Bruit de Fond (Masson, Paris, 1961).

Rigden, J. D.

J. D. Rigden and E. I. Gordon, Proc. IRE 50, 2367 (1962).

Root, W. L.

W. B. Davenport and W. L. Root, Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958).

Skinner, T. J.

T. J. Skinner, J. Opt. Soc. Am. 53, 1351A (1963).

Spizzichino, A.

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).

Wolf, E.

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

Other

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).

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

J. D. Rigden and E. I. Gordon, Proc. IRE 50, 2367 (1962).

B. M. Oliver, Proc. IEEE 51, 220 (1963).

L. Allen and D. G. C. Jones, Phys. Letters 7, 321 (1963).

T. J. Skinner, J. Opt. Soc. Am. 53, 1351A (1963).

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

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

P. Dumontet, Publ. Sci. Univ. Alger, Série B, 203 (1956).

S. Lowenthal, Opt. Acta 12, 261 (1965).

A. W. Lohmann and D. P. Paris, J. Opt. Soc. Am. 55, 1007 (1965).

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

A. Blanc-Lapierre and Robert Fortet, Théorie des Fonctions Aléatoires (Masson, Paris, 1953).

A. Blanc-Lapierre and B. Picinbono, Propriétés Statistiques du Bruit de Fond (Masson, Paris, 1961).

B. Picinbono, Rev. Cethedec 11, 1 (1967).

W. B. Davenport and W. L. Root, Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958).

A. Maréchal and M. Françon, Diffraction: Structure des Images (Ed. Rev. d'Optique, Paris, 1960).

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

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