Abstract

When image plane speckle intensity integrated over a finite aperture is submitted to a logarithmic transformation, the noise becomes additive and signal independent. The first- and second-order moments of the probability distribution are derived. It is found that the logarithm of speckle noise approaches a normal distribution much faster than speckle intensity. The properties of speckle noise are different from those of filmgrain noise; for example, neither Nutting’s law nor Selwyn’s law is satisfied by speckle.

© 1976 Optical Society of America

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  1. H. H. Arsenault and N. Brousseau, "Digital Image Processing and Preprocessing," J. Opt. Soc. Am. 65, 1203 (1975).
  2. J. F. Walkup and R. C. Choens, " Image processing in signal-dependent noise," Opt. Eng. 13, 258 (1974).
  3. L. S. Barbanel, "Signal discrimination and dection in the presence of nonadditive noise," Opt. Spectrosc. (USSR) 33, 1145 (1972).
  4. J. W. Goodman and H. Kato, "Nonlinear filtering in coherent optical systems through halftone screen processes," Appl. Opt. 14, 1813 (1975).
  5. T. G. Stockham, "Image processing in the context of a visual model," Proc. IEEE 60, 828 (1972).
  6. S. Lowenthal and H. H. Arsenault, "Image formation for coherent diffuse objects: statistical properties," J. Opt. Soc. Am. 60, 1478 (1970).
  7. J. W. Goodman, "Some effects of target-induced scintillation on optical radar performance," Proc. IEEE 53, 1688 (1965).
  8. J. W. Goodman, "Statistical properties of laser speckle patterns," in Laser Speckle and Related Phenomena, edited by J. C. Dainty (Springer-Verlag, New York), pp. 9–75.
  9. R. Barakat, "First-order probability densities of laser speckle patterns observed through finite size scanning apertures," Opt. Acta 20, 729 (1973).
  10. M. Abramowitz and I. Stegun, "Handbook of Mathematical Functions," (Dover, New York, 1965), p. 930.
  11. Reference (10), p. 258.
  12. H. J. Gerritsen, W. J. Hannan, and E. G. Ramberg, "Elimination of speckle noise in holograms with redundancy," Appl. Opt. 7, 2301 (1968).
  13. F. C. Billingsley, Noise Considerations in Digital Image Processing Hardware, in Picture Processing and Digital Filtering, edited by T. S. Huang (Springer-Verlag, New York, 1975), p. 259.
  14. H. H. Arsenault and G. April, "Speckle removal by optical and digital processing," J. Opt. Soc. Am. 66, 177 (1976).

1976 (1)

H. H. Arsenault and G. April, "Speckle removal by optical and digital processing," J. Opt. Soc. Am. 66, 177 (1976).

1975 (2)

H. H. Arsenault and N. Brousseau, "Digital Image Processing and Preprocessing," J. Opt. Soc. Am. 65, 1203 (1975).

J. W. Goodman and H. Kato, "Nonlinear filtering in coherent optical systems through halftone screen processes," Appl. Opt. 14, 1813 (1975).

1974 (1)

J. F. Walkup and R. C. Choens, " Image processing in signal-dependent noise," Opt. Eng. 13, 258 (1974).

1973 (1)

R. Barakat, "First-order probability densities of laser speckle patterns observed through finite size scanning apertures," Opt. Acta 20, 729 (1973).

1972 (1)

L. S. Barbanel, "Signal discrimination and dection in the presence of nonadditive noise," Opt. Spectrosc. (USSR) 33, 1145 (1972).

1970 (1)

1968 (1)

Abramowitz, M.

M. Abramowitz and I. Stegun, "Handbook of Mathematical Functions," (Dover, New York, 1965), p. 930.

April, G.

H. H. Arsenault and G. April, "Speckle removal by optical and digital processing," J. Opt. Soc. Am. 66, 177 (1976).

Arsenault, H. H.

H. H. Arsenault and G. April, "Speckle removal by optical and digital processing," J. Opt. Soc. Am. 66, 177 (1976).

H. H. Arsenault and N. Brousseau, "Digital Image Processing and Preprocessing," J. Opt. Soc. Am. 65, 1203 (1975).

S. Lowenthal and H. H. Arsenault, "Image formation for coherent diffuse objects: statistical properties," J. Opt. Soc. Am. 60, 1478 (1970).

Barakat, R.

R. Barakat, "First-order probability densities of laser speckle patterns observed through finite size scanning apertures," Opt. Acta 20, 729 (1973).

Barbanel, L. S.

L. S. Barbanel, "Signal discrimination and dection in the presence of nonadditive noise," Opt. Spectrosc. (USSR) 33, 1145 (1972).

Billingsley, F. C.

F. C. Billingsley, Noise Considerations in Digital Image Processing Hardware, in Picture Processing and Digital Filtering, edited by T. S. Huang (Springer-Verlag, New York, 1975), p. 259.

Brousseau, N.

H. H. Arsenault and N. Brousseau, "Digital Image Processing and Preprocessing," J. Opt. Soc. Am. 65, 1203 (1975).

Choens, R. C.

J. F. Walkup and R. C. Choens, " Image processing in signal-dependent noise," Opt. Eng. 13, 258 (1974).

Gerritsen, H. J.

Goodman, J. W.

J. W. Goodman and H. Kato, "Nonlinear filtering in coherent optical systems through halftone screen processes," Appl. Opt. 14, 1813 (1975).

J. W. Goodman, "Some effects of target-induced scintillation on optical radar performance," Proc. IEEE 53, 1688 (1965).

J. W. Goodman, "Statistical properties of laser speckle patterns," in Laser Speckle and Related Phenomena, edited by J. C. Dainty (Springer-Verlag, New York), pp. 9–75.

Hannan, W. J.

Kato, H.

Lowenthal, S.

Ramberg, E. G.

Stegun, I.

M. Abramowitz and I. Stegun, "Handbook of Mathematical Functions," (Dover, New York, 1965), p. 930.

Stockham, T. G.

T. G. Stockham, "Image processing in the context of a visual model," Proc. IEEE 60, 828 (1972).

Walkup, J. F.

J. F. Walkup and R. C. Choens, " Image processing in signal-dependent noise," Opt. Eng. 13, 258 (1974).

Appl. Opt. (2)

J. Opt. Soc. Am. (3)

S. Lowenthal and H. H. Arsenault, "Image formation for coherent diffuse objects: statistical properties," J. Opt. Soc. Am. 60, 1478 (1970).

H. H. Arsenault and G. April, "Speckle removal by optical and digital processing," J. Opt. Soc. Am. 66, 177 (1976).

H. H. Arsenault and N. Brousseau, "Digital Image Processing and Preprocessing," J. Opt. Soc. Am. 65, 1203 (1975).

Opt. Acta (1)

R. Barakat, "First-order probability densities of laser speckle patterns observed through finite size scanning apertures," Opt. Acta 20, 729 (1973).

Opt. Eng. (1)

J. F. Walkup and R. C. Choens, " Image processing in signal-dependent noise," Opt. Eng. 13, 258 (1974).

Opt. Spectrosc. (1)

L. S. Barbanel, "Signal discrimination and dection in the presence of nonadditive noise," Opt. Spectrosc. (USSR) 33, 1145 (1972).

Other (6)

J. W. Goodman, "Some effects of target-induced scintillation on optical radar performance," Proc. IEEE 53, 1688 (1965).

J. W. Goodman, "Statistical properties of laser speckle patterns," in Laser Speckle and Related Phenomena, edited by J. C. Dainty (Springer-Verlag, New York), pp. 9–75.

M. Abramowitz and I. Stegun, "Handbook of Mathematical Functions," (Dover, New York, 1965), p. 930.

Reference (10), p. 258.

T. G. Stockham, "Image processing in the context of a visual model," Proc. IEEE 60, 828 (1972).

F. C. Billingsley, Noise Considerations in Digital Image Processing Hardware, in Picture Processing and Digital Filtering, edited by T. S. Huang (Springer-Verlag, New York, 1975), p. 259.

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