Abstract

The properties of the image of a nonuniform transparency degraded by speckle noise are studied. Attention is focused on the spatial details of an object that cannot be resolved by a coherent system. Analysis of the power spectrum of the noisy spatial-intensity distribution in the image plane confirms that the bandwidth for coherent diffuse illumination corresponds to the incoherent transfer function of the system. Experimental verification is presented using a Ronchi ruling as a test object.

© 1984 Optical Society of America

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References

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  1. J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, New York, 1975), pp. 9–75.
    [CrossRef]
  2. J. C. Dainty, “The statistics of speckle patterns,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), Vol. 8, pp. 1–46.
  3. V. N. Korwar, J. R. Pierce, “Detection of gratings and small features in speckle imagery,” Appl. Opt. 20, 312–319 (1981).
    [CrossRef] [PubMed]
  4. A. Kozma, C. R. Christensen, “Effect of speckle on resolution,” J. Opt. Soc. Am. 66, 1257–1260 (1976).
    [CrossRef]
  5. N. George, C. R. Christensen, J. S. Bennett, B. D. Guenther, “Speckle noise in displays,” J. Opt. Soc. Am. 66, 1282–1290 (1976).
    [CrossRef]
  6. J. S. Lim, H. Nawab, “Techniques for speckle noise removal,” Proc. Soc. Photo-Opt. Instrum. Eng. 243, 35–45 (1980).
  7. A. K. Jain, C. R. Christensen, “Digital processing of images in speckle noise,” Proc. Soc. Photo-Opt. Instrum. Eng. 243, 46–50 (1980).
  8. V. S. Frost, J. A. Stiles, K. S. Shanmugan, J. C. Holzman, “A model for radar images and its application to adaptive digital filtering of multiplicative noise,” IEEE Trans. Pattern. Anal. Mach. Intell. PAMI-4, 157–166 (1982).
    [CrossRef]
  9. J. S. Lee, “Speckle analysis and smoothing of synthetic aperture radar images,” Comput. Graphic Image Process. 17, 24–32 (1981).
    [CrossRef]
  10. J. S. Lee, “A simple speckle smoothing algorithm for synthetic aperture radar images,” IEEE Trans. Syst. Man Cybern. SMC-13, 85–89 (1983).
    [CrossRef]
  11. B. E. A. Saleh, M. Rabbani, “Linear filtering of speckled images,” Opt. Commun. 35, 327–331 (1980).
    [CrossRef]
  12. M. Tur, K. C. Chin, J. W. Goodman, “When is speckle noise multiplicative?” Appl. Opt. 21, 1157–1159 (1982).
    [CrossRef] [PubMed]
  13. D. T. Kuan, A. A. Sawchuk, T. C. Strand, P. Chavel, “Adaptive restoration of images with speckle,” Proc. Soc. Photo-Opt. Instrum. Eng. 359, 28–38 (1982).
  14. P. Beckman, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963), p. 128.
  15. S. Lowenthal, H. H. Arsenault, “Image formation for coherent diffuse objects: statistical properties,” J. Opt. Soc. Am. 60, 1478–1483 (1970).
    [CrossRef]
  16. M. J. Beran, G. B. Parrent, Theory of Partial Coherence (Society of Photo-Optical Instrumentation Engineers, New York, 1974).
  17. M. G. Miller, A. M. Schneiderman, P. F. Kellen, “Second-order statistics of laser speckle patterns,” J. Opt. Soc. Am. 65, 779–785 (1975).
    [CrossRef]

1983

J. S. Lee, “A simple speckle smoothing algorithm for synthetic aperture radar images,” IEEE Trans. Syst. Man Cybern. SMC-13, 85–89 (1983).
[CrossRef]

1982

V. S. Frost, J. A. Stiles, K. S. Shanmugan, J. C. Holzman, “A model for radar images and its application to adaptive digital filtering of multiplicative noise,” IEEE Trans. Pattern. Anal. Mach. Intell. PAMI-4, 157–166 (1982).
[CrossRef]

M. Tur, K. C. Chin, J. W. Goodman, “When is speckle noise multiplicative?” Appl. Opt. 21, 1157–1159 (1982).
[CrossRef] [PubMed]

D. T. Kuan, A. A. Sawchuk, T. C. Strand, P. Chavel, “Adaptive restoration of images with speckle,” Proc. Soc. Photo-Opt. Instrum. Eng. 359, 28–38 (1982).

1981

J. S. Lee, “Speckle analysis and smoothing of synthetic aperture radar images,” Comput. Graphic Image Process. 17, 24–32 (1981).
[CrossRef]

V. N. Korwar, J. R. Pierce, “Detection of gratings and small features in speckle imagery,” Appl. Opt. 20, 312–319 (1981).
[CrossRef] [PubMed]

1980

J. S. Lim, H. Nawab, “Techniques for speckle noise removal,” Proc. Soc. Photo-Opt. Instrum. Eng. 243, 35–45 (1980).

A. K. Jain, C. R. Christensen, “Digital processing of images in speckle noise,” Proc. Soc. Photo-Opt. Instrum. Eng. 243, 46–50 (1980).

B. E. A. Saleh, M. Rabbani, “Linear filtering of speckled images,” Opt. Commun. 35, 327–331 (1980).
[CrossRef]

1976

1975

1970

Arsenault, H. H.

Beckman, P.

P. Beckman, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963), p. 128.

Bennett, J. S.

Beran, M. J.

M. J. Beran, G. B. Parrent, Theory of Partial Coherence (Society of Photo-Optical Instrumentation Engineers, New York, 1974).

Chavel, P.

D. T. Kuan, A. A. Sawchuk, T. C. Strand, P. Chavel, “Adaptive restoration of images with speckle,” Proc. Soc. Photo-Opt. Instrum. Eng. 359, 28–38 (1982).

Chin, K. C.

Christensen, C. R.

Dainty, J. C.

J. C. Dainty, “The statistics of speckle patterns,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), Vol. 8, pp. 1–46.

Frost, V. S.

V. S. Frost, J. A. Stiles, K. S. Shanmugan, J. C. Holzman, “A model for radar images and its application to adaptive digital filtering of multiplicative noise,” IEEE Trans. Pattern. Anal. Mach. Intell. PAMI-4, 157–166 (1982).
[CrossRef]

George, N.

Goodman, J. W.

M. Tur, K. C. Chin, J. W. Goodman, “When is speckle noise multiplicative?” Appl. Opt. 21, 1157–1159 (1982).
[CrossRef] [PubMed]

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, New York, 1975), pp. 9–75.
[CrossRef]

Guenther, B. D.

Holzman, J. C.

V. S. Frost, J. A. Stiles, K. S. Shanmugan, J. C. Holzman, “A model for radar images and its application to adaptive digital filtering of multiplicative noise,” IEEE Trans. Pattern. Anal. Mach. Intell. PAMI-4, 157–166 (1982).
[CrossRef]

Jain, A. K.

A. K. Jain, C. R. Christensen, “Digital processing of images in speckle noise,” Proc. Soc. Photo-Opt. Instrum. Eng. 243, 46–50 (1980).

Kellen, P. F.

Korwar, V. N.

Kozma, A.

Kuan, D. T.

D. T. Kuan, A. A. Sawchuk, T. C. Strand, P. Chavel, “Adaptive restoration of images with speckle,” Proc. Soc. Photo-Opt. Instrum. Eng. 359, 28–38 (1982).

Lee, J. S.

J. S. Lee, “A simple speckle smoothing algorithm for synthetic aperture radar images,” IEEE Trans. Syst. Man Cybern. SMC-13, 85–89 (1983).
[CrossRef]

J. S. Lee, “Speckle analysis and smoothing of synthetic aperture radar images,” Comput. Graphic Image Process. 17, 24–32 (1981).
[CrossRef]

Lim, J. S.

J. S. Lim, H. Nawab, “Techniques for speckle noise removal,” Proc. Soc. Photo-Opt. Instrum. Eng. 243, 35–45 (1980).

Lowenthal, S.

Miller, M. G.

Nawab, H.

J. S. Lim, H. Nawab, “Techniques for speckle noise removal,” Proc. Soc. Photo-Opt. Instrum. Eng. 243, 35–45 (1980).

Parrent, G. B.

M. J. Beran, G. B. Parrent, Theory of Partial Coherence (Society of Photo-Optical Instrumentation Engineers, New York, 1974).

Pierce, J. R.

Rabbani, M.

B. E. A. Saleh, M. Rabbani, “Linear filtering of speckled images,” Opt. Commun. 35, 327–331 (1980).
[CrossRef]

Saleh, B. E. A.

B. E. A. Saleh, M. Rabbani, “Linear filtering of speckled images,” Opt. Commun. 35, 327–331 (1980).
[CrossRef]

Sawchuk, A. A.

D. T. Kuan, A. A. Sawchuk, T. C. Strand, P. Chavel, “Adaptive restoration of images with speckle,” Proc. Soc. Photo-Opt. Instrum. Eng. 359, 28–38 (1982).

Schneiderman, A. M.

Shanmugan, K. S.

V. S. Frost, J. A. Stiles, K. S. Shanmugan, J. C. Holzman, “A model for radar images and its application to adaptive digital filtering of multiplicative noise,” IEEE Trans. Pattern. Anal. Mach. Intell. PAMI-4, 157–166 (1982).
[CrossRef]

Spizzichino, A.

P. Beckman, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963), p. 128.

Stiles, J. A.

V. S. Frost, J. A. Stiles, K. S. Shanmugan, J. C. Holzman, “A model for radar images and its application to adaptive digital filtering of multiplicative noise,” IEEE Trans. Pattern. Anal. Mach. Intell. PAMI-4, 157–166 (1982).
[CrossRef]

Strand, T. C.

D. T. Kuan, A. A. Sawchuk, T. C. Strand, P. Chavel, “Adaptive restoration of images with speckle,” Proc. Soc. Photo-Opt. Instrum. Eng. 359, 28–38 (1982).

Tur, M.

Appl. Opt.

Comput. Graphic Image Process.

J. S. Lee, “Speckle analysis and smoothing of synthetic aperture radar images,” Comput. Graphic Image Process. 17, 24–32 (1981).
[CrossRef]

IEEE Trans. Pattern. Anal. Mach. Intell.

V. S. Frost, J. A. Stiles, K. S. Shanmugan, J. C. Holzman, “A model for radar images and its application to adaptive digital filtering of multiplicative noise,” IEEE Trans. Pattern. Anal. Mach. Intell. PAMI-4, 157–166 (1982).
[CrossRef]

IEEE Trans. Syst. Man Cybern.

J. S. Lee, “A simple speckle smoothing algorithm for synthetic aperture radar images,” IEEE Trans. Syst. Man Cybern. SMC-13, 85–89 (1983).
[CrossRef]

J. Opt. Soc. Am.

Opt. Commun.

B. E. A. Saleh, M. Rabbani, “Linear filtering of speckled images,” Opt. Commun. 35, 327–331 (1980).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng.

J. S. Lim, H. Nawab, “Techniques for speckle noise removal,” Proc. Soc. Photo-Opt. Instrum. Eng. 243, 35–45 (1980).

A. K. Jain, C. R. Christensen, “Digital processing of images in speckle noise,” Proc. Soc. Photo-Opt. Instrum. Eng. 243, 46–50 (1980).

D. T. Kuan, A. A. Sawchuk, T. C. Strand, P. Chavel, “Adaptive restoration of images with speckle,” Proc. Soc. Photo-Opt. Instrum. Eng. 359, 28–38 (1982).

Other

P. Beckman, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963), p. 128.

M. J. Beran, G. B. Parrent, Theory of Partial Coherence (Society of Photo-Optical Instrumentation Engineers, New York, 1974).

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, New York, 1975), pp. 9–75.
[CrossRef]

J. C. Dainty, “The statistics of speckle patterns,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), Vol. 8, pp. 1–46.

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Figures (4)

Fig. 1
Fig. 1

Formation of the speckled image of a Ronchi ruling using a telecentric optical system.

Fig. 2
Fig. 2

Photographs of the image of a Ronchi ruling in the presence of speckle noise for three chosen values of the coherent cutoff frequency: (a) uc = 7.93 mm−1, (b) uc = 3.96 mm−1, (c) uc = 2.64 mm−1. Sketches of the coherent and incoherent transfer functions are shown on the left.

Fig. 3
Fig. 3

Power spectrum of the speckled image of a Ronchi ruling (uc < u0 < 2uc).

Fig. 4
Fig. 4

Fourier spectra of the speckled images shown in Fig. 2.

Equations (18)

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A ( x ) = - f ( ξ ) d ( ξ ) h ( x - ξ ) d 2 ξ .
S I ( u ) = | - I ( x ) exp ( - 2 π i ux ) d 2 x | 2 ,
S I ( u ) = - I ( x 1 ) I ( x 2 ) × exp [ - 2 π i u ( x 1 - x 2 ) ] d 2 x 1 d 2 x 2 .
I ( x 1 ) I ( x 2 ) = I ( x 1 ) I ( x 2 ) + A ( x 1 ) A * ( x 2 ) 2 .
S I ( u ) = S I ( 1 ) ( u ) + S I ( 2 ) ( u ) ,
S I ( 1 ) ( u ) = | - I ( x ) exp ( - 2 π i ux ) d 2 x | 2
S I ( 2 ) ( u ) = - A ( x 1 ) A * ( x 2 ) 2 × exp [ - 2 π i u ( x 1 - x 2 ) ] d 2 x 1 d 2 x 2 .
S I ( 1 ) ( u ) = F ( u ) H ( u ) 2
S I ( 2 ) ( u ) = - H ( u 1 ) H * ( u - u 1 ) H * ( u 2 ) H ( u - u 2 ) × F ( u 1 - u 2 ) 2 d 2 u 1 d 2 u 2 ,
- S I ( 1 ) ( u ) d 2 u = - S I ( 2 ) ( u ) d 2 u .
f ( ξ , η ) = [ Π ( ξ b ) * 1 2 b III ( ξ 2 b ) ] Π ( ξ c ) Π ( η c ) ,
Π ( x ) = { 1 , x ½ 0 , x > ½
III ( x ) = n = - δ ( x - n ) .
F ( u , v ) = ( c 2 / 2 ) n = - sinc ( n / 2 ) sinc ( c v ) sinc [ c ( u - n u 0 ) ] .
F ( u , v ) 2 = ( c 2 / 4 ) n = - sinc 2 ( n / 2 ) δ ( v ) δ ( u - n u 0 ) .
H ( u , v ) = Π ( u 2 u c ) Π ( v 2 u c ) ,
Î ( u ) = - I ( x ) exp ( - 2 π i ux ) d 2 x ,
Î ( u ) 2 = - I ( x 1 ) I ( x 2 ) exp [ - 2 π i u ( x 1 - x 2 ) ] d 2 x 1 d 2 x 2 ,

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