Abstract

In describing the first-order properties of laser speckle under polarized illumination conditions, it is almost an article of faith that the contrast is unity. In many processing schemes, however, the contrast defined as the quotient of the standard deviation and the mean is calculated over a localized spatial region. In such cases, this local contrast displays a distribution of values that can depart substantially from unity. Properties of this distribution depend on details of the data acquisition and on the size of the local neighborhood over which the contrast is calculated. We demonstrate that this local contrast can be characterized in terms of a log-normal distribution. Further, we show that the two defining parameters of this model can in turn be expressed in terms of the minimum speckle size and the extent of the local neighborhood. Performance of the model is illustrated with some typical optical coherence tomography data.

© 2008 Optical Society of America

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References

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    [CrossRef]
  2. J. W. Goodman, Statistical Optics (Wiley & Sons, 1985).
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    [CrossRef]
  4. T. Durduran, M. G. Burnett, G. Yu, C. Zhou, D. Furuya, A. G. Yodh, J. A. Detre, and J. H. Greenburg, "Spatiotemporal quantification of cerebral blood flow during functional activation in rat somatosensory cortex using laser-speckle flowmetry," J. Cereb. Blood Flow Metab. 24, 518-525 (2004).
    [CrossRef] [PubMed]
  5. H. Isono, S. Kishi, Y. Kimura, N. Hagiwara, N. Konishi, and H. Fuji, "Observation of choroidal circulation using index of erythrocytic velocity," Arch. Ophthalmol. (Chicago) 121, 225-231 (2003).
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  7. H. Rabal, N. Cap, M. Trivi, R. Arizaga, A. Federico, G. E. Galizzi, and G. H. Kaufmann, "Speckle activity images based on the spatial variance of the phase," Appl. Opt. 45, 8733-8738 (2006).
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    [CrossRef]
  9. A. Papoulis and S. U. Pillai, Probability, Random Variables, and Stochastic Processes, 4th edition (McGraw-Hill, 2001).
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    [CrossRef]
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    [CrossRef]

2007 (1)

2006 (3)

2005 (1)

R. Bandyopadhyay, A. S. Gittings, S. S. Suh, P. K. Dixon, and D. J. Durian, "Speckle-visibility spectroscopy: a tool to study time-varying dynamics," Rev. Sci. Instrum. 76, 093110-093110 (2005).
[CrossRef]

2004 (1)

T. Durduran, M. G. Burnett, G. Yu, C. Zhou, D. Furuya, A. G. Yodh, J. A. Detre, and J. H. Greenburg, "Spatiotemporal quantification of cerebral blood flow during functional activation in rat somatosensory cortex using laser-speckle flowmetry," J. Cereb. Blood Flow Metab. 24, 518-525 (2004).
[CrossRef] [PubMed]

2003 (1)

H. Isono, S. Kishi, Y. Kimura, N. Hagiwara, N. Konishi, and H. Fuji, "Observation of choroidal circulation using index of erythrocytic velocity," Arch. Ophthalmol. (Chicago) 121, 225-231 (2003).

2001 (2)

A. Papoulis and S. U. Pillai, Probability, Random Variables, and Stochastic Processes, 4th edition (McGraw-Hill, 2001).

J. D. Briers, "Time-varying laser speckle for measuring motion and flow," Proc. SPIE 4242, 25-39 (2001).
[CrossRef]

1985 (1)

J. W. Goodman, Statistical Optics (Wiley & Sons, 1985).

1981 (1)

A. F. Fercher and J. D. Briers, "Flow visualization by means of single-exposure speckle photography," Opt. Commun. 37, 326-330 (1981).
[CrossRef]

1975 (1)

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

Arizaga, R.

Bandyopadhyay, R.

R. Bandyopadhyay, A. S. Gittings, S. S. Suh, P. K. Dixon, and D. J. Durian, "Speckle-visibility spectroscopy: a tool to study time-varying dynamics," Rev. Sci. Instrum. 76, 093110-093110 (2005).
[CrossRef]

Briers, J. D.

J. D. Briers, "Time-varying laser speckle for measuring motion and flow," Proc. SPIE 4242, 25-39 (2001).
[CrossRef]

A. F. Fercher and J. D. Briers, "Flow visualization by means of single-exposure speckle photography," Opt. Commun. 37, 326-330 (1981).
[CrossRef]

Buck, A.

Burnett, M. G.

T. Durduran, M. G. Burnett, G. Yu, C. Zhou, D. Furuya, A. G. Yodh, J. A. Detre, and J. H. Greenburg, "Spatiotemporal quantification of cerebral blood flow during functional activation in rat somatosensory cortex using laser-speckle flowmetry," J. Cereb. Blood Flow Metab. 24, 518-525 (2004).
[CrossRef] [PubMed]

Cap, N.

Detre, J. A.

T. Durduran, M. G. Burnett, G. Yu, C. Zhou, D. Furuya, A. G. Yodh, J. A. Detre, and J. H. Greenburg, "Spatiotemporal quantification of cerebral blood flow during functional activation in rat somatosensory cortex using laser-speckle flowmetry," J. Cereb. Blood Flow Metab. 24, 518-525 (2004).
[CrossRef] [PubMed]

Dixon, P. K.

R. Bandyopadhyay, A. S. Gittings, S. S. Suh, P. K. Dixon, and D. J. Durian, "Speckle-visibility spectroscopy: a tool to study time-varying dynamics," Rev. Sci. Instrum. 76, 093110-093110 (2005).
[CrossRef]

Duncan, D. D.

Durduran, T.

T. Durduran, M. G. Burnett, G. Yu, C. Zhou, D. Furuya, A. G. Yodh, J. A. Detre, and J. H. Greenburg, "Spatiotemporal quantification of cerebral blood flow during functional activation in rat somatosensory cortex using laser-speckle flowmetry," J. Cereb. Blood Flow Metab. 24, 518-525 (2004).
[CrossRef] [PubMed]

Durian, D. J.

R. Bandyopadhyay, A. S. Gittings, S. S. Suh, P. K. Dixon, and D. J. Durian, "Speckle-visibility spectroscopy: a tool to study time-varying dynamics," Rev. Sci. Instrum. 76, 093110-093110 (2005).
[CrossRef]

Federico, A.

Fercher, A. F.

A. F. Fercher and J. D. Briers, "Flow visualization by means of single-exposure speckle photography," Opt. Commun. 37, 326-330 (1981).
[CrossRef]

Fuji, H.

H. Isono, S. Kishi, Y. Kimura, N. Hagiwara, N. Konishi, and H. Fuji, "Observation of choroidal circulation using index of erythrocytic velocity," Arch. Ophthalmol. (Chicago) 121, 225-231 (2003).

Furuya, D.

T. Durduran, M. G. Burnett, G. Yu, C. Zhou, D. Furuya, A. G. Yodh, J. A. Detre, and J. H. Greenburg, "Spatiotemporal quantification of cerebral blood flow during functional activation in rat somatosensory cortex using laser-speckle flowmetry," J. Cereb. Blood Flow Metab. 24, 518-525 (2004).
[CrossRef] [PubMed]

Galizzi, G. E.

Gittings, A. S.

R. Bandyopadhyay, A. S. Gittings, S. S. Suh, P. K. Dixon, and D. J. Durian, "Speckle-visibility spectroscopy: a tool to study time-varying dynamics," Rev. Sci. Instrum. 76, 093110-093110 (2005).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley & Sons, 1985).

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

Greenburg, J. H.

T. Durduran, M. G. Burnett, G. Yu, C. Zhou, D. Furuya, A. G. Yodh, J. A. Detre, and J. H. Greenburg, "Spatiotemporal quantification of cerebral blood flow during functional activation in rat somatosensory cortex using laser-speckle flowmetry," J. Cereb. Blood Flow Metab. 24, 518-525 (2004).
[CrossRef] [PubMed]

Hagiwara, N.

H. Isono, S. Kishi, Y. Kimura, N. Hagiwara, N. Konishi, and H. Fuji, "Observation of choroidal circulation using index of erythrocytic velocity," Arch. Ophthalmol. (Chicago) 121, 225-231 (2003).

Hinds, M. T.

Isono, H.

H. Isono, S. Kishi, Y. Kimura, N. Hagiwara, N. Konishi, and H. Fuji, "Observation of choroidal circulation using index of erythrocytic velocity," Arch. Ophthalmol. (Chicago) 121, 225-231 (2003).

Kaufmann, G. H.

Kimura, Y.

H. Isono, S. Kishi, Y. Kimura, N. Hagiwara, N. Konishi, and H. Fuji, "Observation of choroidal circulation using index of erythrocytic velocity," Arch. Ophthalmol. (Chicago) 121, 225-231 (2003).

Kirkpatrick, S. J.

Kishi, S.

H. Isono, S. Kishi, Y. Kimura, N. Hagiwara, N. Konishi, and H. Fuji, "Observation of choroidal circulation using index of erythrocytic velocity," Arch. Ophthalmol. (Chicago) 121, 225-231 (2003).

Konishi, N.

H. Isono, S. Kishi, Y. Kimura, N. Hagiwara, N. Konishi, and H. Fuji, "Observation of choroidal circulation using index of erythrocytic velocity," Arch. Ophthalmol. (Chicago) 121, 225-231 (2003).

Li, P.

Luo, Q.

Ni, S.

Papoulis, A.

A. Papoulis and S. U. Pillai, Probability, Random Variables, and Stochastic Processes, 4th edition (McGraw-Hill, 2001).

Pillai, S. U.

A. Papoulis and S. U. Pillai, Probability, Random Variables, and Stochastic Processes, 4th edition (McGraw-Hill, 2001).

Rabal, H.

Scheffold, F.

Suh, S. S.

R. Bandyopadhyay, A. S. Gittings, S. S. Suh, P. K. Dixon, and D. J. Durian, "Speckle-visibility spectroscopy: a tool to study time-varying dynamics," Rev. Sci. Instrum. 76, 093110-093110 (2005).
[CrossRef]

Trivi, M.

Völker, A.

Wang, R. K.

Weber, B.

Yodh, A. G.

T. Durduran, M. G. Burnett, G. Yu, C. Zhou, D. Furuya, A. G. Yodh, J. A. Detre, and J. H. Greenburg, "Spatiotemporal quantification of cerebral blood flow during functional activation in rat somatosensory cortex using laser-speckle flowmetry," J. Cereb. Blood Flow Metab. 24, 518-525 (2004).
[CrossRef] [PubMed]

Yu, G.

T. Durduran, M. G. Burnett, G. Yu, C. Zhou, D. Furuya, A. G. Yodh, J. A. Detre, and J. H. Greenburg, "Spatiotemporal quantification of cerebral blood flow during functional activation in rat somatosensory cortex using laser-speckle flowmetry," J. Cereb. Blood Flow Metab. 24, 518-525 (2004).
[CrossRef] [PubMed]

Zakharov, P.

Zeng, S.

Zhang, L.

Zhou, C.

T. Durduran, M. G. Burnett, G. Yu, C. Zhou, D. Furuya, A. G. Yodh, J. A. Detre, and J. H. Greenburg, "Spatiotemporal quantification of cerebral blood flow during functional activation in rat somatosensory cortex using laser-speckle flowmetry," J. Cereb. Blood Flow Metab. 24, 518-525 (2004).
[CrossRef] [PubMed]

Appl. Opt. (1)

Arch. Ophthalmol. (Chicago) (1)

H. Isono, S. Kishi, Y. Kimura, N. Hagiwara, N. Konishi, and H. Fuji, "Observation of choroidal circulation using index of erythrocytic velocity," Arch. Ophthalmol. (Chicago) 121, 225-231 (2003).

J. Cereb. Blood Flow Metab. (1)

T. Durduran, M. G. Burnett, G. Yu, C. Zhou, D. Furuya, A. G. Yodh, J. A. Detre, and J. H. Greenburg, "Spatiotemporal quantification of cerebral blood flow during functional activation in rat somatosensory cortex using laser-speckle flowmetry," J. Cereb. Blood Flow Metab. 24, 518-525 (2004).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

A. F. Fercher and J. D. Briers, "Flow visualization by means of single-exposure speckle photography," Opt. Commun. 37, 326-330 (1981).
[CrossRef]

Opt. Lett. (2)

Proc. SPIE (1)

J. D. Briers, "Time-varying laser speckle for measuring motion and flow," Proc. SPIE 4242, 25-39 (2001).
[CrossRef]

Rev. Sci. Instrum. (1)

R. Bandyopadhyay, A. S. Gittings, S. S. Suh, P. K. Dixon, and D. J. Durian, "Speckle-visibility spectroscopy: a tool to study time-varying dynamics," Rev. Sci. Instrum. 76, 093110-093110 (2005).
[CrossRef]

Other (3)

A. Papoulis and S. U. Pillai, Probability, Random Variables, and Stochastic Processes, 4th edition (McGraw-Hill, 2001).

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

J. W. Goodman, Statistical Optics (Wiley & Sons, 1985).

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Figures (14)

Fig. 1
Fig. 1

Illustration of a synthetic speckle algorithm.

Fig. 2
Fig. 2

Example of a synthetic speckle pattern.

Fig. 3
Fig. 3

PDF of example speckle pattern and exponential distribution with same mean.

Fig. 4
Fig. 4

Speckle contrast computed over a 7 × 7 pixel region.

Fig. 5
Fig. 5

PDF of local contrast and log-normal distribution having same mean and standard deviation (not a fit).

Fig. 6
Fig. 6

Median parameter of contrast distribution for SI draws from an exponential distribution.

Fig. 7
Fig. 7

Width parameter of contrast distribution for independent draws from an exponential distribution.

Fig. 8
Fig. 8

Median parameter of contrast distribution as a function of local neighborhood and speckle size. Dashed curve denoted “exponential” is the result from Fig. 6, shown here for comparison.

Fig. 9
Fig. 9

Width parameter for contrast distribution as a function of local neighborhood and speckle size. Dashed curve denoted “exponential” is the result from Fig. 7, shown here for comparison.

Fig. 10
Fig. 10

Single frame of OCT movie of a chick embryo.

Fig. 11
Fig. 11

Local contrast computed over a 7 × 7 neighborhood.

Fig. 12
Fig. 12

Image to be segmented.

Fig. 13
Fig. 13

Background and subject contrast PDFs.

Fig. 14
Fig. 14

Global contrast distribution compared to that of background.

Equations (17)

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c = σ I μ I ,
f C ( c ) = 1 2 π c ln σ g exp { ln 2 ( c c m ) 2 ln 2 σ g } ;
E { C v } = c m v exp { v 2 2 ln 2 σ g } ,
σ C μ C = [ exp ( ln 2 σ g ) 1 ] 1 2 .
C = S M ,
M = 1 N s i = 1 N s I i ,
S 2 = 1 N s 1 i = 1 N s ( I i M ) 2 .
S M N s σ μ ,
σ C μ C 0.86 N s 0.46 ,
c m = 1 α N s β .
c m = 1 α ( p N s ) 1 p ,
c m = 1 0.734 ( p N s ) 1 p .
σ g = 1 + α N s β .
σ g = 1 + 0.454 p 0.672 N s 0.373 .
c m = asymptote [ 1 0.769 ( p N s ) 1.09 p ] ,
σ g = 1 + 0.457 p 0.697 N s 0.382 ,
F = C empirical C theoretical ,

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