Abstract

Scattering fluid flux can be quantified with coherent light, either from the contrast of speckle patterns, or from the moments of the power spectrum of intensity fluctuations. We present a theory connecting these approaches for the general case of mixed static-dynamic patterns of boiling speckles without prior assumptions regarding the particle dynamics. An expression is derived and tested relating the speckle contrast to the intensity power spectrum. Our theory demonstrates that in speckle contrast the concentration of moving particles dominates over the contribution of speed to the particle flux. Our theory provides a basis for comparison of both approaches when used for studying tissue perfusion.

© 2010 Optical Society of America

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References

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  1. P. Vennemann, R. Lindken, and J. Westerweel, "In vivo whole-field blood velocity measurement techniques," Exp. Fluids 42(4), 495-511 (2007).
    [CrossRef]
  2. M. J. Draijer, E. Hondebrink, T. G. van Leeuwen, and W. Steenbergen, "Review of laser speckle contrast techniques for visualizing tissue perfusion," Lasers Med. Sci. 24(4), 639-651 (2009).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  5. H. Cheng, Q. Luo, S. Zeng, S. Chen, J. Cen, and H. Gong, "Modified laser speckle imaging method with improved spatial resolution," J. Biomed. Opt. 8(3), 559-564 (2003).
    [CrossRef] [PubMed]
  6. D. A. Boas and A. K. Dunn, "Laser speckle contrast imaging in biomedical optics," J. Biomed. Opt. 15(1), 011109 (2010).
    [CrossRef] [PubMed]
  7. J. D. Briers and S. Webster, "Quasi real-time digital version of single-exposure speckle photography for full-field monitoring of velocity or flow fields," Opt. Commun. 116, 36-42 (1995).
    [CrossRef]
  8. J. C. Ramirez-San-Juan, R. Ramos-Garcia, I. Guizar-Iturbide, G. Martinez-Niconoff, and B. Choi, "Impact of velocity distribution assumption on simplified laser speckle imaging equation," Opt. Express 16(5), 3197-3203 (2008).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  11. G. E. Nilsson, T. Tenland, and P. A. Oberg, "A New Instrument for Continuous Measurement of Tissue Blood Flow by Light Beating Spectroscopy," IEEE Trans. Biomed. Eng. 27(1), 12-18 (1980).
    [CrossRef]
  12. D. D. Duncan and S. J. Kirkpatrick, "Can laser speckle flowmetry be made a quantitative tool?" J. Opt. Soc. Am. A 25(8), 2088-2094 (2008).
    [CrossRef]
  13. P. A. Lynn, Electronic signals and systems (Macmillan, London, 1986).
  14. J. W. Goodman and G. Parry, Laser Speckle and Related Phenomena (Springer-Verlag, New York, 1975).
  15. A. Serov, W. Steenbergen, and F. F. M. de Mul, "Prediction of the photodetector signal generated by Dopplerinduced speckle fluctuations: theory and some validations," J. Opt. Soc. Am. A 18(3), 622-630 (2001).
    [CrossRef]
  16. D. D. Duncan, S. J. Kirkpatrick, and R. K. Wang, "Statistics of local speckle contrast,"J. Opt. Soc. Am. A: Opt. Image Sci. Vis. 25(1), 9-15 (2008).
    [CrossRef]

2010 (1)

D. A. Boas and A. K. Dunn, "Laser speckle contrast imaging in biomedical optics," J. Biomed. Opt. 15(1), 011109 (2010).
[CrossRef] [PubMed]

2009 (1)

M. J. Draijer, E. Hondebrink, T. G. van Leeuwen, and W. Steenbergen, "Review of laser speckle contrast techniques for visualizing tissue perfusion," Lasers Med. Sci. 24(4), 639-651 (2009).
[CrossRef]

2008 (4)

2007 (1)

P. Vennemann, R. Lindken, and J. Westerweel, "In vivo whole-field blood velocity measurement techniques," Exp. Fluids 42(4), 495-511 (2007).
[CrossRef]

2006 (1)

2003 (1)

H. Cheng, Q. Luo, S. Zeng, S. Chen, J. Cen, and H. Gong, "Modified laser speckle imaging method with improved spatial resolution," J. Biomed. Opt. 8(3), 559-564 (2003).
[CrossRef] [PubMed]

2001 (1)

1996 (1)

J. D. Briers and S. Webster, "Laser speckle contrast analysis LASCA): a nonscanning, full-field technique for monitoring capillary blood flow," J. Biomed. Opt. 1, 174-179 (1996).
[CrossRef]

1995 (1)

J. D. Briers and S. Webster, "Quasi real-time digital version of single-exposure speckle photography for full-field monitoring of velocity or flow fields," Opt. Commun. 116, 36-42 (1995).
[CrossRef]

1981 (1)

1980 (1)

G. E. Nilsson, T. Tenland, and P. A. Oberg, "A New Instrument for Continuous Measurement of Tissue Blood Flow by Light Beating Spectroscopy," IEEE Trans. Biomed. Eng. 27(1), 12-18 (1980).
[CrossRef]

Boas, D. A.

D. A. Boas and A. K. Dunn, "Laser speckle contrast imaging in biomedical optics," J. Biomed. Opt. 15(1), 011109 (2010).
[CrossRef] [PubMed]

Bonner, R.

Briers, J. D.

J. D. Briers and S. Webster, "Laser speckle contrast analysis LASCA): a nonscanning, full-field technique for monitoring capillary blood flow," J. Biomed. Opt. 1, 174-179 (1996).
[CrossRef]

J. D. Briers and S. Webster, "Quasi real-time digital version of single-exposure speckle photography for full-field monitoring of velocity or flow fields," Opt. Commun. 116, 36-42 (1995).
[CrossRef]

Buck, A.

Cen, J.

H. Cheng, Q. Luo, S. Zeng, S. Chen, J. Cen, and H. Gong, "Modified laser speckle imaging method with improved spatial resolution," J. Biomed. Opt. 8(3), 559-564 (2003).
[CrossRef] [PubMed]

Chen, S.

H. Cheng, Q. Luo, S. Zeng, S. Chen, J. Cen, and H. Gong, "Modified laser speckle imaging method with improved spatial resolution," J. Biomed. Opt. 8(3), 559-564 (2003).
[CrossRef] [PubMed]

Cheng, H.

H. Cheng, Q. Luo, S. Zeng, S. Chen, J. Cen, and H. Gong, "Modified laser speckle imaging method with improved spatial resolution," J. Biomed. Opt. 8(3), 559-564 (2003).
[CrossRef] [PubMed]

Choi, B.

de Mul, F. F. M.

Draijer, M. J.

M. J. Draijer, E. Hondebrink, T. G. van Leeuwen, and W. Steenbergen, "Review of laser speckle contrast techniques for visualizing tissue perfusion," Lasers Med. Sci. 24(4), 639-651 (2009).
[CrossRef]

Duncan, D. D.

D. D. Duncan, S. J. Kirkpatrick, and R. K. Wang, "Statistics of local speckle contrast,"J. Opt. Soc. Am. A: Opt. Image Sci. Vis. 25(1), 9-15 (2008).
[CrossRef]

D. D. Duncan and S. J. Kirkpatrick, "Can laser speckle flowmetry be made a quantitative tool?" J. Opt. Soc. Am. A 25(8), 2088-2094 (2008).
[CrossRef]

Dunn, A. K.

Gong, H.

H. Cheng, Q. Luo, S. Zeng, S. Chen, J. Cen, and H. Gong, "Modified laser speckle imaging method with improved spatial resolution," J. Biomed. Opt. 8(3), 559-564 (2003).
[CrossRef] [PubMed]

Gopal, A.

Guizar-Iturbide, I.

Hondebrink, E.

M. J. Draijer, E. Hondebrink, T. G. van Leeuwen, and W. Steenbergen, "Review of laser speckle contrast techniques for visualizing tissue perfusion," Lasers Med. Sci. 24(4), 639-651 (2009).
[CrossRef]

Kirkpatrick, S. J.

D. D. Duncan, S. J. Kirkpatrick, and R. K. Wang, "Statistics of local speckle contrast,"J. Opt. Soc. Am. A: Opt. Image Sci. Vis. 25(1), 9-15 (2008).
[CrossRef]

D. D. Duncan and S. J. Kirkpatrick, "Can laser speckle flowmetry be made a quantitative tool?" J. Opt. Soc. Am. A 25(8), 2088-2094 (2008).
[CrossRef]

Lindken, R.

P. Vennemann, R. Lindken, and J. Westerweel, "In vivo whole-field blood velocity measurement techniques," Exp. Fluids 42(4), 495-511 (2007).
[CrossRef]

Luo, Q.

H. Cheng, Q. Luo, S. Zeng, S. Chen, J. Cen, and H. Gong, "Modified laser speckle imaging method with improved spatial resolution," J. Biomed. Opt. 8(3), 559-564 (2003).
[CrossRef] [PubMed]

Martinez-Niconoff, G.

Nilsson, G. E.

G. E. Nilsson, T. Tenland, and P. A. Oberg, "A New Instrument for Continuous Measurement of Tissue Blood Flow by Light Beating Spectroscopy," IEEE Trans. Biomed. Eng. 27(1), 12-18 (1980).
[CrossRef]

Nossal, R.

Oberg, P. A. ¨

G. E. Nilsson, T. Tenland, and P. A. Oberg, "A New Instrument for Continuous Measurement of Tissue Blood Flow by Light Beating Spectroscopy," IEEE Trans. Biomed. Eng. 27(1), 12-18 (1980).
[CrossRef]

Parthasarathy, A. B.

Ramirez-San-Juan, J. C.

Ramos-Garcia, R.

Scheffold, F.

Serov, A.

Steenbergen, W.

M. J. Draijer, E. Hondebrink, T. G. van Leeuwen, and W. Steenbergen, "Review of laser speckle contrast techniques for visualizing tissue perfusion," Lasers Med. Sci. 24(4), 639-651 (2009).
[CrossRef]

A. Serov, W. Steenbergen, and F. F. M. de Mul, "Prediction of the photodetector signal generated by Dopplerinduced speckle fluctuations: theory and some validations," J. Opt. Soc. Am. A 18(3), 622-630 (2001).
[CrossRef]

Tenland, T.

G. E. Nilsson, T. Tenland, and P. A. Oberg, "A New Instrument for Continuous Measurement of Tissue Blood Flow by Light Beating Spectroscopy," IEEE Trans. Biomed. Eng. 27(1), 12-18 (1980).
[CrossRef]

Tom, W. J.

V¨olker, A.

van Leeuwen, T. G.

M. J. Draijer, E. Hondebrink, T. G. van Leeuwen, and W. Steenbergen, "Review of laser speckle contrast techniques for visualizing tissue perfusion," Lasers Med. Sci. 24(4), 639-651 (2009).
[CrossRef]

Vennemann, P.

P. Vennemann, R. Lindken, and J. Westerweel, "In vivo whole-field blood velocity measurement techniques," Exp. Fluids 42(4), 495-511 (2007).
[CrossRef]

Wang, R. K.

D. D. Duncan, S. J. Kirkpatrick, and R. K. Wang, "Statistics of local speckle contrast,"J. Opt. Soc. Am. A: Opt. Image Sci. Vis. 25(1), 9-15 (2008).
[CrossRef]

Weber, B.

Webster, S.

J. D. Briers and S. Webster, "Laser speckle contrast analysis LASCA): a nonscanning, full-field technique for monitoring capillary blood flow," J. Biomed. Opt. 1, 174-179 (1996).
[CrossRef]

J. D. Briers and S. Webster, "Quasi real-time digital version of single-exposure speckle photography for full-field monitoring of velocity or flow fields," Opt. Commun. 116, 36-42 (1995).
[CrossRef]

Westerweel, J.

P. Vennemann, R. Lindken, and J. Westerweel, "In vivo whole-field blood velocity measurement techniques," Exp. Fluids 42(4), 495-511 (2007).
[CrossRef]

Zakharov, P.

Zeng, S.

H. Cheng, Q. Luo, S. Zeng, S. Chen, J. Cen, and H. Gong, "Modified laser speckle imaging method with improved spatial resolution," J. Biomed. Opt. 8(3), 559-564 (2003).
[CrossRef] [PubMed]

Zhang, X.

Appl. Opt. (1)

Exp. Fluids (1)

P. Vennemann, R. Lindken, and J. Westerweel, "In vivo whole-field blood velocity measurement techniques," Exp. Fluids 42(4), 495-511 (2007).
[CrossRef]

IEEE Trans. Biomed. Eng. (1)

G. E. Nilsson, T. Tenland, and P. A. Oberg, "A New Instrument for Continuous Measurement of Tissue Blood Flow by Light Beating Spectroscopy," IEEE Trans. Biomed. Eng. 27(1), 12-18 (1980).
[CrossRef]

J. Biomed. Opt. (3)

J. D. Briers and S. Webster, "Laser speckle contrast analysis LASCA): a nonscanning, full-field technique for monitoring capillary blood flow," J. Biomed. Opt. 1, 174-179 (1996).
[CrossRef]

H. Cheng, Q. Luo, S. Zeng, S. Chen, J. Cen, and H. Gong, "Modified laser speckle imaging method with improved spatial resolution," J. Biomed. Opt. 8(3), 559-564 (2003).
[CrossRef] [PubMed]

D. A. Boas and A. K. Dunn, "Laser speckle contrast imaging in biomedical optics," J. Biomed. Opt. 15(1), 011109 (2010).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. A: Opt. Image Sci. Vis. (1)

D. D. Duncan, S. J. Kirkpatrick, and R. K. Wang, "Statistics of local speckle contrast,"J. Opt. Soc. Am. A: Opt. Image Sci. Vis. 25(1), 9-15 (2008).
[CrossRef]

Lasers Med. Sci. (1)

M. J. Draijer, E. Hondebrink, T. G. van Leeuwen, and W. Steenbergen, "Review of laser speckle contrast techniques for visualizing tissue perfusion," Lasers Med. Sci. 24(4), 639-651 (2009).
[CrossRef]

Opt. Commun. (1)

J. D. Briers and S. Webster, "Quasi real-time digital version of single-exposure speckle photography for full-field monitoring of velocity or flow fields," Opt. Commun. 116, 36-42 (1995).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Other (2)

P. A. Lynn, Electronic signals and systems (Macmillan, London, 1986).

J. W. Goodman and G. Parry, Laser Speckle and Related Phenomena (Springer-Verlag, New York, 1975).

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Figures (5)

Fig. 1:
Fig. 1:

Gain of transfer function |H(T, ν)| for moving average operation with integration times T = 1, 5 and 10 ms.

Fig. 2:
Fig. 2:

Decomposition of the blurred intensity I (solid) into average value 〈I〉 (dotted), static intensity fluctuation Is (dashed) and time-dependent blurred fluctuation IT.

Fig. 3:
Fig. 3:

Power spectrum averaged over an area of 7 × 7 pixels of the artificial speckle pattern used to determine the spatial contrast.

Fig. 4:
Fig. 4:

Measured (open symbols) and predicted (closed symbols) speckle contrast values for temporal (squares) and spatial (circles) contrast as a function of integration time T, for artificial speckles.

Fig. 5:
Fig. 5:

Spectral weighting functions realized by 1 – C2, with C the contrast of integrated speckle for integration times T of 1, 2, 5 and 15 ms.

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

M i ν i P ( ν ) d ν
C σ I = I 2 I 2 I
U ( T , ω ) = 1 i ω T [ 1 exp ( i ω T ) ] F ( ω )
H ( T , ω ) = 1 i ω T [ 1 exp ( i ω T ) ]
| H ( T , ν ) | = 1 T 1 cos ( 2 π ν T ) 2 π 2 ν 2
C 2 = ( I s + I T ) 2 I 2 = ( I s 2 + I T 2 ) I 2
C 2 ( T ) = C 2 ( 0 ) + 0 T d C 2 d T ˜ d T ˜
C 2 ( T ) = 1 + 1 I 2 0 T T ˜ I T 2 d T ˜
I T 2 = P ( ν ) | H ( T , ν ) | 2 d ν
C 2 ( T ) = 1 + 1 I 2 P ( ν ) [ | H ( T , ν ) | 2 ] 0 T d ν
C 2 ( T ) = 1 M 0 I 2 + 1 I 2 P ( ν ) | H ( T , ν ) | 2 d ν
1 C 2 = 1 I 2 ( 1 | H ( T , ν ) | 2 ) P ( ν ) d ν

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