Abstract

One of the major constraints facing laser speckle imaging for blood-flow measurement is reliable measurement of the correlation time (τC) of the back-scattered light and, hence, the blood’s speed in blood vessels. In this Letter, we present a new model expression for integrated speckle contrast, which accounts not only for temporal integration but spatial integration, too, due to the finite size of the pixel of the CCD camera; as a result, we find that a correction factor should be introduced to the measured speckle contrast to properly determine τC; otherwise, the measured blood’s speed is overestimated. Experimental results support our theoretical model.

© 2014 Optical Society of America

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  1. A. Fercher and J. Briers, Opt. Commun. 37, 326 (1981).
    [CrossRef]
  2. A. L. Srienc, Z. L. Kurth-Nelson, and E. A. Newman, Front Neuroenergetics 2, 1 (2010).
  3. B. Choi, N. M. Kang, and J. S. Nelson, Microvasc. Res. 68, 143 (2004).
    [CrossRef]
  4. J. L. Cracowski, F. Gaillard-Bigot, C. Cracowski, M. Roustit, and C. Millet, Microvasc. Res. 82, 333 (2011).
    [CrossRef]
  5. T. Sato, M. Miyazaki, A. Rikuta, and K. Kobayashi, Dent. Mater. J. 23, 284 (2004).
  6. C. Stoianovici, P. Wilder-Smith, and B. Choi, Lasers Surg. Med. 43, 833 (2011).
    [CrossRef]
  7. A. K. Dunn, Ann. Biomed. Eng. 40, 367 (2012).
    [CrossRef]
  8. G. A. Armitage, K. G. Todd, A. Shuaib, and I. R. Winship, J. Cereb. Blood Flow. Metab. 30, 1432 (2010).
    [CrossRef]
  9. S. J. Kirkpatrick, D. Duncan, and M. Wells-Gray, Opt. Lett. 33, 2886 (2008).
    [CrossRef]
  10. R. Bandyopadhyay, A. S. Gittings, S. S. Suh, P. K. Dixon, and D. J. Durian, Rev. Sci. Instrum., 76093110 (2005).
    [CrossRef]
  11. B. Parthasarathy, J. Tom, A. Gopal, X. Zhang, and K. Dunn, Opt. Express 16, 1975 (2008).
    [CrossRef]
  12. J. Goodman, Speckle Phenomena in Optics: Theory and Application, (Roberts & Company, 2007).
  13. P. A. Lemieux and D. J. Durian, J. Opt. Soc. Am. A 16, 1651 (1999).
    [CrossRef]
  14. D. A. Boas, “Diffuse photon probes of structural and dynamical properties of turbid media: theory and biomedical applications,” Ph.D. dissertation in Physics, University of Pennsylvania (1996).
  15. D. A. Boas and A. K. Dunn, J. Biomed. Opt. 15, 011109 (2010).
    [CrossRef]
  16. E. Jakeman, in Photon Correlation and Light Beating Spectroscopy, H. Z. Cummins and E. R. Pike, eds. (Plenum, 1974).
  17. J. D. Briers and S. Webster, Opt. Commun. 116, 36 (1995).
    [CrossRef]
  18. H. Cheng, Q. Lou, S. Zeng, S. Chen, J. Cen, and H. Gong, J. Biomed. Opt. 8, 559 (2003).
    [CrossRef]
  19. A. Ennos, in Laser Speckle and Related Phenomena, J. C. Dainty, eds. (Springer-Verlag, 1975).
  20. O. Thompson, M. Andrews, and E. Hirst, Biomed. Opt. Express 2, 1021 (2011).
    [CrossRef]
  21. J. C. Ramirez-San-Juan, E. Mendez-Aguilar, N. Salazar-Hermenegildo, A. Fuentes-Garcia, R. Ramos-Garcia, and B. Choi, Biomed. Opt. Express 4, 1883 (2013).

2013 (1)

2012 (1)

A. K. Dunn, Ann. Biomed. Eng. 40, 367 (2012).
[CrossRef]

2011 (3)

J. L. Cracowski, F. Gaillard-Bigot, C. Cracowski, M. Roustit, and C. Millet, Microvasc. Res. 82, 333 (2011).
[CrossRef]

C. Stoianovici, P. Wilder-Smith, and B. Choi, Lasers Surg. Med. 43, 833 (2011).
[CrossRef]

O. Thompson, M. Andrews, and E. Hirst, Biomed. Opt. Express 2, 1021 (2011).
[CrossRef]

2010 (3)

A. L. Srienc, Z. L. Kurth-Nelson, and E. A. Newman, Front Neuroenergetics 2, 1 (2010).

G. A. Armitage, K. G. Todd, A. Shuaib, and I. R. Winship, J. Cereb. Blood Flow. Metab. 30, 1432 (2010).
[CrossRef]

D. A. Boas and A. K. Dunn, J. Biomed. Opt. 15, 011109 (2010).
[CrossRef]

2008 (2)

2005 (1)

R. Bandyopadhyay, A. S. Gittings, S. S. Suh, P. K. Dixon, and D. J. Durian, Rev. Sci. Instrum., 76093110 (2005).
[CrossRef]

2004 (2)

B. Choi, N. M. Kang, and J. S. Nelson, Microvasc. Res. 68, 143 (2004).
[CrossRef]

T. Sato, M. Miyazaki, A. Rikuta, and K. Kobayashi, Dent. Mater. J. 23, 284 (2004).

2003 (1)

H. Cheng, Q. Lou, S. Zeng, S. Chen, J. Cen, and H. Gong, J. Biomed. Opt. 8, 559 (2003).
[CrossRef]

1999 (1)

1995 (1)

J. D. Briers and S. Webster, Opt. Commun. 116, 36 (1995).
[CrossRef]

1981 (1)

A. Fercher and J. Briers, Opt. Commun. 37, 326 (1981).
[CrossRef]

Andrews, M.

Armitage, G. A.

G. A. Armitage, K. G. Todd, A. Shuaib, and I. R. Winship, J. Cereb. Blood Flow. Metab. 30, 1432 (2010).
[CrossRef]

Bandyopadhyay, R.

R. Bandyopadhyay, A. S. Gittings, S. S. Suh, P. K. Dixon, and D. J. Durian, Rev. Sci. Instrum., 76093110 (2005).
[CrossRef]

Boas, D. A.

D. A. Boas and A. K. Dunn, J. Biomed. Opt. 15, 011109 (2010).
[CrossRef]

D. A. Boas, “Diffuse photon probes of structural and dynamical properties of turbid media: theory and biomedical applications,” Ph.D. dissertation in Physics, University of Pennsylvania (1996).

Briers, J.

A. Fercher and J. Briers, Opt. Commun. 37, 326 (1981).
[CrossRef]

Briers, J. D.

J. D. Briers and S. Webster, Opt. Commun. 116, 36 (1995).
[CrossRef]

Cen, J.

H. Cheng, Q. Lou, S. Zeng, S. Chen, J. Cen, and H. Gong, J. Biomed. Opt. 8, 559 (2003).
[CrossRef]

Chen, S.

H. Cheng, Q. Lou, S. Zeng, S. Chen, J. Cen, and H. Gong, J. Biomed. Opt. 8, 559 (2003).
[CrossRef]

Cheng, H.

H. Cheng, Q. Lou, S. Zeng, S. Chen, J. Cen, and H. Gong, J. Biomed. Opt. 8, 559 (2003).
[CrossRef]

Choi, B.

J. C. Ramirez-San-Juan, E. Mendez-Aguilar, N. Salazar-Hermenegildo, A. Fuentes-Garcia, R. Ramos-Garcia, and B. Choi, Biomed. Opt. Express 4, 1883 (2013).

C. Stoianovici, P. Wilder-Smith, and B. Choi, Lasers Surg. Med. 43, 833 (2011).
[CrossRef]

B. Choi, N. M. Kang, and J. S. Nelson, Microvasc. Res. 68, 143 (2004).
[CrossRef]

Cracowski, C.

J. L. Cracowski, F. Gaillard-Bigot, C. Cracowski, M. Roustit, and C. Millet, Microvasc. Res. 82, 333 (2011).
[CrossRef]

Cracowski, J. L.

J. L. Cracowski, F. Gaillard-Bigot, C. Cracowski, M. Roustit, and C. Millet, Microvasc. Res. 82, 333 (2011).
[CrossRef]

Dixon, P. K.

R. Bandyopadhyay, A. S. Gittings, S. S. Suh, P. K. Dixon, and D. J. Durian, Rev. Sci. Instrum., 76093110 (2005).
[CrossRef]

Duncan, D.

Dunn, A. K.

A. K. Dunn, Ann. Biomed. Eng. 40, 367 (2012).
[CrossRef]

D. A. Boas and A. K. Dunn, J. Biomed. Opt. 15, 011109 (2010).
[CrossRef]

Dunn, K.

Durian, D. J.

R. Bandyopadhyay, A. S. Gittings, S. S. Suh, P. K. Dixon, and D. J. Durian, Rev. Sci. Instrum., 76093110 (2005).
[CrossRef]

P. A. Lemieux and D. J. Durian, J. Opt. Soc. Am. A 16, 1651 (1999).
[CrossRef]

Ennos, A.

A. Ennos, in Laser Speckle and Related Phenomena, J. C. Dainty, eds. (Springer-Verlag, 1975).

Fercher, A.

A. Fercher and J. Briers, Opt. Commun. 37, 326 (1981).
[CrossRef]

Fuentes-Garcia, A.

Gaillard-Bigot, F.

J. L. Cracowski, F. Gaillard-Bigot, C. Cracowski, M. Roustit, and C. Millet, Microvasc. Res. 82, 333 (2011).
[CrossRef]

Gittings, A. S.

R. Bandyopadhyay, A. S. Gittings, S. S. Suh, P. K. Dixon, and D. J. Durian, Rev. Sci. Instrum., 76093110 (2005).
[CrossRef]

Gong, H.

H. Cheng, Q. Lou, S. Zeng, S. Chen, J. Cen, and H. Gong, J. Biomed. Opt. 8, 559 (2003).
[CrossRef]

Goodman, J.

J. Goodman, Speckle Phenomena in Optics: Theory and Application, (Roberts & Company, 2007).

Gopal, A.

Hirst, E.

Jakeman, E.

E. Jakeman, in Photon Correlation and Light Beating Spectroscopy, H. Z. Cummins and E. R. Pike, eds. (Plenum, 1974).

Kang, N. M.

B. Choi, N. M. Kang, and J. S. Nelson, Microvasc. Res. 68, 143 (2004).
[CrossRef]

Kirkpatrick, S. J.

Kobayashi, K.

T. Sato, M. Miyazaki, A. Rikuta, and K. Kobayashi, Dent. Mater. J. 23, 284 (2004).

Kurth-Nelson, Z. L.

A. L. Srienc, Z. L. Kurth-Nelson, and E. A. Newman, Front Neuroenergetics 2, 1 (2010).

Lemieux, P. A.

Lou, Q.

H. Cheng, Q. Lou, S. Zeng, S. Chen, J. Cen, and H. Gong, J. Biomed. Opt. 8, 559 (2003).
[CrossRef]

Mendez-Aguilar, E.

Millet, C.

J. L. Cracowski, F. Gaillard-Bigot, C. Cracowski, M. Roustit, and C. Millet, Microvasc. Res. 82, 333 (2011).
[CrossRef]

Miyazaki, M.

T. Sato, M. Miyazaki, A. Rikuta, and K. Kobayashi, Dent. Mater. J. 23, 284 (2004).

Nelson, J. S.

B. Choi, N. M. Kang, and J. S. Nelson, Microvasc. Res. 68, 143 (2004).
[CrossRef]

Newman, E. A.

A. L. Srienc, Z. L. Kurth-Nelson, and E. A. Newman, Front Neuroenergetics 2, 1 (2010).

Parthasarathy, B.

Ramirez-San-Juan, J. C.

Ramos-Garcia, R.

Rikuta, A.

T. Sato, M. Miyazaki, A. Rikuta, and K. Kobayashi, Dent. Mater. J. 23, 284 (2004).

Roustit, M.

J. L. Cracowski, F. Gaillard-Bigot, C. Cracowski, M. Roustit, and C. Millet, Microvasc. Res. 82, 333 (2011).
[CrossRef]

Salazar-Hermenegildo, N.

Sato, T.

T. Sato, M. Miyazaki, A. Rikuta, and K. Kobayashi, Dent. Mater. J. 23, 284 (2004).

Shuaib, A.

G. A. Armitage, K. G. Todd, A. Shuaib, and I. R. Winship, J. Cereb. Blood Flow. Metab. 30, 1432 (2010).
[CrossRef]

Srienc, A. L.

A. L. Srienc, Z. L. Kurth-Nelson, and E. A. Newman, Front Neuroenergetics 2, 1 (2010).

Stoianovici, C.

C. Stoianovici, P. Wilder-Smith, and B. Choi, Lasers Surg. Med. 43, 833 (2011).
[CrossRef]

Suh, S. S.

R. Bandyopadhyay, A. S. Gittings, S. S. Suh, P. K. Dixon, and D. J. Durian, Rev. Sci. Instrum., 76093110 (2005).
[CrossRef]

Thompson, O.

Todd, K. G.

G. A. Armitage, K. G. Todd, A. Shuaib, and I. R. Winship, J. Cereb. Blood Flow. Metab. 30, 1432 (2010).
[CrossRef]

Tom, J.

Webster, S.

J. D. Briers and S. Webster, Opt. Commun. 116, 36 (1995).
[CrossRef]

Wells-Gray, M.

Wilder-Smith, P.

C. Stoianovici, P. Wilder-Smith, and B. Choi, Lasers Surg. Med. 43, 833 (2011).
[CrossRef]

Winship, I. R.

G. A. Armitage, K. G. Todd, A. Shuaib, and I. R. Winship, J. Cereb. Blood Flow. Metab. 30, 1432 (2010).
[CrossRef]

Zeng, S.

H. Cheng, Q. Lou, S. Zeng, S. Chen, J. Cen, and H. Gong, J. Biomed. Opt. 8, 559 (2003).
[CrossRef]

Zhang, X.

Ann. Biomed. Eng. (1)

A. K. Dunn, Ann. Biomed. Eng. 40, 367 (2012).
[CrossRef]

Biomed. Opt. Express (2)

Dent. Mater. J. (1)

T. Sato, M. Miyazaki, A. Rikuta, and K. Kobayashi, Dent. Mater. J. 23, 284 (2004).

Front Neuroenergetics (1)

A. L. Srienc, Z. L. Kurth-Nelson, and E. A. Newman, Front Neuroenergetics 2, 1 (2010).

J. Biomed. Opt. (2)

D. A. Boas and A. K. Dunn, J. Biomed. Opt. 15, 011109 (2010).
[CrossRef]

H. Cheng, Q. Lou, S. Zeng, S. Chen, J. Cen, and H. Gong, J. Biomed. Opt. 8, 559 (2003).
[CrossRef]

J. Cereb. Blood Flow. Metab. (1)

G. A. Armitage, K. G. Todd, A. Shuaib, and I. R. Winship, J. Cereb. Blood Flow. Metab. 30, 1432 (2010).
[CrossRef]

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

Lasers Surg. Med. (1)

C. Stoianovici, P. Wilder-Smith, and B. Choi, Lasers Surg. Med. 43, 833 (2011).
[CrossRef]

Microvasc. Res. (2)

B. Choi, N. M. Kang, and J. S. Nelson, Microvasc. Res. 68, 143 (2004).
[CrossRef]

J. L. Cracowski, F. Gaillard-Bigot, C. Cracowski, M. Roustit, and C. Millet, Microvasc. Res. 82, 333 (2011).
[CrossRef]

Opt. Commun. (2)

A. Fercher and J. Briers, Opt. Commun. 37, 326 (1981).
[CrossRef]

J. D. Briers and S. Webster, Opt. Commun. 116, 36 (1995).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Rev. Sci. Instrum. (1)

R. Bandyopadhyay, A. S. Gittings, S. S. Suh, P. K. Dixon, and D. J. Durian, Rev. Sci. Instrum., 76093110 (2005).
[CrossRef]

Other (4)

J. Goodman, Speckle Phenomena in Optics: Theory and Application, (Roberts & Company, 2007).

A. Ennos, in Laser Speckle and Related Phenomena, J. C. Dainty, eds. (Springer-Verlag, 1975).

D. A. Boas, “Diffuse photon probes of structural and dynamical properties of turbid media: theory and biomedical applications,” Ph.D. dissertation in Physics, University of Pennsylvania (1996).

E. Jakeman, in Photon Correlation and Light Beating Spectroscopy, H. Z. Cummins and E. R. Pike, eds. (Plenum, 1974).

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Figures (2)

Fig. 1.
Fig. 1.

Experimental measurements of speckle contrast as a function of M obtained with the (a) temporal and (b) spatial analysis methods. The continuous lines represent the corresponding fit of the data to Eq. (19).

Fig. 2.
Fig. 2.

Corrected speckle contrast obtained after applying the correction factor to the data shown in Fig. 1(a), similar results are obtained for Fig. 1(b).

Equations (20)

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g2(τ)=1+|g1(τ)|2.
K2=βe2x1+2x2x2,
E(t)=Ef(t)eiwt+Eseiwt,
K=β1/2[ρ2e2x1+2x2x2+4ρ(1ρ)ex1+xx2+(1ρ)2]1/2+Cn,
E(x,y,t)=Ef(x,y,t)eiwt+Es(x,y)eiwt.
g2(Δx,Δy,τ)=1+|g1(Δx,Δy,τ)|2=1+α|E(x1,y1,t)E*(x1+Δx,y1+Δy,t+τ)E(x1,y1,t)E*(x1,y1,t)|2=1+αρ2|g1,f(Δx,Δy,τ)|2+2αρ(1ρ)|g1,f(Δx,Δy,τ)||g1,s(Δx,Δy)|+α(1ρ)2|g1,s(Δx,Δy)|2+Cn2,
g1,f(Δx,Δy,τ)=Ef(x1,y1,t)Ef*(x1+Δx,y1+Δy,t+τ)Ef(x1,y1,t)Ef*(x1,y1,t)g1,s(Δx,Δy)=Es(x1,y1)Es*(x1+Δx,y1+Δy)Ef(x1,y1)Es*(x1,y1).
g2(τ)=1+ρ2|g1,f(τ)|2β+2ρ(1ρ)|g1,f(τ)|β+(1ρ)2β+Cn2.
I2=1AD2T20TD(x1,y1)D(x2,y2)I(x1,y1,t1)I(x2,y2,t2)dx1dy1dx2dy2dt1dt2=1AD2T20TD(x1,y1)D(x2,y2)I2g2(Δx,Δy,τ)dx1dy1dx2dy2dt1dt2,
D(x,y)={1in the sensitive area0outside of the sensitive area.
AD=D(x,y)dxdy.
K2I2I2I2=ρ2αAD2T20TKD(Δx,Δy)|g1,f(Δx,Δy,t2t1)|2d(Δx)d(Δy)dt1dt2+2αρ(1ρ)AD2T20TKD(Δx,Δy)|g1,s(Δx,Δy)||g1,f(Δx,Δy,t2t1)|d(Δx)d(Δy)dt1dt2+α(1ρ)2AD2T20TKD(Δx,Δy)|g1,s(Δx,Δy)|2d(Δx)d(Δy)dt1dt2,
KD(Δx,Δy)=D(x1,y1)D(x1Δx,y1Δy)dx1dy1.
|g1,f(Δx,Δy,t2t1)|=|g1,s(Δx,Δy)||gf(t2t1)|.
K2=α{1AD2KD(Δx,Δy)|g1,s(Δx,Δy)|2d(Δx)d(Δy)}×{1T20T[ρ2|gf(t2t1)|+ρ(1ρ)|gf(t2t1)|+(1ρ)2]dt1dt2}.
1AD2KD(Δx,Δy)|gs(Δx,Δy)|2d(Δx)d(Δy)={1Merf(πM)(1πM)(1eπM)}2β(M),
AC=|gs(Δx,Δy)|2d(Δx)d(Δy).
1T20T[ρ2|gf(t2t1)|+ρ(1ρ)|gf(t2t1)|+(1ρ)2]dt1dt2=ρ2e2x1+2x2x2+4ρ(1ρ)ex1+xx2+(1ρ)2Kt(x).
K=α1/2[1Merf(πM)(1πM)(1eπM)][ρ2e2x1+2x2x2+4ρ(1ρ)ex1+xx2+(1ρ)2]1/2+Kn=α1/2β1/2(M)Kt1/2(x)+Kn.
AC[1.22(1+Mag)λ#f]2,

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