Abstract

We present a method for the detection and localization of inhomogeneities embedded within highly scattering media that employs speckle statistics with a partially coherent light source. Variations in speckle contrast as a function of position are used to interrogate inhomogeneities deeply embedded within scattering media. A numerical model based on photon diffusion theory is introduced to predict speckle contrast as a function of scan position. This model uses measured speckle data to determine scattering and absorption parameters.

© 1997 Optical Society of America

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  1. J. G. Fujimoto, S. D. Silvestri, E. Ippen, C. Puliafito, R. Margolis, A. Oseroff, “Eye-length measurement by interferometry with partially coherent light,” Opt. Lett. 11, 150–152 (1986).
    [Crossref]
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    [Crossref] [PubMed]
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  6. J. S. Reynolds, S. Yeung, A. Przadka, K. J. Webb, “Optical diffusion imaging: a comparative numerical and experimental study,” Appl. Opt. 35, 3671–3679 (1996).
    [Crossref] [PubMed]
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    [Crossref]
  8. D. G. Voelz, P. S. Idell, K. A. Bush, “Illumination coherence effects in laser-speckle imaging,” in Laser Radar VI, R. J. Becherer, ed., Proc. SPIE1416, 260–265 (1991).
    [Crossref]
  9. R. Berkovits, S. Feng, “Theory of speckle-pattern tomography in multiple-scattering media,” Phys. Rev. Lett. 65, 3120–3123 (1990).
    [Crossref] [PubMed]
  10. D. A. Boas, L. E. Campbell, A. G. Yodh, “Scattering and imaging with diffusing temporal field correlations,” Phys. Rev. Lett. 75, 1855–1858 (1995).
    [Crossref] [PubMed]
  11. P. Naulleau, D. Dilworth, E. Leith, J. Lopez, “Detection of moving objects embedded within scattering media by use of speckle methods,” Opt. Lett. 20, 498–500 (1995).
    [Crossref] [PubMed]
  12. J. D. Briers, “Speckle fluctuations and biomedical optics: implications and applications,” Opt. Eng. 32, 277–283 (1993).
    [Crossref]
  13. G. Parry, “Some effects of temporal coherence on the first order statistics of speckle,” Opt. Acta 21, 763–772 (1974).
    [Crossref]
  14. D. A. Zimnyakov, V. V. Tuchin, S. R. Utts, “A study of statistical properties of partially developed speckle fields as applied to the diagnostics of structural changes in human skin,” Opt. Spectrosc. (USSR) 76, 838–844 (1994).
  15. M. Rosenbluh, M. Hoshen, I. Freund, M. Kaveh, “Time evolution of universal optical fluctuations,” Phys. Rev. Lett. 58, 2754–2757 (1987).
    [Crossref] [PubMed]
  16. I. Freund, “Image reconstruction through multiple scattering media,” Opt. Commun. 86, 216–227 (1991).
    [Crossref]
  17. A. Z. Genack, “Optical transmission in disordered media,” Phys. Rev. Lett. 58, 2043–2046 (1987).
    [Crossref] [PubMed]
  18. A. Z. Genack, J. M. Drake, “Relationship between optical intensity fluctuations and pulse propagation in random media,” Europhys. Lett. 11, 331–336 (1990).
    [Crossref]
  19. C. A. Thompson, K. J. Webb, A. M. Weiner, “Diffusive media characterization using laser speckle,” Appl. Opt. 36, 3726–3734 (1997).
    [Crossref] [PubMed]
  20. J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed., Vol. 9 of Topics in Applied Physics (Springer-Verlag, Berlin, 1984).
  21. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), p. 316.
  22. I. S. Reed, “On a moment theorem for complex Gaussian processes,” IRE Trans. Inf. Theory 8, 194–195 (1962).
    [Crossref]
  23. J. C. Adams, “mudpack: multigrid portable fortran software for the efficient solution of linear elliptic partial differential equations,” Appl. Math. Comput. 34, 113–146 (1989).
    [Crossref]
  24. J. C. Adams, Multigrid Software for Elliptic Partial Differential Equations (National Center for Atmospheric Research, Boulder, Colo., 1991).
  25. R. A. J. Groenhuis, H. A. Ferwerda, J. J. T. Bosch, “Scattering and absorption of turbid materials determined from reflection measurements. 1: Theory,” Appl. Opt. 22, 2456–2462 (1983).
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  26. W. G. Egan, T. W. Hilgeman, Optical Properties of Inhomogeneous Materials (Academic, New York, 1979).
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    [Crossref]
  28. A. Papoulis, Probability Random Variables and Stochastic Processes (McGraw-Hill, New York, 1984), p. 272.

1997 (1)

1996 (2)

1995 (2)

D. A. Boas, L. E. Campbell, A. G. Yodh, “Scattering and imaging with diffusing temporal field correlations,” Phys. Rev. Lett. 75, 1855–1858 (1995).
[Crossref] [PubMed]

P. Naulleau, D. Dilworth, E. Leith, J. Lopez, “Detection of moving objects embedded within scattering media by use of speckle methods,” Opt. Lett. 20, 498–500 (1995).
[Crossref] [PubMed]

1994 (1)

D. A. Zimnyakov, V. V. Tuchin, S. R. Utts, “A study of statistical properties of partially developed speckle fields as applied to the diagnostics of structural changes in human skin,” Opt. Spectrosc. (USSR) 76, 838–844 (1994).

1993 (3)

1992 (1)

1991 (1)

I. Freund, “Image reconstruction through multiple scattering media,” Opt. Commun. 86, 216–227 (1991).
[Crossref]

1990 (2)

A. Z. Genack, J. M. Drake, “Relationship between optical intensity fluctuations and pulse propagation in random media,” Europhys. Lett. 11, 331–336 (1990).
[Crossref]

R. Berkovits, S. Feng, “Theory of speckle-pattern tomography in multiple-scattering media,” Phys. Rev. Lett. 65, 3120–3123 (1990).
[Crossref] [PubMed]

1989 (2)

J. C. Adams, “mudpack: multigrid portable fortran software for the efficient solution of linear elliptic partial differential equations,” Appl. Math. Comput. 34, 113–146 (1989).
[Crossref]

M. S. Patterson, B. Chance, B. Wilson, “Time resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
[Crossref] [PubMed]

1987 (2)

A. Z. Genack, “Optical transmission in disordered media,” Phys. Rev. Lett. 58, 2043–2046 (1987).
[Crossref] [PubMed]

M. Rosenbluh, M. Hoshen, I. Freund, M. Kaveh, “Time evolution of universal optical fluctuations,” Phys. Rev. Lett. 58, 2754–2757 (1987).
[Crossref] [PubMed]

1986 (1)

1983 (1)

1974 (1)

G. Parry, “Some effects of temporal coherence on the first order statistics of speckle,” Opt. Acta 21, 763–772 (1974).
[Crossref]

1969 (1)

1962 (1)

I. S. Reed, “On a moment theorem for complex Gaussian processes,” IRE Trans. Inf. Theory 8, 194–195 (1962).
[Crossref]

Adams, J. C.

J. C. Adams, “mudpack: multigrid portable fortran software for the efficient solution of linear elliptic partial differential equations,” Appl. Math. Comput. 34, 113–146 (1989).
[Crossref]

J. C. Adams, Multigrid Software for Elliptic Partial Differential Equations (National Center for Atmospheric Research, Boulder, Colo., 1991).

Berkovits, R.

R. Berkovits, S. Feng, “Theory of speckle-pattern tomography in multiple-scattering media,” Phys. Rev. Lett. 65, 3120–3123 (1990).
[Crossref] [PubMed]

Boas, D. A.

D. A. Boas, L. E. Campbell, A. G. Yodh, “Scattering and imaging with diffusing temporal field correlations,” Phys. Rev. Lett. 75, 1855–1858 (1995).
[Crossref] [PubMed]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), p. 316.

Bosch, J. J. T.

Briers, J. D.

J. D. Briers, “Speckle fluctuations and biomedical optics: implications and applications,” Opt. Eng. 32, 277–283 (1993).
[Crossref]

Bush, K. A.

D. G. Voelz, P. S. Idell, K. A. Bush, “Illumination coherence effects in laser-speckle imaging,” in Laser Radar VI, R. J. Becherer, ed., Proc. SPIE1416, 260–265 (1991).
[Crossref]

Campbell, L. E.

D. A. Boas, L. E. Campbell, A. G. Yodh, “Scattering and imaging with diffusing temporal field correlations,” Phys. Rev. Lett. 75, 1855–1858 (1995).
[Crossref] [PubMed]

Chance, B.

Chen, C.

Chen, H.

Chen, Y.

Dilworth, D.

Drake, J. M.

A. Z. Genack, J. M. Drake, “Relationship between optical intensity fluctuations and pulse propagation in random media,” Europhys. Lett. 11, 331–336 (1990).
[Crossref]

Egan, W. G.

W. G. Egan, T. W. Hilgeman, Optical Properties of Inhomogeneous Materials (Academic, New York, 1979).

Feng, S.

R. Berkovits, S. Feng, “Theory of speckle-pattern tomography in multiple-scattering media,” Phys. Rev. Lett. 65, 3120–3123 (1990).
[Crossref] [PubMed]

Ferwerda, H. A.

Fishkin, J. B.

Freund, I.

I. Freund, “Image reconstruction through multiple scattering media,” Opt. Commun. 86, 216–227 (1991).
[Crossref]

M. Rosenbluh, M. Hoshen, I. Freund, M. Kaveh, “Time evolution of universal optical fluctuations,” Phys. Rev. Lett. 58, 2754–2757 (1987).
[Crossref] [PubMed]

Fujimoto, J. G.

Genack, A. Z.

A. Z. Genack, J. M. Drake, “Relationship between optical intensity fluctuations and pulse propagation in random media,” Europhys. Lett. 11, 331–336 (1990).
[Crossref]

A. Z. Genack, “Optical transmission in disordered media,” Phys. Rev. Lett. 58, 2043–2046 (1987).
[Crossref] [PubMed]

Goodman, J. W.

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed., Vol. 9 of Topics in Applied Physics (Springer-Verlag, Berlin, 1984).

Gratton, E.

Groenhuis, R. A. J.

Hee, M. R.

Hilgeman, T. W.

W. G. Egan, T. W. Hilgeman, Optical Properties of Inhomogeneous Materials (Academic, New York, 1979).

Hoshen, M.

M. Rosenbluh, M. Hoshen, I. Freund, M. Kaveh, “Time evolution of universal optical fluctuations,” Phys. Rev. Lett. 58, 2754–2757 (1987).
[Crossref] [PubMed]

Idell, P. S.

D. G. Voelz, P. S. Idell, K. A. Bush, “Illumination coherence effects in laser-speckle imaging,” in Laser Radar VI, R. J. Becherer, ed., Proc. SPIE1416, 260–265 (1991).
[Crossref]

Ippen, E.

Izatt, J. A.

Jacobson, J. M.

Jiang, H.

Kaveh, M.

M. Rosenbluh, M. Hoshen, I. Freund, M. Kaveh, “Time evolution of universal optical fluctuations,” Phys. Rev. Lett. 58, 2754–2757 (1987).
[Crossref] [PubMed]

Leith, E.

Lopez, J.

Margolis, R.

Naulleau, P.

Orchard, S. E.

Oseroff, A.

Osterberg, U. L.

Papoulis, A.

A. Papoulis, Probability Random Variables and Stochastic Processes (McGraw-Hill, New York, 1984), p. 272.

Parry, G.

G. Parry, “Some effects of temporal coherence on the first order statistics of speckle,” Opt. Acta 21, 763–772 (1974).
[Crossref]

Patterson, M. S.

Paulsen, K. D.

Pogue, B. W.

Przadka, A.

Puliafito, C.

Reed, I. S.

I. S. Reed, “On a moment theorem for complex Gaussian processes,” IRE Trans. Inf. Theory 8, 194–195 (1962).
[Crossref]

Reynolds, J. S.

Rosenbluh, M.

M. Rosenbluh, M. Hoshen, I. Freund, M. Kaveh, “Time evolution of universal optical fluctuations,” Phys. Rev. Lett. 58, 2754–2757 (1987).
[Crossref] [PubMed]

Rudd, J.

Silvestri, S. D.

Sun, P. C.

Thompson, C. A.

Tuchin, V. V.

D. A. Zimnyakov, V. V. Tuchin, S. R. Utts, “A study of statistical properties of partially developed speckle fields as applied to the diagnostics of structural changes in human skin,” Opt. Spectrosc. (USSR) 76, 838–844 (1994).

Utts, S. R.

D. A. Zimnyakov, V. V. Tuchin, S. R. Utts, “A study of statistical properties of partially developed speckle fields as applied to the diagnostics of structural changes in human skin,” Opt. Spectrosc. (USSR) 76, 838–844 (1994).

Valdmanis, J.

Voelz, D. G.

D. G. Voelz, P. S. Idell, K. A. Bush, “Illumination coherence effects in laser-speckle imaging,” in Laser Radar VI, R. J. Becherer, ed., Proc. SPIE1416, 260–265 (1991).
[Crossref]

Vossler, G.

Webb, K. J.

Weiner, A. M.

Wilson, B.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), p. 316.

Yeung, S.

Yodh, A. G.

D. A. Boas, L. E. Campbell, A. G. Yodh, “Scattering and imaging with diffusing temporal field correlations,” Phys. Rev. Lett. 75, 1855–1858 (1995).
[Crossref] [PubMed]

Zimnyakov, D. A.

D. A. Zimnyakov, V. V. Tuchin, S. R. Utts, “A study of statistical properties of partially developed speckle fields as applied to the diagnostics of structural changes in human skin,” Opt. Spectrosc. (USSR) 76, 838–844 (1994).

Appl. Math. Comput. (1)

J. C. Adams, “mudpack: multigrid portable fortran software for the efficient solution of linear elliptic partial differential equations,” Appl. Math. Comput. 34, 113–146 (1989).
[Crossref]

Appl. Opt. (4)

Europhys. Lett. (1)

A. Z. Genack, J. M. Drake, “Relationship between optical intensity fluctuations and pulse propagation in random media,” Europhys. Lett. 11, 331–336 (1990).
[Crossref]

IRE Trans. Inf. Theory (1)

I. S. Reed, “On a moment theorem for complex Gaussian processes,” IRE Trans. Inf. Theory 8, 194–195 (1962).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Opt. Acta (1)

G. Parry, “Some effects of temporal coherence on the first order statistics of speckle,” Opt. Acta 21, 763–772 (1974).
[Crossref]

Opt. Commun. (1)

I. Freund, “Image reconstruction through multiple scattering media,” Opt. Commun. 86, 216–227 (1991).
[Crossref]

Opt. Eng. (1)

J. D. Briers, “Speckle fluctuations and biomedical optics: implications and applications,” Opt. Eng. 32, 277–283 (1993).
[Crossref]

Opt. Lett. (3)

Opt. Spectrosc. (USSR) (1)

D. A. Zimnyakov, V. V. Tuchin, S. R. Utts, “A study of statistical properties of partially developed speckle fields as applied to the diagnostics of structural changes in human skin,” Opt. Spectrosc. (USSR) 76, 838–844 (1994).

Phys. Rev. Lett. (4)

M. Rosenbluh, M. Hoshen, I. Freund, M. Kaveh, “Time evolution of universal optical fluctuations,” Phys. Rev. Lett. 58, 2754–2757 (1987).
[Crossref] [PubMed]

A. Z. Genack, “Optical transmission in disordered media,” Phys. Rev. Lett. 58, 2043–2046 (1987).
[Crossref] [PubMed]

R. Berkovits, S. Feng, “Theory of speckle-pattern tomography in multiple-scattering media,” Phys. Rev. Lett. 65, 3120–3123 (1990).
[Crossref] [PubMed]

D. A. Boas, L. E. Campbell, A. G. Yodh, “Scattering and imaging with diffusing temporal field correlations,” Phys. Rev. Lett. 75, 1855–1858 (1995).
[Crossref] [PubMed]

Other (6)

D. G. Voelz, P. S. Idell, K. A. Bush, “Illumination coherence effects in laser-speckle imaging,” in Laser Radar VI, R. J. Becherer, ed., Proc. SPIE1416, 260–265 (1991).
[Crossref]

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed., Vol. 9 of Topics in Applied Physics (Springer-Verlag, Berlin, 1984).

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), p. 316.

J. C. Adams, Multigrid Software for Elliptic Partial Differential Equations (National Center for Atmospheric Research, Boulder, Colo., 1991).

W. G. Egan, T. W. Hilgeman, Optical Properties of Inhomogeneous Materials (Academic, New York, 1979).

A. Papoulis, Probability Random Variables and Stochastic Processes (McGraw-Hill, New York, 1984), p. 272.

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Figures (9)

Fig. 1
Fig. 1

Normalized impulse responses or path-length probability-density functions for three different sets of scattering and absorption parameters for a slab of thickness 3.6 cm.

Fig. 2
Fig. 2

Diagram of the scattering medium with embedded inhomogeneity. Note that scanning implies that the plastic is scanned with a fixed source and detector.

Fig. 3
Fig. 3

Experimental arrangement for speckle measurements.

Fig. 4
Fig. 4

Speckle intensity contrast (σI/μI) as a function of position for the more highly scattering inhomogeneity.

Fig. 5
Fig. 5

Numerically simulated temporal impulse response as a function of scan position for the more highly scattering inhomogeneity.

Fig. 6
Fig. 6

Temporal impulse response for imaging points at the center line and at 2.474 cm from the center for denser inhomogeneity.

Fig. 7
Fig. 7

Numerically computed characteristic time (σt) for the denser inhomogeneity.

Fig. 8
Fig. 8

Experimental mean intensity (solid curve) and scaled integral of the temporal impulse (dashed curve) response versus scanning position for the denser inhomogeneity.

Fig. 9
Fig. 9

Speckle intensity contrast as a function of scan position for the clear inhomogeneity.

Equations (52)

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Iinc=0S(λ)dλ.
U(xi, yi, λ)=Ur(xi, yi, λ)+iUi(xi, yi, λ),
U(xi, yi, λ)=Um(xi, yi, λ)exp[-iϕ(xi, yi, λ)],
Um2(xi, yi, λ)=S(λ)In(xi, yi, λ)=I(xi, yi, λ),
p(I, λ)=12πσI2 exp[-I/(2σI2)],
ϕ(xi, yi, λ)=(2π/λ)l(xi, yi).
I(xi, yi)=0S(λ)In(xi, yi, λ)dλ.
In(xi, yi, λ)=0In(xi, yi, λ)p(I, λ)dI,
I2(xi, yi)=00S(λ)S(λ)In(xi, yi, λ)×In(xi, yi, λ)dλdλ.
ΓI(λ, λ)=In(xi, yi, λ)In(xi, yi, λ).
I(xi, yi)I(xi, yi)=00S(λ)S(λ)In(xi, yi, λ)
×In(xi, yi, λ)dλdλ.
In(xi, yi, λ)In(xi, yi, λ)
=Un(xi, yi, λ)Un*(xi, yi, λ)×Un(xi, yi, λ)Un*(xi, yi, λ).
w1*w2*w3w4=w1*w3w2*w4+w2*w3w1*w4.
In(xi, yi, λ)In(xi, yi, λ)
=In(xi, yi, λ)In(xi, yi, λ)+|Un(xi, yi, λ)Un*(xi, yi, λ)|2.
σI2(xi, yi)=00S(λ)S(λ)|Un(xi, yi, λ)×Un*(xi, yi, λ)|2dλdλ.
σI2=00S(λ)S(λ)|In1/2(λ)In1/2(λ)×exp{-i[ϕ(λ)-ϕ(λ)]}|2dλdλ.
σI2=00S(λ)S(λ)|In1/2(λ)In1/2(λ)|2×|exp{-i[ϕ(λ)-ϕ(λ)]}|2dλdλ=00S(λ)S(λ)|ΓU(λ, λ)|2dλdλ,
In(λ)=I0,
σI2=I02 00S(λ)S(λ)×exp-i2πl1λ-1λ2dλdλ.
μI=I00S(λ)dλ.
σIμI (xi0, yi0)=00S(λ)S(λ)×exp-i2πl1λ-1λ2dλdλ1/2/0S(λ)dλ.
exp-i2πl1λ-1λ
=0p(l)exp-i2πl1λ-1λdl,
Ud(x, y, λ)=U(xi, yi, λ) * K(x, y, xi, yi, λ),
1c t Φ(r, t)-D2Φ(r, t)+μaΦ(r, t)=Q(r, t),
T(r, t)=nˆ[-DΦ(r, t)],
p(l)=T(x, y, z, l/c)0T(x, y, z, l/c)dl.
D2Φn+1x2+2Φn+1y2+2Φn+1z2
-μa+1c 1ΔtΦn+1=-Q-1c 1Δt Φn.
Jin=rdJout.
Φ(xs, ys, zs, t)-D2 Φ(xs, ys, z, t)zz=zs
=rdΦ(xs, ys, zs, t)+D2 Φ(xs, ys, z, t)zz=zs,
1-rd1+rd 12D Φ(xs, ys, zs, t)-Φ(xs, ys, z, t)zz=zs
=0.
rd=0.0636n+0.6681+0.7099n-1-1.4399n-2,
ΓUd(x, y, λ, λ)
=[U(xi, yi, λ) * K(x, y, xi, yi, λ)]×[U*(xi, yi, λ) * K*(x, y, xi, yi, λ)],
ΓUd(x, y, λ, λ)
=U(xi, yi, λ)U*(xi, yi, λ) * [K(x, y, xi, yi, λ)K*(x, y, xi, yi, λ)].
μId(x, y)=0S(λ)In(xi, yi, λ) * |K(x, y, xi, yi, λ)|2dλ.
μId(x, y)=μI(xi, yi) * |K(x, y, xi, yi)|2.
σId2(x, y)=00S(λ)S(λ)|Un(xi, yi, λ)×Un*(xi, yi, λ) * [K(x, y, xi, yi, λ)×K*(x, y, xi, yi, λ)]|2dλdλ.
Un(xi, yi, λ)Un*(xi, yi, λ)
=In(xi, yi)exp{-i[ϕ(xi, yi, λ)-ϕ(xi, yi, λ)]},
σId2(x, y)=00S(λ)S(λ)|In(xi, yi)×exp{-i[ϕ(xi, yi, λ)-ϕ(xi, yi, λ)]} * |K(x, y, xi, yi)|2|2dλdλ.
σId2(x, y)=σI2K02(x, y),
K02(x, y)=xi,yispot|K(x, y, xi, yi)|2dxidyi2.
μId(x, y)=μIK0(x, y).
σIdμId=σIμI.

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