Abstract

The statistical properties of laser speckle with partially coherent light are related to the scattering characteristics of an optically diffuse material. A diffusion equation model is shown to yield a speckle contrast ratio that agrees well with measurements of opaque plastics of varying thicknesses. We show that partially coherent light can be used to determine material parameters for highly scattering media. Measured data for stratified materials with differing scattering properties indicate that this technique may be useful in detecting inhomogeneities.

© 1997 Optical Society of America

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  1. 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]
  2. J. S. Reynolds, S. Yeung, A. Przadka, K. Webb, “Optical diffusion imaging: a comparative numerical and experimental study,” Appl. Opt. 35, 3671–3679 (1996).
    [Crossref] [PubMed]
  3. K. Yoo, R. Alfano, “Time-resolved coherent and incoherent components of forward light scattering in random media,” Opt. Lett. 15, 320–322 (1990).
    [Crossref] [PubMed]
  4. D. G. Voelz, P. S. Idell, K. A. Bush, “Illumination coherence effects in laser-speckle imaging,” in Laser Radar VI, R. J. Bercher, ed., Proc. SPIE1416, 260–265 (1991).
    [Crossref]
  5. 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. 76, 838–844 (1994).
  6. R. Berkovits, S. Feng, “Theory of speckle-pattern tomography in multiple-scattering media,” Phys. Rev. Lett. 65, 3120–3123 (1990).
    [Crossref] [PubMed]
  7. 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]
  8. 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]
  9. J. D. Briers, “Speckle fluctuations and biomedical optics: implications and applications,” Opt. Eng. 32, 277–283 (1993).
    [Crossref]
  10. A. Z. Genack, “Optical transmission in disordered media,” Phys. Rev. Lett. 58, 2043–2046 (1987).
    [Crossref] [PubMed]
  11. T. Bellini, M. A. Glaser, N. A. Clark, V. Degiorgio, “Effects of finite laser coherence in quasi-elastic multiple scattering,” Phys. Rev. A 44, 5215–5223 (1991).
    [Crossref] [PubMed]
  12. J. W. Goodman, “Statical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, Vol. 9 of Topics in Applied Physics, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984).
  13. G. Parry, “Some effects of temporal coherence on the first-order statistics of speckle,” Opt. Acta 21, 763–772 (1974).
    [Crossref]
  14. T. J. Farrell, M. S. Patterson, B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888, (1992).
    [Crossref] [PubMed]
  15. W. G. Egan, T. W. Hilgeman, Optical Properties of Inhomogeneous Materials (Academic, New York, 1979).
  16. S. E. Orchard, “Reflection and transmission of light by diffusing suspensions,” J. Opt. Soc. Am. 59, 1584–1597 (1969).
    [Crossref]
  17. J. W. Goodman, Statistical Optics (Wiley, New York, 1985).
  18. J. R. Mourant, J. P. Freyer, T. M. Johnson, “Measurements of scattering and absorption in mammallian cell suspensions,” in Advances in Laser Light Spectroscopy to Diagnose Cancer and Other Diseases III: Optical Biopsy, R. Alfano, ed., Proc. SPIE2679, 79–91 (1996).
    [Crossref]

1996 (1)

1995 (2)

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]

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]

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. 76, 838–844 (1994).

1993 (1)

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

1992 (1)

T. J. Farrell, M. S. Patterson, B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888, (1992).
[Crossref] [PubMed]

1991 (1)

T. Bellini, M. A. Glaser, N. A. Clark, V. Degiorgio, “Effects of finite laser coherence in quasi-elastic multiple scattering,” Phys. Rev. A 44, 5215–5223 (1991).
[Crossref] [PubMed]

1990 (2)

K. Yoo, R. Alfano, “Time-resolved coherent and incoherent components of forward light scattering in random media,” Opt. Lett. 15, 320–322 (1990).
[Crossref] [PubMed]

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

1989 (1)

1987 (1)

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

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)

Alfano, R.

Bellini, T.

T. Bellini, M. A. Glaser, N. A. Clark, V. Degiorgio, “Effects of finite laser coherence in quasi-elastic multiple scattering,” Phys. Rev. A 44, 5215–5223 (1991).
[Crossref] [PubMed]

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]

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. Bercher, 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.

Clark, N. A.

T. Bellini, M. A. Glaser, N. A. Clark, V. Degiorgio, “Effects of finite laser coherence in quasi-elastic multiple scattering,” Phys. Rev. A 44, 5215–5223 (1991).
[Crossref] [PubMed]

Degiorgio, V.

T. Bellini, M. A. Glaser, N. A. Clark, V. Degiorgio, “Effects of finite laser coherence in quasi-elastic multiple scattering,” Phys. Rev. A 44, 5215–5223 (1991).
[Crossref] [PubMed]

Dilworth, D.

Egan, W. G.

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

Farrell, T. J.

T. J. Farrell, M. S. Patterson, B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888, (1992).
[Crossref] [PubMed]

Feng, S.

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

Freyer, J. P.

J. R. Mourant, J. P. Freyer, T. M. Johnson, “Measurements of scattering and absorption in mammallian cell suspensions,” in Advances in Laser Light Spectroscopy to Diagnose Cancer and Other Diseases III: Optical Biopsy, R. Alfano, ed., Proc. SPIE2679, 79–91 (1996).
[Crossref]

Genack, A. Z.

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

Glaser, M. A.

T. Bellini, M. A. Glaser, N. A. Clark, V. Degiorgio, “Effects of finite laser coherence in quasi-elastic multiple scattering,” Phys. Rev. A 44, 5215–5223 (1991).
[Crossref] [PubMed]

Goodman, J. W.

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

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

Hilgeman, T. W.

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

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. Bercher, ed., Proc. SPIE1416, 260–265 (1991).
[Crossref]

Johnson, T. M.

J. R. Mourant, J. P. Freyer, T. M. Johnson, “Measurements of scattering and absorption in mammallian cell suspensions,” in Advances in Laser Light Spectroscopy to Diagnose Cancer and Other Diseases III: Optical Biopsy, R. Alfano, ed., Proc. SPIE2679, 79–91 (1996).
[Crossref]

Leith, E.

Lopez, J.

Mourant, J. R.

J. R. Mourant, J. P. Freyer, T. M. Johnson, “Measurements of scattering and absorption in mammallian cell suspensions,” in Advances in Laser Light Spectroscopy to Diagnose Cancer and Other Diseases III: Optical Biopsy, R. Alfano, ed., Proc. SPIE2679, 79–91 (1996).
[Crossref]

Naulleau, P.

Orchard, S. E.

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.

T. J. Farrell, M. S. Patterson, B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888, (1992).
[Crossref] [PubMed]

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]

Przadka, A.

Reynolds, J. S.

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. 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. 76, 838–844 (1994).

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. Bercher, ed., Proc. SPIE1416, 260–265 (1991).
[Crossref]

Webb, K.

Wilson, B.

T. J. Farrell, M. S. Patterson, B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888, (1992).
[Crossref] [PubMed]

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]

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]

Yoo, K.

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. 76, 838–844 (1994).

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

Med. Phys. (1)

T. J. Farrell, M. S. Patterson, B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888, (1992).
[Crossref] [PubMed]

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. Eng. (1)

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

Opt. Lett. (2)

Opt. Spectrosc. (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. 76, 838–844 (1994).

Phys. Rev. A (1)

T. Bellini, M. A. Glaser, N. A. Clark, V. Degiorgio, “Effects of finite laser coherence in quasi-elastic multiple scattering,” Phys. Rev. A 44, 5215–5223 (1991).
[Crossref] [PubMed]

Phys. Rev. Lett. (3)

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]

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

Other (5)

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

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

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

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

J. R. Mourant, J. P. Freyer, T. M. Johnson, “Measurements of scattering and absorption in mammallian cell suspensions,” in Advances in Laser Light Spectroscopy to Diagnose Cancer and Other Diseases III: Optical Biopsy, R. Alfano, ed., Proc. SPIE2679, 79–91 (1996).
[Crossref]

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Figures (8)

Fig. 1
Fig. 1

Comparison between the degrees of optical coherence in a medium with heavy scatter. Left, intensity versus radial position; right, intensity histogram (τ is the standard deviation of photon arrival times; τc is the coherence time of the source.)

Fig. 2
Fig. 2

Diagram of photon diffusion through a random medium. Photons are introduced into the medium by a source located at point (xs, ys). The lines indicate example random paths of photons through the medium. Detection is made at some point (xi, yi) on the imaging side of the medium.

Fig. 3
Fig. 3

Schematic of four dipole sources used to produce approximate Φ = 0 boundary conditions on an extrapolated boundary for the diffusion equation model applied to a slab of material. The filled circles represent positive sources, the open circles are negative sources, and the shaded region is the slab of material. The extrapolated boundaries are signified by the dashed lines.

Fig. 4
Fig. 4

Diagram of the speckle imaging system. The system images a 1-mm-square spot from the back side of the scattering medium onto the CCD array.

Fig. 5
Fig. 5

Snapshot showing typical speckle patterns. Top, Acrylite, 0.6 cm thick; bottom, Acrylite, 3.6 cm thick. Note that the intensity is more uniform (σI is smaller) for the thicker sample.

Fig. 6
Fig. 6

Speckle contrast ratio (σII) for various thicknesses of white acrylic. The diamonds represent raw experimental data. The dashed curve is a best fit to the experimental data. This curve gives μa = 0.005 cm-1 and μs′ = 41.0 cm-1. The normalized characteristic time, τ/τc, is plotted on the right axis, where τ is the spread in photon travel times (calculated using μa = 0.005 cm-1 and μs′ = 41.0 cm-1) and τc ≈ 737 ps is the laser coherence time.

Fig. 7
Fig. 7

Example intensity histograms for several Acrylite slab thicknesses. Note that σI reduces as the material thickness increases.

Fig. 8
Fig. 8

Probability density functions for photon path lengths, p(l), through three thicknesses of the Acrylite material (0.6, 1.8, and 3.6 cm), calculated using μs′ = 41cm-1 and μa = 0.005 cm-1. As the material increases in thickness, σl increases.

Tables (1)

Tables Icon

Table 1 Measured Speckle Contrast Ratio for Plexiglas Containing Various Slabs of 1.2-cm thick Center Materiala.

Equations (20)

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

μIxi, yi=0SλInxi, yi, λdλ,
σI2xi, yi=00 SλSλUnxi, yi, λ×Un*xi, yi, λ2dλdλ,
Uxi, yi, λ=j=1M Ujxi, yi, λexp-i2πLjxi, yi, λ,
Uλ=Umλexp-i2πl/λ,
μI=I00Sλdλ.
Unλ=In1/2 exp-iϕλ,
Um2λ=SλI0.
ΓU=Inexp-i2πl1/λ-1/λ.
ΓU=I0exp-i2πl1/λ-1/λ.
μI/σI=000 SλSλ×exp-i2πl1/λ-1/λ2dλdλ1/2Sλdλ.
1/c Φx, y, z, t/t-D2Φx, y, z, t+μaΦx, y, z, t=Qx, y, z, t,
D=3μa+1-gμs-1,
Φx, y, z, t=c4πDct3/2×exp-μactexp-x2+y2+z24Dct.
A=1+rd/1-rd,
rd=-1.440n-2+0.710n-1+0.668+0.0636n.
Φsx, y, z, t=q=-12Φx, y, z-2qd+4q-1zb+zo, t-Φx, y, z-4qd+2q-1zb-zo, t,
Tx, y, d, t=zˆ · -DΦsx, y, z, t|z=d,
ft=Tx, y, d, t0Tx, y, d, tdt.
pl=ft|t=l/c,
exp-i2πl1λ-1λ=0pl×exp-i2πl1λ-1λdl,

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