Abstract

We measured the coherent backscattering of light from milk solutions and biological tissues by using a He–Ne laser (633 nm) and a CCD array as a detector. A coherent peak from the milk solutions could be measured with a single exposure. However, ensemble averaging was required for coherent peaks to be produced from solid media such as tissue samples. By fitting experimental data to an existing model numerically, effective scattering and absorption coefficients were estimated. They were compared with those computed from integrating sphere measurements. Effective scattering coefficients computed by the two different methods were in good agreement for high-scattering media. However, higher absorption was estimated by the coherent peak method.

© 1993 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109, 1492–1505 (1958).
    [CrossRef]
  2. Y. Kuga, A. Ishimaru, “Retroreflection from a dense distribution of spherical particles,” J. Opt. Soc. Am. A 1, 831–835 (1984).
    [CrossRef]
  3. P. E. Wolf, G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phy. Rev. Lett. 55, 2696–2699 (1985).
    [CrossRef]
  4. E. Akkermans, P. E. Wolf, R. Maynard, “Coherent backscattering of light by disordered media; analysis of the peak line shape,” Phy. Rev. Lett. 56, 1471–1474 (1986).
    [CrossRef]
  5. M. P. van Albada, M. B. van der Mark, Ad Lagendijk, “Observation of weak localization of light in a finite slab,” Phy. Rev. Lett. 58, 361–364 (1987).
    [CrossRef]
  6. The fluence rate represents the total light energy at a particular position r in the medium. Multiple scattering generates the light of all solid-angle components, which is usually represented by radiance L(r, ŝ), where ŝ is the directional unit vector. Thus the fluence rate is ∫L(r, ŝ)dω. The integral is done over the solid angle ω.
  7. G. Yoon, S. A. Prahl, A. J. Welch, “Accuracies of the diffusion approximation and its similarity relations for laser irradiated biological media,” Appl. Opt. 28, 2250–2255 (1989).
    [CrossRef] [PubMed]
  8. M. Motamedi, S. Rastegar, G. LeCarpentier, A. J. Welch, “Light and temperature distribution in laser irradiated tissue: the influence of anisotropic scattering and refractice index,” Appl. Opt. 28, 2230–2237 (1989).
    [CrossRef] [PubMed]
  9. M. Keijzer, S. L. Jacques, S. A. Prahl, A. J. Welch, “Light distributions in artery tissue: Monte Carlo simulations for finite-diameter laser beams,” Laser Surg. Med. 9, 148–154 (1989).
    [CrossRef]
  10. W. Egan, T. Hilgeman, Optical Properties of Inhomogeneous Materials (Academic, New York, 1979), Chap. 7.
  11. Y. A. Kravtsov, A. I. Saichev, “Effects of double passage of waves in randomly inhomogeneous media,” Sov. Phys. Usp. 25, 494–508 (1982).
    [CrossRef]
  12. T. Gehrels, T. Coffeen, D. Owings, “Wavelength dependence of polarization III. The lunar surface,” Astron. J. 69, 826–852 (969).
  13. S. John, “Localization of light,” Phys. Today 44(5), 32–40 (1991).
    [CrossRef]
  14. K. M. Yoo, G. C. Tang, R. R. Alfano, “Coherent backscattering of light from biological tissues,” Appl. Opt. 29, 3237–3239 (1990).
    [CrossRef] [PubMed]
  15. S. Etemad, R. Thompson, M. J. Anderjco, “Weak localization of photons: universal fluctuations and ensemble averaging,” Phys. Rev. Lett. 57, 575–578 (1986).
    [CrossRef] [PubMed]
  16. S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).
  17. E. Akkermans, P. E. Wolf, R. Maynard, G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. (France) 49, 77–98 (1988).
    [CrossRef]
  18. K. Levenberg, “A method for the solution of certain problems in least squares,” Q. Appl. Math. 2, 164–168 (1944).
  19. D. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” SIAM J. Appl. Math. 11, 431–441 (1963).
    [CrossRef]
  20. B C. Wilson, M. S. Patterson, S. T. Flock, “Indirect versus direct techniques for the measurement of the optical properties of tissues,” Photochem. Photobiol. 46, 601–608 (1987).
    [CrossRef] [PubMed]
  21. G. Yoon, A. J. Welch, “Determination of optical properties for laser-irradiated tissue,” in Proceedings of the Ninth Annual Conference of the Engineering in Medicine and Biology Society (Institute of Electrical and Electronics Engineers, New York, 1987), pp. 1446–1447.
  22. S. A. Prahl, “Light transport in tissue,” Ph.D. dissertation (University of Texas at Austin, Austin, Tex., December1988).

1991 (1)

S. John, “Localization of light,” Phys. Today 44(5), 32–40 (1991).
[CrossRef]

1990 (1)

1989 (3)

1988 (1)

E. Akkermans, P. E. Wolf, R. Maynard, G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. (France) 49, 77–98 (1988).
[CrossRef]

1987 (2)

M. P. van Albada, M. B. van der Mark, Ad Lagendijk, “Observation of weak localization of light in a finite slab,” Phy. Rev. Lett. 58, 361–364 (1987).
[CrossRef]

B C. Wilson, M. S. Patterson, S. T. Flock, “Indirect versus direct techniques for the measurement of the optical properties of tissues,” Photochem. Photobiol. 46, 601–608 (1987).
[CrossRef] [PubMed]

1986 (2)

S. Etemad, R. Thompson, M. J. Anderjco, “Weak localization of photons: universal fluctuations and ensemble averaging,” Phys. Rev. Lett. 57, 575–578 (1986).
[CrossRef] [PubMed]

E. Akkermans, P. E. Wolf, R. Maynard, “Coherent backscattering of light by disordered media; analysis of the peak line shape,” Phy. Rev. Lett. 56, 1471–1474 (1986).
[CrossRef]

1985 (1)

P. E. Wolf, G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phy. Rev. Lett. 55, 2696–2699 (1985).
[CrossRef]

1984 (1)

1982 (1)

Y. A. Kravtsov, A. I. Saichev, “Effects of double passage of waves in randomly inhomogeneous media,” Sov. Phys. Usp. 25, 494–508 (1982).
[CrossRef]

1963 (1)

D. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” SIAM J. Appl. Math. 11, 431–441 (1963).
[CrossRef]

1958 (1)

P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109, 1492–1505 (1958).
[CrossRef]

1944 (1)

K. Levenberg, “A method for the solution of certain problems in least squares,” Q. Appl. Math. 2, 164–168 (1944).

Akkermans, E.

E. Akkermans, P. E. Wolf, R. Maynard, G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. (France) 49, 77–98 (1988).
[CrossRef]

E. Akkermans, P. E. Wolf, R. Maynard, “Coherent backscattering of light by disordered media; analysis of the peak line shape,” Phy. Rev. Lett. 56, 1471–1474 (1986).
[CrossRef]

Alfano, R. R.

Anderjco, M. J.

S. Etemad, R. Thompson, M. J. Anderjco, “Weak localization of photons: universal fluctuations and ensemble averaging,” Phys. Rev. Lett. 57, 575–578 (1986).
[CrossRef] [PubMed]

Anderson, P. W.

P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109, 1492–1505 (1958).
[CrossRef]

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).

Coffeen, T.

T. Gehrels, T. Coffeen, D. Owings, “Wavelength dependence of polarization III. The lunar surface,” Astron. J. 69, 826–852 (969).

Egan, W.

W. Egan, T. Hilgeman, Optical Properties of Inhomogeneous Materials (Academic, New York, 1979), Chap. 7.

Etemad, S.

S. Etemad, R. Thompson, M. J. Anderjco, “Weak localization of photons: universal fluctuations and ensemble averaging,” Phys. Rev. Lett. 57, 575–578 (1986).
[CrossRef] [PubMed]

Flock, S. T.

B C. Wilson, M. S. Patterson, S. T. Flock, “Indirect versus direct techniques for the measurement of the optical properties of tissues,” Photochem. Photobiol. 46, 601–608 (1987).
[CrossRef] [PubMed]

Gehrels, T.

T. Gehrels, T. Coffeen, D. Owings, “Wavelength dependence of polarization III. The lunar surface,” Astron. J. 69, 826–852 (969).

Hilgeman, T.

W. Egan, T. Hilgeman, Optical Properties of Inhomogeneous Materials (Academic, New York, 1979), Chap. 7.

Ishimaru, A.

Jacques, S. L.

M. Keijzer, S. L. Jacques, S. A. Prahl, A. J. Welch, “Light distributions in artery tissue: Monte Carlo simulations for finite-diameter laser beams,” Laser Surg. Med. 9, 148–154 (1989).
[CrossRef]

John, S.

S. John, “Localization of light,” Phys. Today 44(5), 32–40 (1991).
[CrossRef]

Keijzer, M.

M. Keijzer, S. L. Jacques, S. A. Prahl, A. J. Welch, “Light distributions in artery tissue: Monte Carlo simulations for finite-diameter laser beams,” Laser Surg. Med. 9, 148–154 (1989).
[CrossRef]

Kravtsov, Y. A.

Y. A. Kravtsov, A. I. Saichev, “Effects of double passage of waves in randomly inhomogeneous media,” Sov. Phys. Usp. 25, 494–508 (1982).
[CrossRef]

Kuga, Y.

Lagendijk, Ad

M. P. van Albada, M. B. van der Mark, Ad Lagendijk, “Observation of weak localization of light in a finite slab,” Phy. Rev. Lett. 58, 361–364 (1987).
[CrossRef]

LeCarpentier, G.

Levenberg, K.

K. Levenberg, “A method for the solution of certain problems in least squares,” Q. Appl. Math. 2, 164–168 (1944).

Maret, G.

E. Akkermans, P. E. Wolf, R. Maynard, G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. (France) 49, 77–98 (1988).
[CrossRef]

P. E. Wolf, G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phy. Rev. Lett. 55, 2696–2699 (1985).
[CrossRef]

Marquardt, D.

D. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” SIAM J. Appl. Math. 11, 431–441 (1963).
[CrossRef]

Maynard, R.

E. Akkermans, P. E. Wolf, R. Maynard, G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. (France) 49, 77–98 (1988).
[CrossRef]

E. Akkermans, P. E. Wolf, R. Maynard, “Coherent backscattering of light by disordered media; analysis of the peak line shape,” Phy. Rev. Lett. 56, 1471–1474 (1986).
[CrossRef]

Motamedi, M.

Owings, D.

T. Gehrels, T. Coffeen, D. Owings, “Wavelength dependence of polarization III. The lunar surface,” Astron. J. 69, 826–852 (969).

Patterson, M. S.

B C. Wilson, M. S. Patterson, S. T. Flock, “Indirect versus direct techniques for the measurement of the optical properties of tissues,” Photochem. Photobiol. 46, 601–608 (1987).
[CrossRef] [PubMed]

Prahl, S. A.

M. Keijzer, S. L. Jacques, S. A. Prahl, A. J. Welch, “Light distributions in artery tissue: Monte Carlo simulations for finite-diameter laser beams,” Laser Surg. Med. 9, 148–154 (1989).
[CrossRef]

G. Yoon, S. A. Prahl, A. J. Welch, “Accuracies of the diffusion approximation and its similarity relations for laser irradiated biological media,” Appl. Opt. 28, 2250–2255 (1989).
[CrossRef] [PubMed]

S. A. Prahl, “Light transport in tissue,” Ph.D. dissertation (University of Texas at Austin, Austin, Tex., December1988).

Rastegar, S.

Saichev, A. I.

Y. A. Kravtsov, A. I. Saichev, “Effects of double passage of waves in randomly inhomogeneous media,” Sov. Phys. Usp. 25, 494–508 (1982).
[CrossRef]

Tang, G. C.

Thompson, R.

S. Etemad, R. Thompson, M. J. Anderjco, “Weak localization of photons: universal fluctuations and ensemble averaging,” Phys. Rev. Lett. 57, 575–578 (1986).
[CrossRef] [PubMed]

van Albada, M. P.

M. P. van Albada, M. B. van der Mark, Ad Lagendijk, “Observation of weak localization of light in a finite slab,” Phy. Rev. Lett. 58, 361–364 (1987).
[CrossRef]

van der Mark, M. B.

M. P. van Albada, M. B. van der Mark, Ad Lagendijk, “Observation of weak localization of light in a finite slab,” Phy. Rev. Lett. 58, 361–364 (1987).
[CrossRef]

Welch, A. J.

M. Keijzer, S. L. Jacques, S. A. Prahl, A. J. Welch, “Light distributions in artery tissue: Monte Carlo simulations for finite-diameter laser beams,” Laser Surg. Med. 9, 148–154 (1989).
[CrossRef]

G. Yoon, S. A. Prahl, A. J. Welch, “Accuracies of the diffusion approximation and its similarity relations for laser irradiated biological media,” Appl. Opt. 28, 2250–2255 (1989).
[CrossRef] [PubMed]

M. Motamedi, S. Rastegar, G. LeCarpentier, A. J. Welch, “Light and temperature distribution in laser irradiated tissue: the influence of anisotropic scattering and refractice index,” Appl. Opt. 28, 2230–2237 (1989).
[CrossRef] [PubMed]

G. Yoon, A. J. Welch, “Determination of optical properties for laser-irradiated tissue,” in Proceedings of the Ninth Annual Conference of the Engineering in Medicine and Biology Society (Institute of Electrical and Electronics Engineers, New York, 1987), pp. 1446–1447.

Wilson, B C.

B C. Wilson, M. S. Patterson, S. T. Flock, “Indirect versus direct techniques for the measurement of the optical properties of tissues,” Photochem. Photobiol. 46, 601–608 (1987).
[CrossRef] [PubMed]

Wolf, P. E.

E. Akkermans, P. E. Wolf, R. Maynard, G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. (France) 49, 77–98 (1988).
[CrossRef]

E. Akkermans, P. E. Wolf, R. Maynard, “Coherent backscattering of light by disordered media; analysis of the peak line shape,” Phy. Rev. Lett. 56, 1471–1474 (1986).
[CrossRef]

P. E. Wolf, G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phy. Rev. Lett. 55, 2696–2699 (1985).
[CrossRef]

Yoo, K. M.

Yoon, G.

G. Yoon, S. A. Prahl, A. J. Welch, “Accuracies of the diffusion approximation and its similarity relations for laser irradiated biological media,” Appl. Opt. 28, 2250–2255 (1989).
[CrossRef] [PubMed]

G. Yoon, A. J. Welch, “Determination of optical properties for laser-irradiated tissue,” in Proceedings of the Ninth Annual Conference of the Engineering in Medicine and Biology Society (Institute of Electrical and Electronics Engineers, New York, 1987), pp. 1446–1447.

Appl. Opt. (3)

Astron. J. (1)

T. Gehrels, T. Coffeen, D. Owings, “Wavelength dependence of polarization III. The lunar surface,” Astron. J. 69, 826–852 (969).

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

J. Phys. (France) (1)

E. Akkermans, P. E. Wolf, R. Maynard, G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. (France) 49, 77–98 (1988).
[CrossRef]

Laser Surg. Med. (1)

M. Keijzer, S. L. Jacques, S. A. Prahl, A. J. Welch, “Light distributions in artery tissue: Monte Carlo simulations for finite-diameter laser beams,” Laser Surg. Med. 9, 148–154 (1989).
[CrossRef]

Photochem. Photobiol. (1)

B C. Wilson, M. S. Patterson, S. T. Flock, “Indirect versus direct techniques for the measurement of the optical properties of tissues,” Photochem. Photobiol. 46, 601–608 (1987).
[CrossRef] [PubMed]

Phy. Rev. Lett. (3)

P. E. Wolf, G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phy. Rev. Lett. 55, 2696–2699 (1985).
[CrossRef]

E. Akkermans, P. E. Wolf, R. Maynard, “Coherent backscattering of light by disordered media; analysis of the peak line shape,” Phy. Rev. Lett. 56, 1471–1474 (1986).
[CrossRef]

M. P. van Albada, M. B. van der Mark, Ad Lagendijk, “Observation of weak localization of light in a finite slab,” Phy. Rev. Lett. 58, 361–364 (1987).
[CrossRef]

Phys. Rev. (1)

P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109, 1492–1505 (1958).
[CrossRef]

Phys. Rev. Lett. (1)

S. Etemad, R. Thompson, M. J. Anderjco, “Weak localization of photons: universal fluctuations and ensemble averaging,” Phys. Rev. Lett. 57, 575–578 (1986).
[CrossRef] [PubMed]

Phys. Today (1)

S. John, “Localization of light,” Phys. Today 44(5), 32–40 (1991).
[CrossRef]

Q. Appl. Math. (1)

K. Levenberg, “A method for the solution of certain problems in least squares,” Q. Appl. Math. 2, 164–168 (1944).

SIAM J. Appl. Math. (1)

D. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” SIAM J. Appl. Math. 11, 431–441 (1963).
[CrossRef]

Sov. Phys. Usp. (1)

Y. A. Kravtsov, A. I. Saichev, “Effects of double passage of waves in randomly inhomogeneous media,” Sov. Phys. Usp. 25, 494–508 (1982).
[CrossRef]

Other (5)

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).

The fluence rate represents the total light energy at a particular position r in the medium. Multiple scattering generates the light of all solid-angle components, which is usually represented by radiance L(r, ŝ), where ŝ is the directional unit vector. Thus the fluence rate is ∫L(r, ŝ)dω. The integral is done over the solid angle ω.

W. Egan, T. Hilgeman, Optical Properties of Inhomogeneous Materials (Academic, New York, 1979), Chap. 7.

G. Yoon, A. J. Welch, “Determination of optical properties for laser-irradiated tissue,” in Proceedings of the Ninth Annual Conference of the Engineering in Medicine and Biology Society (Institute of Electrical and Electronics Engineers, New York, 1987), pp. 1446–1447.

S. A. Prahl, “Light transport in tissue,” Ph.D. dissertation (University of Texas at Austin, Austin, Tex., December1988).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Experimental setup for measuring the CP.

Fig. 2
Fig. 2

CP’s measured from milk at 633 nm. VV polarization, no polarization, and VH polarization are compared. Also shown are isointensity lines of the VV polarization: 1, 95%; 2, 87%; 3, 75%; 4, 65% from inside the inset.

Fig. 3
Fig. 3

CP’s from different concentrations of milk in water: 100%, 50%, and 10% from the top.

Fig. 4
Fig. 4

CP’s from chicken breast: single exposure (dotted curve), ensemble averaged (solid curve).

Fig. 5
Fig. 5

Computed coherent peaks and the smooth peaks caused by a detector resolution of 0.18 mrad FWHM. The transport coefficient μt, is 40/cm, and the absorption coefficient μa is 0, 1/cm, and 10/cm from the top.

Fig. 6
Fig. 6

Measured (filled squares) and numerical-fit (solid curve) coherent peaks for the human forearm.

Fig. 7
Fig. 7

Effective scattering and absorption coefficients measured from the CP (solid curve) and the integrating sphere (dotted curve) methods.

Equations (2)

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

α ( θ ) = 1 + { 1 + [ 1 exp ( 1 . 4 q / μ t ) ] / ( q / μ t ) } / [ 2 . 4 ( 1 + q / μ t ) 2 ] ,
α ( θ ) | = α ( θ ) exp [ c ( θ θ ) 2 / FWHM 2 ] d θ .

Metrics