Abstract

The diffusion of correlation is used to detect, localize, and characterize dynamical and optical spatial inhomogeneities in turbid media and is accurately modeled by a correlation diffusion equation. We demonstrate experimentally and with Monte Carlo simulations that the transport of correlation can be viewed as a correlation wave {analogous to a diffuse photon-density wave [Phys. Today 48, 34 (1995)]} that propagates spherically outward from sources and scatters from macroscopic spatial variations in dynamical and/or optical properties. We demonstrate the utility of inverse scattering algorithms for reconstructing images of the spatially varying dynamical properties of turbid media. The biomedical applicability of this diffuse correlation probe is illustrated in studies of the depth of burned tissues.

© 1997 Optical Society of America

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  1. A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48, 34–40 (1995).
    [CrossRef]
  2. B. Chance, ed., Photon Migration in Tissues (Plenum, New York, 1989).
  3. B. J. Tromberg, L. O. Svaasand, T. Tsay, R. C. Haskell, “Properties of photon density waves in multiple-scattering media,” Appl. Opt. 32, 607–616 (1993).
    [CrossRef] [PubMed]
  4. M. S. Patterson, B. Chance, B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
    [CrossRef] [PubMed]
  5. G. A. Millikan, “Experiments on muscle haemoglobin in vivo: the instantaneous measurement of muscle metabolism,” Proc. R. Soc. London, Sect. B 129, 218–241 (1937).
    [CrossRef]
  6. G. A. Millikan, “The oximeter, an instrument for measuring continuously the oxygen saturation of arterial blood in man,” Rev. Sci. Instrum. 13, 434–444 (1942).
    [CrossRef]
  7. F. F. Jobsis, “Noninvasive, infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters,” Science 198, 1264–1267 (1977).
    [CrossRef] [PubMed]
  8. J. M. Schmitt, “Simple photon diffusion analysis of the effects of multiple scattering on pulse oximetry,” IEEE Trans. Biomed. Eng. 38, 1194–1203 (1991).
    [CrossRef] [PubMed]
  9. M. R. Neuman, “Pulse oximetry: physical principles technical realization and present limitations,” Adv. Exp. Med. Biol. 220, 135–144 (1987).
  10. J. W. Severinghaus, “History and recent developments in pulse oximetry,” Scand. J. Clin. Lab. Invest. 53, 105–111 (1993).
    [PubMed]
  11. W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
    [CrossRef]
  12. B. C. Wilson, E. M. Sevick, M. S. Patterson, B. Chance, “Time-dependent optical spectroscopy and imaging for biomedical applications,” Proc. IEEE 80, 918–930 (1992).
    [CrossRef]
  13. See related studies by S. R. Arridge, et al. J. P. Kaltenbach, et al. R. L. Barbour et al., in Medical Optical Tomography: Functional Imaging and Monitoring, G. Müller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, P. van der Zee, eds., Institute Series of SPIE Optical Engineering (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 31–143.
  14. S. R. Arridge, P. van der Zee, M. Cope, D. T. Delpy, “Reconstruction methods for infra-red absorption imaging,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, ed., Proc. SPIE1431, 204–215 (1991).
    [CrossRef]
  15. S. P. Gopinath, C. S. Robertson, R. G. Grossman, B. Chance, “Near-infrared spectroscopic localization of intracranial hematomas,” J. Neurosurg. 79, 43–47 (1993).
    [CrossRef]
  16. A. P. Shepherd, P. A. Oberg, eds., Laser-Doppler Blood Flowmetry (Kluwer Academic, Boston, Mass., 1990).
  17. L. E. Drain, The Laser Doppler Technique (Wiley, New York, 1980).
  18. G. V. Belcaro, U. Hoffmann, A. Bollinger, A. N. Nicolaides, eds., Laser Doppler (Med-Orion, London, 1994).
  19. A. D. Edwards, C. Richardson, P. van der Zee, M. Cope, D. T. Delpy, “Measurement of hemoglobin flow and blood flow by near-infrared spectroscopy,” J. Appl. Physiol. 75, 1884–1889 (1993).
    [PubMed]
  20. N. A. Clark, J. H. Lunacek, G. B. Benedek, “A study of Brownian motion using light scattering,” Am. J. Phys. 38, 575–585 (1970).
    [CrossRef]
  21. P. J. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976).
  22. B. J. Berne, R. Pecora, in Dynamic Light Scattering with Applications to Chemistry, Biology, and Physics (Krieger, Malabar, Fla., 1990).
  23. W. Brown, ed., Dynamic Light Scattering: The Method and Some Applications (Clarendon, New York, 1993).
  24. G. G. Fuller, J. M. Rallison, R. L. Schmidt, L. G. Leal, “The measurement of velocity gradients in laminar flow by homodyne light-scattering spectroscopy,” J. Fluid Mech. 100, 555–575 (1980).
    [CrossRef]
  25. P. Tong, W. I. Goldburg, C. K. Chan, A. Sirivat, “Turbulent transition by photon-correlation spectroscopy,” Phys. Rev. A 37, 2125–2133 (1988).
    [CrossRef] [PubMed]
  26. M. Bertolotti, B. Crosignani, P. Di, Porto, D. Sette, “Light scattering by particles suspended in a turbulent fluid,” J. Phys. A 2, 126–128 (1969).
    [CrossRef]
  27. P. J. Bourke, J. Butterworth, L. E. Drain, P. A. Egelstaff, E. Jakeman, E. R. Pike, “A study of the spatial structure of turbulent flow by intensity-fluctuation spectroscopy,” J. Phys. A 3, 216–228 (1970).
    [CrossRef]
  28. T. Tanaka, C. Riva, I. Ben-Sira, “Blood velocity measurements in human retinal vessels,” Science 186, 830–831 (1974).
    [CrossRef] [PubMed]
  29. M. Stern, In vivo evaluation of microcirculation by coherent light scattering,” Nature (London) 254, 56–58 (1975).
    [CrossRef]
  30. R. Bonner, R. Nossal, “Model for laser Doppler measurements of blood flow in tissue,” Appl. Opt. 20, 2097–2107 (1981).
    [CrossRef] [PubMed]
  31. H. Z. Cummings, E. R. Pike, eds., Photon Correlation and Light-Beating Spectroscopy, Vol. 3 of NATO Advanced Study Institute Series B: Physics (Plenum, New York, 1974).
  32. D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
    [CrossRef] [PubMed]
  33. F. C. MacKintosh, S. John, “Diffusing-wave spectroscopy and multiple scattering of light in correlated random media,” Phys. Rev. B 40, 2382–2406 (1989).
    [CrossRef]
  34. G. Maret, P. E. Wolf, “Multiple light scattering from disordered media. The effect of Brownian motion of scatterers,” Z. Phys. B 65, 409–413 (1987).
    [CrossRef]
  35. A. Y. Val’kov, V. P. Romanov, “Characteristics of propagation and scattering of light in nematic liquid crystals,” Sov. Phys. JETP 63, 737–743 (1986) [Zh. Eksp. Teor. Fiz. 90, 1264–1274 (1986)].
  36. P. N. Pusey, J. M. Vaughan, “Light scattering and intensity fluctuation spectroscopy,” in Specialist Periodical Report, Vol. 2 of Dielectric and Related Molecular Processes. M. Davies, ed. (The Chemical Society, London, 1975).
  37. S. O. Rice, “Mathematical analysis of random noise,” in Noise and Stochastic Processes, N. Wax, ed. (Dover, New York, 1954), p. 133.
  38. 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]
  39. D. A. Boas, “Diffuse photon probes of structural and dynamical properties of turbid media: theory and biomedical applications,” Ph.D. dissertation (Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pa., 1996).
  40. D. A. Boas, I. V. Meglinsky, L. Zemany, L. E. Campbell, B. Chance, A. G. Yodh, “Diffusion of temporal field correlation with selected applications,” in Coherence-Domain Methods in Biomedical Optics, V. V. Tuchin, ed., Proc. SPIE2732, 34–46 (1996).
    [CrossRef]
  41. D. A. Weitz, D. J. Pine, P. N. Pusey, R. J. A. Tough, “Nondiffusive Brownian motion studied by diffusing-wave spectroscopy,” Phys. Rev. Lett. 63, 1747–1750 (1989).
    [CrossRef] [PubMed]
  42. X. Qiu, X. L. Wu, J. Z. Xue, D. J. Pine, D. A. Weitz, P. M. Chaikin, “Hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 65, 516–518 (1990).
    [CrossRef] [PubMed]
  43. P. D. Kaplan, A. G. Yodh, D. J. Pine, “Diffusion and structure in dense binary suspensions.” Phys. Rev. Lett. 68, 393–396 (1992).
    [CrossRef] [PubMed]
  44. J. X. Zhu, D. J. Durian, J. Muller, D. A. Weitz, D. J. Pine, “Scaling of transient hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 68, 2559–2562 (1992).
    [CrossRef] [PubMed]
  45. M. H. Kao, A. G. Yodh, D. J. Pine, “Observation of Brownian motion on the time scale of hydrodynamic interactions,” Phys. Rev. Lett. 70, 242–245 (1993).
    [CrossRef] [PubMed]
  46. S. J. Nilsen, A. P. Gast, “The influence of structure on diffusion in screened Coulombic suspensions,” J. Chem. Phys. 101, 4975–4985 (1994).
    [CrossRef]
  47. A. J. C. Ladd, H. Gang, J. X. Zhu, D. A. Weitz, “Time-dependent collective diffusion of colloidal particles,” Phys. Rev. Lett. 74, 318–321 (1995).
    [CrossRef] [PubMed]
  48. D. J. Durian, D. A. Weitz, D. J. Pine, “Multiple light scattering probes of foam structure and dynamics,” Science 252, 686–688 (1991).
    [CrossRef] [PubMed]
  49. A. D. Gopal, D. J. Durian, “Nonlinear bubble dynamics in a slowly driven foam,” Phys. Rev. Lett. 75, 2610–2613 (1995).
    [CrossRef] [PubMed]
  50. H. Gang, A. H. Krall, D. A. Weitz, “Shape fluctuations of interacting fluid droplets,” Phys. Rev. Lett. 73, 3435–3438 (1994).
    [CrossRef] [PubMed]
  51. P. D. Kaplan, A. G. Yodh, D. F. Townsend, “Noninvasive study of gel formation in polymer-stabilized dense colloids using multiply scattered light,” J. Colloid Interface Sci. 155, 319–324 (1993).
    [CrossRef]
  52. J. D. Briers, “Laser Doppler and time-varying speckle: a reconciliation,” J. Opt. Soc. Am. A 13, 345–350 (1996).
    [CrossRef]
  53. H. Z. Cummings, H. L. Swinney, “Light beating spectroscopy,” Prog. Opt. 8, 133–200 (1970).
    [CrossRef]
  54. P. N. Pusey, J. M. Vaughan, D. V. Willets, “Effect of spatial incoherence of the laser in photon-counting spectroscopy,” J. Opt. Soc. Am. 73, 1012–1017 (1983).
    [CrossRef]
  55. T. Bellini, M. A. Glaser, N. A. Clark, V. Degiorgio, “Effects of finite laser coherence in quasielastic multiple scattering,” Phys. Rev. A 44, 5215–5223 (1991).
    [CrossRef] [PubMed]
  56. X. L. Wu, D. J. Pine, P. M. Chaikin, J. S. Huang, D. A. Weitz, “Diffusing-wave spectroscopy in a shear flow,” J. Opt. Soc. Am. B 7, 15–20 (1990).
    [CrossRef]
  57. D. J. Pine, D. A. Weitz, J. X. Zhu, E. Herbolzheimer, “Diffusing-wave spectroscopy: dynamic light scattering in the multiple scattering limit,” J. Phys. (Paris) 51, 2101–2127 (1990).
    [CrossRef]
  58. K. Katayama, G. Nishimura, M. Kinjo, M. Tamura, “Absorbance measurements in turbid media by the photon correlation method,” Appl. Opt. 34, 7419–7427 (1995).
    [CrossRef] [PubMed]
  59. G. Nishimura, K. Katayama, M. Kinjo, M. Tamura, “Diffusing-wave absorption spectroscopy in the homogeneous turbid media,” Opt. Commun. 128, 99–107 (1996).
    [CrossRef]
  60. M. J. Stephen, “Temporal fluctuations in wave propagation in random media,” Phys. Rev. B 37, 1–5 (1988).
    [CrossRef]
  61. B. J. Ackerson, R. L. Dougherty, N. M. Reguigui, U. Nobbman, “Correlation transfer: application of radiative transfer solution methods to photon correlation problems,” J. Thermophys. Heat Transfer 6, 577–588 (1992).
    [CrossRef]
  62. R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorri-Nowkoorani, U. Nobbmann, “Correlation transfer: development and application,” J. Quant. Spectrosc. Radiat. Transfer. 52, 713–727 (1994).
    [CrossRef]
  63. S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).
  64. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).
  65. H. S. Carslaw, J. Jaeger, Conduction of Heat in Solids (Oxford U. Press, New York, 1986).
  66. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  67. J. Z. Xue, D. J. Pine, S. T. Milner, X. L. Wu, P. M. Chaikin, “Nonergodicity and light scattering from polymer gels,” Phys. Rev. A 46, 6550–6563 (1992).
    [CrossRef] [PubMed]
  68. K. Schatzel, “Accuracy of photon correlation measurements on nonergodic samples,” Appl. Opt. 32, 3880–3885 (1993).
    [CrossRef] [PubMed]
  69. J. G. H. Joosten, E. T. F. Gelade, P. N. Pusey, “Dynamic light scattering by nonergodic media: Brownian particles trapped in polyacrylamide gels,” Phys. Rev. A 42, 2161–2175 (1990).
    [CrossRef] [PubMed]
  70. P. N. Pusey, W. Van Megen, Dynamic light scattering by non-ergodic media,” Physica A 157, 705–742 (1989).
    [CrossRef]
  71. E. R. Van Keuren, H. Wiese, D. Horn, “Diffusing-wave spectroscopy in concentrated latex dispersions: an investigation using single-mode fibers,” Colloids Surf. A 77, 29–37 (1993).
    [CrossRef]
  72. J. Ricka, “Dynamic light scattering with single-mode and multimode fibers,” Appl. Opt. 32, 2860–2875 (1993).
    [CrossRef]
  73. R. G. Brown, “Dynamic light scattering using monomode optical fibers,” Appl. Opt. 26, 4846–4851 (1987).
    [CrossRef] [PubMed]
  74. A. A. Middleton, D. S. Fisher, “Discrete scatterers and autocorrelations of multiply scattered light,” Phys. Rev. B 43, 5934–5938 (1991).
    [CrossRef]
  75. D. J. Durian, “Accuracy of diffusing-wave spectroscopy theories,” Phys. Rev. E 51, 3350–3358 (1995).
    [CrossRef]
  76. M. H. Koelink, F. F. M. de Mul, J. Greve, R. Graaff, A. C. M. Dassel, J. G. Aarnoudse, “Laser Doppler blood flowmetry using two wavelengths: Monte Carlo simulations and measurements,” Appl. Opt. 33, 3549–3558 (1994).
    [CrossRef] [PubMed]
  77. R. Graaff, M. H. Koelink, F. F. M. de Mul, W. G. Zijlstra, A. C. M. Dassel, J. G. Aarnoudse, “Condensed Monte Carlo simulations for the description of light transport,” Appl. Opt. 32, 426–434 (1993).
    [CrossRef] [PubMed]
  78. S. L. Jacques, L. Wang, “Monte Carlo modeling of light transport in tissues,” in Optical-Thermal Response of Laser-Irradiated Tissue, A. J. Welch, M. J. C. van Gemert, eds. (Plenum, New York, 1995), pp. 73–100.
  79. L. Wang, S. L. Jacques, L. Zheng, “MCML-Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Prog. Biomed. 47, 131–146 (1995).
  80. L. G. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
    [CrossRef]
  81. D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneties within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
    [CrossRef]
  82. P. N. den Outer, T. M. Nieuwenhuizen, A. Lagendijk, “Location of objects in multiple-scattering media,” J. Opt. Soc. Am. A 10, 1209–1218 (1993).
    [CrossRef]
  83. R. C. Haskell, L. O. Svaasand, T. Tsay, T. Feng, M. S. McAdams, B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11, 2727–2741 (1994).
    [CrossRef]
  84. A. C. Kak, M. Slaney, in Principles of Computerized Tomographic Imaging (Institute of Electrical and Electronics Engineers, New York, 1988).
  85. R. Nossal, S. H. Chen, C. C. Lai, “Use of laser scattering for quantitative determinations of bacterial motility,” Opt. Commun. 4, 35–39 (1971).
    [CrossRef]
  86. D. Bicout, R. Maynard, “Diffusing wave spectroscopy in inhomogeneous flows,” Physica A 199, 387–411 (1993).
    [CrossRef]
  87. D. Bicout, G. Maret, “Multiple light scattering in Taylor–Couette flow,” Physica A 210, 87–112 (1994).
    [CrossRef]
  88. D. J. Bicout, R. Maynard, “Multiple light scattering in turbulent flow,” Physica B 204, 20–26 (1995).
    [CrossRef]
  89. D. Bicout, “Non-Newtonian behavior of colloidal suspensions from multiple light scattering,” Phys. Lett. A 180, 375–378 (1993).
    [CrossRef]
  90. The Intralipid used here can be obtained from Kabi Pharmacia, Clayton, North Carolina.
  91. R. Nossal, R. F. Bonner, G. H. Weiss, “Influence of path length on remote optical sensing of properties of biological tissue,” Appl. Opt. 28, 2238–2244 (1989).
    [CrossRef] [PubMed]
  92. H. A. Green, E. E. Burd, N. S. Nishioka, C. C. Compton, “Skin-graft take and healing following 193-nm excimer, continuous-wave carbon dioxide (CO2), pulsed CO2, or pulsed holmium-YAG laser-ablation of the graft bed,” Arch. Dermatol. 129, 979–988 (1993).
  93. K. M. Case, P. F. Zweifel, Linear Transport Theory (Addison-Wesley, Reading, Mass., 1967).
  94. B. Davison, J. B. Sykes, Neutron Transport Theory (Oxford U. Press, London, 1957).
  95. S. Glasstone, M. C. Edlund, The Elements of Nuclear Reactor Theory (Van Nostrand, Princeton, N.J., 1952).
  96. J. M. Kaltenbach, M. Kaschke, “Frequency and time domain modelling of light transport in random media,” in Medical Optical Imaging: Functional Imaging and Monitoring, Institute Series of SPIE Optical Engineering (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 65–86.
  97. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), Chap. 3.6.
  98. G. B. Arfken, in Mathematical Methods for Physicists (Academic, Orlando, Fla., 1985), Chap. 12.9.

1996

G. Nishimura, K. Katayama, M. Kinjo, M. Tamura, “Diffusing-wave absorption spectroscopy in the homogeneous turbid media,” Opt. Commun. 128, 99–107 (1996).
[CrossRef]

J. D. Briers, “Laser Doppler and time-varying speckle: a reconciliation,” J. Opt. Soc. Am. A 13, 345–350 (1996).
[CrossRef]

1995

D. J. Bicout, R. Maynard, “Multiple light scattering in turbulent flow,” Physica B 204, 20–26 (1995).
[CrossRef]

K. Katayama, G. Nishimura, M. Kinjo, M. Tamura, “Absorbance measurements in turbid media by the photon correlation method,” Appl. Opt. 34, 7419–7427 (1995).
[CrossRef] [PubMed]

D. J. Durian, “Accuracy of diffusing-wave spectroscopy theories,” Phys. Rev. E 51, 3350–3358 (1995).
[CrossRef]

L. Wang, S. L. Jacques, L. Zheng, “MCML-Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Prog. Biomed. 47, 131–146 (1995).

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. J. C. Ladd, H. Gang, J. X. Zhu, D. A. Weitz, “Time-dependent collective diffusion of colloidal particles,” Phys. Rev. Lett. 74, 318–321 (1995).
[CrossRef] [PubMed]

A. D. Gopal, D. J. Durian, “Nonlinear bubble dynamics in a slowly driven foam,” Phys. Rev. Lett. 75, 2610–2613 (1995).
[CrossRef] [PubMed]

A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48, 34–40 (1995).
[CrossRef]

1994

H. Gang, A. H. Krall, D. A. Weitz, “Shape fluctuations of interacting fluid droplets,” Phys. Rev. Lett. 73, 3435–3438 (1994).
[CrossRef] [PubMed]

S. J. Nilsen, A. P. Gast, “The influence of structure on diffusion in screened Coulombic suspensions,” J. Chem. Phys. 101, 4975–4985 (1994).
[CrossRef]

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneties within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef]

R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorri-Nowkoorani, U. Nobbmann, “Correlation transfer: development and application,” J. Quant. Spectrosc. Radiat. Transfer. 52, 713–727 (1994).
[CrossRef]

M. H. Koelink, F. F. M. de Mul, J. Greve, R. Graaff, A. C. M. Dassel, J. G. Aarnoudse, “Laser Doppler blood flowmetry using two wavelengths: Monte Carlo simulations and measurements,” Appl. Opt. 33, 3549–3558 (1994).
[CrossRef] [PubMed]

R. C. Haskell, L. O. Svaasand, T. Tsay, T. Feng, M. S. McAdams, B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11, 2727–2741 (1994).
[CrossRef]

D. Bicout, G. Maret, “Multiple light scattering in Taylor–Couette flow,” Physica A 210, 87–112 (1994).
[CrossRef]

1993

P. N. den Outer, T. M. Nieuwenhuizen, A. Lagendijk, “Location of objects in multiple-scattering media,” J. Opt. Soc. Am. A 10, 1209–1218 (1993).
[CrossRef]

D. Bicout, “Non-Newtonian behavior of colloidal suspensions from multiple light scattering,” Phys. Lett. A 180, 375–378 (1993).
[CrossRef]

H. A. Green, E. E. Burd, N. S. Nishioka, C. C. Compton, “Skin-graft take and healing following 193-nm excimer, continuous-wave carbon dioxide (CO2), pulsed CO2, or pulsed holmium-YAG laser-ablation of the graft bed,” Arch. Dermatol. 129, 979–988 (1993).

K. Schatzel, “Accuracy of photon correlation measurements on nonergodic samples,” Appl. Opt. 32, 3880–3885 (1993).
[CrossRef] [PubMed]

J. Ricka, “Dynamic light scattering with single-mode and multimode fibers,” Appl. Opt. 32, 2860–2875 (1993).
[CrossRef]

R. Graaff, M. H. Koelink, F. F. M. de Mul, W. G. Zijlstra, A. C. M. Dassel, J. G. Aarnoudse, “Condensed Monte Carlo simulations for the description of light transport,” Appl. Opt. 32, 426–434 (1993).
[CrossRef] [PubMed]

B. J. Tromberg, L. O. Svaasand, T. Tsay, R. C. Haskell, “Properties of photon density waves in multiple-scattering media,” Appl. Opt. 32, 607–616 (1993).
[CrossRef] [PubMed]

D. Bicout, R. Maynard, “Diffusing wave spectroscopy in inhomogeneous flows,” Physica A 199, 387–411 (1993).
[CrossRef]

E. R. Van Keuren, H. Wiese, D. Horn, “Diffusing-wave spectroscopy in concentrated latex dispersions: an investigation using single-mode fibers,” Colloids Surf. A 77, 29–37 (1993).
[CrossRef]

M. H. Kao, A. G. Yodh, D. J. Pine, “Observation of Brownian motion on the time scale of hydrodynamic interactions,” Phys. Rev. Lett. 70, 242–245 (1993).
[CrossRef] [PubMed]

P. D. Kaplan, A. G. Yodh, D. F. Townsend, “Noninvasive study of gel formation in polymer-stabilized dense colloids using multiply scattered light,” J. Colloid Interface Sci. 155, 319–324 (1993).
[CrossRef]

J. W. Severinghaus, “History and recent developments in pulse oximetry,” Scand. J. Clin. Lab. Invest. 53, 105–111 (1993).
[PubMed]

S. P. Gopinath, C. S. Robertson, R. G. Grossman, B. Chance, “Near-infrared spectroscopic localization of intracranial hematomas,” J. Neurosurg. 79, 43–47 (1993).
[CrossRef]

A. D. Edwards, C. Richardson, P. van der Zee, M. Cope, D. T. Delpy, “Measurement of hemoglobin flow and blood flow by near-infrared spectroscopy,” J. Appl. Physiol. 75, 1884–1889 (1993).
[PubMed]

1992

B. C. Wilson, E. M. Sevick, M. S. Patterson, B. Chance, “Time-dependent optical spectroscopy and imaging for biomedical applications,” Proc. IEEE 80, 918–930 (1992).
[CrossRef]

P. D. Kaplan, A. G. Yodh, D. J. Pine, “Diffusion and structure in dense binary suspensions.” Phys. Rev. Lett. 68, 393–396 (1992).
[CrossRef] [PubMed]

J. X. Zhu, D. J. Durian, J. Muller, D. A. Weitz, D. J. Pine, “Scaling of transient hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 68, 2559–2562 (1992).
[CrossRef] [PubMed]

B. J. Ackerson, R. L. Dougherty, N. M. Reguigui, U. Nobbman, “Correlation transfer: application of radiative transfer solution methods to photon correlation problems,” J. Thermophys. Heat Transfer 6, 577–588 (1992).
[CrossRef]

J. Z. Xue, D. J. Pine, S. T. Milner, X. L. Wu, P. M. Chaikin, “Nonergodicity and light scattering from polymer gels,” Phys. Rev. A 46, 6550–6563 (1992).
[CrossRef] [PubMed]

1991

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

A. A. Middleton, D. S. Fisher, “Discrete scatterers and autocorrelations of multiply scattered light,” Phys. Rev. B 43, 5934–5938 (1991).
[CrossRef]

D. J. Durian, D. A. Weitz, D. J. Pine, “Multiple light scattering probes of foam structure and dynamics,” Science 252, 686–688 (1991).
[CrossRef] [PubMed]

J. M. Schmitt, “Simple photon diffusion analysis of the effects of multiple scattering on pulse oximetry,” IEEE Trans. Biomed. Eng. 38, 1194–1203 (1991).
[CrossRef] [PubMed]

1990

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

X. Qiu, X. L. Wu, J. Z. Xue, D. J. Pine, D. A. Weitz, P. M. Chaikin, “Hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 65, 516–518 (1990).
[CrossRef] [PubMed]

D. J. Pine, D. A. Weitz, J. X. Zhu, E. Herbolzheimer, “Diffusing-wave spectroscopy: dynamic light scattering in the multiple scattering limit,” J. Phys. (Paris) 51, 2101–2127 (1990).
[CrossRef]

J. G. H. Joosten, E. T. F. Gelade, P. N. Pusey, “Dynamic light scattering by nonergodic media: Brownian particles trapped in polyacrylamide gels,” Phys. Rev. A 42, 2161–2175 (1990).
[CrossRef] [PubMed]

X. L. Wu, D. J. Pine, P. M. Chaikin, J. S. Huang, D. A. Weitz, “Diffusing-wave spectroscopy in a shear flow,” J. Opt. Soc. Am. B 7, 15–20 (1990).
[CrossRef]

1989

R. Nossal, R. F. Bonner, G. H. Weiss, “Influence of path length on remote optical sensing of properties of biological tissue,” Appl. Opt. 28, 2238–2244 (1989).
[CrossRef] [PubMed]

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

P. N. Pusey, W. Van Megen, Dynamic light scattering by non-ergodic media,” Physica A 157, 705–742 (1989).
[CrossRef]

D. A. Weitz, D. J. Pine, P. N. Pusey, R. J. A. Tough, “Nondiffusive Brownian motion studied by diffusing-wave spectroscopy,” Phys. Rev. Lett. 63, 1747–1750 (1989).
[CrossRef] [PubMed]

F. C. MacKintosh, S. John, “Diffusing-wave spectroscopy and multiple scattering of light in correlated random media,” Phys. Rev. B 40, 2382–2406 (1989).
[CrossRef]

1988

D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
[CrossRef] [PubMed]

P. Tong, W. I. Goldburg, C. K. Chan, A. Sirivat, “Turbulent transition by photon-correlation spectroscopy,” Phys. Rev. A 37, 2125–2133 (1988).
[CrossRef] [PubMed]

M. J. Stephen, “Temporal fluctuations in wave propagation in random media,” Phys. Rev. B 37, 1–5 (1988).
[CrossRef]

1987

R. G. Brown, “Dynamic light scattering using monomode optical fibers,” Appl. Opt. 26, 4846–4851 (1987).
[CrossRef] [PubMed]

M. R. Neuman, “Pulse oximetry: physical principles technical realization and present limitations,” Adv. Exp. Med. Biol. 220, 135–144 (1987).

G. Maret, P. E. Wolf, “Multiple light scattering from disordered media. The effect of Brownian motion of scatterers,” Z. Phys. B 65, 409–413 (1987).
[CrossRef]

1986

A. Y. Val’kov, V. P. Romanov, “Characteristics of propagation and scattering of light in nematic liquid crystals,” Sov. Phys. JETP 63, 737–743 (1986) [Zh. Eksp. Teor. Fiz. 90, 1264–1274 (1986)].

1983

1981

1980

G. G. Fuller, J. M. Rallison, R. L. Schmidt, L. G. Leal, “The measurement of velocity gradients in laminar flow by homodyne light-scattering spectroscopy,” J. Fluid Mech. 100, 555–575 (1980).
[CrossRef]

1977

F. F. Jobsis, “Noninvasive, infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters,” Science 198, 1264–1267 (1977).
[CrossRef] [PubMed]

1975

M. Stern, In vivo evaluation of microcirculation by coherent light scattering,” Nature (London) 254, 56–58 (1975).
[CrossRef]

1974

T. Tanaka, C. Riva, I. Ben-Sira, “Blood velocity measurements in human retinal vessels,” Science 186, 830–831 (1974).
[CrossRef] [PubMed]

1971

R. Nossal, S. H. Chen, C. C. Lai, “Use of laser scattering for quantitative determinations of bacterial motility,” Opt. Commun. 4, 35–39 (1971).
[CrossRef]

1970

P. J. Bourke, J. Butterworth, L. E. Drain, P. A. Egelstaff, E. Jakeman, E. R. Pike, “A study of the spatial structure of turbulent flow by intensity-fluctuation spectroscopy,” J. Phys. A 3, 216–228 (1970).
[CrossRef]

N. A. Clark, J. H. Lunacek, G. B. Benedek, “A study of Brownian motion using light scattering,” Am. J. Phys. 38, 575–585 (1970).
[CrossRef]

H. Z. Cummings, H. L. Swinney, “Light beating spectroscopy,” Prog. Opt. 8, 133–200 (1970).
[CrossRef]

1969

M. Bertolotti, B. Crosignani, P. Di, Porto, D. Sette, “Light scattering by particles suspended in a turbulent fluid,” J. Phys. A 2, 126–128 (1969).
[CrossRef]

1942

G. A. Millikan, “The oximeter, an instrument for measuring continuously the oxygen saturation of arterial blood in man,” Rev. Sci. Instrum. 13, 434–444 (1942).
[CrossRef]

1941

L. G. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

1937

G. A. Millikan, “Experiments on muscle haemoglobin in vivo: the instantaneous measurement of muscle metabolism,” Proc. R. Soc. London, Sect. B 129, 218–241 (1937).
[CrossRef]

Aarnoudse, J. G.

Ackerson, B. J.

R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorri-Nowkoorani, U. Nobbmann, “Correlation transfer: development and application,” J. Quant. Spectrosc. Radiat. Transfer. 52, 713–727 (1994).
[CrossRef]

B. J. Ackerson, R. L. Dougherty, N. M. Reguigui, U. Nobbman, “Correlation transfer: application of radiative transfer solution methods to photon correlation problems,” J. Thermophys. Heat Transfer 6, 577–588 (1992).
[CrossRef]

Arfken, G. B.

G. B. Arfken, in Mathematical Methods for Physicists (Academic, Orlando, Fla., 1985), Chap. 12.9.

Arridge, S. R.

See related studies by S. R. Arridge, et al. J. P. Kaltenbach, et al. R. L. Barbour et al., in Medical Optical Tomography: Functional Imaging and Monitoring, G. Müller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, P. van der Zee, eds., Institute Series of SPIE Optical Engineering (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 31–143.

S. R. Arridge, P. van der Zee, M. Cope, D. T. Delpy, “Reconstruction methods for infra-red absorption imaging,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, ed., Proc. SPIE1431, 204–215 (1991).
[CrossRef]

Barbour, R. L.

See related studies by S. R. Arridge, et al. J. P. Kaltenbach, et al. R. L. Barbour et al., in Medical Optical Tomography: Functional Imaging and Monitoring, G. Müller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, P. van der Zee, eds., Institute Series of SPIE Optical Engineering (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 31–143.

Bellini, T.

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

Benedek, G. B.

N. A. Clark, J. H. Lunacek, G. B. Benedek, “A study of Brownian motion using light scattering,” Am. J. Phys. 38, 575–585 (1970).
[CrossRef]

Ben-Sira, I.

T. Tanaka, C. Riva, I. Ben-Sira, “Blood velocity measurements in human retinal vessels,” Science 186, 830–831 (1974).
[CrossRef] [PubMed]

Berne, B. J.

B. J. Berne, R. Pecora, in Dynamic Light Scattering with Applications to Chemistry, Biology, and Physics (Krieger, Malabar, Fla., 1990).

Berne, P. J.

P. J. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976).

Bertolotti, M.

M. Bertolotti, B. Crosignani, P. Di, Porto, D. Sette, “Light scattering by particles suspended in a turbulent fluid,” J. Phys. A 2, 126–128 (1969).
[CrossRef]

Bicout, D.

D. Bicout, G. Maret, “Multiple light scattering in Taylor–Couette flow,” Physica A 210, 87–112 (1994).
[CrossRef]

D. Bicout, “Non-Newtonian behavior of colloidal suspensions from multiple light scattering,” Phys. Lett. A 180, 375–378 (1993).
[CrossRef]

D. Bicout, R. Maynard, “Diffusing wave spectroscopy in inhomogeneous flows,” Physica A 199, 387–411 (1993).
[CrossRef]

Bicout, D. J.

D. J. Bicout, R. Maynard, “Multiple light scattering in turbulent flow,” Physica B 204, 20–26 (1995).
[CrossRef]

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]

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneties within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef]

D. A. Boas, I. V. Meglinsky, L. Zemany, L. E. Campbell, B. Chance, A. G. Yodh, “Diffusion of temporal field correlation with selected applications,” in Coherence-Domain Methods in Biomedical Optics, V. V. Tuchin, ed., Proc. SPIE2732, 34–46 (1996).
[CrossRef]

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

Bonner, R.

Bonner, R. F.

Bourke, P. J.

P. J. Bourke, J. Butterworth, L. E. Drain, P. A. Egelstaff, E. Jakeman, E. R. Pike, “A study of the spatial structure of turbulent flow by intensity-fluctuation spectroscopy,” J. Phys. A 3, 216–228 (1970).
[CrossRef]

Briers, J. D.

Brown, R. G.

Burd, E. E.

H. A. Green, E. E. Burd, N. S. Nishioka, C. C. Compton, “Skin-graft take and healing following 193-nm excimer, continuous-wave carbon dioxide (CO2), pulsed CO2, or pulsed holmium-YAG laser-ablation of the graft bed,” Arch. Dermatol. 129, 979–988 (1993).

Butterworth, J.

P. J. Bourke, J. Butterworth, L. E. Drain, P. A. Egelstaff, E. Jakeman, E. R. Pike, “A study of the spatial structure of turbulent flow by intensity-fluctuation spectroscopy,” J. Phys. A 3, 216–228 (1970).
[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]

D. A. Boas, I. V. Meglinsky, L. Zemany, L. E. Campbell, B. Chance, A. G. Yodh, “Diffusion of temporal field correlation with selected applications,” in Coherence-Domain Methods in Biomedical Optics, V. V. Tuchin, ed., Proc. SPIE2732, 34–46 (1996).
[CrossRef]

Carslaw, H. S.

H. S. Carslaw, J. Jaeger, Conduction of Heat in Solids (Oxford U. Press, New York, 1986).

Case, K. M.

K. M. Case, P. F. Zweifel, Linear Transport Theory (Addison-Wesley, Reading, Mass., 1967).

Chaikin, P. M.

J. Z. Xue, D. J. Pine, S. T. Milner, X. L. Wu, P. M. Chaikin, “Nonergodicity and light scattering from polymer gels,” Phys. Rev. A 46, 6550–6563 (1992).
[CrossRef] [PubMed]

X. Qiu, X. L. Wu, J. Z. Xue, D. J. Pine, D. A. Weitz, P. M. Chaikin, “Hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 65, 516–518 (1990).
[CrossRef] [PubMed]

X. L. Wu, D. J. Pine, P. M. Chaikin, J. S. Huang, D. A. Weitz, “Diffusing-wave spectroscopy in a shear flow,” J. Opt. Soc. Am. B 7, 15–20 (1990).
[CrossRef]

D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
[CrossRef] [PubMed]

Chan, C. K.

P. Tong, W. I. Goldburg, C. K. Chan, A. Sirivat, “Turbulent transition by photon-correlation spectroscopy,” Phys. Rev. A 37, 2125–2133 (1988).
[CrossRef] [PubMed]

Chance, B.

A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48, 34–40 (1995).
[CrossRef]

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneties within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef]

S. P. Gopinath, C. S. Robertson, R. G. Grossman, B. Chance, “Near-infrared spectroscopic localization of intracranial hematomas,” J. Neurosurg. 79, 43–47 (1993).
[CrossRef]

B. C. Wilson, E. M. Sevick, M. S. Patterson, B. Chance, “Time-dependent optical spectroscopy and imaging for biomedical applications,” Proc. IEEE 80, 918–930 (1992).
[CrossRef]

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

D. A. Boas, I. V. Meglinsky, L. Zemany, L. E. Campbell, B. Chance, A. G. Yodh, “Diffusion of temporal field correlation with selected applications,” in Coherence-Domain Methods in Biomedical Optics, V. V. Tuchin, ed., Proc. SPIE2732, 34–46 (1996).
[CrossRef]

Chandrasekhar, S.

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

Chen, S. H.

R. Nossal, S. H. Chen, C. C. Lai, “Use of laser scattering for quantitative determinations of bacterial motility,” Opt. Commun. 4, 35–39 (1971).
[CrossRef]

Cheong, W. F.

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Clark, N. A.

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

N. A. Clark, J. H. Lunacek, G. B. Benedek, “A study of Brownian motion using light scattering,” Am. J. Phys. 38, 575–585 (1970).
[CrossRef]

Compton, C. C.

H. A. Green, E. E. Burd, N. S. Nishioka, C. C. Compton, “Skin-graft take and healing following 193-nm excimer, continuous-wave carbon dioxide (CO2), pulsed CO2, or pulsed holmium-YAG laser-ablation of the graft bed,” Arch. Dermatol. 129, 979–988 (1993).

Cope, M.

A. D. Edwards, C. Richardson, P. van der Zee, M. Cope, D. T. Delpy, “Measurement of hemoglobin flow and blood flow by near-infrared spectroscopy,” J. Appl. Physiol. 75, 1884–1889 (1993).
[PubMed]

S. R. Arridge, P. van der Zee, M. Cope, D. T. Delpy, “Reconstruction methods for infra-red absorption imaging,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, ed., Proc. SPIE1431, 204–215 (1991).
[CrossRef]

Crosignani, B.

M. Bertolotti, B. Crosignani, P. Di, Porto, D. Sette, “Light scattering by particles suspended in a turbulent fluid,” J. Phys. A 2, 126–128 (1969).
[CrossRef]

Cummings, H. Z.

H. Z. Cummings, H. L. Swinney, “Light beating spectroscopy,” Prog. Opt. 8, 133–200 (1970).
[CrossRef]

Dassel, A. C. M.

Davison, B.

B. Davison, J. B. Sykes, Neutron Transport Theory (Oxford U. Press, London, 1957).

de Mul, F. F. M.

Degiorgio, V.

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

Delpy, D. T.

A. D. Edwards, C. Richardson, P. van der Zee, M. Cope, D. T. Delpy, “Measurement of hemoglobin flow and blood flow by near-infrared spectroscopy,” J. Appl. Physiol. 75, 1884–1889 (1993).
[PubMed]

S. R. Arridge, P. van der Zee, M. Cope, D. T. Delpy, “Reconstruction methods for infra-red absorption imaging,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, ed., Proc. SPIE1431, 204–215 (1991).
[CrossRef]

den Outer, P. N.

Di, P.

M. Bertolotti, B. Crosignani, P. Di, Porto, D. Sette, “Light scattering by particles suspended in a turbulent fluid,” J. Phys. A 2, 126–128 (1969).
[CrossRef]

Dorri-Nowkoorani, F.

R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorri-Nowkoorani, U. Nobbmann, “Correlation transfer: development and application,” J. Quant. Spectrosc. Radiat. Transfer. 52, 713–727 (1994).
[CrossRef]

Dougherty, R. L.

R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorri-Nowkoorani, U. Nobbmann, “Correlation transfer: development and application,” J. Quant. Spectrosc. Radiat. Transfer. 52, 713–727 (1994).
[CrossRef]

B. J. Ackerson, R. L. Dougherty, N. M. Reguigui, U. Nobbman, “Correlation transfer: application of radiative transfer solution methods to photon correlation problems,” J. Thermophys. Heat Transfer 6, 577–588 (1992).
[CrossRef]

Drain, L. E.

P. J. Bourke, J. Butterworth, L. E. Drain, P. A. Egelstaff, E. Jakeman, E. R. Pike, “A study of the spatial structure of turbulent flow by intensity-fluctuation spectroscopy,” J. Phys. A 3, 216–228 (1970).
[CrossRef]

L. E. Drain, The Laser Doppler Technique (Wiley, New York, 1980).

Durian, D. J.

A. D. Gopal, D. J. Durian, “Nonlinear bubble dynamics in a slowly driven foam,” Phys. Rev. Lett. 75, 2610–2613 (1995).
[CrossRef] [PubMed]

D. J. Durian, “Accuracy of diffusing-wave spectroscopy theories,” Phys. Rev. E 51, 3350–3358 (1995).
[CrossRef]

J. X. Zhu, D. J. Durian, J. Muller, D. A. Weitz, D. J. Pine, “Scaling of transient hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 68, 2559–2562 (1992).
[CrossRef] [PubMed]

D. J. Durian, D. A. Weitz, D. J. Pine, “Multiple light scattering probes of foam structure and dynamics,” Science 252, 686–688 (1991).
[CrossRef] [PubMed]

Edlund, M. C.

S. Glasstone, M. C. Edlund, The Elements of Nuclear Reactor Theory (Van Nostrand, Princeton, N.J., 1952).

Edwards, A. D.

A. D. Edwards, C. Richardson, P. van der Zee, M. Cope, D. T. Delpy, “Measurement of hemoglobin flow and blood flow by near-infrared spectroscopy,” J. Appl. Physiol. 75, 1884–1889 (1993).
[PubMed]

Egelstaff, P. A.

P. J. Bourke, J. Butterworth, L. E. Drain, P. A. Egelstaff, E. Jakeman, E. R. Pike, “A study of the spatial structure of turbulent flow by intensity-fluctuation spectroscopy,” J. Phys. A 3, 216–228 (1970).
[CrossRef]

Feng, T.

Fisher, D. S.

A. A. Middleton, D. S. Fisher, “Discrete scatterers and autocorrelations of multiply scattered light,” Phys. Rev. B 43, 5934–5938 (1991).
[CrossRef]

Fuller, G. G.

G. G. Fuller, J. M. Rallison, R. L. Schmidt, L. G. Leal, “The measurement of velocity gradients in laminar flow by homodyne light-scattering spectroscopy,” J. Fluid Mech. 100, 555–575 (1980).
[CrossRef]

Gang, H.

A. J. C. Ladd, H. Gang, J. X. Zhu, D. A. Weitz, “Time-dependent collective diffusion of colloidal particles,” Phys. Rev. Lett. 74, 318–321 (1995).
[CrossRef] [PubMed]

H. Gang, A. H. Krall, D. A. Weitz, “Shape fluctuations of interacting fluid droplets,” Phys. Rev. Lett. 73, 3435–3438 (1994).
[CrossRef] [PubMed]

Gast, A. P.

S. J. Nilsen, A. P. Gast, “The influence of structure on diffusion in screened Coulombic suspensions,” J. Chem. Phys. 101, 4975–4985 (1994).
[CrossRef]

Gelade, E. T. F.

J. G. H. Joosten, E. T. F. Gelade, P. N. Pusey, “Dynamic light scattering by nonergodic media: Brownian particles trapped in polyacrylamide gels,” Phys. Rev. A 42, 2161–2175 (1990).
[CrossRef] [PubMed]

Glaser, M. A.

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

Glasstone, S.

S. Glasstone, M. C. Edlund, The Elements of Nuclear Reactor Theory (Van Nostrand, Princeton, N.J., 1952).

Goldburg, W. I.

P. Tong, W. I. Goldburg, C. K. Chan, A. Sirivat, “Turbulent transition by photon-correlation spectroscopy,” Phys. Rev. A 37, 2125–2133 (1988).
[CrossRef] [PubMed]

Gopal, A. D.

A. D. Gopal, D. J. Durian, “Nonlinear bubble dynamics in a slowly driven foam,” Phys. Rev. Lett. 75, 2610–2613 (1995).
[CrossRef] [PubMed]

Gopinath, S. P.

S. P. Gopinath, C. S. Robertson, R. G. Grossman, B. Chance, “Near-infrared spectroscopic localization of intracranial hematomas,” J. Neurosurg. 79, 43–47 (1993).
[CrossRef]

Graaff, R.

Green, H. A.

H. A. Green, E. E. Burd, N. S. Nishioka, C. C. Compton, “Skin-graft take and healing following 193-nm excimer, continuous-wave carbon dioxide (CO2), pulsed CO2, or pulsed holmium-YAG laser-ablation of the graft bed,” Arch. Dermatol. 129, 979–988 (1993).

Greenstein, J. L.

L. G. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Greve, J.

Grossman, R. G.

S. P. Gopinath, C. S. Robertson, R. G. Grossman, B. Chance, “Near-infrared spectroscopic localization of intracranial hematomas,” J. Neurosurg. 79, 43–47 (1993).
[CrossRef]

Haskell, R. C.

Henyey, L. G.

L. G. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Herbolzheimer, E.

D. J. Pine, D. A. Weitz, J. X. Zhu, E. Herbolzheimer, “Diffusing-wave spectroscopy: dynamic light scattering in the multiple scattering limit,” J. Phys. (Paris) 51, 2101–2127 (1990).
[CrossRef]

D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
[CrossRef] [PubMed]

Horn, D.

E. R. Van Keuren, H. Wiese, D. Horn, “Diffusing-wave spectroscopy in concentrated latex dispersions: an investigation using single-mode fibers,” Colloids Surf. A 77, 29–37 (1993).
[CrossRef]

Huang, J. S.

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), Chap. 3.6.

Jacques, S. L.

L. Wang, S. L. Jacques, L. Zheng, “MCML-Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Prog. Biomed. 47, 131–146 (1995).

S. L. Jacques, L. Wang, “Monte Carlo modeling of light transport in tissues,” in Optical-Thermal Response of Laser-Irradiated Tissue, A. J. Welch, M. J. C. van Gemert, eds. (Plenum, New York, 1995), pp. 73–100.

Jaeger, J.

H. S. Carslaw, J. Jaeger, Conduction of Heat in Solids (Oxford U. Press, New York, 1986).

Jakeman, E.

P. J. Bourke, J. Butterworth, L. E. Drain, P. A. Egelstaff, E. Jakeman, E. R. Pike, “A study of the spatial structure of turbulent flow by intensity-fluctuation spectroscopy,” J. Phys. A 3, 216–228 (1970).
[CrossRef]

Jobsis, F. F.

F. F. Jobsis, “Noninvasive, infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters,” Science 198, 1264–1267 (1977).
[CrossRef] [PubMed]

John, S.

F. C. MacKintosh, S. John, “Diffusing-wave spectroscopy and multiple scattering of light in correlated random media,” Phys. Rev. B 40, 2382–2406 (1989).
[CrossRef]

Joosten, J. G. H.

J. G. H. Joosten, E. T. F. Gelade, P. N. Pusey, “Dynamic light scattering by nonergodic media: Brownian particles trapped in polyacrylamide gels,” Phys. Rev. A 42, 2161–2175 (1990).
[CrossRef] [PubMed]

Kak, A. C.

A. C. Kak, M. Slaney, in Principles of Computerized Tomographic Imaging (Institute of Electrical and Electronics Engineers, New York, 1988).

Kaltenbach, J. M.

J. M. Kaltenbach, M. Kaschke, “Frequency and time domain modelling of light transport in random media,” in Medical Optical Imaging: Functional Imaging and Monitoring, Institute Series of SPIE Optical Engineering (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 65–86.

Kaltenbach, J. P.

See related studies by S. R. Arridge, et al. J. P. Kaltenbach, et al. R. L. Barbour et al., in Medical Optical Tomography: Functional Imaging and Monitoring, G. Müller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, P. van der Zee, eds., Institute Series of SPIE Optical Engineering (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 31–143.

Kao, M. H.

M. H. Kao, A. G. Yodh, D. J. Pine, “Observation of Brownian motion on the time scale of hydrodynamic interactions,” Phys. Rev. Lett. 70, 242–245 (1993).
[CrossRef] [PubMed]

Kaplan, P. D.

P. D. Kaplan, A. G. Yodh, D. F. Townsend, “Noninvasive study of gel formation in polymer-stabilized dense colloids using multiply scattered light,” J. Colloid Interface Sci. 155, 319–324 (1993).
[CrossRef]

P. D. Kaplan, A. G. Yodh, D. J. Pine, “Diffusion and structure in dense binary suspensions.” Phys. Rev. Lett. 68, 393–396 (1992).
[CrossRef] [PubMed]

Kaschke, M.

J. M. Kaltenbach, M. Kaschke, “Frequency and time domain modelling of light transport in random media,” in Medical Optical Imaging: Functional Imaging and Monitoring, Institute Series of SPIE Optical Engineering (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 65–86.

Katayama, K.

G. Nishimura, K. Katayama, M. Kinjo, M. Tamura, “Diffusing-wave absorption spectroscopy in the homogeneous turbid media,” Opt. Commun. 128, 99–107 (1996).
[CrossRef]

K. Katayama, G. Nishimura, M. Kinjo, M. Tamura, “Absorbance measurements in turbid media by the photon correlation method,” Appl. Opt. 34, 7419–7427 (1995).
[CrossRef] [PubMed]

Kinjo, M.

G. Nishimura, K. Katayama, M. Kinjo, M. Tamura, “Diffusing-wave absorption spectroscopy in the homogeneous turbid media,” Opt. Commun. 128, 99–107 (1996).
[CrossRef]

K. Katayama, G. Nishimura, M. Kinjo, M. Tamura, “Absorbance measurements in turbid media by the photon correlation method,” Appl. Opt. 34, 7419–7427 (1995).
[CrossRef] [PubMed]

Koelink, M. H.

Krall, A. H.

H. Gang, A. H. Krall, D. A. Weitz, “Shape fluctuations of interacting fluid droplets,” Phys. Rev. Lett. 73, 3435–3438 (1994).
[CrossRef] [PubMed]

Ladd, A. J. C.

A. J. C. Ladd, H. Gang, J. X. Zhu, D. A. Weitz, “Time-dependent collective diffusion of colloidal particles,” Phys. Rev. Lett. 74, 318–321 (1995).
[CrossRef] [PubMed]

Lagendijk, A.

Lai, C. C.

R. Nossal, S. H. Chen, C. C. Lai, “Use of laser scattering for quantitative determinations of bacterial motility,” Opt. Commun. 4, 35–39 (1971).
[CrossRef]

Leal, L. G.

G. G. Fuller, J. M. Rallison, R. L. Schmidt, L. G. Leal, “The measurement of velocity gradients in laminar flow by homodyne light-scattering spectroscopy,” J. Fluid Mech. 100, 555–575 (1980).
[CrossRef]

Lunacek, J. H.

N. A. Clark, J. H. Lunacek, G. B. Benedek, “A study of Brownian motion using light scattering,” Am. J. Phys. 38, 575–585 (1970).
[CrossRef]

MacKintosh, F. C.

F. C. MacKintosh, S. John, “Diffusing-wave spectroscopy and multiple scattering of light in correlated random media,” Phys. Rev. B 40, 2382–2406 (1989).
[CrossRef]

Maret, G.

D. Bicout, G. Maret, “Multiple light scattering in Taylor–Couette flow,” Physica A 210, 87–112 (1994).
[CrossRef]

G. Maret, P. E. Wolf, “Multiple light scattering from disordered media. The effect of Brownian motion of scatterers,” Z. Phys. B 65, 409–413 (1987).
[CrossRef]

Maynard, R.

D. J. Bicout, R. Maynard, “Multiple light scattering in turbulent flow,” Physica B 204, 20–26 (1995).
[CrossRef]

D. Bicout, R. Maynard, “Diffusing wave spectroscopy in inhomogeneous flows,” Physica A 199, 387–411 (1993).
[CrossRef]

McAdams, M. S.

Meglinsky, I. V.

D. A. Boas, I. V. Meglinsky, L. Zemany, L. E. Campbell, B. Chance, A. G. Yodh, “Diffusion of temporal field correlation with selected applications,” in Coherence-Domain Methods in Biomedical Optics, V. V. Tuchin, ed., Proc. SPIE2732, 34–46 (1996).
[CrossRef]

Middleton, A. A.

A. A. Middleton, D. S. Fisher, “Discrete scatterers and autocorrelations of multiply scattered light,” Phys. Rev. B 43, 5934–5938 (1991).
[CrossRef]

Millikan, G. A.

G. A. Millikan, “The oximeter, an instrument for measuring continuously the oxygen saturation of arterial blood in man,” Rev. Sci. Instrum. 13, 434–444 (1942).
[CrossRef]

G. A. Millikan, “Experiments on muscle haemoglobin in vivo: the instantaneous measurement of muscle metabolism,” Proc. R. Soc. London, Sect. B 129, 218–241 (1937).
[CrossRef]

Milner, S. T.

J. Z. Xue, D. J. Pine, S. T. Milner, X. L. Wu, P. M. Chaikin, “Nonergodicity and light scattering from polymer gels,” Phys. Rev. A 46, 6550–6563 (1992).
[CrossRef] [PubMed]

Muller, J.

J. X. Zhu, D. J. Durian, J. Muller, D. A. Weitz, D. J. Pine, “Scaling of transient hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 68, 2559–2562 (1992).
[CrossRef] [PubMed]

Neuman, M. R.

M. R. Neuman, “Pulse oximetry: physical principles technical realization and present limitations,” Adv. Exp. Med. Biol. 220, 135–144 (1987).

Nieuwenhuizen, T. M.

Nilsen, S. J.

S. J. Nilsen, A. P. Gast, “The influence of structure on diffusion in screened Coulombic suspensions,” J. Chem. Phys. 101, 4975–4985 (1994).
[CrossRef]

Nishimura, G.

G. Nishimura, K. Katayama, M. Kinjo, M. Tamura, “Diffusing-wave absorption spectroscopy in the homogeneous turbid media,” Opt. Commun. 128, 99–107 (1996).
[CrossRef]

K. Katayama, G. Nishimura, M. Kinjo, M. Tamura, “Absorbance measurements in turbid media by the photon correlation method,” Appl. Opt. 34, 7419–7427 (1995).
[CrossRef] [PubMed]

Nishioka, N. S.

H. A. Green, E. E. Burd, N. S. Nishioka, C. C. Compton, “Skin-graft take and healing following 193-nm excimer, continuous-wave carbon dioxide (CO2), pulsed CO2, or pulsed holmium-YAG laser-ablation of the graft bed,” Arch. Dermatol. 129, 979–988 (1993).

Nobbman, U.

B. J. Ackerson, R. L. Dougherty, N. M. Reguigui, U. Nobbman, “Correlation transfer: application of radiative transfer solution methods to photon correlation problems,” J. Thermophys. Heat Transfer 6, 577–588 (1992).
[CrossRef]

Nobbmann, U.

R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorri-Nowkoorani, U. Nobbmann, “Correlation transfer: development and application,” J. Quant. Spectrosc. Radiat. Transfer. 52, 713–727 (1994).
[CrossRef]

Nossal, R.

O’Leary, M. A.

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneties within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef]

Patterson, M. S.

B. C. Wilson, E. M. Sevick, M. S. Patterson, B. Chance, “Time-dependent optical spectroscopy and imaging for biomedical applications,” Proc. IEEE 80, 918–930 (1992).
[CrossRef]

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

Pecora, R.

B. J. Berne, R. Pecora, in Dynamic Light Scattering with Applications to Chemistry, Biology, and Physics (Krieger, Malabar, Fla., 1990).

P. J. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976).

Pike, E. R.

P. J. Bourke, J. Butterworth, L. E. Drain, P. A. Egelstaff, E. Jakeman, E. R. Pike, “A study of the spatial structure of turbulent flow by intensity-fluctuation spectroscopy,” J. Phys. A 3, 216–228 (1970).
[CrossRef]

Pine, D. J.

M. H. Kao, A. G. Yodh, D. J. Pine, “Observation of Brownian motion on the time scale of hydrodynamic interactions,” Phys. Rev. Lett. 70, 242–245 (1993).
[CrossRef] [PubMed]

P. D. Kaplan, A. G. Yodh, D. J. Pine, “Diffusion and structure in dense binary suspensions.” Phys. Rev. Lett. 68, 393–396 (1992).
[CrossRef] [PubMed]

J. X. Zhu, D. J. Durian, J. Muller, D. A. Weitz, D. J. Pine, “Scaling of transient hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 68, 2559–2562 (1992).
[CrossRef] [PubMed]

J. Z. Xue, D. J. Pine, S. T. Milner, X. L. Wu, P. M. Chaikin, “Nonergodicity and light scattering from polymer gels,” Phys. Rev. A 46, 6550–6563 (1992).
[CrossRef] [PubMed]

D. J. Durian, D. A. Weitz, D. J. Pine, “Multiple light scattering probes of foam structure and dynamics,” Science 252, 686–688 (1991).
[CrossRef] [PubMed]

X. Qiu, X. L. Wu, J. Z. Xue, D. J. Pine, D. A. Weitz, P. M. Chaikin, “Hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 65, 516–518 (1990).
[CrossRef] [PubMed]

D. J. Pine, D. A. Weitz, J. X. Zhu, E. Herbolzheimer, “Diffusing-wave spectroscopy: dynamic light scattering in the multiple scattering limit,” J. Phys. (Paris) 51, 2101–2127 (1990).
[CrossRef]

X. L. Wu, D. J. Pine, P. M. Chaikin, J. S. Huang, D. A. Weitz, “Diffusing-wave spectroscopy in a shear flow,” J. Opt. Soc. Am. B 7, 15–20 (1990).
[CrossRef]

D. A. Weitz, D. J. Pine, P. N. Pusey, R. J. A. Tough, “Nondiffusive Brownian motion studied by diffusing-wave spectroscopy,” Phys. Rev. Lett. 63, 1747–1750 (1989).
[CrossRef] [PubMed]

D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
[CrossRef] [PubMed]

Porto,

M. Bertolotti, B. Crosignani, P. Di, Porto, D. Sette, “Light scattering by particles suspended in a turbulent fluid,” J. Phys. A 2, 126–128 (1969).
[CrossRef]

Prahl, S. A.

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Pusey, P. N.

J. G. H. Joosten, E. T. F. Gelade, P. N. Pusey, “Dynamic light scattering by nonergodic media: Brownian particles trapped in polyacrylamide gels,” Phys. Rev. A 42, 2161–2175 (1990).
[CrossRef] [PubMed]

D. A. Weitz, D. J. Pine, P. N. Pusey, R. J. A. Tough, “Nondiffusive Brownian motion studied by diffusing-wave spectroscopy,” Phys. Rev. Lett. 63, 1747–1750 (1989).
[CrossRef] [PubMed]

P. N. Pusey, W. Van Megen, Dynamic light scattering by non-ergodic media,” Physica A 157, 705–742 (1989).
[CrossRef]

P. N. Pusey, J. M. Vaughan, D. V. Willets, “Effect of spatial incoherence of the laser in photon-counting spectroscopy,” J. Opt. Soc. Am. 73, 1012–1017 (1983).
[CrossRef]

P. N. Pusey, J. M. Vaughan, “Light scattering and intensity fluctuation spectroscopy,” in Specialist Periodical Report, Vol. 2 of Dielectric and Related Molecular Processes. M. Davies, ed. (The Chemical Society, London, 1975).

Qiu, X.

X. Qiu, X. L. Wu, J. Z. Xue, D. J. Pine, D. A. Weitz, P. M. Chaikin, “Hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 65, 516–518 (1990).
[CrossRef] [PubMed]

Rallison, J. M.

G. G. Fuller, J. M. Rallison, R. L. Schmidt, L. G. Leal, “The measurement of velocity gradients in laminar flow by homodyne light-scattering spectroscopy,” J. Fluid Mech. 100, 555–575 (1980).
[CrossRef]

Reguigui, N. M.

R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorri-Nowkoorani, U. Nobbmann, “Correlation transfer: development and application,” J. Quant. Spectrosc. Radiat. Transfer. 52, 713–727 (1994).
[CrossRef]

B. J. Ackerson, R. L. Dougherty, N. M. Reguigui, U. Nobbman, “Correlation transfer: application of radiative transfer solution methods to photon correlation problems,” J. Thermophys. Heat Transfer 6, 577–588 (1992).
[CrossRef]

Rice, S. O.

S. O. Rice, “Mathematical analysis of random noise,” in Noise and Stochastic Processes, N. Wax, ed. (Dover, New York, 1954), p. 133.

Richardson, C.

A. D. Edwards, C. Richardson, P. van der Zee, M. Cope, D. T. Delpy, “Measurement of hemoglobin flow and blood flow by near-infrared spectroscopy,” J. Appl. Physiol. 75, 1884–1889 (1993).
[PubMed]

Ricka, J.

Riva, C.

T. Tanaka, C. Riva, I. Ben-Sira, “Blood velocity measurements in human retinal vessels,” Science 186, 830–831 (1974).
[CrossRef] [PubMed]

Robertson, C. S.

S. P. Gopinath, C. S. Robertson, R. G. Grossman, B. Chance, “Near-infrared spectroscopic localization of intracranial hematomas,” J. Neurosurg. 79, 43–47 (1993).
[CrossRef]

Romanov, V. P.

A. Y. Val’kov, V. P. Romanov, “Characteristics of propagation and scattering of light in nematic liquid crystals,” Sov. Phys. JETP 63, 737–743 (1986) [Zh. Eksp. Teor. Fiz. 90, 1264–1274 (1986)].

Schatzel, K.

Schmidt, R. L.

G. G. Fuller, J. M. Rallison, R. L. Schmidt, L. G. Leal, “The measurement of velocity gradients in laminar flow by homodyne light-scattering spectroscopy,” J. Fluid Mech. 100, 555–575 (1980).
[CrossRef]

Schmitt, J. M.

J. M. Schmitt, “Simple photon diffusion analysis of the effects of multiple scattering on pulse oximetry,” IEEE Trans. Biomed. Eng. 38, 1194–1203 (1991).
[CrossRef] [PubMed]

Sette, D.

M. Bertolotti, B. Crosignani, P. Di, Porto, D. Sette, “Light scattering by particles suspended in a turbulent fluid,” J. Phys. A 2, 126–128 (1969).
[CrossRef]

Severinghaus, J. W.

J. W. Severinghaus, “History and recent developments in pulse oximetry,” Scand. J. Clin. Lab. Invest. 53, 105–111 (1993).
[PubMed]

Sevick, E. M.

B. C. Wilson, E. M. Sevick, M. S. Patterson, B. Chance, “Time-dependent optical spectroscopy and imaging for biomedical applications,” Proc. IEEE 80, 918–930 (1992).
[CrossRef]

Sirivat, A.

P. Tong, W. I. Goldburg, C. K. Chan, A. Sirivat, “Turbulent transition by photon-correlation spectroscopy,” Phys. Rev. A 37, 2125–2133 (1988).
[CrossRef] [PubMed]

Slaney, M.

A. C. Kak, M. Slaney, in Principles of Computerized Tomographic Imaging (Institute of Electrical and Electronics Engineers, New York, 1988).

Stephen, M. J.

M. J. Stephen, “Temporal fluctuations in wave propagation in random media,” Phys. Rev. B 37, 1–5 (1988).
[CrossRef]

Stern, M.

M. Stern, In vivo evaluation of microcirculation by coherent light scattering,” Nature (London) 254, 56–58 (1975).
[CrossRef]

Svaasand, L. O.

Swinney, H. L.

H. Z. Cummings, H. L. Swinney, “Light beating spectroscopy,” Prog. Opt. 8, 133–200 (1970).
[CrossRef]

Sykes, J. B.

B. Davison, J. B. Sykes, Neutron Transport Theory (Oxford U. Press, London, 1957).

Tamura, M.

G. Nishimura, K. Katayama, M. Kinjo, M. Tamura, “Diffusing-wave absorption spectroscopy in the homogeneous turbid media,” Opt. Commun. 128, 99–107 (1996).
[CrossRef]

K. Katayama, G. Nishimura, M. Kinjo, M. Tamura, “Absorbance measurements in turbid media by the photon correlation method,” Appl. Opt. 34, 7419–7427 (1995).
[CrossRef] [PubMed]

Tanaka, T.

T. Tanaka, C. Riva, I. Ben-Sira, “Blood velocity measurements in human retinal vessels,” Science 186, 830–831 (1974).
[CrossRef] [PubMed]

Tong, P.

P. Tong, W. I. Goldburg, C. K. Chan, A. Sirivat, “Turbulent transition by photon-correlation spectroscopy,” Phys. Rev. A 37, 2125–2133 (1988).
[CrossRef] [PubMed]

Tough, R. J. A.

D. A. Weitz, D. J. Pine, P. N. Pusey, R. J. A. Tough, “Nondiffusive Brownian motion studied by diffusing-wave spectroscopy,” Phys. Rev. Lett. 63, 1747–1750 (1989).
[CrossRef] [PubMed]

Townsend, D. F.

P. D. Kaplan, A. G. Yodh, D. F. Townsend, “Noninvasive study of gel formation in polymer-stabilized dense colloids using multiply scattered light,” J. Colloid Interface Sci. 155, 319–324 (1993).
[CrossRef]

Tromberg, B. J.

Tsay, T.

Val’kov, A. Y.

A. Y. Val’kov, V. P. Romanov, “Characteristics of propagation and scattering of light in nematic liquid crystals,” Sov. Phys. JETP 63, 737–743 (1986) [Zh. Eksp. Teor. Fiz. 90, 1264–1274 (1986)].

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

van der Zee, P.

A. D. Edwards, C. Richardson, P. van der Zee, M. Cope, D. T. Delpy, “Measurement of hemoglobin flow and blood flow by near-infrared spectroscopy,” J. Appl. Physiol. 75, 1884–1889 (1993).
[PubMed]

S. R. Arridge, P. van der Zee, M. Cope, D. T. Delpy, “Reconstruction methods for infra-red absorption imaging,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, ed., Proc. SPIE1431, 204–215 (1991).
[CrossRef]

Van Keuren, E. R.

E. R. Van Keuren, H. Wiese, D. Horn, “Diffusing-wave spectroscopy in concentrated latex dispersions: an investigation using single-mode fibers,” Colloids Surf. A 77, 29–37 (1993).
[CrossRef]

Van Megen, W.

P. N. Pusey, W. Van Megen, Dynamic light scattering by non-ergodic media,” Physica A 157, 705–742 (1989).
[CrossRef]

Vaughan, J. M.

P. N. Pusey, J. M. Vaughan, D. V. Willets, “Effect of spatial incoherence of the laser in photon-counting spectroscopy,” J. Opt. Soc. Am. 73, 1012–1017 (1983).
[CrossRef]

P. N. Pusey, J. M. Vaughan, “Light scattering and intensity fluctuation spectroscopy,” in Specialist Periodical Report, Vol. 2 of Dielectric and Related Molecular Processes. M. Davies, ed. (The Chemical Society, London, 1975).

Wang, L.

L. Wang, S. L. Jacques, L. Zheng, “MCML-Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Prog. Biomed. 47, 131–146 (1995).

S. L. Jacques, L. Wang, “Monte Carlo modeling of light transport in tissues,” in Optical-Thermal Response of Laser-Irradiated Tissue, A. J. Welch, M. J. C. van Gemert, eds. (Plenum, New York, 1995), pp. 73–100.

Weiss, G. H.

Weitz, D. A.

A. J. C. Ladd, H. Gang, J. X. Zhu, D. A. Weitz, “Time-dependent collective diffusion of colloidal particles,” Phys. Rev. Lett. 74, 318–321 (1995).
[CrossRef] [PubMed]

H. Gang, A. H. Krall, D. A. Weitz, “Shape fluctuations of interacting fluid droplets,” Phys. Rev. Lett. 73, 3435–3438 (1994).
[CrossRef] [PubMed]

J. X. Zhu, D. J. Durian, J. Muller, D. A. Weitz, D. J. Pine, “Scaling of transient hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 68, 2559–2562 (1992).
[CrossRef] [PubMed]

D. J. Durian, D. A. Weitz, D. J. Pine, “Multiple light scattering probes of foam structure and dynamics,” Science 252, 686–688 (1991).
[CrossRef] [PubMed]

X. Qiu, X. L. Wu, J. Z. Xue, D. J. Pine, D. A. Weitz, P. M. Chaikin, “Hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 65, 516–518 (1990).
[CrossRef] [PubMed]

D. J. Pine, D. A. Weitz, J. X. Zhu, E. Herbolzheimer, “Diffusing-wave spectroscopy: dynamic light scattering in the multiple scattering limit,” J. Phys. (Paris) 51, 2101–2127 (1990).
[CrossRef]

X. L. Wu, D. J. Pine, P. M. Chaikin, J. S. Huang, D. A. Weitz, “Diffusing-wave spectroscopy in a shear flow,” J. Opt. Soc. Am. B 7, 15–20 (1990).
[CrossRef]

D. A. Weitz, D. J. Pine, P. N. Pusey, R. J. A. Tough, “Nondiffusive Brownian motion studied by diffusing-wave spectroscopy,” Phys. Rev. Lett. 63, 1747–1750 (1989).
[CrossRef] [PubMed]

D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
[CrossRef] [PubMed]

Welch, A. J.

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Wiese, H.

E. R. Van Keuren, H. Wiese, D. Horn, “Diffusing-wave spectroscopy in concentrated latex dispersions: an investigation using single-mode fibers,” Colloids Surf. A 77, 29–37 (1993).
[CrossRef]

Willets, D. V.

Wilson, B. C.

B. C. Wilson, E. M. Sevick, M. S. Patterson, B. Chance, “Time-dependent optical spectroscopy and imaging for biomedical applications,” Proc. IEEE 80, 918–930 (1992).
[CrossRef]

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

Wolf, P. E.

G. Maret, P. E. Wolf, “Multiple light scattering from disordered media. The effect of Brownian motion of scatterers,” Z. Phys. B 65, 409–413 (1987).
[CrossRef]

Wu, X. L.

J. Z. Xue, D. J. Pine, S. T. Milner, X. L. Wu, P. M. Chaikin, “Nonergodicity and light scattering from polymer gels,” Phys. Rev. A 46, 6550–6563 (1992).
[CrossRef] [PubMed]

X. Qiu, X. L. Wu, J. Z. Xue, D. J. Pine, D. A. Weitz, P. M. Chaikin, “Hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 65, 516–518 (1990).
[CrossRef] [PubMed]

X. L. Wu, D. J. Pine, P. M. Chaikin, J. S. Huang, D. A. Weitz, “Diffusing-wave spectroscopy in a shear flow,” J. Opt. Soc. Am. B 7, 15–20 (1990).
[CrossRef]

Xue, J. Z.

J. Z. Xue, D. J. Pine, S. T. Milner, X. L. Wu, P. M. Chaikin, “Nonergodicity and light scattering from polymer gels,” Phys. Rev. A 46, 6550–6563 (1992).
[CrossRef] [PubMed]

X. Qiu, X. L. Wu, J. Z. Xue, D. J. Pine, D. A. Weitz, P. M. Chaikin, “Hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 65, 516–518 (1990).
[CrossRef] [PubMed]

Yodh, A.

A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48, 34–40 (1995).
[CrossRef]

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]

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneties within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef]

M. H. Kao, A. G. Yodh, D. J. Pine, “Observation of Brownian motion on the time scale of hydrodynamic interactions,” Phys. Rev. Lett. 70, 242–245 (1993).
[CrossRef] [PubMed]

P. D. Kaplan, A. G. Yodh, D. F. Townsend, “Noninvasive study of gel formation in polymer-stabilized dense colloids using multiply scattered light,” J. Colloid Interface Sci. 155, 319–324 (1993).
[CrossRef]

P. D. Kaplan, A. G. Yodh, D. J. Pine, “Diffusion and structure in dense binary suspensions.” Phys. Rev. Lett. 68, 393–396 (1992).
[CrossRef] [PubMed]

D. A. Boas, I. V. Meglinsky, L. Zemany, L. E. Campbell, B. Chance, A. G. Yodh, “Diffusion of temporal field correlation with selected applications,” in Coherence-Domain Methods in Biomedical Optics, V. V. Tuchin, ed., Proc. SPIE2732, 34–46 (1996).
[CrossRef]

Zemany, L.

D. A. Boas, I. V. Meglinsky, L. Zemany, L. E. Campbell, B. Chance, A. G. Yodh, “Diffusion of temporal field correlation with selected applications,” in Coherence-Domain Methods in Biomedical Optics, V. V. Tuchin, ed., Proc. SPIE2732, 34–46 (1996).
[CrossRef]

Zheng, L.

L. Wang, S. L. Jacques, L. Zheng, “MCML-Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Prog. Biomed. 47, 131–146 (1995).

Zhu, J. X.

A. J. C. Ladd, H. Gang, J. X. Zhu, D. A. Weitz, “Time-dependent collective diffusion of colloidal particles,” Phys. Rev. Lett. 74, 318–321 (1995).
[CrossRef] [PubMed]

J. X. Zhu, D. J. Durian, J. Muller, D. A. Weitz, D. J. Pine, “Scaling of transient hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 68, 2559–2562 (1992).
[CrossRef] [PubMed]

D. J. Pine, D. A. Weitz, J. X. Zhu, E. Herbolzheimer, “Diffusing-wave spectroscopy: dynamic light scattering in the multiple scattering limit,” J. Phys. (Paris) 51, 2101–2127 (1990).
[CrossRef]

Zijlstra, W. G.

Zweifel, P. F.

K. M. Case, P. F. Zweifel, Linear Transport Theory (Addison-Wesley, Reading, Mass., 1967).

Adv. Exp. Med. Biol.

M. R. Neuman, “Pulse oximetry: physical principles technical realization and present limitations,” Adv. Exp. Med. Biol. 220, 135–144 (1987).

Am. J. Phys.

N. A. Clark, J. H. Lunacek, G. B. Benedek, “A study of Brownian motion using light scattering,” Am. J. Phys. 38, 575–585 (1970).
[CrossRef]

Appl. Opt.

R. Bonner, R. Nossal, “Model for laser Doppler measurements of blood flow in tissue,” Appl. Opt. 20, 2097–2107 (1981).
[CrossRef] [PubMed]

R. G. Brown, “Dynamic light scattering using monomode optical fibers,” Appl. Opt. 26, 4846–4851 (1987).
[CrossRef] [PubMed]

R. Nossal, R. F. Bonner, G. H. Weiss, “Influence of path length on remote optical sensing of properties of biological tissue,” Appl. Opt. 28, 2238–2244 (1989).
[CrossRef] [PubMed]

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

J. Ricka, “Dynamic light scattering with single-mode and multimode fibers,” Appl. Opt. 32, 2860–2875 (1993).
[CrossRef]

R. Graaff, M. H. Koelink, F. F. M. de Mul, W. G. Zijlstra, A. C. M. Dassel, J. G. Aarnoudse, “Condensed Monte Carlo simulations for the description of light transport,” Appl. Opt. 32, 426–434 (1993).
[CrossRef] [PubMed]

B. J. Tromberg, L. O. Svaasand, T. Tsay, R. C. Haskell, “Properties of photon density waves in multiple-scattering media,” Appl. Opt. 32, 607–616 (1993).
[CrossRef] [PubMed]

M. H. Koelink, F. F. M. de Mul, J. Greve, R. Graaff, A. C. M. Dassel, J. G. Aarnoudse, “Laser Doppler blood flowmetry using two wavelengths: Monte Carlo simulations and measurements,” Appl. Opt. 33, 3549–3558 (1994).
[CrossRef] [PubMed]

K. Katayama, G. Nishimura, M. Kinjo, M. Tamura, “Absorbance measurements in turbid media by the photon correlation method,” Appl. Opt. 34, 7419–7427 (1995).
[CrossRef] [PubMed]

K. Schatzel, “Accuracy of photon correlation measurements on nonergodic samples,” Appl. Opt. 32, 3880–3885 (1993).
[CrossRef] [PubMed]

Arch. Dermatol.

H. A. Green, E. E. Burd, N. S. Nishioka, C. C. Compton, “Skin-graft take and healing following 193-nm excimer, continuous-wave carbon dioxide (CO2), pulsed CO2, or pulsed holmium-YAG laser-ablation of the graft bed,” Arch. Dermatol. 129, 979–988 (1993).

Astrophys. J.

L. G. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Colloids Surf. A

E. R. Van Keuren, H. Wiese, D. Horn, “Diffusing-wave spectroscopy in concentrated latex dispersions: an investigation using single-mode fibers,” Colloids Surf. A 77, 29–37 (1993).
[CrossRef]

Comput. Methods Prog. Biomed.

L. Wang, S. L. Jacques, L. Zheng, “MCML-Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Prog. Biomed. 47, 131–146 (1995).

IEEE J. Quantum Electron.

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

IEEE Trans. Biomed. Eng.

J. M. Schmitt, “Simple photon diffusion analysis of the effects of multiple scattering on pulse oximetry,” IEEE Trans. Biomed. Eng. 38, 1194–1203 (1991).
[CrossRef] [PubMed]

J. Appl. Physiol.

A. D. Edwards, C. Richardson, P. van der Zee, M. Cope, D. T. Delpy, “Measurement of hemoglobin flow and blood flow by near-infrared spectroscopy,” J. Appl. Physiol. 75, 1884–1889 (1993).
[PubMed]

J. Chem. Phys.

S. J. Nilsen, A. P. Gast, “The influence of structure on diffusion in screened Coulombic suspensions,” J. Chem. Phys. 101, 4975–4985 (1994).
[CrossRef]

J. Colloid Interface Sci.

P. D. Kaplan, A. G. Yodh, D. F. Townsend, “Noninvasive study of gel formation in polymer-stabilized dense colloids using multiply scattered light,” J. Colloid Interface Sci. 155, 319–324 (1993).
[CrossRef]

J. Fluid Mech.

G. G. Fuller, J. M. Rallison, R. L. Schmidt, L. G. Leal, “The measurement of velocity gradients in laminar flow by homodyne light-scattering spectroscopy,” J. Fluid Mech. 100, 555–575 (1980).
[CrossRef]

J. Neurosurg.

S. P. Gopinath, C. S. Robertson, R. G. Grossman, B. Chance, “Near-infrared spectroscopic localization of intracranial hematomas,” J. Neurosurg. 79, 43–47 (1993).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

J. Phys. (Paris)

D. J. Pine, D. A. Weitz, J. X. Zhu, E. Herbolzheimer, “Diffusing-wave spectroscopy: dynamic light scattering in the multiple scattering limit,” J. Phys. (Paris) 51, 2101–2127 (1990).
[CrossRef]

J. Phys. A

M. Bertolotti, B. Crosignani, P. Di, Porto, D. Sette, “Light scattering by particles suspended in a turbulent fluid,” J. Phys. A 2, 126–128 (1969).
[CrossRef]

P. J. Bourke, J. Butterworth, L. E. Drain, P. A. Egelstaff, E. Jakeman, E. R. Pike, “A study of the spatial structure of turbulent flow by intensity-fluctuation spectroscopy,” J. Phys. A 3, 216–228 (1970).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer.

R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorri-Nowkoorani, U. Nobbmann, “Correlation transfer: development and application,” J. Quant. Spectrosc. Radiat. Transfer. 52, 713–727 (1994).
[CrossRef]

J. Thermophys. Heat Transfer

B. J. Ackerson, R. L. Dougherty, N. M. Reguigui, U. Nobbman, “Correlation transfer: application of radiative transfer solution methods to photon correlation problems,” J. Thermophys. Heat Transfer 6, 577–588 (1992).
[CrossRef]

Nature (London)

M. Stern, In vivo evaluation of microcirculation by coherent light scattering,” Nature (London) 254, 56–58 (1975).
[CrossRef]

Opt. Commun.

R. Nossal, S. H. Chen, C. C. Lai, “Use of laser scattering for quantitative determinations of bacterial motility,” Opt. Commun. 4, 35–39 (1971).
[CrossRef]

G. Nishimura, K. Katayama, M. Kinjo, M. Tamura, “Diffusing-wave absorption spectroscopy in the homogeneous turbid media,” Opt. Commun. 128, 99–107 (1996).
[CrossRef]

Phys. Lett. A

D. Bicout, “Non-Newtonian behavior of colloidal suspensions from multiple light scattering,” Phys. Lett. A 180, 375–378 (1993).
[CrossRef]

Phys. Rev. A

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

J. Z. Xue, D. J. Pine, S. T. Milner, X. L. Wu, P. M. Chaikin, “Nonergodicity and light scattering from polymer gels,” Phys. Rev. A 46, 6550–6563 (1992).
[CrossRef] [PubMed]

J. G. H. Joosten, E. T. F. Gelade, P. N. Pusey, “Dynamic light scattering by nonergodic media: Brownian particles trapped in polyacrylamide gels,” Phys. Rev. A 42, 2161–2175 (1990).
[CrossRef] [PubMed]

P. Tong, W. I. Goldburg, C. K. Chan, A. Sirivat, “Turbulent transition by photon-correlation spectroscopy,” Phys. Rev. A 37, 2125–2133 (1988).
[CrossRef] [PubMed]

Phys. Rev. B

F. C. MacKintosh, S. John, “Diffusing-wave spectroscopy and multiple scattering of light in correlated random media,” Phys. Rev. B 40, 2382–2406 (1989).
[CrossRef]

A. A. Middleton, D. S. Fisher, “Discrete scatterers and autocorrelations of multiply scattered light,” Phys. Rev. B 43, 5934–5938 (1991).
[CrossRef]

M. J. Stephen, “Temporal fluctuations in wave propagation in random media,” Phys. Rev. B 37, 1–5 (1988).
[CrossRef]

Phys. Rev. E

D. J. Durian, “Accuracy of diffusing-wave spectroscopy theories,” Phys. Rev. E 51, 3350–3358 (1995).
[CrossRef]

Phys. Rev. Lett.

D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
[CrossRef] [PubMed]

A. D. Gopal, D. J. Durian, “Nonlinear bubble dynamics in a slowly driven foam,” Phys. Rev. Lett. 75, 2610–2613 (1995).
[CrossRef] [PubMed]

H. Gang, A. H. Krall, D. A. Weitz, “Shape fluctuations of interacting fluid droplets,” Phys. Rev. Lett. 73, 3435–3438 (1994).
[CrossRef] [PubMed]

A. J. C. Ladd, H. Gang, J. X. Zhu, D. A. Weitz, “Time-dependent collective diffusion of colloidal particles,” Phys. Rev. Lett. 74, 318–321 (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]

D. A. Weitz, D. J. Pine, P. N. Pusey, R. J. A. Tough, “Nondiffusive Brownian motion studied by diffusing-wave spectroscopy,” Phys. Rev. Lett. 63, 1747–1750 (1989).
[CrossRef] [PubMed]

X. Qiu, X. L. Wu, J. Z. Xue, D. J. Pine, D. A. Weitz, P. M. Chaikin, “Hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 65, 516–518 (1990).
[CrossRef] [PubMed]

P. D. Kaplan, A. G. Yodh, D. J. Pine, “Diffusion and structure in dense binary suspensions.” Phys. Rev. Lett. 68, 393–396 (1992).
[CrossRef] [PubMed]

J. X. Zhu, D. J. Durian, J. Muller, D. A. Weitz, D. J. Pine, “Scaling of transient hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 68, 2559–2562 (1992).
[CrossRef] [PubMed]

M. H. Kao, A. G. Yodh, D. J. Pine, “Observation of Brownian motion on the time scale of hydrodynamic interactions,” Phys. Rev. Lett. 70, 242–245 (1993).
[CrossRef] [PubMed]

Phys. Today

A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48, 34–40 (1995).
[CrossRef]

Physica A

P. N. Pusey, W. Van Megen, Dynamic light scattering by non-ergodic media,” Physica A 157, 705–742 (1989).
[CrossRef]

D. Bicout, R. Maynard, “Diffusing wave spectroscopy in inhomogeneous flows,” Physica A 199, 387–411 (1993).
[CrossRef]

D. Bicout, G. Maret, “Multiple light scattering in Taylor–Couette flow,” Physica A 210, 87–112 (1994).
[CrossRef]

Physica B

D. J. Bicout, R. Maynard, “Multiple light scattering in turbulent flow,” Physica B 204, 20–26 (1995).
[CrossRef]

Proc. IEEE

B. C. Wilson, E. M. Sevick, M. S. Patterson, B. Chance, “Time-dependent optical spectroscopy and imaging for biomedical applications,” Proc. IEEE 80, 918–930 (1992).
[CrossRef]

Proc. Natl. Acad. Sci. USA

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneties within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef]

Proc. R. Soc. London, Sect. B

G. A. Millikan, “Experiments on muscle haemoglobin in vivo: the instantaneous measurement of muscle metabolism,” Proc. R. Soc. London, Sect. B 129, 218–241 (1937).
[CrossRef]

Prog. Opt.

H. Z. Cummings, H. L. Swinney, “Light beating spectroscopy,” Prog. Opt. 8, 133–200 (1970).
[CrossRef]

Rev. Sci. Instrum.

G. A. Millikan, “The oximeter, an instrument for measuring continuously the oxygen saturation of arterial blood in man,” Rev. Sci. Instrum. 13, 434–444 (1942).
[CrossRef]

Scand. J. Clin. Lab. Invest.

J. W. Severinghaus, “History and recent developments in pulse oximetry,” Scand. J. Clin. Lab. Invest. 53, 105–111 (1993).
[PubMed]

Science

F. F. Jobsis, “Noninvasive, infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters,” Science 198, 1264–1267 (1977).
[CrossRef] [PubMed]

T. Tanaka, C. Riva, I. Ben-Sira, “Blood velocity measurements in human retinal vessels,” Science 186, 830–831 (1974).
[CrossRef] [PubMed]

D. J. Durian, D. A. Weitz, D. J. Pine, “Multiple light scattering probes of foam structure and dynamics,” Science 252, 686–688 (1991).
[CrossRef] [PubMed]

Sov. Phys. JETP

A. Y. Val’kov, V. P. Romanov, “Characteristics of propagation and scattering of light in nematic liquid crystals,” Sov. Phys. JETP 63, 737–743 (1986) [Zh. Eksp. Teor. Fiz. 90, 1264–1274 (1986)].

Z. Phys. B

G. Maret, P. E. Wolf, “Multiple light scattering from disordered media. The effect of Brownian motion of scatterers,” Z. Phys. B 65, 409–413 (1987).
[CrossRef]

Other

P. N. Pusey, J. M. Vaughan, “Light scattering and intensity fluctuation spectroscopy,” in Specialist Periodical Report, Vol. 2 of Dielectric and Related Molecular Processes. M. Davies, ed. (The Chemical Society, London, 1975).

S. O. Rice, “Mathematical analysis of random noise,” in Noise and Stochastic Processes, N. Wax, ed. (Dover, New York, 1954), p. 133.

H. Z. Cummings, E. R. Pike, eds., Photon Correlation and Light-Beating Spectroscopy, Vol. 3 of NATO Advanced Study Institute Series B: Physics (Plenum, New York, 1974).

See related studies by S. R. Arridge, et al. J. P. Kaltenbach, et al. R. L. Barbour et al., in Medical Optical Tomography: Functional Imaging and Monitoring, G. Müller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, P. van der Zee, eds., Institute Series of SPIE Optical Engineering (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 31–143.

S. R. Arridge, P. van der Zee, M. Cope, D. T. Delpy, “Reconstruction methods for infra-red absorption imaging,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, ed., Proc. SPIE1431, 204–215 (1991).
[CrossRef]

A. P. Shepherd, P. A. Oberg, eds., Laser-Doppler Blood Flowmetry (Kluwer Academic, Boston, Mass., 1990).

L. E. Drain, The Laser Doppler Technique (Wiley, New York, 1980).

G. V. Belcaro, U. Hoffmann, A. Bollinger, A. N. Nicolaides, eds., Laser Doppler (Med-Orion, London, 1994).

P. J. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976).

B. J. Berne, R. Pecora, in Dynamic Light Scattering with Applications to Chemistry, Biology, and Physics (Krieger, Malabar, Fla., 1990).

W. Brown, ed., Dynamic Light Scattering: The Method and Some Applications (Clarendon, New York, 1993).

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

D. A. Boas, I. V. Meglinsky, L. Zemany, L. E. Campbell, B. Chance, A. G. Yodh, “Diffusion of temporal field correlation with selected applications,” in Coherence-Domain Methods in Biomedical Optics, V. V. Tuchin, ed., Proc. SPIE2732, 34–46 (1996).
[CrossRef]

B. Chance, ed., Photon Migration in Tissues (Plenum, New York, 1989).

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

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).

H. S. Carslaw, J. Jaeger, Conduction of Heat in Solids (Oxford U. Press, New York, 1986).

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

The Intralipid used here can be obtained from Kabi Pharmacia, Clayton, North Carolina.

S. L. Jacques, L. Wang, “Monte Carlo modeling of light transport in tissues,” in Optical-Thermal Response of Laser-Irradiated Tissue, A. J. Welch, M. J. C. van Gemert, eds. (Plenum, New York, 1995), pp. 73–100.

A. C. Kak, M. Slaney, in Principles of Computerized Tomographic Imaging (Institute of Electrical and Electronics Engineers, New York, 1988).

K. M. Case, P. F. Zweifel, Linear Transport Theory (Addison-Wesley, Reading, Mass., 1967).

B. Davison, J. B. Sykes, Neutron Transport Theory (Oxford U. Press, London, 1957).

S. Glasstone, M. C. Edlund, The Elements of Nuclear Reactor Theory (Van Nostrand, Princeton, N.J., 1952).

J. M. Kaltenbach, M. Kaschke, “Frequency and time domain modelling of light transport in random media,” in Medical Optical Imaging: Functional Imaging and Monitoring, Institute Series of SPIE Optical Engineering (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 65–86.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), Chap. 3.6.

G. B. Arfken, in Mathematical Methods for Physicists (Academic, Orlando, Fla., 1985), Chap. 12.9.

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Figures (20)

Fig. 1
Fig. 1

Schematic of system in which light is incident upon a dilute suspension of scatterers. The suspension is dilute enough that photons are scattered no more than once. Scattered light is measured at an angle θ defined by two pinholes and is monitored with a photodetector.

Fig. 2
Fig. 2

Schematic of system in which light is incident upon a concentrated suspension of scatterers. Photons on average are scattered many times before emerging from the system. A single speckle of transmitted light is imaged with pinholes (or is gathered by a single-mode fiber) and is monitored with a photodetector.

Fig. 3
Fig. 3

Ensemble-average correlation function from a nonergodic turbid medium. The medium is a solid, highly scattering slab with a cylindrical vein through which a highly scattering colloid flows. The early τ decay corresponds to the flow dynamics, whereas the long τ decay results from the ensemble averaging. The three curves come from three different flow speeds, with the solid, the dotted, and the dashed curves corresponding to flow speeds of 0.08, 0.24, and 0.88 cm s-1, respectively. The early τ decay rate increases with the flow speed. The longer τ decay depends only on the rate of ensemble averaging, which is held constant. The intermediate plateau reveals the relative magnitudes of 〈Ic〉 and 〈If〉 and tells us what fraction of the detected photons have sampled the dynamic region. Here Ic/(Ic+Ic)0.8, which reveals that 80% of the photons have not sampled the dynamic region. This is independent of the flow speed, as expected.

Fig. 4
Fig. 4

Experimental setup for photon correlation spectroscopy. Amp/Disc., amplifier–discriminator.

Fig. 5
Fig. 5

Setup for performing the ensemble average.

Fig. 6
Fig. 6

Setup of an experiment in which a 514-nm line from an Ar-ion laser (operated at 2.0 W with an étalon) is coupled into a multimode fiber-optic cable and is delivered to the surface of a solid slab of TiO2 suspended in resin. The slab has dimensions of 15 × 15 × 8 cm. A spherical cavity with a diameter of 2.5 cm is located 1.8 cm below the center of the upper surface. The cavity is filled with a 0.2% suspension of 0.296-µm-diameter polystyrene spheres at 25 °C, resulting in μs=6.67 cm-1, μa=0.002 cm-1, and DB=1.5×10-8 cm2 s-1. For the solid slab, μs=4.55 cm-1 and μa=0.002 cm-1. A single-mode fiber collects light at a known position and delivers it to a PMT whose output enters a digital autocorrelator to obtain the temporal intensity correlation function. The temporal intensity correlation function is related to the temporal field correlation function by the Siegert relation.32,34,37 The fibers can be moved to any position on the sample surface.

Fig. 7
Fig. 7

Experimental measurements of the temporal intensity autocorrelation function for three different source–detector pairs with a colloid present and one source–detector position without the colloid. The dotted–dashed curve illustrates the correlation function decay that is due to ensemble averaging (i.e., no colloid is present in the spherical cavity). This decay is independent of the source–detector position. The dashed, dotted, and solid curves correspond to g2(τ) measured with a colloid in the cavity and the source–detector positions at 1, 2, and 3, respectively, as indicated in Fig. 8.

Fig. 8
Fig. 8

Experimental measurements of the normalized temporal field autocorrelation function for three different source–detector pairs in comparison with theory. The geometry is illustrated in (a) and (b). With respect to an x–y coordinate system whose origin lies directly above the center of the spherical cavity, the source–detector axis was aligned parallel to the y axis with the source at y=1.0 cm and the detector at y=-0.75 cm. Keeping the source–detector separation fixed at 1.75 cm, we made measurements at x=0.0, 1.0, 2.0 cm, indicated by the symbols ⋄, +, and *, respectively. The uncertainty for these measurements is 3% and arises from uncertainty in the position of the source and the detector. The curves were calculated with the known experimental parameters, with DB being a free parameter (see Fig. 6). Note that larger and more rapid decays are observed when the source and the detector are nearest the dynamic sphere.

Fig. 9
Fig. 9

Experimental measurements of the normalized field correlation function for a dynamical region (a) with three different μs values plotted and (b) for three different DB values. The source and the detector were separated by 1.5 cm and were centered over the position of the sphere. In (a) the symbols ⋄, +, and * correspond to μs=3.5, 4.5, 9.0 cm-1, respectively. The curves were calculated with the known experimental parameters, with DB being a free parameter. In (b) the symbols, ⋄, +, and * correspond to a=0.813, 0.300, 0.137 µm, respectively.

Fig. 10
Fig. 10

(a) Image reconstructed from experimental measurements of the scattered correlation function. The system was a 4.6-cm-diameter cylinder with l*=0.25 cm, μa=0.002 cm-1, and DB=0 [see illustration in (b)]. A 1.3-cm-diameter spherical cavity was centered at x=0.7 cm, y=0, and z=0 and was filled with a colloid with l*=0.25 cm, μa=0.002 cm-1, and DB=1.5×10-8 cm2 s-1. A slice of the image at z=0 cm is presented in (a). The values of the reconstructed particle diffusion coefficients are indicated by the legend in units of square centimeters per second.

Fig. 11
Fig. 11

Same experimental system as that described in Fig. 6, except that the TiO2 slab now has a 6-mm-diameter cylindrical cavity instead of a spherical cavity. The cylindrical cavity is centered 13 mm below the surface of the slab, and 0.5% Intralipid is pumped through the cavity at flow speeds of 0.442, 0.884, and 1.77 cm s-1. For the solid slab, μs=4.0 cm-1 and μa=0.002 cm-1. For the Intralipid, the optical properties are assumed to be the same as those of the TiO2 slab. The correlation function is measured with the source and the detector separated by 2.0 cm, i.e., the source is 1.0 cm to the left of the vein, and the detector is 1.0 cm to the right.

Fig. 12
Fig. 12

Experimental measurements of the normalized temporal field correlation function for three different flow speeds in comparison with theory. Measurements for flow speeds of 0.442, 0.884, and 1.77 cm s-1 are indicated by the symbols +, *, and ⋄, respectively. The curves, from top to bottom, are calculated with the experimental parameters given in Fig. 11 and with effective shear rates of 3.0, 6.0, and 12.0 s-1, respectively.

Fig. 13
Fig. 13

(a) Schematic of the burn phantom. In (b) the natural log of the normalized field correlation function is plotted versus the square root (sqrt) of the correlation time for different Teflon thicknesses. The source–detector separation was held fixed at 1.2 mm. The solid curve is for a thickness of 0.132 mm. The other curves, in order of decreasing slope, are for thicknesses of 0.258, 0.408, 0.517, 0.650, and 0.802 mm.

Fig. 14
Fig. 14

Comparisons between the experimental data and those predicted by theory for different thicknesses and separations. Each graph shows the results for a particular thickness of Teflon. The solid curves are the experimental data, and the dotted curves are theoretical data. Results for separations of 0.4, 0.8, 1.2, and 1.8 mm are given.

Fig. 15
Fig. 15

Comparison between Monte Carlo simulations for correlation diffusion in a homogeneous medium and predictions of theory for different source–detector separations. Monte Carlo results are given by the symbols. The solid curves are calculated from diffusion theory. μs=10.0 cm-1, μa=0.05 cm-1, and DB=1.0×10-8 cm2 s-1.

Fig. 16
Fig. 16

Comparison between Monte Carlo results for the g1(τ) (symbols) and correlation diffusion theory (solid curves) for the system depicted in (a). An isotropic point source is positioned 1.0 cm from the center of a spherical inhomogeneity. The sphere has a diameter of 1 cm. Detectors are positioned 1.0 cm away along the z axis and are displaced off the z axis at ρ=1, 2, 3 cm. The optical properties are spatially uniform. In (b), (c), and (d) the absorption coefficient μa=0.02, 0.05, 0.10 cm-1, respectively. The ρ position of the detector is indicated in the legend.

Fig. 17
Fig. 17

Comparison of Monte Carlo simulations and correlation diffusion theory for random flow in a static tissuelike matrix. The probability of scattering from a flow particle (blood) is 0.1.

Fig. 18
Fig. 18

Experimental setup for the pig experiments. The shaded areas on the pig indicate burns of various depths.

Fig. 19
Fig. 19

Plot of temporal field correlation functions obtained from the 48-h-old burns for a source–detector separation of 800 µm. The correlation functions for the 3-s (solid curve), 5-s (dotted curve), 7-s (dashed curve), 12-s (dotted–dashed curve), and the 20-s (top curve) burns are presented.

Fig. 20
Fig. 20

Graph of decay rate of the correlation function versus source–detector separation for different burns. The burn depths are indicated in the legend.

Tables (1)

Tables Icon

Table 1 Burn Depths Were Assessed from Biopsied Tissue by Use of a Lactate Dehydrogenase Staina

Equations (80)

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

E=EoF(q)n=1N exp(ikin·rn)exp[ikout·(Rd-rn)]=EoF(q)exp(ikout·Rd)n=1N exp(-iq·rn).
G2(τ)=I(t)I(t+τ),
S(ω)=I22π- cos(ωτ)[g2(τ)-1]dτ,
G2(τ)=I2+β|G1(τ)|2,
g1(τ)=E(0)E*(τ)|E(0)|2.
g1(τ)=exp[- q2Δr2(τ)].
g1(s)(τ)=exp[- ko2Δr2(τ)(s/l*)],
g1(τ)=0P(s)exp- ko2Δr2(τ) sl*ds,
g1(τ)=exp-[3µal*+ko2Δr2(τ)]1/2 |r-rs|l*,
·G1T(r, Ωˆ, τ)Ωˆ+μtG1T(r, Ωˆ, τ)
=μsG1T(r, Ωˆ, τ)g1s(Ωˆ, Ωˆ, τ)f(Ωˆ, Ωˆ)dΩˆ
+S(r, Ωˆ).
[Dγ2-vμa- vμsko2Δr2(τ)]G1(r, τ)=-vS(r).
[2+K2(τ)]G1(r, τ)=-vSDγδ3(r-rs),
G1(r, τ)
=vS exp-[3µal*+ko2Δr2(τ)]1/2 |r-rs|l*4πDγ|r-rs|.
E(t)=Ec(t)+Ef(t).
g2(τ)=1+2βIcIf|g1,f(τ)|+βIf2|g1,f(τ)|2(Ic+If)2.
g2(τ)=1+β [Ic|g1,c(τ)|+If|g1,f(τ)|]2(Ic+If)2.
g2(τ)=1+β [Ic+If|g1,f(τ)|]2(Ic+If)2,
g1(τ)=[Ic+If|g1,f(τ)|](Ic+If).
g1s(τ)=exp[-q2Δr2(τ)],
g1(α)(τ)=exp-16j=1nqα,j2Δr2(τ].
Yn1-cos θ=nll*=sl*=S.
g1(τ)=0P(S)exp[ko2Δr2(τ)S/3]dS.
g1(τ)=0P(Y)exp13Yko2Δr2(τ)dY.
G1out(rs, rd, τ)=S exp[iKout(τ)|rd-rs|]4πDγ|rd-rs|+l=0Alhl(1)×[Kout(τ)rd][Kout(τ)rd]Yl0(θ, ϕ).
Al=-ivSKoutDγouthl(1)(Koutzs)Yl0*(π, 0)×Dγoutxjl(x)jl(y)-Dγinyjl(x)jl(y)Dγoutxhl(1)(x)jl(y)-Dγinyhl(1)(x)jl(y),
2G1(rs, r, τ)-vμa,oDγ,oG1(rs, r, τ)
-2vμsko2DB,oτDγ,oG1(rs, r, τ)
=-vDγ(r)Soδ(rs-r)+1μs,oδμs(r)·G1(rs, r, τ)+vδμa(r)Dγ,oG1(rs, r, τ)+2vμsko2δDB(r)τDγ,oG1(rs, r, τ)+3µa,oδμsG1(rs, r, τ).
Φs(rs, rd, τ)=-1G1o(rs, rd, τ)×d3r2vμsko2τδDB(r)Dγ,o×H(r, rd, τ)G1o(rs, r, τ)+vδμa(r)Dγ,oH(r, rd, τ)G1o(rs, r, τ)+δDγ(r)Dγ,oG1o(rs, r)·H(r, rd).
(Dγ2-vμa-2vμsDBko2τ- vμsΔV2ko2τ2-⅟₁₅vμs-1Γeff2ko2τ2)G1(r, τ)=-vS(r).
G1scatt(r, θ, z)=-vS2π2Dγn=10dp cos(nθ)cos(pz)×Kn[p2-(Kout)2r]Kn[p2-(Kout)2rs]×DγoutxIn(x)In(y)-DγinyIn(x)In(y)DγoutxKn(x)In(y)-DγinyKn(x)In(y),
G1(r, τ)=exp[-k1(τ)ρ2+zo2]4πρ2+zo2-exp[-k1(τ)ρ2+(zo+2zb)2]4πρ2+(zo+2zb)2+0λdλA(λ)J0(λρ) sin[k12(τ)-λ2(z+zb)]k12(τ)-λ2.
A(λ)=-{exp[iX(λ)(d-zo)]-exp[iX(λ)(d+2zb+zo)]}×Dγ(2)Y(λ)-Dγ(1)X(λ)Dγ(1)X(λ)cos[X(λ)(d+zb)]-iDγ(2)Y(λ)sin[X(λ)(d+zb)],
G1(r, τ)=0λdλJ0(λρ) -2iDγ(2) exp[iY(λ)(zo-d)]Dγ(1)X(λ)cos[X(λ)(d+zb)]-iDγ(2)Y sin[X(λ)(d+zb)]sin[X(λ)zb].
μs(randomflowcomponent)μs(randomflowcomponent)+μs(staticcomponent).
g1(τ)=0dYP(Y)exp-13Yko2Δr2(τ).
(Dγ2-vμa-Pbloodvμsko2ΔV2τ2)G1(r, τ)
=-vS(r).
Pblood=μs(blood)μs(blood)+μs(staticcomponent).
·G1T(r, Ωˆ, τ)Ωˆ+μtG1T(r, Ωˆ, τ)
=μsG1T(r, Ωˆ, τ)g1s(Ωˆ, Ωˆ, τ)f(Ωˆ, Ωˆ)dΩˆ
+S(r, Ωˆ).
G1(r, t)=dΩˆG1T(r, Ωˆ, τ),
Jg(r, t)=dΩˆG1T(r, Ωˆ, τ)Ωˆ.
G1T(r, Ωˆ, τ)=l=0Nm=-llΓl,m(r, τ)Yl,m(Ωˆ),
S(r, Ωˆ)=l=0Nm=-llql,m(r)Yl,m(Ωˆ).
f(Ωˆ·Ωˆ)=l=0 2l+14πglPl(Ωˆ·Ωˆ)=l=0m=-llglYl,m*(Ωˆ)Yl,m(Ωˆ),
g1s(Ωˆ, Ωˆ, τ)=exp[-q2Δr2(τ)]=exp[-ko2Δr2(τ)(1-Ωˆ·Ωˆ)],
g1s(Ωˆ, Ωˆ, τ)=1-2DBko2τ+2DBko2τ(Ωˆ·Ωˆ)=1-2DBko2τ+2DBko2τ 4π3×m=-11Y1,m*(Ωˆ)Y1,m(Ωˆ).
l=0Nm=-ll(Ωˆ·+μt)Γl,m(r, τ)Yl,m(Ωˆ)-ql,mYl,m(Ωˆ)-μsdΩˆΓl,m(r, τ)Yl,m(Ωˆ)×l=0Nm=-llglYl,m*(Ωˆ)Yl,m(Ωˆ)1-2DBko2τ+2DBko2τ 4π3m=-11Yl,m*(Ωˆ)Y1,m(Ωˆ)=0.
l=0Nm=-ll[Ωˆ·+μt(l)+glkc]Γl,m(r, τ)Yl,m(Ωˆ)
-ql,mYl,m(Ωˆ)-kcdΩˆΓl,m(r, τ)Yl,m(Ωˆ)
×l=0Nm=-llglYl,m*(Ωˆ)Yl,m(Ωˆ)
×4π3m=-11Y1,m*(Ωˆ)Y1,m(Ωˆ)=0.
Yl,m(Ωˆ)Y1,-1(Ωˆ)=38π Bl+1m-1Yl+1,m-1(Ωˆ)-38π Bl-mYl-1,m-1(Ωˆ),
Yl,m(Ωˆ)Y1,0(Ωˆ)=34π Al+1mYl+1,m(Ωˆ)
+34π AlmYl-1,m(Ωˆ), 
Yl,m(Ωˆ)Y1,1(Ωˆ)=38π Bl+1-m-1Yl+1,m+1(Ωˆ)
-38π BlmYl-1,m+1(Ωˆ).
4π3lmglYlm*(Ωˆ)Ylm(Ωˆ)m=-11Y1m*(Ωˆ)Y1m(Ωˆ)=4π3lmgl38π[Bl+1m-1Yl+1m-1*(Ωˆ)-Bl-mYl-1m-1*(Ωˆ)][Bl+1m-1Yl+1m-1(Ωˆ)-Bl-mYl-1m-1(Ωˆ)]+34π[Al+1mYl+1m*(Ωˆ)+AlmYl-1m*(Ωˆ)][Al+1mYl+1m(Ωˆ)+AlmYl-1m(Ωˆ)]-38π×[Bl+1-m-1Yl+1m+1*(Ωˆ)-BlmYl-1m+1*(Ωˆ)][Bl+1-m-1Yl+1m+1(Ωˆ)-BlmYl-1m+1(Ωˆ)].
l=0Nm=-ll[Ωˆ·+μt(l)+glkc]Γl,m(r, τ)Yl,m(Ωˆ)
-ql,mYl,m(Ωˆ)-kcΓl,m 4π3×38πgl-1Blm[BlmYlm(Ωˆ)-Bl-1-m-1Yl-2m(Ωˆ)]-38πgl+1Bl+1-m-1[Bl+2mYl+2m(Ωˆ)-Bl+1-m-1Ylm(Ωˆ)]+34πgl-1Alm[AlmYlm(Ωˆ)+Al-1mYl-2m(Ωˆ)]+34πgl+1Al+1m[Al+2mYl+2m(Ωˆ)+Al+1mYlm(Ωˆ)]-38πgl-1Bl-m[-Bl-mYlm(Ωˆ)+Bl-1m-1Yl-2m(Ωˆ)]+38πgl+1Bl+1m-1×[-Bl+2-mYl+2m(Ωˆ)+Bl+1m-1Ylm(Ωˆ)]=0.
μt(α)Γα,β+gαkcΓα,β-kc12(gα-1BαβBαβΓα,β-gα+1Bα+2βBα+1-β-1Γα+2,β)-12(gα-1Bα-1-β-1BαβΓα-2,β-gα+1Bα+1-β-1Bα+1-β-1Γα,β)+(gα-1AαβAαβΓα,β+gα+1Aα+2βAα+1βΓα+2,β)+(gα-1Aα-1βAαβΓα-2,β+gα+1Aα+1βAα+1βΓα,β)-12(-gα-1BBα-βBα-β×Γα,β+gα+1Bα+2-βBα+1β-1Γα+2,β)+12(-gα-1Bα-1β-1Bα-βΓα-2,β+gα+1Bα+1β-1Bα+1β-1Γα,β)+12Bα+1β-1×x-i yΓα+1,β-1-12Bα-βx-i y×Γα-1,β-1-12Bα+1-β-1x+i y×Γα+1,β+1+12Bαβx+i yΓα-1,β+1+Aα+1β zΓα+1,β+Aαβ zΓα-1,β=qα,β.
μaΓ0,0+kc(1-g1)Γ0,0+1223 x-i yΓ1,-1
-1223 x+i yΓ1,1+13 zΓ1,0=q0,0,
μt(1)Γ1,-1+(g1-)kcΓ1,-1+1223 x+i yΓ0,0
=q1,-1,
μt(1)Γ1,0+(g1-)kcΓ1,0+13 zΓ0,0=q1,0,
μt(1)Γ1,1+(g1-)kcΓ1,1-1223 x-i yΓ0,0
=q1,1.
μaG1(r, τ)+ μsko2Δr2(τ)G1(r, τ)+·Jg(r, τ)
=S0(r),
μt(1)Jg(r, τ)+ μs(g1-)ko2Δr2(τ)Jg(r, τ)
+G1(r, τ)=S1(r).
μsJg(r, τ)+G1(r, τ)=S1(r).
-·1vDγ+μa+13μsko2Δr2(τ)G1(r, τ)
=S0(r)-·3vDγS1(r),

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