Properties of the light emerging from a diffusive medium: angular dependence and flux at the external boundary.

By using the diffusion approximation of the radiative transfer equation and the partial-current boundary condition, an analytical expression for the angular dependence of the specific intensity emerging from a diffusive medium has been obtained. The analytical expression for the angular distribution has been validated by comparisons with the results of Monte Carlo simulations. By using the diffusion equation and the extrapolated boundary condition, an heuristic analytical expression for the diffuse time-resolved reflectance has also been obtained by assuming that the photon flux is simply proportional to the fluence rate. For the case of the semi-infinite medium, comparisons with Monte Carlo results are presented and time-resolved reflectance data are fitted with the simple fluence rate formula. The results obtained show that the simple expression correctly describes the time-resolved reflectance giving an error in the retrieved optical parameters smaller than that of other commonly used expressions.

[1]  R R Alfano,et al.  Should the photon flux or the photon density be used to describe the temporal profiles of scattered ultrashort laser pulses in random media? , 1993, Optics letters.

[2]  E. Gratton,et al.  Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry , 1995 .

[3]  Frank K. Tittel,et al.  The influence of boundary conditions on the accuracy of diffusion theory in time-resolved reflectance spectroscopy of biological tissues , 1995, Physics in medicine and biology.

[4]  M. Patterson,et al.  Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite turbid medium. , 1997, Journal of the Optical Society of America. A, Optics, image science, and vision.

[5]  D. Durian,et al.  Angular distribution of diffusely transmitted light. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[6]  D Contini,et al.  Photon migration through a turbid slab described by a model based on diffusion approximation. I. Theory. , 1997, Applied optics.

[7]  A Taddeucci,et al.  Photon migration through a turbid slab described by a model based on diffusion approximation. II. Comparison with Monte Carlo results. , 1997, Applied optics.

[8]  S R Arridge,et al.  The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis. , 1992, Physics in medicine and biology.

[9]  L. O. Svaasand,et al.  Boundary conditions for the diffusion equation in radiative transfer. , 1994, Journal of the Optical Society of America. A, Optics, image science, and vision.

[10]  Kevin Wells,et al.  UCL multichannel time-resolved system for optical tomography , 1997, Photonics West - Biomedical Optics.

[11]  Akira Ishimaru,et al.  Wave propagation and scattering in random media , 1997 .

[12]  R. Steiner,et al.  Spatially resolved absolute diffuse reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue. , 1996, Applied optics.

[13]  S R Arridge,et al.  An investigation of light transport through scattering bodies with non-scattering regions. , 1996, Physics in medicine and biology.

[14]  B. Wilson,et al.  A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo. , 1992, Medical physics.

[15]  B. Wilson,et al.  Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties. , 1989, Applied optics.

[16]  J. Feng.  Alternative scheme for studying gap solitons in an infinite periodic Kerr medium. , 1993, Optics letters.

[17]  G Zaccanti,et al.  Monte Carlo study of light propagation in optically thick media: point source case. , 1991, Applied optics.