Light diffusion through a turbid parallelepiped.

Solutions of the diffusion approximation to the radiative transport equation are derived for a turbid (rectangular) parallelepiped using the method of image sources and applying extrapolated boundary conditions. The derived solutions are compared with Monte Carlo simulations in the steady-state and time domains. It is found that the diffusion theory is in good agreement with Monte Carlo simulations provided that the light is detected sufficiently far from the incident beam. Applications of the derived solutions, including the determination of the optical properties of the turbid parallelepiped, are discussed.

[1]  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.

[2]  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.

[3]  J. C. Jaeger,et al.  Conduction of Heat in Solids , 1952 .

[4]  Alwin Kienle,et al.  Determination of the optical properties of tissue by spatially resolved transmission measurements and Monte Carlo simulations , 1994, Other Conferences.

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

[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]  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.

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

[9]  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.

[10]  J. Vesecky,et al.  Wave propagation and scattering. , 1989 .

[11]  Thomas E. Milner,et al.  A three-dimensional modular adaptable grid numerical model for light propagation during laser irradiation of skin tissue , 1996 .

[12]  Alex H. Barnett,et al.  A fast numerical method for time-resolved photon diffusion in general stratified turbid media , 2004 .

[13]  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.

[14]  Yukio Yamada,et al.  Solution of the time-dependent diffusion equation for layered diffusive media by the eigenfunction method. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.