Analytical approach for solving the radiative transfer equation in two-dimensional layered media

Abstract This study presents an analytical approach for obtaining Green's function of the two-dimensional radiative transfer equation to the boundary-value problem of a layered medium. A conventional Fourier transform and a modified Fourier series which is defined in a rotated reference frame are applied to derive an analytical solution of the radiance in the transformed space. The Monte Carlo method was used for a successful validation of the derived solutions.

[1]  L Wang,et al.  MCML--Monte Carlo modeling of light transport in multi-layered tissues. , 1995, Computer methods and programs in biomedicine.

[2]  Simon R. Arridge,et al.  Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements , 2011, J. Comput. Phys..

[3]  Vadim A. Markel,et al.  The Green's function for the radiative transport equation in the slab geometry , 2010 .

[4]  R. Alcouffe,et al.  Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues. , 1998, Physics in medicine and biology.

[5]  V. Budak,et al.  Narrow-beam propagation in a two-dimensional scattering medium. , 2011, Journal of the Optical Society of America. A, Optics, image science, and vision.

[6]  L. Barichello,et al.  An analytical approach for a nodal scheme of two-dimensional neutron transport problems , 2011 .

[7]  Simon Arridge,et al.  Anisotropic effects in highly scattering media. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Vadim A. Markel.  Modified spherical harmonics method for solving the radiative transport equation , 2004 .

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

[10]  S. Kumar,et al.  Discrete-ordinates solution of short-pulsed laser transport in two-dimensional turbid media. , 2001, Applied optics.

[11]  Alwin Kienle,et al.  Radiative transfer in two-dimensional infinitely extended scattering media , 2011 .

[12]  G. C. Pomraning,et al.  Linear Transport Theory , 1967 .

[13]  John C. Schotland,et al.  Radiative transport equation in rotated reference frames , 2006 .

[14]  A. Kienle,et al.  Green's functions for the two-dimensional radiative transfer equation in bounded media , 2012 .

[15]  Alexander D. Klose,et al.  Reprint of: Optical tomography using the time-independent equation of radiative transfer --- Part 1: Forward model , 2010 .