Finite-difference time-domain and steady-state analysis with novel boundary conditions of optical transport in a three-dimensional scattering medium illuminated by an isotropic point source

Abstract

We evaluate the numerical accuracy of finite-difference time-domain (FDTD) analysis of optical transport in a three-dimensional scattering medium illuminated by an isotropic point source. This analysis employs novel boundary conditions for the diffusion equation. The power radiated from an isotropic point source located at a depth equal to the reciprocal of the reduced scattering coefficient (1/μ'(s)) below the surface at the irradiated position is introduced to the integral form of the diffusion equation. Finite-difference approximations of the diffusion equation for a surface cell are derived by utilizing new boundary conditions that include an isotropic source even in a surface cell. Steady-state and time-resolved reflectances are calculated by FDTD analysis for a semi-infinite uniform scattering medium illuminated by an isotropic point source. The numerical results agree reasonably with the analytical solutions for μ'(s)=1-3 mm(-1) without resizing the mesh elements.