[OPTICAL REVIEW Vol. 16, No. 3 (2009) 283-289]
© 2009 The Optical Society of Japan
Alternative Boundary Conditions for Solving Optical Diffusion Equations by a Finite Difference Time Domain Analysis in Three-Dimensional Scattering Medium
Department of Electrical and Electronics Engineering, Kitami Institute of Technology, 165 Koen-cho, Kitami, Hokkaido 090-8507, Japan
(Received July 22, 2008; Accepted January 23, 2009)
Alternative boundary conditions for solving optical diffusion equations in three-dimensional (3-D) scattering medium by a finite difference time domain (FDTD) analysis formulated by the author are proposed. The previous boundary conditions were defined only by fluence rate, which, although essential, is only one factor needed to solve approximated diffusion equations for fluence rate. In this paper, alternative boundary conditions defined both by fluence rate and radiant flux have been proposed for use in the FDTD analysis, which is derived from the two coupled differential equations for fluence rate and radiant flux. It has been become clear that these boundary conditions are almost equivalent to the previous boundary conditions in the FDTD analysis for sufficiently fine grid spacing. For the analysis with coarser grid spacing, the proposed boundary conditions suppress analytical errors, especially in intensity of time-resolved reflectance and transmittance.
Key words: boundary conditions, diffusion equations, finite difference time domain (FDTD) analysis, 3-D scattering media, time-resolved reflectance, time-resolved transmittance