<title>Study of the failure of the time-independent diffuse equation near a point source</title>

Abstract

The diffusion equation (DE) is widely used in biomedical optics for describing light propagation in tissue. However, the DE yields inaccurate results near sources. This drawback is important in practical situations, when it is of primary interest to calculate the dose of light applied or to retrieve the optical properties of the tissue near the light source, e.g., the distal end of an optical fiber. To study this problem we derived a diffusion equation for constant refractive index and rays of arbitrary divergence (DErad) from a modified radiative transfer equation for spatially varying refractive index. We solve the DErad for a time-independent point source in near field and far field, which are defined by a parameter Rcrit. The far-field solution is the solution to the time-independent DE, the near-field solution agrees well with Monte Carlo simulation results and the R crit coincides with the reported radius of inaccuracy of the DE. These results suggest that the inaccuracy of the time-independent DE near a point source is due to a non-negligible ray divergence.© (2004) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.