Index mismatch for diffuse photon density waves at both flat and rough diffuse-diffuse interfaces

By means of a surface-integral formalism we derive the integral equations f or diffuse photon density waves with boundary conditions corresponding to a diffuse-diffuse interface with index mismatch and solve them numerically w ithout any approximation. These numerical results are verified with Monte C arlo simulations for the planar interface case. Since the application of th e boundary condition to index-mismatched. media is difficult, an approximat ion that yields very accurate values is found. This approximation can be ea sily introduced into analytical models, and a study of its limit of validit y is shown. We demonstrate with numerical results that the multiple-scatter ing contribution that is due to surface roughness can be neglected, even wh en index mismatch is present. (C) 1999 Optical Society of America [S0740-32 32(99)01308-3].