Modified reciprocity relation for the time dependent diffusion equation

The classical reciprocity relation of radiative transfer fails for two points placed in regions having different indices of refraction. A modified reciprocity relation that involves the relative refractive index between the two points con- sidered was previously derived for the continuous wave (cw) radiative transfer equation and for the cw diffusion equation (DE) [J. Opt. Soc. Am. A 14, 486 (1997)]. In this paper, we extend these findings to the time-dependent DE and we discuss some implications to diffuse optical tomography.