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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 considered was previously derived for the continuous wave (cw) radiative transfer equation and for the cw diffusion equation (DE) [J. Opt. Soc. Am. A14, 486 (1997)]. In this paper, we extend these findings to the time-dependent DE and we discuss some implications to diffuse optical tomography.