Expressions of the peak time for time-domain boundary measurements of diffuse light

Light propagation through diffusive media can be described by the diffusion equation in a space–time domain. Furthermore, fluorescence can be described by a system of coupled diffusion equations. This paper analyzes time-domain measurements. In particular, the temporal point-spread function is measured at the boundary of a diffusive medium. Moreover, the temporal profile of fluorescence is considered. In both cases, we refer to the maximum temporal position of measured light as the peak time. In this paper, we provide proofs of the existence and uniqueness of the peak time and give explicit expressions of the peak time. The relationship between the peak time and the object position in a medium is clarified.