Light propagation through diffusive media can be described by the diffusion equation in a space-time domain. Further, fluorescence can be described by a system of coupled diffusion equations. This paper analyzes time-domain measurements, which measure the temporal point-spread function (TPSF), at a boundary of such diffusive media with a given source and detector. We focus on the temporal position of the TPSF maximum, which we refer to as the peak time. Although some unique properties of solutions of this system have been numerically studied, we give a mathematical analysis of peak time, providing proof of the existence, uniqueness, and the explicit expression of the peak time. We clearly show the relationship between the peak time and the object position in a medium.

翻译：通过 diffusive 介质的光传播可以通过一个时空域的传播方程式来描述。 此外, 荧光可以通过一个混合扩散方程式系统来描述。 本文分析时间- 域测量, 测量时间- 范围功能( TPSF), 与给定源和探测器相交 。 我们集中关注 TPSF 最大值的时间位置, 我们称之为峰值时间 。 虽然已经对这个系统解决方案的某些独特特性进行了数字化研究, 但我们对峰值时间进行了数学分析, 提供了峰值时间的存在、 独特性以及峰值时间的清晰表达。 我们清楚地展示了峰值时间与介质对象位置之间的关系 。