The exact solution of the time-dependent equation of radiative transfer in a semi-infinite atmosphere

Abstract

The exact solution of the time-dependent equation of radiative transfer was obtained for the emergent intensity of radiation from a homogeneous semi-infinite atmosphere whose surface is illuminated by a pulsed beam of radiation, allowing for two parameters having dimension of time: the mean time of temporal capture and the mean free time. The solution is expressed in the form of convergent infinite series. Each term is a product of two known functions whose numerical values are known or can be computed. Using the simple expression of the time-dependent emergent intensity, we can derive the fundamental relations for it.