The accuracy of numerical inversion of the Laplace transform applied to the time-dependent reflection function from a semi-infinite atmosphere

In order to check the accuracy of the numerical inversion of the Laplace transform when it is applied to evaluate the time-dependent diffuse reflection function from a semi-infinite atmosphere, numerical experiments are done in virtue of comparing the numerical value with the exact one. It becomes clear that the numerical inversion method is sufficiently applicable if the time dependence of incident radiation is given by the Dirac δ function. A technique which reduces the error of the numerical inversion is proposed. It gives a remarkable improvement.