Transient response of a layer of discrete random media over a dielectric half space

A solution is presented in the time domain for the scattering of a short pulse incident on a layer of discrete random media. The layer consists of identical, but randomly oriented particles situated above a homogeneous (i.e. deterministic) half-space. A solution is found for the backscattered pulse when the incident pulse is obliquely incident on the layer. The solution is obtained in the case of low particle density using the distorted Born approximation. The short pulse solution is an approximation to the impulse response (Green´s function) for the layer and as such can be used to compute the response to pulses of arbitrary shape