Backscatter modified Mueller matrix elements from layered stratified medium

Backscatter specific intensities for irregular stratified structures consisting of three media are presented. They are expressed in terms of the modified Mueller (phase) matrix. The modified Mueller matrix relates the scattered (modified) Stokes vector to the incident (modified) Stokes vector. We consider the case in which the uppermost interface (facing the source) is a random rough surface. In addition to scattering and depolarization upon reflection, the incident wave also undergoes scattering and depolarization upon transmission across the rough interface. For isotropic surfaces six independent backscatter Mueller matrix elements are presented as functions of the incident angle with different roughness parameters. These modified Mueller matrix elements can be used to select the optimum backscatter angle and the wavelength that could be used to remotely detect the presence of coating materials deposited upon flat substrates.