Emission polarization from rough surfaces

Abstract

We revisit the theoretical model for emission polarization from rough surfaces to improve previous models. Previous models treat the directional emissivity σ s as 1- r s where r s is directional reflectivity and s stands for perpendicular or parallel component to the incident surface. The directional emissivity is based on the Kirchhoff's law and the energy conservation between incident, reflected and transmitted light. This emission model considers only linear polarization as it does not allow the cross term of parallel and perpendicular components of Fresnel reflection coefficients. In this paper, we formulate the four emission Stokes parameters with emission wave amplitudes to describe the complete emission polarization content of dielectric as well as conduction media. The emission wave amplitudes are derived from the energy conservation and are functions of Fresnel transmission coefficients and incident and refraction angles. For a conducting medium which has a complex indices of refraction, the refraction angle is redefined to avoid the physically unreasonable complex angle. The emission Stokes parameters are averaged over time and then over the roughness of the surface. The time average of the cross terms of the perpendicular and parallel emission electric fields is assumed to be zero as the emission is an incoherent process. It is found that the emission S2 is zero for a smooth surface or a surface with isotropic roughness and S3 is zero regardless of surface roughness if the time average of the cross terms is assumed to be zero. Our results are compared with previous theoretical models and lab measurements and reasonable agreement is found.