A globally flat, locally rough, reflecting surface scatters incident radiation in all angular directions. This scattered radiation is depolarized, that is, it is transformed into a different state of polarization from that of the incident radiation. The expected state of polarization of the scattered radiation (described by a Stokes vector where each element is an ensemble average), is different for different materials and for different angles of incidence and detection (where the scattered radiation is measured). The surface properties are described by a Mueller matrix, so that the Stokes vector of the scattered radiation can be obtained by multiplying the Stokes vector of the incident radiation to the matrix. Many elements in the matrix are always zero, or only sometimes zero, depending on the material and the angle of incidence and detection. An experiment that measures how the nonzero elements change with angles of incidence and scatter for two rough surfaces whose surface profiles have the same statistics is described; however, one is a conductor and the other is a nonconductor. The actual results for the experimental geometry in which the angle, where the scattered radiation is detected, is equal and opposite to the angle of incidence (called specular scatter) are included. In this geometry the angular behavior of the various nonzero matrix elements show marked differences for the two surfaces. The authors postulate that the differences are primarily dependent on the material properties, rather than surface roughness, and that the differences are sufficiently gross to enable them to distinguish a conducting from a nonconducting rough surface. This postulate is reinforced by plotting, for comparison purposes, the theoretical Mueller matrix for a flat dielectric mirror (calculated from the Fresnel reflection coefficients) and the same for a flat metallic mirror. Comparing the polarized state of radiation reflected from a flat surface with the polarized state of radiation scattered from a rough surface shows that the state is largely independent of the roughness and dependent on the conducting properties of the surface.
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