Polarization in reflectance imaging

The Sinclair and Kennaugh matrices are widely used in the remote sensing discipline for signals detected in the backward direction. The connections between the Jones matrix and the Sinclair matrix, and between the Mueller matrix and the Kennaugh matrix, are explored. Different operations on the Jones matrix and their corresponding effects on the Mueller matrix, coherency matrix, and coherence vector are derived. As an example, the Sinclair matrix leads to a Mueller-Sinclair matrix, and a transformed coherence vector. The Kennaugh matrix is not, however, a Mueller matrix, but can be determined from the Mueller or Mueller-Sinclair matrices. We consider backscattering through a medium on a perfect mirror. We propose that backscattering from a uniform medium can be modeled as an effective uniform medium situated on a perfectly reflective substrate, and the elementary polarization properties derived. In this way, the concept of a uniform polarizing medium can be extended to the reflectance geometry. An experimental Mueller matrix from the literature is considered as an example.