Merit functions and measurement schemes for single parameter depolarization models

Mueller polarized bi-directional scattering distribution functions (pBSDFs) are 4 × 4 matrix-valued functions which depend on acquisition geometry. A widely used backscattering pBSDF model proposed by Priest and Meier [Opt. Eng.41, 988 (2002)10.1117/1.1467360] is a weighted sum between a Fresnel matrix and an ideal depolarizer. This work's main contribution is relating the relative weight between an ideal depolarizer and Fresnel matrix to a single depolarization parameter. Rather than a 16-dimensional matrix norm, this parameter can form a one-dimensional merit function. Then, instead of a full Mueller matrix measurement, a scheme for pBSDF fitting to only two polarimetric measurements is introduced. Depolarization can be mathematically expressed as the incoherent addition of coherent states [J. Opt. Soc. Am. A30, 691 (2013)10.1364/JOSAA.30.000691]. This work shows that, for a Mueller matrix to be in the span of a Fresnel matrix and an ideal depolarizer, the weights in the incoherent addition are triply degenerate. This triple degeneracy is observed in five different colored opaque plastics treated with nine different surface textures and measured at varying acquisition geometries and wavebands.