  Mueller polarized bi-directional scattering distribution functions (pBSDFs)
are 4x4 matrix-valued functions which depend on acquisition geometry. The most
popular pBSDF 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. 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.
