Conversion of 3×3 Mueller matrix to 4×4 Mueller matrix for non-depolarizing samples

Abstract

A minimum of 16 measurements involving both linear and circularly polarized light are required to determine the Mueller matrix of a sample which completely describes the polarization properties of the sample. In contrast a 3×3 partial Mueller matrix, devoid of last row and column of conventional Mueller matrix, can be obtained by using nine linear polarization measurements. Further, with only linear polarization measurements the limitation on spectral coverage imposed by quarter wave plates required for circular polarization measurements is avoided. However, a drawback of this approach is that the data analysis tools developed for 4×4 Mueller matrix cannot be applied in this case. To address this issue we show that for non-depolarizing media the various symmetry constraints on Muller matrix elements can be used to obtain the 4×4 Mueller matrix from the measured 3×3 Mueller matrix. This method should prove particularly useful for measurement of Mueller matrix in the spectral region for which retarders are either not readily available or inconvenient to use.