Bilinear constraints between elements of the 4 x 4 Mueller-Jones transfer matrix of polarization theory

Abstract

When the 4 x 4 Mueller matrix of an optical system represents a situation in which the polarization of the light is unchanged, then the elements of the Mueller matrix are derivable from a 2 x 2 Jones matrix. The general Mueller matrix contains 16 independent parameters, whereas the Jones matrix contains 7 independent parameters. Consequently, 9 identities exist between the 16 matrix elements. The purpose of this note is to display explicitly these 9 nonlinear (bilinear) equations. These equations are then used to study the number of independent parameters of a recent experimental determination by Howell of the Mueller matrix of a collimator-radiometer system.