Jones and Mueller matrices: structure, symmetry relations and information content

Abstract

When light propagates through a linear medium, its polarization properties can be described either by the Stokes vector or, under definite conditions, by Jones vector formalisms. The effect of medium on the light is then to transform the Stokes or Jones vector, so that the medium can be represented by a transformation matrix. This transformation is usually known as the Mueller matrix (Bohren and Huffman, 1983; Brosseau; 1998) when it acts on the four-dimensional Stokes vector or as the Jones matrix (Azzam and Bashara, 1987; Collett, 1993; Shurcliff, 1962) when it acts on Jones vector. Information contained in the Mueller matrix has many useful applications in such diverse fields as interaction with various optical systems (Shurcliff, 1962; Azzam and Bashara, 1977; Collett, 1993; Brosseau, 1998), cloud diagnostics (van de Hulst, 1957; Bohren and Huffman, 1983; Mishchenko et al., 2000, 2002; Kokhanovsky, 2003b), remote sensing in the ocean, atmosphere and terrestrial (Boerner, 1992; Kokhanovsky, 2001, 2003a, 2003b; Muttiah, 2002), and tissue optics (Priezzhev et al., 1989; Tuchin, 2002, 2004).