Real bivector representation of target backscattering matrix and the Mueller matrix construction

Vector decomposition of the coherent backscattering matrix conveniently leads to generalisation to partially coherent scattering via the Hermitian covariance matrix. Recently, it was shown how this formalism could be incorporated within the Stokes-Mueller calculus, but the requirement for complex vectors and covariance matrices leads to some problems in defining transformation laws. These are overcome by obtaining a closely related real representation of the coherent scattering matrix as a four-dimensional bivector. This permits a description of coherent scattering within an extended Stokes algebra, and a particularly simple construction of the Mueller matrix in terms of the bivector