## Abstract

We propose a new algorithm, the pseudopolar decomposition, to decompose a Jones or a Mueller–Jones matrix into a sequence of matrix factors: $\mathbf{J}\cong {\mathbf{J}}_{R}{\mathbf{J}}_{D}{\mathbf{J}}_{1C}{\mathbf{J}}_{2C}$ or $\mathbf{M}\cong {\mathbf{M}}_{R}{\mathbf{M}}_{D}{\mathbf{M}}_{1C}{\mathbf{M}}_{2C}$. The matrices ${\mathbf{J}}_{R}$
$\left({\mathbf{M}}_{R}\right)$ and ${\mathbf{J}}_{D}$
$\left({\mathbf{M}}_{D}\right)$ parameterize, respectively, the retardation and dichroic properties of **J**
$\left(\mathbf{M}\right)$ in a good approximation, while ${\mathbf{J}}_{iC}$
$\left({\mathbf{M}}_{iC}\right)$ are correction factors that arise from the noncommutativity of the polarization properties. The exponential versions of the general Jones matrix are used to demonstrate the pseudopolar decomposition and to calculate each one of the matrix factors. The decomposition preserves all the polarization properties of the system on the factorized ${\mathbf{J}}_{R}$
$\left({\mathbf{M}}_{R}\right)$ and ${\mathbf{J}}_{D}$
$\left({\mathbf{M}}_{D}\right)$ matrix terms. The algorithm that calculates the pseudopolar decomposition for experimentally determined Mueller matrices is presented.

© 2009 Optical Society of America

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