Mueller matrix roots algorithm and computational considerations

H. D. Noble, R. A. Chipman

Research output: Contribution to journalArticle

27 Scopus citations

Abstract

Recently, an order-independent Mueller matrix decomposition was proposed in an effort to elucidate the nine depolarization degrees of freedom [Handbook of Optics, Vol. 1 of Mueller Matrices (2009)]. This paper addresses the critical computational issues involved in applying this Mueller matrix roots decomposition, along with a review of the principal matrix root and common methods for its calculation. The calculation of the pth matrix root is optimized around p = 105 for a 53 digit binary double precision calculation. A matrix roots algorithm is provided which incorporates these computational results. It is applied to a statistically significant number of randomly generated physical Mueller matrices in order to gain insight on the typical ranges of the depolarizing Matrix roots parameters. Computational techniques are proposed which allow singular Mueller matrices and Mueller matrices with a half-wave of retardance to be evaluated with the matrix roots decomposition.

Original languageEnglish (US)
Pages (from-to)17-31
Number of pages15
JournalOptics Express
Volume20
Issue number1
DOIs
StatePublished - Jan 2 2012

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

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