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Mueller matrix cone and its application to filtering

: Zander, Tim; Beyerer, Jürgen

Fulltext urn:nbn:de:0011-n-5958193 (299 KByte PDF)
MD5 Fingerprint: 21391dc5b9a912527121274abc88d617
Created on: 10.7.2020

OSA continuum 3 (2020), No.6, pp.1376-1384
ISSN: 2578-7519
Journal Article, Electronic Publication
Fraunhofer IOSB ()

We show that there is an isometry between the real ambient space of all Mueller matrices and the space of all Hermitian matrices that maps the Mueller matrices onto the positive semidefinite matrices. We use this to establish an optimality result for the filtering of Mueller matrices, which roughly says that it is always enough to filter the eigenvalues of the corresponding “coherency matrix.” Then we further explain how the knowledge of the cone of Hermitian positive semidefinite matrices can be transferred to the cone of Mueller matrices with a special emphasis towards optimisation. In particular, we suggest that means of Mueller matrices should be computed within the corresponding Riemannian geometry.