On the equivalence of optimization metrics in Stokes polarimetry

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Title: On the equivalence of optimization metrics in Stokes polarimetry
Authors: Foreman, MR
Goudail, F
Item Type: Journal Article
Abstract: Optimization of polarimeters has historically been achieved using an assortment of performance metrics. Selection of an optimization parameter is, however, frequently made on an ad hoc basis. We rigorously demonstrate that optimization strategies in Stokes polarimetry based on three common metrics, namely the Frobenius condition number of the instrument matrix, the determinant of the associated Gram matrix, or the equally weighted variance, are frequently formally equivalent. In particular, using each metric, we derive the same set of constraints on the measurement states, correcting a previously reported proof, and show that these can be satisfied using spherical 2 designs. Discussion of scenarios in which equivalence between the metrics breaks down is also given. Our conclusions are equally applicable to optimization of the illumination states in Mueller matrix polarimetry.
Issue Date: 5-Mar-2019
Date of Acceptance: 14-Feb-2019
URI: http://hdl.handle.net/10044/1/69319
DOI: https://doi.org/10.1117/1.oe.58.8.082410
ISSN: 0091-3286
Publisher: Society of Photo-optical Instrumentation Engineers
Journal / Book Title: Optical Engineering
Volume: 58
Issue: 8
Copyright Statement: © 2019 Society of Photo-Optical Instrumentation Engineers (SPIE) [DOI: 10.1117/1.OE.58.8.082410].
Sponsor/Funder: The Royal Society
Royal Society
Funder's Grant Number: UF150335
University Research Fellowship
Keywords: 0205 Optical Physics
0906 Electrical and Electronic Engineering
0801 Artificial Intelligence and Image Processing
Optics
Publication Status: Published
Online Publication Date: 2019-03-05
Appears in Collections:Physics
Photonics
Faculty of Natural Sciences



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