On the equivalence of optimization metrics in Stokes polarimetry
File(s)
Author(s)
Foreman, Matthew R
Goudail, François
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.
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.
Date Issued
2019-03-05
Date Acceptance
2019-02-14
Citation
Optical Engineering, 2019, 58 (8)
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
The Royal Society
Royal Society
Grant Number
UF150335
University Research Fellowship
Subjects
0205 Optical Physics
0906 Electrical and Electronic Engineering
0801 Artificial Intelligence and Image Processing
Optics
Publication Status
Published
Date Publish Online
2019-03-05