Robust polarimetry via convex optimization

Jacob M. Leamer; Wenlei Zhang; Ravi K. Saripalli; Ryan T. Glasser; Denys I. Bondar

doi:10.1364/AO.400431

Applied Optics
Vol. 59,
Issue 28,
pp. 8886-8894
(2020)
•https://doi.org/10.1364/AO.400431

Robust polarimetry via convex optimization

Jacob M. Leamer, Wenlei Zhang, Ravi K. Saripalli, Ryan T. Glasser, and Denys I. Bondar

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Jacob M. Leamer, Wenlei Zhang, Ravi K. Saripalli, Ryan T. Glasser, and Denys I. Bondar, "Robust polarimetry via convex optimization," Appl. Opt. 59, 8886-8894 (2020)

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- Instrumentation and Measurements
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About this Article
History
- Original Manuscript: June 16, 2020
- Revised Manuscript: August 26, 2020
- Manuscript Accepted: August 28, 2020
- Published: September 29, 2020

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Abstract

We present mathematical methods, based on convex optimization, for correcting non-physical coherency matrices measured in polarimetry. We also develop the method for recovering the coherency matrices corresponding to the smallest and largest values of the degree of polarization given the experimental data and a specified tolerance. We use experimental non-physical results obtained with the standard polarimetry scheme and a commercial polarimeter to illustrate these methods. Our techniques are applied in post-processing, which complements other experimental methods for robust polarimetry.

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Supplementary Material (1)

Name	Description
Code 1	Repository for code used to solve the convex optimization problems developed in the paper.

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Linearly Polarized Data
	Measured				Corrected
Data Set	$θ$	$s_{1} / s_{0}$	$s_{2} / s_{0}$	$s_{3} / s_{0}$	$s_{1} / s_{0}$	$s_{2} / s_{0}$	$s_{3} / s_{0}$
High Intensity Standard	5	−0.928	−0.382	−0.033	−0.924	−0.381	−0.033
	35	0.781	−0.644	−0.002	0.772	−0.636	−0.002
	40	0.945	−0.335	−0.005	0.942	−0.334	−0.005
High Intensity Polarimeter	5	−0.947	−0.325	−0.038	−0.945	−0.325	−0.038
	10	−0.771	−0.639	−0.038	−0.770	−0.637	−0.038
	15	−0.503	−0.866	−0.039	−0.502	−0.864	−0.038
	20	−0.199	−0.982	−0.039	−0.199	−0.979	−0.039
	25	0.160	−0.989	−0.036	0.160	−0.987	−0.036
	30	0.494	−0.869	−0.033	0.494	−0.869	−0.033
Low Intensity Polarimeter	0	−0.999	−0.010	−0.043	−0.999	−0.010	−0.043
Low Intensity Polarimeter	90	−0.999	−0.005	−0.056	−0.998	−0.005	−0.056

Elliptically Polarized Data
	Measured				Corrected
Data Set	$θ$	$s_{1} / s_{0}$	$s_{2} / s_{0}$	$s_{3} / s_{0}$	$s_{1} / s_{0}$	$s_{2} / s_{0}$	$s_{3} / s_{0}$
Low Intensity Standard	0	−0.990	0.105	0.139	−0.985	0.104	0.138
	10	−0.944	−0.232	0.384	−0.903	−0.222	0.369
	20	−0.683	−0.473	0.590	−0.670	−0.464	0.579
	50	−0.042	0.070	1.00	−0.042	0.070	0.997
	60	−0.196	0.354	1.02	−0.179	0.324	0.929
	70	−0.513	0.496	0.944	−0.434	0.419	0.798
	80	−0.826	0.333	0.703	−0.728	0.294	0.620
	90	−0.993	0.075	0.344	−0.943	0.071	0.326
	180	−0.992	0.117	0.112	−0.987	0.117	0.111
High Intensity Standard	0	−0.999	0.058	0.013	−0.998	0.058	0.013
	70	−0.616	0.558	0.663	−0.580	0.525	0.623
	80	−0.908	0.356	0.402	−0.861	0.338	0.381
	120	−0.225	−0.438	−0.896	−0.220	−0.429	−0.876
	130	−0.020	−0.185	−0.991	−0.020	−0.184	−0.983
Low Intensity Polarimeter	10	−0.917	−0.356	−0.232	−0.907	−0.353	−0.230
	20	−0.640	−0.549	−0.555	−0.634	−0.544	−0.550
	30	−0.295	−0.510	−0.813	−0.293	−0.508	−0.810
	40	−0.062	−0.264	−0.967	−0.062	−0.263	−0.963
	90	−0.992	−0.073	−0.114	−0.991	−0.073	−0.114
	100	−0.894	−0.408	0.237	−0.884	−0.404	0.234
	110	−0.595	−0.602	0.565	−0.585	−0.591	0.556
	120	−0.246	−0.554	0.821	−0.241	−0.543	0.805
	130	−0.008	−0.291	0.960	−0.008	−0.290	0.957
High Intensity Polarimeter	10	−0.904	−0.342	−0.278	−0.899	−0.340	−0.277
	20	−0.610	−0.529	−0.602	−0.606	−0.525	−0.598
	30	−0.262	−0.474	−0.847	−0.261	−0.471	−0.843
	40	−0.032	−0.223	−0.979	−0.031	−0.222	−0.975
	50	−0.019	0.110	−0.995	−0.019	0.110	−0.994
	100	−0.877	−0.399	0.299	−0.869	−0.396	0.296
	110	−0.578	−0.569	0.609	−0.570	−0.561	0.600
	120	−0.224	−0.502	0.851	−0.221	−0.496	0.840
	130	0.010	−0.222	0.985	0.010	−0.219	0.976
	140	0.010	0.116	0.994	0.010	0.116	0.993

Linearly Polarized Data
	Measured				Corrected
Data Set	$θ$	$s_{1} / s_{0}$	$s_{2} / s_{0}$	$s_{3} / s_{0}$	$s_{1} / s_{0}$	$s_{2} / s_{0}$	$s_{3} / s_{0}$
High Intensity Standard	5	−0.928	−0.382	−0.033	−0.924	−0.381	−0.033
	35	0.781	−0.644	−0.002	0.772	−0.636	−0.002
	40	0.945	−0.335	−0.005	0.942	−0.334	−0.005
High Intensity Polarimeter	5	−0.947	−0.325	−0.038	−0.945	−0.325	−0.038
	10	−0.771	−0.639	−0.038	−0.770	−0.637	−0.038
	15	−0.503	−0.866	−0.039	−0.502	−0.864	−0.038
	20	−0.199	−0.982	−0.039	−0.199	−0.979	−0.039
	25	0.160	−0.989	−0.036	0.160	−0.987	−0.036
	30	0.494	−0.869	−0.033	0.494	−0.869	−0.033
Low Intensity Polarimeter	0	−0.999	−0.010	−0.043	−0.999	−0.010	−0.043
Low Intensity Polarimeter	90	−0.999	−0.005	−0.056	−0.998	−0.005	−0.056

Elliptically Polarized Data
	Measured				Corrected
Data Set	$θ$	$s_{1} / s_{0}$	$s_{2} / s_{0}$	$s_{3} / s_{0}$	$s_{1} / s_{0}$	$s_{2} / s_{0}$	$s_{3} / s_{0}$
Low Intensity Standard	0	−0.990	0.105	0.139	−0.985	0.104	0.138
	10	−0.944	−0.232	0.384	−0.903	−0.222	0.369
	20	−0.683	−0.473	0.590	−0.670	−0.464	0.579
	50	−0.042	0.070	1.00	−0.042	0.070	0.997
	60	−0.196	0.354	1.02	−0.179	0.324	0.929
	70	−0.513	0.496	0.944	−0.434	0.419	0.798
	80	−0.826	0.333	0.703	−0.728	0.294	0.620
	90	−0.993	0.075	0.344	−0.943	0.071	0.326
	180	−0.992	0.117	0.112	−0.987	0.117	0.111
High Intensity Standard	0	−0.999	0.058	0.013	−0.998	0.058	0.013
	70	−0.616	0.558	0.663	−0.580	0.525	0.623
	80	−0.908	0.356	0.402	−0.861	0.338	0.381
	120	−0.225	−0.438	−0.896	−0.220	−0.429	−0.876
	130	−0.020	−0.185	−0.991	−0.020	−0.184	−0.983
Low Intensity Polarimeter	10	−0.917	−0.356	−0.232	−0.907	−0.353	−0.230
	20	−0.640	−0.549	−0.555	−0.634	−0.544	−0.550
	30	−0.295	−0.510	−0.813	−0.293	−0.508	−0.810
	40	−0.062	−0.264	−0.967	−0.062	−0.263	−0.963
	90	−0.992	−0.073	−0.114	−0.991	−0.073	−0.114
	100	−0.894	−0.408	0.237	−0.884	−0.404	0.234
	110	−0.595	−0.602	0.565	−0.585	−0.591	0.556
	120	−0.246	−0.554	0.821	−0.241	−0.543	0.805
	130	−0.008	−0.291	0.960	−0.008	−0.290	0.957
High Intensity Polarimeter	10	−0.904	−0.342	−0.278	−0.899	−0.340	−0.277
	20	−0.610	−0.529	−0.602	−0.606	−0.525	−0.598
	30	−0.262	−0.474	−0.847	−0.261	−0.471	−0.843
	40	−0.032	−0.223	−0.979	−0.031	−0.222	−0.975
	50	−0.019	0.110	−0.995	−0.019	0.110	−0.994
	100	−0.877	−0.399	0.299	−0.869	−0.396	0.296
	110	−0.578	−0.569	0.609	−0.570	−0.561	0.600
	120	−0.224	−0.502	0.851	−0.221	−0.496	0.840
	130	0.010	−0.222	0.985	0.010	−0.219	0.976
	140	0.010	0.116	0.994	0.010	0.116	0.993

Abstract

Supplementary Material (1)

Cited By

Figures (6)

Tables (2)

Equations (18)

Applied Optics