Mueller matrix polarimetry with four photoelastic modulators: theory and calibration

Oriol Arteaga; John Freudenthal; Baoliang Wang; Bart Kahr

doi:10.1364/AO.51.006805

Applied Optics
Vol. 51,
Issue 28,
pp. 6805-6817
(2012)
•https://doi.org/10.1364/AO.51.006805

Mueller matrix polarimetry with four photoelastic modulators: theory and calibration

Oriol Arteaga, John Freudenthal, Baoliang Wang, and Bart Kahr

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Oriol Arteaga, John Freudenthal, Baoliang Wang, and Bart Kahr, "Mueller matrix polarimetry with four photoelastic modulators: theory and calibration," Appl. Opt. 51, 6805-6817 (2012)

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Table of Contents Category
- Instrumentation, Measurement, and Metrology
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About this Article
History
- Original Manuscript: June 7, 2012
- Revised Manuscript: August 16, 2012
- Manuscript Accepted: August 20, 2012
- Published: September 26, 2012

Abstract

A spectroscopic Mueller matrix polarimeter with four photoelastic modulators (PEMs) and no moving parts is introduced. In the 4-PEM polarimeter, all the elements of the Mueller matrix are simultaneously determined from the analysis of the frequencies of the time-dependent intensity of the light beam.

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Element	Harmonic	$Ω_{k}$	Frequency (kHz)	$\prod_{i = 0}^{3} J_{x} (A_{i})$
$m_{01}$	$X_{0 δ} X_{1 δ}$	b $ω_{0} + ω_{1}$	109.508	0.270
		c $- ω_{0} + ω_{1}$	9.940	0.201
$m_{02}$	$Y_{0 δ}$	b,c $2 ω_{0}$	99.568	0.432
$m_{03}$	$X_{0 δ} Y_{1 δ}$	b $- ω_{0} - 2 ω_{1}$	169.232	0.224
		c $ω_{0}$	49.784	0.430
$m_{10}$	$X_{2 δ} X_{3 δ}$	b $ω_{2} + ω_{3}$	89.169	0.270
		c $ω_{2} + ω_{3}$	89.169	0.201
$m_{11}$	$X_{0 δ} X_{1 δ} X_{2 δ} X_{3 δ}$	b $ω_{0} + ω_{1} - ω_{2} + ω_{3}$	114.523	0.073
		c $ω_{0} + ω_{1} - ω_{2} + ω_{3}$	114.523	0.041
$m_{12}$	$Y_{0 δ} X_{2 δ} X_{3 δ}$	b $2 ω_{0} + ω_{2} + ω_{3}$	188.737	0.116
		c $2 ω_{0} + ω_{2} + ω_{3}$	188.737	0.087
$m_{13}$	$X_{0 δ} Y_{1 δ} X_{2 δ} X_{3 δ}$	b $ω_{0} - 2 ω_{1} + ω_{2} + ω_{3}$	$19.505$	0.060
		c $ω_{0} + ω_{2} + ω_{3}$	138.953	0.086
$m_{20}$	$Y_{3 δ}$	b,c $2 ω_{3}$	94.184	0.432
$m_{21}$	$X_{0 δ} X_{1 δ} Y_{3 δ}$	b $- ω_{0} + ω_{1} - 2 ω_{3}$	102.124	0.116
		c $- ω_{0} + ω_{1} + 2 ω_{3}$	84.244	0.087
$m_{22}$	$Y_{0 δ} Y_{3 δ}$	b,c $2 ω_{0} - 2 ω_{3}$	5.384	0.186
$m_{23}$	$X_{0 δ} Y_{1 δ} Y_{3 δ}$	b $ω_{0} - 2 ω_{1} - 2 ω_{3}$	163.848	0.097
		c $ω_{0} - 2 ω_{3}$	44.400	0.185
$m_{30}$	$Y_{2 δ} X_{3 δ}$	b $- ω_{2} + ω 3$	37.062	0.224
		c $ω 3$	47.092	0.430
$m_{31}$	$X_{0 δ} X_{1 δ} Y_{2 δ} X_{3 δ}$	b $ω_{0} + ω_{1} - 2 ω_{2} + ω_{3}$	72.446	0.270
		c $ω_{0} + ω_{1} + ω_{3}$	156.600	0.270
$m_{32}$	$Y_{0 δ} Y_{2 δ} X_{3 δ}$	b $2 ω_{0} + 2 ω_{2} - ω 3$	136.630	0.060
		c $2 ω_{0} - ω 3$	52.476	0.086
$m_{33}$	$X_{0 δ} Y_{1 δ} Y_{2 δ} X_{3 δ}$	b $ω_{0} + 2 ω_{1} - 2 ω_{2} + ω_{3}$	132.170	0.050
		c $ω_{0} + ω_{3}$	96.876	0.184
cal0d	$X_{0 δ} Y_{2 δ} X_{3 δ}$	b $ω_{0} + 2 ω 2 + ω 3$	216.324	0.116
		c $ω_{0} + 2 ω 2 + ω 3$	86.846	0.019
cal1	$X_{0 δ} Y_{1 δ} X_{3 δ}$	b $ω_{0} + 2 ω 1 - ω 3$	181.030	0.116
		c $ω_{0} + 2 ω 1 - ω 3$	122.140	0.019
cal2	$Y_{0 δ} X_{3 δ}$	b,c $- 2 ω_{0} + ω_{3}$	52.476	0.224
cal3	$X_{0 δ} Y_{3 δ}$	b,c $ω_{0} - 2 ω_{3}$	44.400	0.224
cal4	$Y_{1 δ} X_{2 δ} X_{3 δ}$	b $2 ω_{1} - ω_{2} + ω_{3}$	124.463	0.116
		c $- ω_{2} + ω_{3}$	5.015	0.167
cal5	$X_{0 δ} Y_{1 δ} X_{2 δ}$	b $- ω_{0} + {2 ω}_{1} - ω_{2}$	111.741	0.116
		c $- ω_{0} + ω_{2}$	7.707	0.167
cal6	$Y_{0 δ} X_{1 δ} Y_{2 δ} X_{3 δ}$	b $2 ω_{0} + ω_{1} - 2 ω_{2} + ω_{3}$	122.230	0.072
		c $- 2 ω_{0} + ω_{1} + ω_{3}$	7.248	0.270
cal7	$X_{0 δ} X_{1 δ} X_{2 δ} Y_{3 δ}$	b $ω_{0} + ω_{1} - 2 ω_{2} - 2 ω_{3}$	68.830	0.050
		c $ω_{0} + ω_{1} - 2 ω_{3}$	15.324	0.072

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Applied Optics