Multi-carrier channeled polarimetry for photoelastic modulator systems

Andrey S. Alenin; Farhana Bashar; Michael E. Gehm; J. Scott Tyo

doi:10.1364/OL.43.005789

Optics Letters
Vol. 43,
Issue 23,
pp. 5789-5792
(2018)
•https://doi.org/10.1364/OL.43.005789

Multi-carrier channeled polarimetry for photoelastic modulator systems

Andrey S. Alenin, Farhana Bashar, Michael E. Gehm, and J. Scott Tyo

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Andrey S. Alenin, Farhana Bashar, Michael E. Gehm, and J. Scott Tyo, "Multi-carrier channeled polarimetry for photoelastic modulator systems," Opt. Lett. 43, 5789-5792 (2018)

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Abstract

Photoelastic modulator-based polarimeters use multi-carrier modulation schemes that are more complicated than the single carriers of rotating optics. Current state-of-the-art reconstruction implementations favor mathematical simplicity by using significantly abridged subsets of channels. In this Letter, we extend our generalized channeled polarimetry principles to address the challenges associated with multi-carrier modulation schemes. We demonstrate the performance forfeited by existing systems through the use of an incomplete set of information channels, as well as propose a set of more optimal system parameters that achieve better reconstruction noise characteristics. The overall improvement corresponds to a better sensitivity of up to a factor of six.

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$m_{i j}$	Harmonic	$ν_{(kHz)}$	A Amplitude	B Amplitude
$m_{00}$	DC	0	1.0000	1.0000
$m_{01}$	$ν_{1} + ν_{2}$	110	0.2009	0.2695
$m_{02}$	$2 ν_{1}$	100	0.4318	0.4318
$m_{03}$	$- ν_{1} - 2 ν_{2}$	−170	0.4299	0.2241
$m_{10}$	$ν_{3} + ν_{4}$	89	0.2009	0.2695
$m_{11}$	$ν_{1} + ν_{2} - ν_{3} + ν_{4}$	115	0.0404	0.0726
$m_{12}$	$2 ν_{1} + ν_{3} + ν_{4}$	189	0.0868	0.1164
$m_{13}$	$ν_{1} - 2 ν_{2} + ν_{3} + ν_{4}$	19	0.0864	0.0604
$m_{20}$	$2 ν_{4}$	94	0.4318	0.4318
$m_{21}$	$- ν_{1} + ν_{2} - 2 ν_{4}$	−84	0.0868	0.1164
$m_{22}$	$2 ν_{1} - 2 ν_{4}$	6	0.1864	0.1864
$m_{23}$	$ν_{1} - 2 ν_{2} - 2 ν_{4}$	−164	0.1856	0.0968
$m_{30}$	$- 2 ν_{3} + ν_{4}$	−37	0.4299	0.2241
$m_{31}$	$ν_{1} + ν_{2} - 2 ν_{3} + ν_{4}$	73	0.0864	0.0604
$m_{32}$	$2 ν_{1} + 2 ν_{3} - ν_{4}$	137	0.1856	0.0968
$m_{33}$	$ν_{1} + 2 ν_{2} - 2 ν_{3} + ν_{4}$	133	0.1848	0.0502

System	$δ_{1} = δ_{4}$	$δ_{2} = δ_{3}$	$ς_{16, 0}^{2}$	$ς_{16, 1}^{2}$	$ς_{16, 2}^{2}$	$ς_{16, 3}^{2}$	${EWV}_{16}$	$ς_{\infty, 0}^{2}$	$ς_{\infty, 1}^{2}$	$ς_{\infty, 2}^{2}$	$ς_{\infty, 3}^{2}$	${EWV}_{\infty}$
A	0.3827	0.1350	1.000	24.770	5.365	5.410	1335.5	1.000	5.389	2.623	2.308	128.15
B	0.3827	0.3827	1.000	13.767	5.365	19.904	1602.8	1.000	2.612	2.623	4.239	109.71
C	0.3827	0.4393	1.000	20.766	5.365	16.462	1900.3	1.000	3.233	2.623	3.232	101.76
D	0.3699	0.4393	1.010	19.521	5.718	15.475	1740.9	1.005	3.117	2.805	3.116	100.87

$d_{i}$	$A_{16}$	$B_{16}$	$C_{16}$	$D_{16}$	$A_{\infty}$	$B_{\infty}$	$C_{\infty}$	$D_{\infty}$
$d_{1} / d_{7}$	1.76	1.31	1.61	1.57	0.82	0.57	0.63	0.62
$d_{2} / d_{8}$	0.82	0.82	0.82	0.85	0.57	0.57	0.57	0.59
$d_{3} / d_{9}$	0.82	1.57	1.43	1.39	0.54	0.73	0.64	0.63
$d_{4} / d_{10}$	1.91	3.66	3.33	3.32	0.87	1.18	1.03	1.04
$d_{5} / d_{11}$	4.09	5.86	6.53	6.14	1.24	1.18	1.14	1.11
$d_{6} / d_{12}$	4.08	3.03	3.73	3.74	1.33	0.92	1.03	1.04
$d_{13}$	6.35	3.69	5.35	5.08	1.50	0.93	1.05	1.05
$d_{14}$	3.97	6.12	5.66	5.34	1.09	1.34	1.11	1.09
$d_{15}$	5.29	5.06	5.51	5.22	1.31	1.15	1.08	1.07

$m_{i j}$	Harmonic	$ν_{(kHz)}$	A Amplitude	B Amplitude
$m_{00}$	DC	0	1.0000	1.0000
$m_{01}$	$ν_{1} + ν_{2}$	110	0.2009	0.2695
$m_{02}$	$2 ν_{1}$	100	0.4318	0.4318
$m_{03}$	$- ν_{1} - 2 ν_{2}$	−170	0.4299	0.2241
$m_{10}$	$ν_{3} + ν_{4}$	89	0.2009	0.2695
$m_{11}$	$ν_{1} + ν_{2} - ν_{3} + ν_{4}$	115	0.0404	0.0726
$m_{12}$	$2 ν_{1} + ν_{3} + ν_{4}$	189	0.0868	0.1164
$m_{13}$	$ν_{1} - 2 ν_{2} + ν_{3} + ν_{4}$	19	0.0864	0.0604
$m_{20}$	$2 ν_{4}$	94	0.4318	0.4318
$m_{21}$	$- ν_{1} + ν_{2} - 2 ν_{4}$	−84	0.0868	0.1164
$m_{22}$	$2 ν_{1} - 2 ν_{4}$	6	0.1864	0.1864
$m_{23}$	$ν_{1} - 2 ν_{2} - 2 ν_{4}$	−164	0.1856	0.0968
$m_{30}$	$- 2 ν_{3} + ν_{4}$	−37	0.4299	0.2241
$m_{31}$	$ν_{1} + ν_{2} - 2 ν_{3} + ν_{4}$	73	0.0864	0.0604
$m_{32}$	$2 ν_{1} + 2 ν_{3} - ν_{4}$	137	0.1856	0.0968
$m_{33}$	$ν_{1} + 2 ν_{2} - 2 ν_{3} + ν_{4}$	133	0.1848	0.0502

System	$δ_{1} = δ_{4}$	$δ_{2} = δ_{3}$	$ς_{16, 0}^{2}$	$ς_{16, 1}^{2}$	$ς_{16, 2}^{2}$	$ς_{16, 3}^{2}$	${EWV}_{16}$	$ς_{\infty, 0}^{2}$	$ς_{\infty, 1}^{2}$	$ς_{\infty, 2}^{2}$	$ς_{\infty, 3}^{2}$	${EWV}_{\infty}$
A	0.3827	0.1350	1.000	24.770	5.365	5.410	1335.5	1.000	5.389	2.623	2.308	128.15
B	0.3827	0.3827	1.000	13.767	5.365	19.904	1602.8	1.000	2.612	2.623	4.239	109.71
C	0.3827	0.4393	1.000	20.766	5.365	16.462	1900.3	1.000	3.233	2.623	3.232	101.76
D	0.3699	0.4393	1.010	19.521	5.718	15.475	1740.9	1.005	3.117	2.805	3.116	100.87

Abstract

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Equations (15)

Optics Letters