Preflight calibration of the Imaging Magnetograph eXperiment
polarization modulation package
based on liquid-crystal variable
retarders

Néstor Uribe-Patarroyo; Alberto Alvarez-Herrero; Valentín Martínez Pillet

doi:10.1364/AO.51.004954

Applied Optics
Vol. 51,
Issue 21,
pp. 4954-4970
(2012)
•https://doi.org/10.1364/AO.51.004954

Preflight calibration of the Imaging Magnetograph eXperiment polarization modulation package based on liquid-crystal variable retarders

Néstor Uribe-Patarroyo, Alberto Alvarez-Herrero, and Valentín Martínez Pillet

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Néstor Uribe-Patarroyo, Alberto Alvarez-Herrero, and Valentín Martínez Pillet, "Preflight calibration of the Imaging Magnetograph eXperiment polarization modulation package based on liquid-crystal variable retarders," Appl. Opt. 51, 4954-4970 (2012)

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Abstract

We present the study, characterization, and calibration of the polarization modulation package (PMP) of the Imaging Magnetograph eXperiment (IMaX) instrument, a successful Stokes spectropolarimeter on board the SUNRISE balloon project within the NASA Long Duration Balloon program. IMaX was designed to measure the Stokes parameters of incoming light with a signal-to-noise ratio of at least $10^{3}$ , using as polarization modulators two nematic liquid-crystal variable retarders (LCVRs). An ad hoc calibration system that reproduced the optical and environmental characteristics of IMaX was designed, assembled, and aligned. The system recreates the optical beam that IMaX receives from SUNRISE with known polarization across the image plane, as well as an optical system with the same characteristics of IMaX. The system was used to calibrate the IMaX PMP in vacuum and at different temperatures, with a thermal control resembling the in-flight one. The efficiencies obtained were very high, near theoretical maximum values: the total efficiency in vacuum calibration at nominal temperature was 0.972 (1 being the theoretical maximum). The condition number of the demodulation matrix of the same calibration was 0.522 (0.577 theoretical maximum). Some inhomogeneities of the LCVRs were clear during the pixel-by-pixel calibration of the PMP, but it can be concluded that the mere information of a pixel-per-pixel calibration is sufficient to maintain high efficiencies in spite of inhomogeneities of the LCVRs.

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LCVR1: $ρ$ [deg]	LCVR2: $σ$ [deg]
315.00	234.74
315.00	125.26
225.00	54.74
225.00	305.26

Illumination System
Item	Length [mm]
$l_{1}$	24
$l_{2}$	129
$l_{P}$	50
$l_{3}$	237
$l_{4}$	210
$l_{C}$	4
$l_{5}$	188
Total	842
Detection System
Item	Length [mm]
$l_{6}$	43
$l_{7}$	12
$l_{8}$	186
$l_{W 2}$	9
$l_{9}$	50
$l_{10}$	150
$l_{A}$	50
$l_{11}$	450
$l_{12}$	400
Total	1350

Mueller Matrix Element	Mean	SD
A at 0 deg
$M_{11}^{'}$	$\equiv 1$	—
$M_{12}^{'}$	1.001	0.001
$M_{13}^{'}$	0.002	0.001
$M_{14}^{'}$	0.004	0.002
A at 45 deg
$M_{11}^{''}$	$\equiv 1$	—
$M_{12}^{''}$	0.000	0.000
$M_{13}^{''}$	1.009	0.001
$M_{14}^{''}$	$- 0.022$	0.001

V1 [volts]	LCVR1 [deg]	V2 [volts]	LCVR2 [deg]
2.540	304	2.535	242
2.540	318	9.000	127
3.120	230	4.300	54
3.120	220	2.900	309

Mean Modulation Matrix
1.003	0.462	$- 0.641$	$- 0.528$
0.999	0.605	0.515	0.607
0.996	$- 0.590$	0.664	$- 0.442$
1.002	$- 0.623$	$- 0.499$	0.555
Modulation Matrix SD
0.003	0.034	0.019	0.019
0.003	0.011	0.013	0.008
0.002	0.019	0.011	0.010
0.003	0.022	0.022	0.016

Demodulation Matrix				Efficiencies
0.292	0.243	0.253	0.213	0.993
0.376	0.491	$- 0.383$	$- 0.486$	0.571
-0.430	0.368	0.488	$- 0.422$	0.582
$- 0.490$	0.445	$- 0.448$	0.492	0.533
Total efficiency				0.974
Demodulation Matrix SD				Efficiencies SD
0.003	0.008	0.008	0.004	0.001
0.010	0.008	0.008	0.014	0.006
0.017	0.020	0.018	0.016	0.006
0.011	0.009	0.012	0.012	0.007

Mean Modulation Matrix
1.008	0.494	$- 0.616$	$- 0.538$
1.001	0.615	0.491	0.617
0.991	$- 0.593$	0.663	$- 0.421$
1.000	$- 0.604$	$- 0.510$	0.552
Modulation Matrix SD
0.003	0.034	0.018	0.020
0.003	0.012	0.015	0.008
0.003	0.019	0.012	0.009
0.003	0.022	0.022	0.016

Demodulation Matrix				Efficiencies
0.288	0.234	0.261	0.217	0.994
0.370	0.487	$- 0.385$	$- 0.479$	0.577
$- 0.418$	0.375	0.497	$- 0.447$	0.572
$- 0.502$	0.456	$- 0.435$	0.480	0.533
Total efficiency				0.972
Demodulation Matrix SD				Efficiencies SD
0.003	0.007	0.007	0.004	0.001
0.010	0.009	0.009	0.014	0.006
0.016	0.020	0.019	0.014	0.006
0.011	0.010	0.012	0.013	0.007

Mean Modulation Matrix Difference				Mean Demodulation Matrix Difference				$〈 δ S_{i} 〉$
$O_{vacuum} - O_{ambient pressure}$				$Δ D = D_{vacuum} - D_{ambient pressure}$				$〈 δ S_{i} 〉$
0.005	0.032	0.025	$- 0.010$	$- 0.004$	$- 0.009$	0.008	0.005	0.000
0.002	0.010	$- 0.024$	0.010	$- 0.006$	$- 0.005$	$- 0.002$	0.007	$- 0.006$
$- 0.005$	$- 0.002$	$- 0.001$	0.021	0.012	0.007	0.010	$- 0.025$	0.003
$- 0.002$	0.019	$- 0.012$	$- 0.003$	$- 0.012$	0.011	0.013	$- 0.012$	0.000

Mean Modulation Matrix
1.004	0.448	$- 0.645$	$- 0.541$
1.004	0.626	0.506	0.602
0.997	$- 0.574$	0.672	$- 0.443$
0.995	$- 0.647$	$- 0.492$	0.545
Modulation Matrix SD
0.003	0.034	0.018	0.019
0.003	0.011	0.014	0.009
0.002	0.019	0.011	0.010
0.003	0.021	0.022	0.016

Mean Modulation Matrix
1.003	0.654	$- 0.423$	$- 0.527$
1.000	0.601	0.337	0.720
0.995	$- 0.661$	0.695	$- 0.229$
1.002	$- 0.459$	$- 0.690$	0.494
Modulation Matrix SD
0.003	0.038	0.025	0.032
0.003	0.018	0.016	0.015
0.003	0.022	0.017	0.011
0.003	0.035	0.027	0.016

Demodulation Matrix				Efficiencies
0.302	0.175	0.311	0.212	0.973
0.391	0.452	$- 0.412$	$- 0.434$	0.591
$- 0.266$	0.375	0.496	$- 0.601$	0.552
$- 0.622$	0.593	$- 0.319$	0.349	0.510
Total efficiency				0.956
Demodulation Matrix SD				Efficiencies SD
0.005	0.011	0.010	0.005	0.006
0.019	0.019	0.010	0.015	0.006
0.020	0.024	0.024	0.019	0.006
0.012	0.017	0.012	0.017	0.008

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Applied Optics