Optimization of fast spectrally encoded Mueller polarimeters for real-time monitoring

Sylvain Rivet; Matthieu Dubreuil; Yann Le Grand

doi:10.1364/JOSAA.36.0000C9

Journal of the Optical Society of America A
Vol. 36,
Issue 11,
pp. C9-C17
(2019)
•https://doi.org/10.1364/JOSAA.36.0000C9

Optimization of fast spectrally encoded Mueller polarimeters for real-time monitoring

Sylvain Rivet, Matthieu Dubreuil, and Yann Le Grand

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Sylvain Rivet, Matthieu Dubreuil, and Yann Le Grand, "Optimization of fast spectrally encoded Mueller polarimeters for real-time monitoring," J. Opt. Soc. Am. A 36, C9-C17 (2019)

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About this Article
History
- Original Manuscript: June 12, 2019
- Revised Manuscript: August 19, 2019
- Manuscript Accepted: September 5, 2019
- Published: October 7, 2019
Virtual Issues
JOSA A Feature Issue: Classical Optics in France (2019)

Abstract

In this paper, we report a generalized theoretical framework on spectrally encoded polarimeters to display in real time both linear and circular retardance as well as linear and circular diattenuation on the basis of a recent experimental work detailed in Sci. Rep. 9, 3972 (2019) [CrossRef] . The considered polarimeters use a broadband light source and wavelength-dependent retarders whose thicknesses are selected to guarantee minimal noise propagation and reduced data processing for real-time display of pure polarimetric effects.

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Peaks	Complex Value
$P_{a \pm b} \to P_{D_{L}}^{r o w}$	$- \frac{1}{4} (\pm m_{02} - i m_{01})$
$P_{c \pm d} \to P_{D_{L}}^{c o l u m n}$	$\pm \frac{1}{4} (m_{20} + i m_{10})$
$P_{a} \to P_{D_{C}}^{r o w}$	$- \frac{1}{2} m_{0 3}$
$P_{d} \to P_{D_{C}}^{c o l u m n}$	$\frac{1}{2} m_{30}$
$P_{a \pm (c + d)} \to P_{R_{L}}^{c o l u m n}$	$- \frac{1}{8} (m_{23} \pm i m_{13})$
$P_{a \pm (c - d)} \to P_{R_{L}}^{c o l u m n}$	$\frac{1}{8} (m_{23} \pm i m_{13})$
$P_{a \pm (b + d)} \to P_{R_{L}}^{r o w}$	$- \frac{1}{8} (\pm m_{32} - i m_{31})$
$P_{a \pm (b - d)} \to P_{R_{L}}^{r o w}$	$- \frac{1}{8} (\pm m_{32} - i m_{31})$
$P_{a \pm (b + c) + d} \to P_{R_{C}}$	$\frac{1}{16} (- (m_{11} + m_{22}) \pm i (m_{21} - m_{12}))$
$P_{a \pm (b + c) - d} \to P_{R_{C}}$	$\frac{1}{16} (m_{11} + m_{22} \pm i (m_{12} - m_{21}))$

$(a + b + c + d) f_{0}$	Configurations	$P_{R_{L}}$	$P_{R_{C}}$	$P_{D_{L}}$	$P_{D_{C}}$
$20 f_{0}$	( $2 e$ , $e$ , $5 e$ , $12 e$ ) or ( $12 e$ , $5 e$ , $e$ , $2 e$ )	$5 f_{0}$ , $11 f_{0}$ , $13 f_{0}$ , $19 f_{0}$	$4 f_{0}$ , $8 f_{0}$ , $16 f_{0}$ , $20 f_{0}$	$f_{0}$ , $3 f_{0}$ , $7 f_{0}$ , $17 f_{0}$	$2 f_{0}$ , $12 f_{0}$
$21 f_{0}$	( $e$ , $3 e$ , $5 e$ , $12 e$ ) or ( $12 e$ , $5 e$ , $3 e$ , $e$ )	$6 f_{0}$ , $10 f_{0}$ , $14 f_{0}$ , $18 f_{0}$	$3 f_{0}$ , $5 f_{0}$ , $19 f_{0}$ , $21 f_{0}$	$2 f_{0}$ , $4 f_{0}$ , $7 f_{0}$ , $17 f_{0}$	$f_{0}$ , $12 f_{0}$
$21 f_{0}$	( $2 e$ , $e$ , $5 e$ , $13 e$ ) or ( $13 e$ , $5 e$ , $e$ , $2 e$ )	$6 f_{0}$ , $12 f_{0}$ , $14 f_{0}$ , $20 f_{0}$	$5 f_{0}$ , $9 f_{0}$ , $17 f_{0}$ , $21 f_{0}$	$f_{0}$ , $3 f_{0}$ , $8 f_{0}$ , $18 f_{0}$	$2 f_{0}$ , $13 f_{0}$
$22 f_{0}$	( $2 e$ , $e$ , $5 e$ , $14 e$ ) or ( $14 e$ , $5 e$ , $e$ , $2 e$ )	$7 f_{0}$ , $13 f_{0}$ , $15 f_{0}$ , $21 f_{0}$	$6 f_{0}$ , $10 f_{0}$ , $18 f_{0}$ , $22 f_{0}$	$f_{0}$ , $3 f_{0}$ , $9 f_{0}$ , $19 f_{0}$	$2 f_{0}$ , $14 f_{0}$
$22 f_{0}$	( $2 e$ , $e$ , $6 e$ , $13 e$ ) or ( $13 e$ , $6 e$ , $e$ , $2 e$ )	$5 f_{0}$ , $9 f_{0}$ , $17 f_{0}$ , $21 f_{0}$ , $12 f_{0}$ , $14 f_{0}$	$4 f_{0}$ , $8 f_{0}$ , $18 f_{0}$ , $22 f_{0}$	$f_{0}$ , $3 f_{0}$ , $7 f_{0}$ , $19 f_{0}$	$2 f_{0}$ , $13 f_{0}$

Peaks	Complex Value
$P_{a \pm b} \to P_{D_{L}}^{r o w}$	$- \frac{1}{4} (\pm m_{02} - i m_{01})$
$P_{c \pm d} \to P_{D_{L}}^{c o l u m n}$	$\pm \frac{1}{4} (m_{20} + i m_{10})$
$P_{a} \to P_{D_{C}}^{r o w}$	$- \frac{1}{2} m_{0 3}$
$P_{d} \to P_{D_{C}}^{c o l u m n}$	$\frac{1}{2} m_{30}$
$P_{a \pm (c + d)} \to P_{R_{L}}^{c o l u m n}$	$- \frac{1}{8} (m_{23} \pm i m_{13})$
$P_{a \pm (c - d)} \to P_{R_{L}}^{c o l u m n}$	$\frac{1}{8} (m_{23} \pm i m_{13})$
$P_{a \pm (b + d)} \to P_{R_{L}}^{r o w}$	$- \frac{1}{8} (\pm m_{32} - i m_{31})$
$P_{a \pm (b - d)} \to P_{R_{L}}^{r o w}$	$- \frac{1}{8} (\pm m_{32} - i m_{31})$
$P_{a \pm (b + c) + d} \to P_{R_{C}}$	$\frac{1}{16} (- (m_{11} + m_{22}) \pm i (m_{21} - m_{12}))$
$P_{a \pm (b + c) - d} \to P_{R_{C}}$	$\frac{1}{16} (m_{11} + m_{22} \pm i (m_{12} - m_{21}))$

$(a + b + c + d) f_{0}$	Configurations	$P_{R_{L}}$	$P_{R_{C}}$	$P_{D_{L}}$	$P_{D_{C}}$
$20 f_{0}$	( $2 e$ , $e$ , $5 e$ , $12 e$ ) or ( $12 e$ , $5 e$ , $e$ , $2 e$ )	$5 f_{0}$ , $11 f_{0}$ , $13 f_{0}$ , $19 f_{0}$	$4 f_{0}$ , $8 f_{0}$ , $16 f_{0}$ , $20 f_{0}$	$f_{0}$ , $3 f_{0}$ , $7 f_{0}$ , $17 f_{0}$	$2 f_{0}$ , $12 f_{0}$
$21 f_{0}$	( $e$ , $3 e$ , $5 e$ , $12 e$ ) or ( $12 e$ , $5 e$ , $3 e$ , $e$ )	$6 f_{0}$ , $10 f_{0}$ , $14 f_{0}$ , $18 f_{0}$	$3 f_{0}$ , $5 f_{0}$ , $19 f_{0}$ , $21 f_{0}$	$2 f_{0}$ , $4 f_{0}$ , $7 f_{0}$ , $17 f_{0}$	$f_{0}$ , $12 f_{0}$
$21 f_{0}$	( $2 e$ , $e$ , $5 e$ , $13 e$ ) or ( $13 e$ , $5 e$ , $e$ , $2 e$ )	$6 f_{0}$ , $12 f_{0}$ , $14 f_{0}$ , $20 f_{0}$	$5 f_{0}$ , $9 f_{0}$ , $17 f_{0}$ , $21 f_{0}$	$f_{0}$ , $3 f_{0}$ , $8 f_{0}$ , $18 f_{0}$	$2 f_{0}$ , $13 f_{0}$
$22 f_{0}$	( $2 e$ , $e$ , $5 e$ , $14 e$ ) or ( $14 e$ , $5 e$ , $e$ , $2 e$ )	$7 f_{0}$ , $13 f_{0}$ , $15 f_{0}$ , $21 f_{0}$	$6 f_{0}$ , $10 f_{0}$ , $18 f_{0}$ , $22 f_{0}$	$f_{0}$ , $3 f_{0}$ , $9 f_{0}$ , $19 f_{0}$	$2 f_{0}$ , $14 f_{0}$
$22 f_{0}$	( $2 e$ , $e$ , $6 e$ , $13 e$ ) or ( $13 e$ , $6 e$ , $e$ , $2 e$ )	$5 f_{0}$ , $9 f_{0}$ , $17 f_{0}$ , $21 f_{0}$ , $12 f_{0}$ , $14 f_{0}$	$4 f_{0}$ , $8 f_{0}$ , $18 f_{0}$ , $22 f_{0}$	$f_{0}$ , $3 f_{0}$ , $7 f_{0}$ , $19 f_{0}$	$2 f_{0}$ , $13 f_{0}$

Abstract

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Figures (11)

Tables (2)

Equations (30)

Journal of the Optical Society of America A