Analysis of Phase Error of Retarders in Spectrally Encoded Mueller Matrix Measurement

Shuqiang Huang; Xiumei Jiang; Yuanhua Feng

doi:10.3788/LOP202158.1926001

Laser & Optoelectronics Progress, Volume. 58, Issue 19, 1926001(2021)

Analysis of Phase Error of Retarders in Spectrally Encoded Mueller Matrix Measurement

Shuqiang Huang¹, Xiumei Jiang¹, and Yuanhua Feng^2,3、*

¹Department of Optoelectronic Engineering, College of Science and Engineering, Jinan University, Guangzhou , Guangdong 510632, China

²Department of Electronic Engineering, College of Information Science and Technology, Jinan University, Guangzhou , Guangdong 510632, China

³State Key Laboratory of Integrated Optoelectronics, Beijing 100083, China

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Figures & Tables(7)

Fig. 1. Schematic of experimental setup of spectrally encoded Mueller matrix measurement system

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Fig. 2. Measurement spectrum with 0° polarizer as sample

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Fig. 3. Influence of phase $ϕ_{w}$ on the Mueller matrix for different samples

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Fig. 4. The value of each element of the Muller matrix with the compensation of polarizer from 0° to 90°

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Table 1. Influence of $Δ ϕ_{2}$ , $Δ ϕ_{3}$ ,and $Δ ϕ_{4}$ on the Mueller matrix for different samples and the compensation effect

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Table 1. Influence of $Δ ϕ_{2}$ , $Δ ϕ_{3}$ ,and $Δ ϕ_{4}$ on the Mueller matrix for different samples and the compensation effect

$ϕ_{2} / r a d$		$ϕ_{3} / r a d$	$ϕ_{4} / r a d$	$E_{R M S}$ of vacuum		$E_{R M S}$ of polarizer（ $θ = 45 °$ ）		$E_{R M S}$ of quarter waveplate（ $θ = 45 °$ ）
$ϕ_{2} / r a d$		$ϕ_{3} / r a d$	$ϕ_{4} / r a d$	Without compensation	With compensation	Without compensation	With compensation	Without compensation	With compensation
0.01	0		0	0.0030	0.0013	0.0040	0.0024	0.0051	0.0023
0.1	0		0	0.0330	0.0013	0.0351	0.0024	0.0366	0.0023
0	0.01		0	0.0030	0.0013	0.0040	0.0024	0.0045	0.0023
0	0.1		0	0.0330	0.0013	0.0351	0.0024	0.0358	0.0023
0	0		0.01	0.0030	0.0013	0.0040	0.0024	0.0051	0.0023
0	0		0.1	0.0330	0.0013	0.0351	0.0024	0.0436	0.0023
0.01	0.01		0.01	0.0106	0.0013	0.0079	0.0024	0.0093	0.0023
0.1	0.1		0.1	0.1083	0.0013	0.0790	0.0024	0.0836	0.0023
0.1	0.1		-0.1	0.0432	0.0013	0.0355	0.0024	0.0444	0.0023

Table 2. Comparison with and without compensation of different samples using polarizer method

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Table 2. Comparison with and without compensation of different samples using polarizer method

Sample	Theoretical Muellermatrix	Experimental Mueller matrix		Mueller matrix element error
Sample	Theoretical Muellermatrix	Without compensation	With compensation	$E_{R M S}$	E_max
Vacuum	$[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{matrix}]$	$[\begin{matrix} 1.0000 & 0.0431 & - 0.0518 & 0.1440 \\ 0.0439 & 0.9774 & 0.0142 & 0.0095 \\ 0.0265 & 0.0261 & 0.8505 & - 0.3377 \\ 0.0175 & 0.0351 & 0.3343 & 0.9301 \end{matrix}]$	$[\begin{matrix} 1.0000 & 0.0487 & - 0.0494 & - 0.0019 \\ 0.0473 & 0.9899 & - 0.0153 & - 0.0143 \\ 0.0074 & - 0.0071 & 0.9669 & - 0.0106 \\ 0.0304 & 0.0431 & - 0.0605 & 0.9314 \end{matrix}]$	0.0354	0.0686
Polarizer 0°	$[\begin{matrix} 1 & 1 & 0 & 0 \\ 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{matrix}]$	$[\begin{matrix} 1.0000 & 0.9922 & 0.0077 & 0.0129 \\ 0.9823 & 0.9820 & 0.0067 & - 0.0048 \\ - 0.0314 & 0.0405 & 0.0431 & 0.0286 \\ 0.0136 & - 0.0157 & - 0.0148 & 0.0035 \end{matrix}]$	$[\begin{matrix} 1.0000 & 0.9943 & 0.0227 & 0.0094 \\ 0.9859 & 0.9838 & - 0.0067 & - 0.0058 \\ 0.0156 & 0.0003 & - 0.0671 & 0.0537 \\ - 0.0212 & 0.0070 & - 0.0330 & - 0.0597 \end{matrix}]$	0.0199	0.0471
Polarizer 45°	$[\begin{matrix} 1 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 \\ 1 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 \end{matrix}]$	$[\begin{matrix} 1.0000 & 0.0362 & 1.2229 & - 0.5937 \\ 0.0174 & - 0.0043 & 0.0415 & - 0.0556 \\ - 0.1386 & - 0.0399 & - 0.1625 & - 0.0154 \\ 1.3922 & 0.0492 & 1.4881 & - 0.7976 \end{matrix}]$	$[\begin{matrix} 1.0000 & 0.0411 & 0.9998 & 0.0080 \\ 0.0113 & - 0.0061 & 0.0042 & 0.0035 \\ 1.0584 & 0.0056 & 1.0248 & - 0.0449 \\ - 0.0044 & 0.0332 & - 0.0409 & 0.0324 \end{matrix}]$	0.0271	0.0584
Quarter-wave plate 0°	$[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & - 1 \\ 0 & 0 & 1 & 0 \end{matrix}]$	$[\begin{matrix} 1.0000 & - 2024 & 0.0630 & - 0.0780 \\ 0.0266 & - 0.0853 & - 0.8329 & - 0.3081 \\ 0.0013 & 0.4204 & 0.3130 & - 0.6268 \\ 0.0958 & 0.9229 & - 0.1780 & 0.7461 \end{matrix}]$	$[\begin{matrix} 1.0000 & 0.0616 & - 0.0022 & - 0.0603 \\ 0.0584 & 0.9860 & 0.0181 & - 0.0035 \\ 0.0014 & 0.0430 & 0.0041 & 1.0197 \\ 0.0236 & 0.0036 & - 0.9539 & - 0.0676 \end{matrix}]$	0.0389	0.0676
Quarter-wave plate 90°	$[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & - 1 \\ 0 & 0 & 1 & 0 \end{matrix}]$	$[\begin{matrix} 1.0000 & 0.0564 & - 0.1682 & 0.0825 \\ 0.0480 & 0.9769 & 0.0150 & 0.0102 \\ 0.0097 & 0.0028 & - 0.4047 & - 0.7883 \\ 0.0066 & 0.0400 & 0.8655 & - 0.3518 \end{matrix}]$	$[\begin{matrix} 1.0000 & 0.0651 & - 0.0252 & 0.0612 \\ 0.0541 & 0.9911 & - 0.0144 & 0.0126 \\ 0.0007 & - 0.0243 & 0.0193 & - 0.9452 \\ 0.0066 & 0.0319 & 0.9688 & 0.0630 \end{matrix}]$	0.0375	0.0630
Half-wave plate 0°	$[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & - 1 & 0 \\ 0 & 0 & 0 & - 1 \end{matrix}]$	$[\begin{matrix} 1.0000 & 0.0867 & 0.0537 & 0.1629 \\ 0.0676 & 0.9870 & 0.0020 & - 0.0112 \\ - 0.0323 & 0.0003 & - 0.8732 & 0.3927 \\ - 0.0260 & 0.0124 & - 0.2852 & - 0.9353 \end{matrix}]$	$[\begin{matrix} 1.0000 & 0.0694 & 0.0394 & 0.0190 \\ 0.0625 & 0.9972 & 0.0020 & - 0.0002 \\ - 0.0054 & - 0.0087 & - 1.0308 & - 0.0211 \\ - 0.0408 & 0.0089 & 0.0340 & - 0.9569 \end{matrix}]$	0.0325	0.0694

Table 3. Comparison of compensation results for different samples with 45° quarter-wave plate

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Table 3. Comparison of compensation results for different samples with 45° quarter-wave plate

Sample	Theoretical Mueller matrix	Experimental Mueller matrix（with compensation）	Mueller Matrix element error
Sample	Theoretical Mueller matrix	Experimental Mueller matrix（with compensation）	$E_{R M S}$	E_max
Vacuum	$[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{matrix}]$	$[\begin{matrix} 1.0000 & 0.0454 & 0.0343 & - 0.0381 \\ 0.0470 & 0.9905 & - 0.0136 & - 0.0137 \\ - 0.0340 & - 0.0076 & 0.9772 & 0.0086 \\ 0.0484 & 0.0406 & - 0.0783 & 0.9281 \end{matrix}]$	0.0391	0.0783
Polarizer 0°	$[\begin{matrix} 1 & 1 & 0 & 0 \\ 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{matrix}]$	$[\begin{matrix} 1.0000 & 1.0015 & - 0.0331 & 0.0076 \\ 0.9887 & 0.9859 & 0.0108 & - 0.0039 \\ 0.0070 & 0.0156 & - 0.0451 & 0.0698 \\ 0.0296 & 0.0231 & - 0.0771 & - 0.0365 \end{matrix}]$	0.0331	0.0698
Half-wave plate 0°	$[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & - 1 & 0 \\ 0 & 0 & 0 & - 1 \end{matrix}]$	$[\begin{matrix} 1.0000 & 0.0590 & - 0.0490 & 0.0516 \\ 0.0707 & 0.9943 & 0.0066 & - 0.0011 \\ 0.0383 & - 0.0090 & - 1.0275 & - 0.0469 \\ - 0.0534 & 0.0135 & 0.0423 & - 0.9543 \end{matrix}]$	0.0396	0.0707
Quarter-wave plate 0°	$[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & - 1 \\ 0 & 0 & 1 & 0 \end{matrix}]$	$[\begin{matrix} 1.0000 & 0.0658 & 0.0345 & 0.0294 \\ 0.0569 & 0.9870 & 0.0193 & - 0.0024 \\ 0.0119 & 0.0418 & - 0.0176 & 1.0281 \\ 0.0628 & 0.0074 & - 0.9530 & - 0.0635 \end{matrix}]$	0.0382	0.0658

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Shuqiang Huang, Xiumei Jiang, Yuanhua Feng. Analysis of Phase Error of Retarders in Spectrally Encoded Mueller Matrix Measurement[J]. Laser & Optoelectronics Progress, 2021, 58(19): 1926001

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Paper Information

Category: Physical Optics

Received: Jan. 21, 2021

Accepted: Feb. 12, 2021

Published Online: Oct. 14, 2021

The Author Email: Feng Yuanhua (favinfeng@163.com)

DOI:10.3788/LOP202158.1926001

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Influence of Δϕ2,Δϕ3,and Δϕ4 on the Mueller matrix for different samples and the compensation effect

Table 1. Influence of Δϕ2,Δϕ3,and Δϕ4 on the Mueller matrix for different samples and the compensation effect

Table 2. Comparison with and without compensation of different samples using polarizer method

Table 2. Comparison with and without compensation of different samples using polarizer method

Table 3. Comparison of compensation results for different samples with 45° quarter-wave plate

Table 3. Comparison of compensation results for different samples with 45° quarter-wave plate

Table 1. Influence of $Δ ϕ_{2}$ , $Δ ϕ_{3}$ ,and $Δ ϕ_{4}$ on the Mueller matrix for different samples and the compensation effect

Table 1. Influence of $Δ ϕ_{2}$ , $Δ ϕ_{3}$ ,and $Δ ϕ_{4}$ on the Mueller matrix for different samples and the compensation effect