Acta Optica Sinica, Volume. 39, Issue 9, 0911002(2019)
Simplified Analytical Method for Error Sources in Mueller Matrix Imaging Polarimeter
Figures & Tables(13)
Fig. 1. Structure of Mueller matrix imaging polarimeter for measuring polarization aberration
Fig. 3. Statistics of prediction errors by using model of delay error of retarder. (a) Mean value; (b) standard deviation
Fig. 4. Statistics of prediction errors by using model of polarization attenuation error of retarder. (a) Mean value; (b) standard deviation
Fig. 5. Statistics of prediction errors by using model of azimuthal-angle error of retarder. (a) Mean value; (b) standard deviation
Fig. 6. Statistics of error distribution of Mueller matrix caused by two kinds of random error sources. (a) Image sensor noise; (b) random azimuthal-angle errors of retarders
Fig. 7. Relationship between original and predicted intensity errors and random azimuthal-angle error of retarder
Fig. 8. Errors of Mueller matrix caused by noise of image sensor. (a) Original values; (b) predicted values
Fig. 9. Errors of Mueller matrix caused by random azimuthal-angle errors of retarders. (a) Original values; (b) predicted values
Table 1. Error sources in Mueller matrix imaging polarimeter
View tableTable 1. Error sources in Mueller matrix imaging polarimeter
Error type Element Error parameter Typical value Quarter-wave plates Retardance error δ 0.001π Q1, Q2 Diattenuation error ε 0.01 Systematic Azimuthal angle error Δ θ /(°)0.1 Polarizers Diattenuation error ε 0.01 P1, P2 Retardance error δ 0.001π Azimuthal angle error Δ θ /(°)0.1 Random Image sensor CCD Noise σ (ΔI )0.003 (normal distribution) Q1, Q2 Azimuthal angle error σ (Δθ R) /(°)0.1
Table 2. Fourier coefficients of light intensity influenced by delay errorof retarder
View tableTable 2. Fourier coefficients of light intensity influenced by delay errorof retarder
Order Term Coefficient of Fourier series Approximate coefficient 0 1 m 11/4+(1-s1) (m 12+m 21)/8+(1-s 1)2m 22/16m 11/4+(1-s 1) (m 12+m 21)/8+(1-2s 1)m 22/161 cos(2 θ )0 0 2 sin(2 θ )- c 1m 14/4-c 1 (1-s 1)m 24/8- m 14/4-(1-s 1)m 24/83 cos(2 kθ )0 0 4 sin(2 kθ )c 1m 41/4+c 1 (1-s 1)m 42/8m 41/4+(1-s 1)m 42/85 cos[2(1+ k )θ ]c 12m 44/8m 44/ 86 sin[2(1+ k )θ ]0 0 7 cos[2(1- k )θ ]- c 12m 44/8- m 44/ 88 sin[2(1- k )θ ]0 0 9 cos(4 θ )(1- s 12)m 22/16+(1+s 1)m 12/8m 22/16+(1+s 1)m 12/810 sin(4 θ )(1- s 12)m 23/16+(1+s 1)m 13/8m 23/16+(1+s 1)m 13/811 cos(4 kθ )(1- s 12)m 22/16+(1+s 1)m 21/8m 22/16+(1+s 1)m 21/812 sin(4 kθ )(1- s 12)m 32/16+(1+s1)m 31/8m 32/16+(1+s 1)m 31/813 cos[4(1+ k )θ ](1+ s 1)2 (m 22-m 33)/32(1+2 s 1) (m 22-m 33)/3214 sin[4(1+ k )θ ](1+ s 1)2 (m 23+m 32)/32(1+2 s 1) (m 23+m 32)/3215 cos[4(1- k )θ ](1+ s 1)2 (m 22+m 33)/32(1+2 s 1) (m 22+m 33)/3216 sin[4(1- k )θ ](1+ s 1)2 (m 23-m 32)/32(1+2 s 1) (m 23-m 32)/3217 cos[2(1+2 k )θ ]c 1 (1+s 1)m 34/16(1+ s 1)m 34/1618 sin[2(1+2 k )θ ]- c 1 (1+s 1)m 24/16-(1+ s 1)m 24/1619 cos[2(1-2 k )θ ]- c 1 (1+s 1)m 34/16-(1+ s 1)m 34/1620 sin[2(1-2 k )θ ]- c 1 (1+s 1)m 24/16-(1+ s 1)m 24/1621 cos[2(2+ k )θ ]- c 1 (1+s 1)m 43/16-(1+ s 1)m 43/1622 sin[2(2+ k )θ ]c 1 (1+s 1)m 42/16(1+ s 1)m 42/1623 cos[2(2- k )θ ]c 1 (1+s 1)m 43/16(1+ s 1)m 43/1624 sin[2(2- k )θ ]- c 1 (1+s 1)m 42/16-(1+ s 1)m 42/16
Table 3. Fourier coefficients of light intensity influenced by diattenuation and azimuthal-angle error of retarder
View tableTable 3. Fourier coefficients of light intensity influenced by diattenuation and azimuthal-angle error of retarder
Order Term Approximate coefficient ( ε )Approximate coefficient ( θ )0 1 (1-2 s 2) (m 11/4+(m 12+m 21)/8+m 22/16)m 11/4+(m 12+m 21)/8+m 22/161 cos(2 θ )s 2 (m 11/4+m 12/4+m 21/8+m 22/8)-s3 ( m 14/4+m 24/8)2 sin(2 θ )-( m 14/4+m 24/8)+s 2 (m 14/2+m 24/4+m 13/4+m 23/8)-( m 14/4+m 24/8)3 cos(2 kθ )s 2 (m 11/4+m 21/4+m 12/8+m 22/8)s 3 (m 41/4+m 42/8)4 sin(2 kθ )( m 41/4+m 42/8)-s 2 (m 41/2+m 42/4-m 31/4-m 32/8)( m 41/4+m 42/8)5 cos[2(1+ k )θ ]m 44/8-s 2 (m 44/4-m 34/8+m 43/8)m 44/86 sin[2(1+ k )θ ]- s 2 (m 14/8+m 24/8-m 41/8-m 42/8)- s 3m 44/47 cos[2(1- k )θ ]- m 44/8+s 2 (m 44/4-m 34/8+m 43/8)- m 44/88 sin[2(1- k )θ ]- s 2 (m 14/8+m 24/8+m 41/8+m 42/8)0 9 cos(4 θ )(1-2 s 2) (m 12/8+m 22/16)( m 12/8+m 22/16)+s 3 (m 13/4+m 23/8)10 sin(4 θ )(1-2 s 2) (m 13/8+m 23/16)( m 13/8+m 23/16)-s 3 (m 12/4+) 11 cos(4 kθ )(1-2 s 2) (m 21/8+m 22/16)( m 21/8+m 22/16)+s 3 (m 31/4+m 32/8)12 sin(4 kθ )(1-2 s 2) (m 31/8+m 32/16)( m 31/8+m 32/16)-s 3 (m 21/4+) 13 cos[4(1+ k )θ ](1-2 s 2) (m 22-m 33)/32( m 22-m 33)/32+s 3 (m 23+m 32)/814 sin[4(1+ k )θ ](1-2 s 2) (m 23+m 32)/32( m 23+m 32)/32-s3 (m 22-m 33)/815 cos[4(1- k )θ ](1-2 s 2) (m 22+m 33)/32( m 22+m 33)/3216 sin[4(1- k )θ ](1-2 s 2) (m 23-m 32)/32(m23- m 32)/3217 cos[2(1+2 k )θ ]m 34/16-s 2 (m 34/8+- m 21/16-m 22/16)m 34/16-3s 3m 24/1618 sin[2(1+2 k )θ ]- m 24/16+s 2 (m 24/8+m 23/16+m 31/16+m 32/16)- m 24/16-3s 3m 34/1619 cos[2(1-2 k )θ ]- m 34/16+s2 (m 34/8++ m 21/16+m 22/16)- m 34/16+s 3m 24/1620 sin[2(1-2 k )θ ]- m 24/16+s 2 (m 24/8+m 23/16-m 31/16-m 32/16)- m 24/16-s 3m 34/1621 cos[2(2+ k )θ ]- m 43/16+s 2 (m 43/8-+ m 12/16+m 22/16)- m 43/16+3s 3m 42/1622 sin[2(2+ k )θ ]m 42/16-s 2 (m 42/8-m 32/16-m 13/16-m 23/16)m 42/16+3s 3m 43/1623 cos[2(2- k )θ ]m 43/16-s 2 (m 43/8-- m 12/16-m 22/16)m 43/16-s 3m 42/1624 sin[2(2- k )θ ]- m 42/16+s2 (m 42/8-m 32/16+m 13/16+m 23/16)- m 42/16-s 3m 43/16
Table 4. Angle configuration of polarization element
View tableTable 4. Angle configuration of polarization element
Configuration Angle of P1 θ 1 /(°)Angle of Q1 ϕ 1 /(°)Angle of Q2 ϕ 2 /(°)Angle of P2 θ 2 /(°)1×144×1 0 0, 1.25, 2.5, …, 178.75 6 ϕ 10
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Zejiang Meng, Sikun Li, Xiangzhao Wang, Yang Bu, Fengzhao Dai, Chaoxing Yang. Simplified Analytical Method for Error Sources in Mueller Matrix Imaging Polarimeter[J]. Acta Optica Sinica, 2019, 39(9): 0911002
Paper Information
Category: Imaging Systems
Received: Apr. 17, 2019
Accepted: May. 21, 2019
Published Online: Sep. 9, 2019
The Author Email: Li Sikun (lisikun@siom.ac.cn), Wang Xiangzhao (wxz26267@siom.ac.cn)
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