Abstract

A division of focal plane (DoFP) polarimeter includes an array of polarized pixels. The response characteristics of polarized pixels are directly affected by inherent defects of a DoFP polarimeter. Correspondingly, the response characteristics are crucial to correction of the inherent defects. However, research on the response characteristics is rarely reported. Therefore, this paper proposes a pixel response model for a DoFP polarimeter. The response model combines the response characteristics of a traditional photoelectric imager and a micro-polarizer array. The proposed model includes six input parameters. They are the major polarization responsivity, minor polarization responsivity, polarization orientation, exposure time, conversion gain, and gamma correction. An experimental setup is constructed to measure the response of a DoFP polarimeter. The proposed model is evaluated by comparing the calculated results and the measured results. The compared results under different artificial parameters show that the each average root-mean-square error value is less than one gray value, which proves the validity of the proposed model.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (8)

R. Liu, D. J. Wang, P. Jia, and X. Che, “Gradient sky scene based nonuniformity correction and local weighted filter based denoising,” Optik 174, 748–756 (2018).
[Crossref]

D. B. Chenault, J. P. Vaden, D. A. Mitchell, and E. D. Demicco, “Infrared polarimetric sensing of oil on water,” Mar. Technol. Soc. J. 52, 13–22 (2018).
[Crossref]

S. B. Powell, R. Garnett, J. Marshall, C. Rizk, and V. Gruev, “Bioinspired polarization vision enables underwater geolocalization,” Sci. Adv. 4, eaao6841 (2018).
[Crossref]

M. Garcia, T. Davis, S. Blair, N. Cui, and V. Gruev, “Bioinspired polarization imager with high dynamic range,” Optica 5, 1240–1246 (2018).
[Crossref]

H. Fei, F.-M. Li, W.-C. Chen, R. Zhang, and C.-S. Chen, “Calibration method for division of focal plane polarimeters,” Appl. Opt. 57, 4992–4996 (2018).
[Crossref]

B. Feng, Z. Shi, H. Liu, L. Liu, Y. Zhao, and J. Zhang, “Polarized-pixel performance model for DoFP polarimeter,” J. Opt. 20, 065703 (2018).
[Crossref]

S. Roussel, M. Boffety, and F. Goudail, “Polarimetric precision of a micropolarizer grid-based camera in the presence of additive and Poisson shot noise,” Opt. Express 26, 29968–29982 (2018).
[Crossref]

H. Sun, D. Wang, C. Chen, K. Long, and X. Sun, “Effect of sensor SNR and extinction ratio on polarimetric imaging error for nanowire-based systems,” Appl. Opt. 57, 7344–7351 (2018).
[Crossref]

2017 (6)

2016 (5)

2015 (2)

2014 (3)

2013 (2)

S. B. Powell and V. Gruev, “Calibration methods for division-of-focal-plane polarimeters,” Opt. Express 21, 21039–21055 (2013).
[Crossref]

J. Duan, Q. Fu, C. Mo, Y. Zhu, and D. Liu, “Review of polarization imaging for international military application,” Proc. SPIE 8908, 890813 (2013)
[Crossref]

2012 (1)

2011 (1)

2009 (1)

1998 (1)

Ahmed, A.

Antonelli, M.-R.

Balakrishnan, K.

Benali, A.

Bermak, A.

Blair, S.

Boffety, M.

Brock, N.

Cao, E.

L. Guo, E. Cao, G. Gu, X. Hu, W. Qian, M. Wan, and R. Zhao, “Target recognition method based on polarization parameters,” Proc. SPIE 10155, 101552N (2016).
[Crossref]

Chang, Z.

Che, X.

R. Liu, D. J. Wang, P. Jia, and X. Che, “Gradient sky scene based nonuniformity correction and local weighted filter based denoising,” Optik 174, 748–756 (2018).
[Crossref]

Chen, C.

Chen, C.-S.

Chen, W.-C.

Chen, Z.

Chenault, D. B.

D. B. Chenault, J. P. Vaden, D. A. Mitchell, and E. D. Demicco, “Infrared polarimetric sensing of oil on water,” Mar. Technol. Soc. J. 52, 13–22 (2018).
[Crossref]

Chipman, R. A.

Compain, E.

Cui, N.

Davis, T.

De Martino, A.

Demicco, E. D.

D. B. Chenault, J. P. Vaden, D. A. Mitchell, and E. D. Demicco, “Infrared polarimetric sensing of oil on water,” Mar. Technol. Soc. J. 52, 13–22 (2018).
[Crossref]

Drevillon, B.

Duan, J.

J. Duan, Q. Fu, C. Mo, Y. Zhu, and D. Liu, “Review of polarization imaging for international military application,” Proc. SPIE 8908, 890813 (2013)
[Crossref]

Edmiston, C.

Elson, D. S.

J. Qi and D. S. Elson, “Mueller polarimetric imaging for surgical and diagnostic applications: a review,” J. Biophoton. 10, 950–982 (2017).
[Crossref]

Fang, S.

Fei, H.

Feng, B.

B. Feng, Z. Shi, H. Liu, L. Liu, Y. Zhao, and J. Zhang, “Polarized-pixel performance model for DoFP polarimeter,” J. Opt. 20, 065703 (2018).
[Crossref]

B. Feng, Z. Shi, H. Liu, Y. Zhao, and J. Liu, “Calibration method for equivalent extinction ratio of polarized pixel in integrated micropolarizer array camera,” Proc. SPIE 10605, 106051B (2017).
[Crossref]

Fu, Q.

J. Duan, Q. Fu, C. Mo, Y. Zhu, and D. Liu, “Review of polarization imaging for international military application,” Proc. SPIE 8908, 890813 (2013)
[Crossref]

Garcia, M.

Garnett, R.

S. B. Powell, R. Garnett, J. Marshall, C. Rizk, and V. Gruev, “Bioinspired polarization vision enables underwater geolocalization,” Sci. Adv. 4, eaao6841 (2018).
[Crossref]

Gayet, B.

Goudail, F.

Gruev, V.

Gu, G.

L. Guo, E. Cao, G. Gu, X. Hu, W. Qian, M. Wan, and R. Zhao, “Target recognition method based on polarization parameters,” Proc. SPIE 10155, 101552N (2016).
[Crossref]

Guo, L.

L. Guo, E. Cao, G. Gu, X. Hu, W. Qian, M. Wan, and R. Zhao, “Target recognition method based on polarization parameters,” Proc. SPIE 10155, 101552N (2016).
[Crossref]

Han, J.

Hsu, W.-L.

Hu, H.

Hu, X.

L. Guo, E. Cao, G. Gu, X. Hu, W. Qian, M. Wan, and R. Zhao, “Target recognition method based on polarization parameters,” Proc. SPIE 10155, 101552N (2016).
[Crossref]

Huang, B.

Hui, B.

Ibn-Elhaj, M.

Jia, P.

R. Liu, D. J. Wang, P. Jia, and X. Che, “Gradient sky scene based nonuniformity correction and local weighted filter based denoising,” Optik 174, 748–756 (2018).
[Crossref]

LaCasse, C.

Li, F.-M.

Liang, R.

Liu, D.

J. Duan, Q. Fu, C. Mo, Y. Zhu, and D. Liu, “Review of polarization imaging for international military application,” Proc. SPIE 8908, 890813 (2013)
[Crossref]

Liu, H.

B. Feng, Z. Shi, H. Liu, L. Liu, Y. Zhao, and J. Zhang, “Polarized-pixel performance model for DoFP polarimeter,” J. Opt. 20, 065703 (2018).
[Crossref]

B. Feng, Z. Shi, H. Liu, Y. Zhao, and J. Liu, “Calibration method for equivalent extinction ratio of polarized pixel in integrated micropolarizer array camera,” Proc. SPIE 10605, 106051B (2017).
[Crossref]

Liu, J.

B. Feng, Z. Shi, H. Liu, Y. Zhao, and J. Liu, “Calibration method for equivalent extinction ratio of polarized pixel in integrated micropolarizer array camera,” Proc. SPIE 10605, 106051B (2017).
[Crossref]

Liu, L.

B. Feng, Z. Shi, H. Liu, L. Liu, Y. Zhao, and J. Zhang, “Polarized-pixel performance model for DoFP polarimeter,” J. Opt. 20, 065703 (2018).
[Crossref]

Liu, R.

R. Liu, D. J. Wang, P. Jia, and X. Che, “Gradient sky scene based nonuniformity correction and local weighted filter based denoising,” Optik 174, 748–756 (2018).
[Crossref]

Liu, T.

Long, K.

Luo, H.

Marinov, R.

Marshall, J.

S. B. Powell, R. Garnett, J. Marshall, C. Rizk, and V. Gruev, “Bioinspired polarization vision enables underwater geolocalization,” Sci. Adv. 4, eaao6841 (2018).
[Crossref]

Mitchell, D. A.

D. B. Chenault, J. P. Vaden, D. A. Mitchell, and E. D. Demicco, “Infrared polarimetric sensing of oil on water,” Mar. Technol. Soc. J. 52, 13–22 (2018).
[Crossref]

Mo, C.

J. Duan, Q. Fu, C. Mo, Y. Zhu, and D. Liu, “Review of polarization imaging for international military application,” Proc. SPIE 8908, 890813 (2013)
[Crossref]

Myhre, G.

Namer, E.

Ninkov, Z.

D. Vorobiev, Z. Ninkov, N. Brock, and R. West, “On-sky performance evaluation and calibration of a polarization-sensitive focal plane array,” Proc. SPIE 9912, 99125X (2016).
[Crossref]

Novikova, T.

Pacheco, S.

Pau, S.

Peinado, A.

Pierangelo, A.

Powell, S. B.

S. B. Powell, R. Garnett, J. Marshall, C. Rizk, and V. Gruev, “Bioinspired polarization vision enables underwater geolocalization,” Sci. Adv. 4, eaao6841 (2018).
[Crossref]

S. B. Powell and V. Gruev, “Calibration methods for division-of-focal-plane polarimeters,” Opt. Express 21, 21039–21055 (2013).
[Crossref]

Qi, J.

J. Qi and D. S. Elson, “Mueller polarimetric imaging for surgical and diagnostic applications: a review,” J. Biophoton. 10, 950–982 (2017).
[Crossref]

Qian, W.

L. Guo, E. Cao, G. Gu, X. Hu, W. Qian, M. Wan, and R. Zhao, “Target recognition method based on polarization parameters,” Proc. SPIE 10155, 101552N (2016).
[Crossref]

Rizk, C.

S. B. Powell, R. Garnett, J. Marshall, C. Rizk, and V. Gruev, “Bioinspired polarization vision enables underwater geolocalization,” Sci. Adv. 4, eaao6841 (2018).
[Crossref]

Roussel, S.

Schechner, Y. Y.

Shi, Z.

B. Feng, Z. Shi, H. Liu, L. Liu, Y. Zhao, and J. Zhang, “Polarized-pixel performance model for DoFP polarimeter,” J. Opt. 20, 065703 (2018).
[Crossref]

B. Feng, Z. Shi, H. Liu, Y. Zhao, and J. Liu, “Calibration method for equivalent extinction ratio of polarized pixel in integrated micropolarizer array camera,” Proc. SPIE 10605, 106051B (2017).
[Crossref]

Shwartz, S.

Sun, H.

Sun, X.

Vaden, J. P.

D. B. Chenault, J. P. Vaden, D. A. Mitchell, and E. D. Demicco, “Infrared polarimetric sensing of oil on water,” Mar. Technol. Soc. J. 52, 13–22 (2018).
[Crossref]

Vail, A.

Validire, P.

Vorobiev, D.

D. Vorobiev, Z. Ninkov, N. Brock, and R. West, “On-sky performance evaluation and calibration of a polarization-sensitive focal plane array,” Proc. SPIE 9912, 99125X (2016).
[Crossref]

Wan, M.

L. Guo, E. Cao, G. Gu, X. Hu, W. Qian, M. Wan, and R. Zhao, “Target recognition method based on polarization parameters,” Proc. SPIE 10155, 101552N (2016).
[Crossref]

Wang, D.

Wang, D. J.

R. Liu, D. J. Wang, P. Jia, and X. Che, “Gradient sky scene based nonuniformity correction and local weighted filter based denoising,” Optik 174, 748–756 (2018).
[Crossref]

Wang, X.

West, R.

D. Vorobiev, Z. Ninkov, N. Brock, and R. West, “On-sky performance evaluation and calibration of a polarization-sensitive focal plane array,” Proc. SPIE 9912, 99125X (2016).
[Crossref]

Xia, X.

Xing, H.

Zhang, J.

Zhang, R.

Zhao, R.

L. Guo, E. Cao, G. Gu, X. Hu, W. Qian, M. Wan, and R. Zhao, “Target recognition method based on polarization parameters,” Proc. SPIE 10155, 101552N (2016).
[Crossref]

Zhao, X.

Zhao, Y.

B. Feng, Z. Shi, H. Liu, L. Liu, Y. Zhao, and J. Zhang, “Polarized-pixel performance model for DoFP polarimeter,” J. Opt. 20, 065703 (2018).
[Crossref]

B. Feng, Z. Shi, H. Liu, Y. Zhao, and J. Liu, “Calibration method for equivalent extinction ratio of polarized pixel in integrated micropolarizer array camera,” Proc. SPIE 10605, 106051B (2017).
[Crossref]

Zhou, W.

Zhu, Y.

J. Duan, Q. Fu, C. Mo, Y. Zhu, and D. Liu, “Review of polarization imaging for international military application,” Proc. SPIE 8908, 890813 (2013)
[Crossref]

Appl. Opt. (6)

J. Biophoton. (1)

J. Qi and D. S. Elson, “Mueller polarimetric imaging for surgical and diagnostic applications: a review,” J. Biophoton. 10, 950–982 (2017).
[Crossref]

J. Opt. (1)

B. Feng, Z. Shi, H. Liu, L. Liu, Y. Zhao, and J. Zhang, “Polarized-pixel performance model for DoFP polarimeter,” J. Opt. 20, 065703 (2018).
[Crossref]

J. Opt. Soc. Am. A (2)

Mar. Technol. Soc. J. (1)

D. B. Chenault, J. P. Vaden, D. A. Mitchell, and E. D. Demicco, “Infrared polarimetric sensing of oil on water,” Mar. Technol. Soc. J. 52, 13–22 (2018).
[Crossref]

Opt. Express (11)

A. Pierangelo, A. Benali, M.-R. Antonelli, T. Novikova, P. Validire, B. Gayet, and A. De Martino, “Ex-vivo characterization of human colon cancer by Mueller polarimetric imaging,” Opt. Express 19, 1582–1593 (2011).
[Crossref]

W.-L. Hsu, G. Myhre, K. Balakrishnan, N. Brock, M. Ibn-Elhaj, and S. Pau, “Full-Stokes imaging polarimeter using an array of elliptical polarizer,” Opt. Express 22, 3063–3074 (2014).
[Crossref]

G. Myhre, W.-L. Hsu, A. Peinado, C. LaCasse, N. Brock, R. A. Chipman, and S. Pau, “Liquid crystal polymer full-Stokes division of focal plane polarimeter,” Opt. Express 20, 27393–27409 (2012).
[Crossref]

J. Zhang, H. Luo, B. Hui, and Z. Chang, “Image interpolation for division of focal plane polarimeters with intensity correlation,” Opt. Express 24, 20799–20807 (2016).
[Crossref]

E. Namer, S. Shwartz, and Y. Y. Schechner, “Skyless polarimetric calibration and visibility enhancement,” Opt. Express 17, 472–493 (2009).
[Crossref]

S. Fang, X. Xia, H. Xing, and C. Chen, “Image dehazing using polarization effects of objects and airlight,” Opt. Express 22, 19523–19537 (2014).
[Crossref]

B. Huang, T. Liu, J. Han, and H. Hu, “Polarimetric target detection under uneven illumination,” Opt. Express 23, 23603–23612 (2015).
[Crossref]

J. Zhang, H. Luo, R. Liang, W. Zhou, B. Hui, and Z. Chang, “PCA-based denoising method for division of focal plane polarimeters,” Opt. Express 25, 2391–2400 (2017).
[Crossref]

S. Roussel, M. Boffety, and F. Goudail, “Polarimetric precision of a micropolarizer grid-based camera in the presence of additive and Poisson shot noise,” Opt. Express 26, 29968–29982 (2018).
[Crossref]

S. B. Powell and V. Gruev, “Calibration methods for division-of-focal-plane polarimeters,” Opt. Express 21, 21039–21055 (2013).
[Crossref]

A. Ahmed, X. Zhao, V. Gruev, J. Zhang, and A. Bermak, “Residual interpolation for division of focal plane polarization image sensors,” Opt. Express 25, 10651–10662 (2017).
[Crossref]

Optica (2)

Optik (1)

R. Liu, D. J. Wang, P. Jia, and X. Che, “Gradient sky scene based nonuniformity correction and local weighted filter based denoising,” Optik 174, 748–756 (2018).
[Crossref]

Proc. SPIE (4)

L. Guo, E. Cao, G. Gu, X. Hu, W. Qian, M. Wan, and R. Zhao, “Target recognition method based on polarization parameters,” Proc. SPIE 10155, 101552N (2016).
[Crossref]

J. Duan, Q. Fu, C. Mo, Y. Zhu, and D. Liu, “Review of polarization imaging for international military application,” Proc. SPIE 8908, 890813 (2013)
[Crossref]

D. Vorobiev, Z. Ninkov, N. Brock, and R. West, “On-sky performance evaluation and calibration of a polarization-sensitive focal plane array,” Proc. SPIE 9912, 99125X (2016).
[Crossref]

B. Feng, Z. Shi, H. Liu, Y. Zhao, and J. Liu, “Calibration method for equivalent extinction ratio of polarized pixel in integrated micropolarizer array camera,” Proc. SPIE 10605, 106051B (2017).
[Crossref]

Sci. Adv. (1)

S. B. Powell, R. Garnett, J. Marshall, C. Rizk, and V. Gruev, “Bioinspired polarization vision enables underwater geolocalization,” Sci. Adv. 4, eaao6841 (2018).
[Crossref]

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Figures (13)

Fig. 1.
Fig. 1. Signal transmission process of the photoelectric imaging system. A/D, analog-to-digital.
Fig. 2.
Fig. 2. Structure of the polarization detector.
Fig. 3.
Fig. 3. Polarized transmission direction of linearly polarized light and polarized pixels.
Fig. 4.
Fig. 4. Conversion diagram of optical radiation signal to electrical signal.
Fig. 5.
Fig. 5. Optical diagram of our experimental setup.
Fig. 6.
Fig. 6. Constructed experimental setup.
Fig. 7.
Fig. 7. Response of a super-pixel under reference conditions.
Fig. 8.
Fig. 8. Comparison between calculated values and measured values under different exposure times and different linearly polarized light.
Fig. 9.
Fig. 9. Comparison between calculated values and measured values under different exposure times and given linearly polarized light.
Fig. 10.
Fig. 10. Comparison between calculated values and measured values under different gains and different linearly polarized light.
Fig. 11.
Fig. 11. Comparison between calculated values and measured values under different gains and given linearly polarized light.
Fig. 12.
Fig. 12. Comparison between calculated values and measured values under different gamma values and different linearly polarized light.
Fig. 13.
Fig. 13. Comparison between calculated values and measured values under different gamma values and given linearly polarized light.

Tables (7)

Tables Icon

Table 1. Experimental Setup Model

Tables Icon

Table 2. RMSE Values between Calculated Results and Measured Results at Different Exposure Times

Tables Icon

Table 3. RMSE Values between Calculated Results and Measured Results at Different Gains

Tables Icon

Table 4. RMSE Values between Calculated Results and Measured Results at Different Gamma Values

Tables Icon

Table 5. Average RMSE of Polarized Pixels for Each Polarization Orientation at Different Exposure Times

Tables Icon

Table 6. Average RMSE of Polarized Pixels for Each Polarization Orientation at Different Gains

Tables Icon

Table 7. Average RMSE of Polarized Pixels for Each Polarization Orientation at Different Gamma Values

Equations (25)

Equations on this page are rendered with MathJax. Learn more.

S = c r γ ,
S = c ( r + ε ) γ .
L o u t = μ ( i , j ) I cos ( φ z θ ( i , j ) ) 2 + μ ( i , j ) I sin ( φ z θ ( i , j ) ) 2 ,
d ( i , j , z ) = g L o u t + b ( i , j ) ,
d ( i , j , z ) = β g β t g L o u t + b ( i , j ) .
d ( i , j , z ) = β g β t { g [ μ ( i , j ) I cos ( φ z θ ( i , j ) ) 2 + μ ( i , j ) I sin ( φ z θ ( i , j ) ) 2 ] } + b ( i , j ) .
η ( i , j ) = g μ ( i , j ) ,
η ( i , j ) = g μ ( i , j ) .
d ( i , j , z ) = β g β t [ η ( i , j ) I cos ( φ z θ ( i , j ) ) 2 + η ( i , j ) I sin ( φ z θ ( i , j ) ) 2 ] + b ( i , j ) ,
S ( i , j , z ) = { β g β t [ η ( i , j ) I cos ( φ z θ ( i , j ) ) 2 + η ( i , j ) I sin ( φ z θ ( i , j ) ) 2 ] + b ( i , j ) } γ .
cos ( φ z θ ( i , j ) ) 2 = 1 + cos [ 2 ( φ z θ ( i , j ) ) ] 2 ,
sin ( φ z θ ( i , j ) ) 2 = 1 cos [ 2 ( φ z θ ( i , j ) ) ] 2 .
S ( i , j , z ) = { 1 2 β g β t I [ ( η ( i , j ) + η ( i , j ) ) + ( η ( i , j ) η ( i , j ) ) × cos ( 2 φ z 2 θ ( i , j ) ) [ ( η ( i , j ) + η ( i , j ) ) + ( η ( i , j ) η ( i , j ) ) ] + b ( i , j ) } γ ,
η ( i , j ) + = 1 2 ( η ( i , j ) + η ( i , j ) ) ,
η ( i , j ) = 1 2 ( η ( i , j ) η ( i , j ) ) ,
S ( i , j , z ) = { [ β g β t I ( η ( i , j ) + + η ( i , j ) cos 2 φ z cos 2 θ ( i , j ) + η ( i , j ) sin 2 φ z sin 2 θ ( i , j ) ) ] + b ( i , j ) } γ ,
[ S ( i , j , z ) 1 S ( i , j , z ) 2 S ( i , j , z ) n ] [ b ( i , j ) 1 b ( i , j ) 2 b ( i , j ) n ] = I [ 1 1 1 cos 2 φ 1 cos 2 φ 2 cos 2 φ n sin 2 φ 1 sin 2 φ 2 sin 2 φ n ] [ η ( i , j ) + η ( i , j ) cos 2 θ ( i , j ) η ( i , j ) sin 2 θ ( i , j ) ] .
[ y ( i , j ) 1 y ( i , j ) 2 y ( i , j ) n ] = [ S ( i , j , z ) 1 S ( i , j , z ) 2 S ( i , j , z ) n ] [ b ( i , j ) 1 b ( i , j ) 2 b ( i . j ) n ] ,
[ q 1 q 2 q 3 ] = [ η ( i , j ) + η ( i , j ) cos 2 θ ( i , j ) η ( i , j ) sin 2 θ ( i , j ) ] .
[ q 1 q 2 q 3 ] = 1 I [ 1 1 1 cos 2 φ 1 cos 2 φ 2 cos 2 φ n sin 2 φ 1 sin 2 φ 2 sin 2 φ n ] [ y ( i , j ) 1 y ( i , j ) 2 y ( i , j ) n ] .
θ ( i , j ) = 1 2 arctan ( q 3 q 2 ) ,
η ( i , j ) = q 1 2 + q 2 2 cos 2 θ ( i , j ) ,
η ( i , j ) = q 1 2 q 2 2 cos 2 θ ( i , j ) ,
R M S E = 1 n i = 1 n [ y i ϕ ( x i ) ] 2 ,
20 log ( y ) = ( x ) d B ,