Abstract

Polarization imaging technology provides information about not only the irradiance of a target but also the polarization degree and angle of polarization, which indicates extensive application potential. However, polarization imaging theory is based on paraxial optics. When a beam of obliquely incident light passes an analyser, the direction of light propagation is not perpendicular to the surface of the analyser and the applicability of the traditional paraxial optical polarization imaging theory is challenged. This paper investigates a theoretical model of a polarization imaging system with obliquely incident light and establishes a polarization imaging transmission model with a large field of obliquely incident light. In an imaging experiment with an integrating sphere light source and rotatable polarizer, the polarization imaging transmission model is verified and analysed for two cases of natural light and linearly polarized light incidence. Although the results indicate that the theoretical model is consistent with the experimental results, the theoretical model distinctly differs from the traditional paraxial approximation model. The results prove the accuracy and necessity of the theoretical model and the theoretical guiding significance for theoretical and systematic research of large field polarization imaging.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2012 (1)

M. Kulkarni and V. Gruev, “A division-of-focal-plane spectral-polarization imaging sensor,” Proc. SPIE 8364, 83640K (2012).
[Crossref]

2009 (1)

J. L. Pezzaniti, D. Chenault, M. Roche, J. Reinhardt, and H. Schultz, “Wave slope measurement using imaging polarimetry,” Proc. SPIE 7317, 73170B (2009).
[Crossref]

2008 (3)

C. J. Zappa, M. L. Banner, H. Schultz, A. C. Emmanuel, L. B. Wolffet, and J. Yalcin, “Retrieval of short ocean wave slope using polarimetric imaging,” Meas. Sci. Technol. 19(5), 055503 (2008).
[Crossref]

K. S. Kawabata, O. Nagae, S. Chiyonobu, H. Tanaka, H. Nakaya, M. Suzuki, Y. Kamata, S. Miyazaki, K. Hiragi, H. Miyamoto, M. Yamanaka, A. Arai, T. Yamashita, M. Uemura, T. Ohsugi, M. Isogai, Y. Ishitobi, and S. Sato, “Wide-field one-shot optical polarimeter: HOWPol,” Proc. SPIE 7014, 70144L (2008).
[Crossref]

P. Terrier, V. Devlaminck, and J. M. Charbois, “Segmentation of rough surfaces using a polarization imaging system,” J. Opt. Soc. Am. A 25(2), 423–430 (2008).
[Crossref] [PubMed]

2006 (1)

X. Y. Chen and M. San, “Description of effect of polarimeter with slanting ray,” Opt. Technol. 32(3), 425–427 (2006).

2005 (1)

J. S. Harchanko and D. B. Chenault, “Water-surface object detection and classification using imaging polarimetry,” Proc. SPIE 5888, 588815 (2005).
[Crossref]

2003 (1)

C. Pernechele, E. Giro, and D. Fantinel, “Device for optical linear polarization measurements with a single exposure,” Proc. SPIE 4843, 156–164 (2003).
[Crossref]

2002 (1)

J. S. Baba, J. R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Coté, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7(3), 341–349 (2002).
[Crossref] [PubMed]

2001 (1)

T. Hamamoto, H. Toyota, and H. Kikuta, “Microretarder array for imaging polarimetry in the visible wavelength region.Lithographic and Micromachining Techniques for Optical Component Fabrication,” Proc. SPIE 4440, 293–301 (2001).
[Crossref]

1997 (1)

E. Oliva, “Wedged double Wollaston, a device for single shot polarimetric measurements,” Astron. Astrophys. Suppl. Ser. 123(3), 589–592 (1997).
[Crossref]

1996 (1)

E. H. Geyer, K. Jockers, N. N. Kiselev, and G. P. Chernova, “A novel quadruple beam imaging polarimeter and its application to Comet Tanaka-Machholz 1992 X,” Astrophys. Space Sci. 239(2), 259–274 (1996).
[Crossref]

Arai, A.

K. S. Kawabata, O. Nagae, S. Chiyonobu, H. Tanaka, H. Nakaya, M. Suzuki, Y. Kamata, S. Miyazaki, K. Hiragi, H. Miyamoto, M. Yamanaka, A. Arai, T. Yamashita, M. Uemura, T. Ohsugi, M. Isogai, Y. Ishitobi, and S. Sato, “Wide-field one-shot optical polarimeter: HOWPol,” Proc. SPIE 7014, 70144L (2008).
[Crossref]

Baba, J. S.

J. S. Baba, J. R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Coté, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7(3), 341–349 (2002).
[Crossref] [PubMed]

Banner, M. L.

C. J. Zappa, M. L. Banner, H. Schultz, A. C. Emmanuel, L. B. Wolffet, and J. Yalcin, “Retrieval of short ocean wave slope using polarimetric imaging,” Meas. Sci. Technol. 19(5), 055503 (2008).
[Crossref]

Burl, M. C.

L. M. Novak, M. C. Burl, W. W. Irving, and G. J. Owirka, “Optimal polarimetric processing for enhanced target detection,” inProceedings of IEEE Conference on Telesystems (IEEE, 1991), pp. 69–75.
[Crossref]

Cameron, B. D.

J. S. Baba, J. R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Coté, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7(3), 341–349 (2002).
[Crossref] [PubMed]

Charbois, J. M.

Chen, X. Y.

X. Y. Chen and M. San, “Description of effect of polarimeter with slanting ray,” Opt. Technol. 32(3), 425–427 (2006).

Chenault, D.

J. L. Pezzaniti, D. Chenault, M. Roche, J. Reinhardt, and H. Schultz, “Wave slope measurement using imaging polarimetry,” Proc. SPIE 7317, 73170B (2009).
[Crossref]

Chenault, D. B.

J. S. Harchanko and D. B. Chenault, “Water-surface object detection and classification using imaging polarimetry,” Proc. SPIE 5888, 588815 (2005).
[Crossref]

Chernova, G. P.

E. H. Geyer, K. Jockers, N. N. Kiselev, and G. P. Chernova, “A novel quadruple beam imaging polarimeter and its application to Comet Tanaka-Machholz 1992 X,” Astrophys. Space Sci. 239(2), 259–274 (1996).
[Crossref]

Chiyonobu, S.

K. S. Kawabata, O. Nagae, S. Chiyonobu, H. Tanaka, H. Nakaya, M. Suzuki, Y. Kamata, S. Miyazaki, K. Hiragi, H. Miyamoto, M. Yamanaka, A. Arai, T. Yamashita, M. Uemura, T. Ohsugi, M. Isogai, Y. Ishitobi, and S. Sato, “Wide-field one-shot optical polarimeter: HOWPol,” Proc. SPIE 7014, 70144L (2008).
[Crossref]

Chung, J. R.

J. S. Baba, J. R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Coté, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7(3), 341–349 (2002).
[Crossref] [PubMed]

Coté, G. L.

J. S. Baba, J. R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Coté, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7(3), 341–349 (2002).
[Crossref] [PubMed]

DeLaughter, A. H.

J. S. Baba, J. R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Coté, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7(3), 341–349 (2002).
[Crossref] [PubMed]

Devlaminck, V.

Emmanuel, A. C.

C. J. Zappa, M. L. Banner, H. Schultz, A. C. Emmanuel, L. B. Wolffet, and J. Yalcin, “Retrieval of short ocean wave slope using polarimetric imaging,” Meas. Sci. Technol. 19(5), 055503 (2008).
[Crossref]

Fantinel, D.

C. Pernechele, E. Giro, and D. Fantinel, “Device for optical linear polarization measurements with a single exposure,” Proc. SPIE 4843, 156–164 (2003).
[Crossref]

Geyer, E. H.

E. H. Geyer, K. Jockers, N. N. Kiselev, and G. P. Chernova, “A novel quadruple beam imaging polarimeter and its application to Comet Tanaka-Machholz 1992 X,” Astrophys. Space Sci. 239(2), 259–274 (1996).
[Crossref]

Giro, E.

C. Pernechele, E. Giro, and D. Fantinel, “Device for optical linear polarization measurements with a single exposure,” Proc. SPIE 4843, 156–164 (2003).
[Crossref]

Gruev, V.

M. Kulkarni and V. Gruev, “A division-of-focal-plane spectral-polarization imaging sensor,” Proc. SPIE 8364, 83640K (2012).
[Crossref]

Hamamoto, T.

T. Hamamoto, H. Toyota, and H. Kikuta, “Microretarder array for imaging polarimetry in the visible wavelength region.Lithographic and Micromachining Techniques for Optical Component Fabrication,” Proc. SPIE 4440, 293–301 (2001).
[Crossref]

Harchanko, J. S.

J. S. Harchanko and D. B. Chenault, “Water-surface object detection and classification using imaging polarimetry,” Proc. SPIE 5888, 588815 (2005).
[Crossref]

Hiragi, K.

K. S. Kawabata, O. Nagae, S. Chiyonobu, H. Tanaka, H. Nakaya, M. Suzuki, Y. Kamata, S. Miyazaki, K. Hiragi, H. Miyamoto, M. Yamanaka, A. Arai, T. Yamashita, M. Uemura, T. Ohsugi, M. Isogai, Y. Ishitobi, and S. Sato, “Wide-field one-shot optical polarimeter: HOWPol,” Proc. SPIE 7014, 70144L (2008).
[Crossref]

Irving, W. W.

L. M. Novak, M. C. Burl, W. W. Irving, and G. J. Owirka, “Optimal polarimetric processing for enhanced target detection,” inProceedings of IEEE Conference on Telesystems (IEEE, 1991), pp. 69–75.
[Crossref]

Ishitobi, Y.

K. S. Kawabata, O. Nagae, S. Chiyonobu, H. Tanaka, H. Nakaya, M. Suzuki, Y. Kamata, S. Miyazaki, K. Hiragi, H. Miyamoto, M. Yamanaka, A. Arai, T. Yamashita, M. Uemura, T. Ohsugi, M. Isogai, Y. Ishitobi, and S. Sato, “Wide-field one-shot optical polarimeter: HOWPol,” Proc. SPIE 7014, 70144L (2008).
[Crossref]

Isogai, M.

K. S. Kawabata, O. Nagae, S. Chiyonobu, H. Tanaka, H. Nakaya, M. Suzuki, Y. Kamata, S. Miyazaki, K. Hiragi, H. Miyamoto, M. Yamanaka, A. Arai, T. Yamashita, M. Uemura, T. Ohsugi, M. Isogai, Y. Ishitobi, and S. Sato, “Wide-field one-shot optical polarimeter: HOWPol,” Proc. SPIE 7014, 70144L (2008).
[Crossref]

Jockers, K.

E. H. Geyer, K. Jockers, N. N. Kiselev, and G. P. Chernova, “A novel quadruple beam imaging polarimeter and its application to Comet Tanaka-Machholz 1992 X,” Astrophys. Space Sci. 239(2), 259–274 (1996).
[Crossref]

Kamata, Y.

K. S. Kawabata, O. Nagae, S. Chiyonobu, H. Tanaka, H. Nakaya, M. Suzuki, Y. Kamata, S. Miyazaki, K. Hiragi, H. Miyamoto, M. Yamanaka, A. Arai, T. Yamashita, M. Uemura, T. Ohsugi, M. Isogai, Y. Ishitobi, and S. Sato, “Wide-field one-shot optical polarimeter: HOWPol,” Proc. SPIE 7014, 70144L (2008).
[Crossref]

Kawabata, K. S.

K. S. Kawabata, O. Nagae, S. Chiyonobu, H. Tanaka, H. Nakaya, M. Suzuki, Y. Kamata, S. Miyazaki, K. Hiragi, H. Miyamoto, M. Yamanaka, A. Arai, T. Yamashita, M. Uemura, T. Ohsugi, M. Isogai, Y. Ishitobi, and S. Sato, “Wide-field one-shot optical polarimeter: HOWPol,” Proc. SPIE 7014, 70144L (2008).
[Crossref]

Kikuta, H.

T. Hamamoto, H. Toyota, and H. Kikuta, “Microretarder array for imaging polarimetry in the visible wavelength region.Lithographic and Micromachining Techniques for Optical Component Fabrication,” Proc. SPIE 4440, 293–301 (2001).
[Crossref]

Kiselev, N. N.

E. H. Geyer, K. Jockers, N. N. Kiselev, and G. P. Chernova, “A novel quadruple beam imaging polarimeter and its application to Comet Tanaka-Machholz 1992 X,” Astrophys. Space Sci. 239(2), 259–274 (1996).
[Crossref]

Kulkarni, M.

M. Kulkarni and V. Gruev, “A division-of-focal-plane spectral-polarization imaging sensor,” Proc. SPIE 8364, 83640K (2012).
[Crossref]

Miyamoto, H.

K. S. Kawabata, O. Nagae, S. Chiyonobu, H. Tanaka, H. Nakaya, M. Suzuki, Y. Kamata, S. Miyazaki, K. Hiragi, H. Miyamoto, M. Yamanaka, A. Arai, T. Yamashita, M. Uemura, T. Ohsugi, M. Isogai, Y. Ishitobi, and S. Sato, “Wide-field one-shot optical polarimeter: HOWPol,” Proc. SPIE 7014, 70144L (2008).
[Crossref]

Miyazaki, S.

K. S. Kawabata, O. Nagae, S. Chiyonobu, H. Tanaka, H. Nakaya, M. Suzuki, Y. Kamata, S. Miyazaki, K. Hiragi, H. Miyamoto, M. Yamanaka, A. Arai, T. Yamashita, M. Uemura, T. Ohsugi, M. Isogai, Y. Ishitobi, and S. Sato, “Wide-field one-shot optical polarimeter: HOWPol,” Proc. SPIE 7014, 70144L (2008).
[Crossref]

Nagae, O.

K. S. Kawabata, O. Nagae, S. Chiyonobu, H. Tanaka, H. Nakaya, M. Suzuki, Y. Kamata, S. Miyazaki, K. Hiragi, H. Miyamoto, M. Yamanaka, A. Arai, T. Yamashita, M. Uemura, T. Ohsugi, M. Isogai, Y. Ishitobi, and S. Sato, “Wide-field one-shot optical polarimeter: HOWPol,” Proc. SPIE 7014, 70144L (2008).
[Crossref]

Nakaya, H.

K. S. Kawabata, O. Nagae, S. Chiyonobu, H. Tanaka, H. Nakaya, M. Suzuki, Y. Kamata, S. Miyazaki, K. Hiragi, H. Miyamoto, M. Yamanaka, A. Arai, T. Yamashita, M. Uemura, T. Ohsugi, M. Isogai, Y. Ishitobi, and S. Sato, “Wide-field one-shot optical polarimeter: HOWPol,” Proc. SPIE 7014, 70144L (2008).
[Crossref]

Narasimhan, S. G.

Y. Y. Schechner, S. G. Narasimhan, and S. K. Nayar, “Instant dehazing of images using polarization,” inProceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2001).

Nayar, S. K.

Y. Y. Schechner, S. G. Narasimhan, and S. K. Nayar, “Instant dehazing of images using polarization,” inProceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2001).

Novak, L. M.

L. M. Novak, M. C. Burl, W. W. Irving, and G. J. Owirka, “Optimal polarimetric processing for enhanced target detection,” inProceedings of IEEE Conference on Telesystems (IEEE, 1991), pp. 69–75.
[Crossref]

Ohsugi, T.

K. S. Kawabata, O. Nagae, S. Chiyonobu, H. Tanaka, H. Nakaya, M. Suzuki, Y. Kamata, S. Miyazaki, K. Hiragi, H. Miyamoto, M. Yamanaka, A. Arai, T. Yamashita, M. Uemura, T. Ohsugi, M. Isogai, Y. Ishitobi, and S. Sato, “Wide-field one-shot optical polarimeter: HOWPol,” Proc. SPIE 7014, 70144L (2008).
[Crossref]

Oliva, E.

E. Oliva, “Wedged double Wollaston, a device for single shot polarimetric measurements,” Astron. Astrophys. Suppl. Ser. 123(3), 589–592 (1997).
[Crossref]

Owirka, G. J.

L. M. Novak, M. C. Burl, W. W. Irving, and G. J. Owirka, “Optimal polarimetric processing for enhanced target detection,” inProceedings of IEEE Conference on Telesystems (IEEE, 1991), pp. 69–75.
[Crossref]

Pernechele, C.

C. Pernechele, E. Giro, and D. Fantinel, “Device for optical linear polarization measurements with a single exposure,” Proc. SPIE 4843, 156–164 (2003).
[Crossref]

Pezzaniti, J. L.

J. L. Pezzaniti, D. Chenault, M. Roche, J. Reinhardt, and H. Schultz, “Wave slope measurement using imaging polarimetry,” Proc. SPIE 7317, 73170B (2009).
[Crossref]

Reinhardt, J.

J. L. Pezzaniti, D. Chenault, M. Roche, J. Reinhardt, and H. Schultz, “Wave slope measurement using imaging polarimetry,” Proc. SPIE 7317, 73170B (2009).
[Crossref]

Roche, M.

J. L. Pezzaniti, D. Chenault, M. Roche, J. Reinhardt, and H. Schultz, “Wave slope measurement using imaging polarimetry,” Proc. SPIE 7317, 73170B (2009).
[Crossref]

San, M.

X. Y. Chen and M. San, “Description of effect of polarimeter with slanting ray,” Opt. Technol. 32(3), 425–427 (2006).

Sato, S.

K. S. Kawabata, O. Nagae, S. Chiyonobu, H. Tanaka, H. Nakaya, M. Suzuki, Y. Kamata, S. Miyazaki, K. Hiragi, H. Miyamoto, M. Yamanaka, A. Arai, T. Yamashita, M. Uemura, T. Ohsugi, M. Isogai, Y. Ishitobi, and S. Sato, “Wide-field one-shot optical polarimeter: HOWPol,” Proc. SPIE 7014, 70144L (2008).
[Crossref]

Schechner, Y. Y.

Y. Y. Schechner, S. G. Narasimhan, and S. K. Nayar, “Instant dehazing of images using polarization,” inProceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2001).

Schultz, H.

J. L. Pezzaniti, D. Chenault, M. Roche, J. Reinhardt, and H. Schultz, “Wave slope measurement using imaging polarimetry,” Proc. SPIE 7317, 73170B (2009).
[Crossref]

C. J. Zappa, M. L. Banner, H. Schultz, A. C. Emmanuel, L. B. Wolffet, and J. Yalcin, “Retrieval of short ocean wave slope using polarimetric imaging,” Meas. Sci. Technol. 19(5), 055503 (2008).
[Crossref]

Suzuki, M.

K. S. Kawabata, O. Nagae, S. Chiyonobu, H. Tanaka, H. Nakaya, M. Suzuki, Y. Kamata, S. Miyazaki, K. Hiragi, H. Miyamoto, M. Yamanaka, A. Arai, T. Yamashita, M. Uemura, T. Ohsugi, M. Isogai, Y. Ishitobi, and S. Sato, “Wide-field one-shot optical polarimeter: HOWPol,” Proc. SPIE 7014, 70144L (2008).
[Crossref]

Tanaka, H.

K. S. Kawabata, O. Nagae, S. Chiyonobu, H. Tanaka, H. Nakaya, M. Suzuki, Y. Kamata, S. Miyazaki, K. Hiragi, H. Miyamoto, M. Yamanaka, A. Arai, T. Yamashita, M. Uemura, T. Ohsugi, M. Isogai, Y. Ishitobi, and S. Sato, “Wide-field one-shot optical polarimeter: HOWPol,” Proc. SPIE 7014, 70144L (2008).
[Crossref]

Terrier, P.

Toyota, H.

T. Hamamoto, H. Toyota, and H. Kikuta, “Microretarder array for imaging polarimetry in the visible wavelength region.Lithographic and Micromachining Techniques for Optical Component Fabrication,” Proc. SPIE 4440, 293–301 (2001).
[Crossref]

Uemura, M.

K. S. Kawabata, O. Nagae, S. Chiyonobu, H. Tanaka, H. Nakaya, M. Suzuki, Y. Kamata, S. Miyazaki, K. Hiragi, H. Miyamoto, M. Yamanaka, A. Arai, T. Yamashita, M. Uemura, T. Ohsugi, M. Isogai, Y. Ishitobi, and S. Sato, “Wide-field one-shot optical polarimeter: HOWPol,” Proc. SPIE 7014, 70144L (2008).
[Crossref]

Wolffet, L. B.

C. J. Zappa, M. L. Banner, H. Schultz, A. C. Emmanuel, L. B. Wolffet, and J. Yalcin, “Retrieval of short ocean wave slope using polarimetric imaging,” Meas. Sci. Technol. 19(5), 055503 (2008).
[Crossref]

Yalcin, J.

C. J. Zappa, M. L. Banner, H. Schultz, A. C. Emmanuel, L. B. Wolffet, and J. Yalcin, “Retrieval of short ocean wave slope using polarimetric imaging,” Meas. Sci. Technol. 19(5), 055503 (2008).
[Crossref]

Yamanaka, M.

K. S. Kawabata, O. Nagae, S. Chiyonobu, H. Tanaka, H. Nakaya, M. Suzuki, Y. Kamata, S. Miyazaki, K. Hiragi, H. Miyamoto, M. Yamanaka, A. Arai, T. Yamashita, M. Uemura, T. Ohsugi, M. Isogai, Y. Ishitobi, and S. Sato, “Wide-field one-shot optical polarimeter: HOWPol,” Proc. SPIE 7014, 70144L (2008).
[Crossref]

Yamashita, T.

K. S. Kawabata, O. Nagae, S. Chiyonobu, H. Tanaka, H. Nakaya, M. Suzuki, Y. Kamata, S. Miyazaki, K. Hiragi, H. Miyamoto, M. Yamanaka, A. Arai, T. Yamashita, M. Uemura, T. Ohsugi, M. Isogai, Y. Ishitobi, and S. Sato, “Wide-field one-shot optical polarimeter: HOWPol,” Proc. SPIE 7014, 70144L (2008).
[Crossref]

Zappa, C. J.

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Figures (8)

Fig. 1
Fig. 1 Imaging relations of a point on-axis (a) and off-axis (b).
Fig. 2
Fig. 2 (a, b) Relationship between the polarizer coordinate system and the light wave coordinate system. (c) Decomposition of the incident light vector.
Fig. 3
Fig. 3 (a) The relationship among β, θ and ψ. (b) The relationship among ρN, θ and ψ. (c) For θ = 0°, the relationship between ρP, ϕ and ψ. (d) For θ = 30°, the relationship between ρP, ϕ and ψ.
Fig. 4
Fig. 4 (a) Schematic (left) and physical image (right) of the verification experiments. (b) Spectral transmissivity of the two polarizers. (c) Spectral transmissivity when the two polarizers have different angles. (d) Relationship between the grey level and irradiance.
Fig. 5
Fig. 5 (a) Integrating sphere images captured by the camera, the natural light image (left) and the image of natural light that passes through the polarizer 1 (right). (b) ψ = 0°; the relationship between ρN and θ, experimental fitting (left, the mean of ρN is M = 0.3936, the mean square error of ρN is σ = 5.61 × 10−3, the same below). Theoretical model, original model and experimental results (right). (c) ψ = 90°; the relationship between ρN and θ, experimental fitting (left, M = 0.3899, σ = 4.63 × 10−3), comparison of three results (right). (d) θ = 5.5°; the relationship between ρN and ψ, experimental fitting (left, M = 0.3917, σ = 3.21 × 10−3), comparison of three results (right).
Fig. 6
Fig. 6 The angle between polarizer 1 and polarizer 2 is 0°. (a) Images captured by the camera, without polarizer 2 (left); the angle of the two polarizers is 0° (middle), and the angle of the two polarizers is 30° (right). (b) ψ = 0°; the relationship between ρP and θ, experimental fitting (left, M = 0.8218, σ = 8.93 × 10−3), comparison of three results (right). (c) ψ = 90°; the relationship between ρP and θ, experimental fitting (left, M = 0.8187, σ = 9.45 × 10−3), comparison of three results (right). (d) θ = 5.5°; the relationship between ρP and ψ, experimental fitting (left, M = 0.8205, σ = 4.99 × 10−3), comparison of three results (right).
Fig. 7
Fig. 7 The angle between polarizer 1 and polarizer 2 is 30°. (a) ψ = 0°; the relationship between ρP and θ, experimental fitting (left, M = 0.6387, σ = 7.57 × 10−3), comparison of three results (right). (b) ψ = 90°; the relationship between ρP and θ, experimental fitting (left, M = 0.6363, σ = 5.69 × 10−3), comparison of three results (right). (c) θ = 5.5°; the relationship between ρP and ψ, experimental fitting (left, M = 0.6370, σ = 4.24 × 10−3), comparison of three results (right).
Fig. 8
Fig. 8 (a) ψ = 0° and θ = 5.5°; the relationship between ρP and ϕ, experimental fitting (left), comparison of three results (right). (b) ψ = 30° and θ = 5.5°; the relationship between ρP and ϕ, experimental fitting (left), comparison of three results (right).

Equations (20)

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E=π L 0 τ n 1 2 n 0 2 sin 2 u 1 .
E =π L 0 τ n 1 2 n 0 2 sin 2 u 1 cos 4 θ.
E =E cos 4 θ.
{ e ζ =sinθsinψisinθcosψj+cosθk e ξ =( cosψcosϕcosθsinψsinϕ )i+( sinψcosϕ+cosθcosψsinϕ )j+( sinθsinϕ )k e η =( cosψsinϕ+cosθsinψcosϕ )i( sinψsinϕcosθcosψcosϕ )j+( sinθcosϕ )k .
{ e b = e y × e ζ / sin γ y = ( cosθisinθsinψk )/ sin γ y e c = e ζ × e x / sin γ x = ( cosθj+sinθcosψk )/ sin γ x .
γ x =arccos(sinθsinψ).
γ y =arccos(sinθcosψ).
cosβ= sin 2 θsin(2ψ)/ (2sin γ x sin γ y ) .
oE=cosα sinα/ tanβ .
cosα= e b e ξ = ( cosθcosψcosϕsinψsinϕ )/ sin γ y .
cosδ= e b e x = cosθ sin γ y .
oF=oE e x =(cosα sinα/ tanβ )cosδ.
oF=cosψcosϕcosθsinψsinϕ.
I N = 0 2π I Nα cos 4 θ (cosα sinα/ tanβ ) 2 cos 2 δdα.
I N = I N 2 cos 4 θ(1+ 1 tan 2 β ) cos 2 δ.
ρ N = I N I Nl = 1 2 (1+ 1 tan 2 β ) cos 2 δ.
ρ N = 1 2 ( 1 sin 2 θ sin 2 ψ ).
| ρ N0 ρ N | ρ N0 = sin 2 θ sin 2 ψ.
I P = I P cos 4 θ ( cosα sinα tanβ ) 2 cos 2 δ.
ρ P = I P I Pl =o F 2 = (cosψcosϕcosθsinψsinϕ) 2 .

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