Abstract

Single-snapshot full-Stokes imaging polarimetry is a powerful tool for the acquisition of the spatial polarization information in real time. According to the general linear model of a polarimeter, to recover full Stokes parameters at least four polarimetric intensities should be measured. In this paper, four types of single-snapshot full-Stokes division-of-aperture imaging polarimeter with four subapertures are presented and compared, with maximum spatial resolution for each polarimetric image on a single area-array detector. By using the error propagation theories for different incident states of polarization, the performance of four polarimeters are evaluated for several main sources of error, including retardance error, alignment error of retarders, and noise perturbation. The results show that the configuration of four 132° retarders with angular positions of ( ± 51.7°, ± 15.1°) is an optimal choice for the configuration of four subaperture single-snapshot full-Stokes imaging polarimeter. The tolerance and uncertainty of this configuration are analyzed.

© 2015 Optical Society of America

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References

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2014 (6)

T. Mu, C. Zhang, Q. Li, Y. Wei, Q. Chen, and C. Jia, “Snapshot full-Stokes imaging spectropolarimetry based on division-ofaperture polarimetry and integral-field spectroscopy,” Proc. SPIE 9298, 92980D (2014).
[Crossref]

T. Mu, C. Zhang, Q. Li, Y. Wei, Q. Chen, and C. Jia, “The polarization-difference interference imaging spectrometer-I. concept, principle, and operation,” Acta Phys. Sin. 63, 110704 (2014).

T. Mu, C. Zhang, Q. Li, Y. Wei, Q. Chen, and C. Jia, “The polarization-difference interference imaging spectrometer-II. optical design and analysis,” Acta Phys. Sin. 63, 110705 (2014).

E. Chironi and C. Iemmi, “Bounding the relative errors associated with a complete Stokes polarimeter,” J. Opt. Soc. Am. A 31(1), 75–80 (2014).
[Crossref] [PubMed]

H. Dai and C. Yan, “Measurement errors resulted from misalignment errors of the retarder in a rotating-retarder complete Stokes polarimeter,” Opt. Express 22(10), 11869–11883 (2014).
[Crossref] [PubMed]

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(3), 3063–3074 (2014).
[Crossref] [PubMed]

2013 (3)

2012 (2)

2011 (1)

2010 (1)

2009 (2)

2006 (3)

2005 (1)

J. L. Pezzaniti and D. B. Chenault, “A Division of Aperture MWIR Imaging Polarimeter,” Proc. SPIE 5888, 58880V (2005).
[Crossref]

2003 (1)

2002 (3)

V. L. Gamiz and J. F. Belsher, “Performance limitations of a four-channel polarimeter in the presence of detection noise,” Opt. Eng. 41(5), 973–980 (2002).
[Crossref]

S. N. Savenkov, “Optimization and structuring of the instrument matrix for polarimetric measurements,” Opt. Eng. 41(5), 965–972 (2002).
[Crossref]

J. S. Tyo, “Design of optimal polarimeters: maximization of signal-to-noise ratio and minimization of systematic error,” Appl. Opt. 41(4), 619–630 (2002).
[Crossref] [PubMed]

2000 (2)

1999 (1)

1995 (2)

A. Ambirajan and D. C. Look, “Optimum angles for a polarimeter: part I,” Opt. Eng. 34(6), 1651–1655 (1995).
[Crossref]

A. Ambirajan and D. C. Look, “Optimum angles for a polarimeter: part II,” Opt. Eng. 34(6), 1656–1658 (1995).
[Crossref]

Ambirajan, A.

A. Ambirajan and D. C. Look, “Optimum angles for a polarimeter: part I,” Opt. Eng. 34(6), 1651–1655 (1995).
[Crossref]

A. Ambirajan and D. C. Look, “Optimum angles for a polarimeter: part II,” Opt. Eng. 34(6), 1656–1658 (1995).
[Crossref]

Balakrishnan, K.

Belsher, J. F.

V. L. Gamiz and J. F. Belsher, “Performance limitations of a four-channel polarimeter in the presence of detection noise,” Opt. Eng. 41(5), 973–980 (2002).
[Crossref]

Brock, N.

Campos, J.

Chen, Q.

T. Mu, C. Zhang, Q. Li, Y. Wei, Q. Chen, and C. Jia, “The polarization-difference interference imaging spectrometer-II. optical design and analysis,” Acta Phys. Sin. 63, 110705 (2014).

T. Mu, C. Zhang, Q. Li, Y. Wei, Q. Chen, and C. Jia, “Snapshot full-Stokes imaging spectropolarimetry based on division-ofaperture polarimetry and integral-field spectroscopy,” Proc. SPIE 9298, 92980D (2014).
[Crossref]

T. Mu, C. Zhang, Q. Li, Y. Wei, Q. Chen, and C. Jia, “The polarization-difference interference imaging spectrometer-I. concept, principle, and operation,” Acta Phys. Sin. 63, 110704 (2014).

Chenault, D. B.

Chironi, E.

Compain, E.

Dai, H.

De Martino, A.

Dereniak, E. L.

Descour, M. R.

Dong, H.

Drevillon, B.

Drévillon, B.

Gamiz, V. L.

V. L. Gamiz and J. F. Belsher, “Performance limitations of a four-channel polarimeter in the presence of detection noise,” Opt. Eng. 41(5), 973–980 (2002).
[Crossref]

Garcia-Caurel, E.

Goldstein, D. L.

Gong, Y.

Goudail, F.

Hsu, W.-L.

Ibn-Elhaj, M.

Iemmi, C.

Jia, C.

T. Mu, C. Zhang, Q. Li, Y. Wei, Q. Chen, and C. Jia, “The polarization-difference interference imaging spectrometer-II. optical design and analysis,” Acta Phys. Sin. 63, 110705 (2014).

T. Mu, C. Zhang, Q. Li, Y. Wei, Q. Chen, and C. Jia, “The polarization-difference interference imaging spectrometer-I. concept, principle, and operation,” Acta Phys. Sin. 63, 110704 (2014).

T. Mu, C. Zhang, Q. Li, Y. Wei, Q. Chen, and C. Jia, “Snapshot full-Stokes imaging spectropolarimetry based on division-ofaperture polarimetry and integral-field spectroscopy,” Proc. SPIE 9298, 92980D (2014).
[Crossref]

T. Mu, C. Zhang, W. Ren, C. Jia, L. Zhang, and Q. Li, “Compact and static Fourier transform imaging spectropolarimeters using birefringent elements,” Proc. SPIE 8910, 89101A (2013).
[Crossref]

T. Mu, C. Zhang, C. Jia, and W. Ren, “Static hyperspectral imaging polarimeter for full linear Stokes parameters,” Opt. Express 20(16), 18194–18201 (2012).
[Crossref] [PubMed]

T. Mu, C. Zhang, W. Ren, and C. Jia, “Static polarization-difference interference imaging spectrometer,” Opt. Lett. 37(17), 3507–3509 (2012).
[Crossref] [PubMed]

Kemme, S. A.

Kim, Y.-K.

Lara, D.

Laude, B.

Li, Q.

T. Mu, C. Zhang, Q. Li, Y. Wei, Q. Chen, and C. Jia, “Snapshot full-Stokes imaging spectropolarimetry based on division-ofaperture polarimetry and integral-field spectroscopy,” Proc. SPIE 9298, 92980D (2014).
[Crossref]

T. Mu, C. Zhang, Q. Li, Y. Wei, Q. Chen, and C. Jia, “The polarization-difference interference imaging spectrometer-I. concept, principle, and operation,” Acta Phys. Sin. 63, 110704 (2014).

T. Mu, C. Zhang, Q. Li, Y. Wei, Q. Chen, and C. Jia, “The polarization-difference interference imaging spectrometer-II. optical design and analysis,” Acta Phys. Sin. 63, 110705 (2014).

T. Mu, C. Zhang, W. Ren, C. Jia, L. Zhang, and Q. Li, “Compact and static Fourier transform imaging spectropolarimeters using birefringent elements,” Proc. SPIE 8910, 89101A (2013).
[Crossref]

Lizana, A.

Look, D. C.

A. Ambirajan and D. C. Look, “Optimum angles for a polarimeter: part I,” Opt. Eng. 34(6), 1651–1655 (1995).
[Crossref]

A. Ambirajan and D. C. Look, “Optimum angles for a polarimeter: part II,” Opt. Eng. 34(6), 1656–1658 (1995).
[Crossref]

Mu, T.

T. Mu, C. Zhang, Q. Li, Y. Wei, Q. Chen, and C. Jia, “Snapshot full-Stokes imaging spectropolarimetry based on division-ofaperture polarimetry and integral-field spectroscopy,” Proc. SPIE 9298, 92980D (2014).
[Crossref]

T. Mu, C. Zhang, Q. Li, Y. Wei, Q. Chen, and C. Jia, “The polarization-difference interference imaging spectrometer-I. concept, principle, and operation,” Acta Phys. Sin. 63, 110704 (2014).

T. Mu, C. Zhang, Q. Li, Y. Wei, Q. Chen, and C. Jia, “The polarization-difference interference imaging spectrometer-II. optical design and analysis,” Acta Phys. Sin. 63, 110705 (2014).

T. Mu, C. Zhang, W. Ren, C. Jia, L. Zhang, and Q. Li, “Compact and static Fourier transform imaging spectropolarimeters using birefringent elements,” Proc. SPIE 8910, 89101A (2013).
[Crossref]

T. Mu, C. Zhang, C. Jia, and W. Ren, “Static hyperspectral imaging polarimeter for full linear Stokes parameters,” Opt. Express 20(16), 18194–18201 (2012).
[Crossref] [PubMed]

T. Mu, C. Zhang, W. Ren, and C. Jia, “Static polarization-difference interference imaging spectrometer,” Opt. Lett. 37(17), 3507–3509 (2012).
[Crossref] [PubMed]

Myhre, G.

Paterson, C.

Pau, S.

Peinado, A.

Pezzaniti, J. L.

J. L. Pezzaniti and D. B. Chenault, “A Division of Aperture MWIR Imaging Polarimeter,” Proc. SPIE 5888, 58880V (2005).
[Crossref]

Phipps, G. S.

Poirier, S.

Ren, W.

S, A.

J. Zallat, A. S, and M. P. Stoll, “Optimal configurations for imaging polarimeters: impact of image noise and systematic errors,” J. Opt. A, Pure Appl. Opt. 8(9), 807–814 (2006).
[Crossref]

Sabatke, D. S.

Savenkov, S. N.

S. N. Savenkov, “Optimization and structuring of the instrument matrix for polarimetric measurements,” Opt. Eng. 41(5), 965–972 (2002).
[Crossref]

Shaw, J. A.

Stoll, M. P.

J. Zallat, A. S, and M. P. Stoll, “Optimal configurations for imaging polarimeters: impact of image noise and systematic errors,” J. Opt. A, Pure Appl. Opt. 8(9), 807–814 (2006).
[Crossref]

Sweatt, W. C.

Tang, M.

Tyo, J. S.

Vidal, J.

Wei, H.

Wei, Y.

T. Mu, C. Zhang, Q. Li, Y. Wei, Q. Chen, and C. Jia, “The polarization-difference interference imaging spectrometer-II. optical design and analysis,” Acta Phys. Sin. 63, 110705 (2014).

T. Mu, C. Zhang, Q. Li, Y. Wei, Q. Chen, and C. Jia, “The polarization-difference interference imaging spectrometer-I. concept, principle, and operation,” Acta Phys. Sin. 63, 110704 (2014).

T. Mu, C. Zhang, Q. Li, Y. Wei, Q. Chen, and C. Jia, “Snapshot full-Stokes imaging spectropolarimetry based on division-ofaperture polarimetry and integral-field spectroscopy,” Proc. SPIE 9298, 92980D (2014).
[Crossref]

Yan, C.

Zallat, J.

J. Zallat, A. S, and M. P. Stoll, “Optimal configurations for imaging polarimeters: impact of image noise and systematic errors,” J. Opt. A, Pure Appl. Opt. 8(9), 807–814 (2006).
[Crossref]

Zhang, C.

T. Mu, C. Zhang, Q. Li, Y. Wei, Q. Chen, and C. Jia, “Snapshot full-Stokes imaging spectropolarimetry based on division-ofaperture polarimetry and integral-field spectroscopy,” Proc. SPIE 9298, 92980D (2014).
[Crossref]

T. Mu, C. Zhang, Q. Li, Y. Wei, Q. Chen, and C. Jia, “The polarization-difference interference imaging spectrometer-II. optical design and analysis,” Acta Phys. Sin. 63, 110705 (2014).

T. Mu, C. Zhang, Q. Li, Y. Wei, Q. Chen, and C. Jia, “The polarization-difference interference imaging spectrometer-I. concept, principle, and operation,” Acta Phys. Sin. 63, 110704 (2014).

T. Mu, C. Zhang, W. Ren, C. Jia, L. Zhang, and Q. Li, “Compact and static Fourier transform imaging spectropolarimeters using birefringent elements,” Proc. SPIE 8910, 89101A (2013).
[Crossref]

T. Mu, C. Zhang, C. Jia, and W. Ren, “Static hyperspectral imaging polarimeter for full linear Stokes parameters,” Opt. Express 20(16), 18194–18201 (2012).
[Crossref] [PubMed]

T. Mu, C. Zhang, W. Ren, and C. Jia, “Static polarization-difference interference imaging spectrometer,” Opt. Lett. 37(17), 3507–3509 (2012).
[Crossref] [PubMed]

Zhang, L.

T. Mu, C. Zhang, W. Ren, C. Jia, L. Zhang, and Q. Li, “Compact and static Fourier transform imaging spectropolarimeters using birefringent elements,” Proc. SPIE 8910, 89101A (2013).
[Crossref]

Acta Phys. Sin. (2)

T. Mu, C. Zhang, Q. Li, Y. Wei, Q. Chen, and C. Jia, “The polarization-difference interference imaging spectrometer-I. concept, principle, and operation,” Acta Phys. Sin. 63, 110704 (2014).

T. Mu, C. Zhang, Q. Li, Y. Wei, Q. Chen, and C. Jia, “The polarization-difference interference imaging spectrometer-II. optical design and analysis,” Acta Phys. Sin. 63, 110705 (2014).

Appl. Opt. (6)

J. Opt. A, Pure Appl. Opt. (1)

J. Zallat, A. S, and M. P. Stoll, “Optimal configurations for imaging polarimeters: impact of image noise and systematic errors,” J. Opt. A, Pure Appl. Opt. 8(9), 807–814 (2006).
[Crossref]

J. Opt. Soc. Am. A (1)

Opt. Eng. (4)

A. Ambirajan and D. C. Look, “Optimum angles for a polarimeter: part I,” Opt. Eng. 34(6), 1651–1655 (1995).
[Crossref]

A. Ambirajan and D. C. Look, “Optimum angles for a polarimeter: part II,” Opt. Eng. 34(6), 1656–1658 (1995).
[Crossref]

V. L. Gamiz and J. F. Belsher, “Performance limitations of a four-channel polarimeter in the presence of detection noise,” Opt. Eng. 41(5), 973–980 (2002).
[Crossref]

S. N. Savenkov, “Optimization and structuring of the instrument matrix for polarimetric measurements,” Opt. Eng. 41(5), 965–972 (2002).
[Crossref]

Opt. Express (6)

Opt. Lett. (5)

Proc. SPIE (3)

J. L. Pezzaniti and D. B. Chenault, “A Division of Aperture MWIR Imaging Polarimeter,” Proc. SPIE 5888, 58880V (2005).
[Crossref]

T. Mu, C. Zhang, W. Ren, C. Jia, L. Zhang, and Q. Li, “Compact and static Fourier transform imaging spectropolarimeters using birefringent elements,” Proc. SPIE 8910, 89101A (2013).
[Crossref]

T. Mu, C. Zhang, Q. Li, Y. Wei, Q. Chen, and C. Jia, “Snapshot full-Stokes imaging spectropolarimetry based on division-ofaperture polarimetry and integral-field spectroscopy,” Proc. SPIE 9298, 92980D (2014).
[Crossref]

Other (5)

J. C. D. T. Iniesta, Introduction to Spectropolarimetry (Cambridge University, 2003).

J. R. Schott, Fundamentals of Polarimetric Remote Sensing (SPIE, 2009).

V. V. Tuchin, L. V. Wang, and D. A. Zimnyakov, Optical Polarization in Biomedical Applications (Springer, 2009).

D. H. Goldstein, Polarized Light, Third Edition (CRC, 2011).

P. R. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, Third Edition (McGraw-Hill, 2003).

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Figures (10)

Fig. 1
Fig. 1 Scheme of DoAP using optimal four-quadrant polarization array. (a) A retarder array R plus a polarizer, and (b) two retarder arrays R1 and R2 plus a polarizer.
Fig. 2
Fig. 2 (a) Uniform sampling of SOPs along a spiral locus around the Poincare sphere, and (b) the normalized intensity for each sampling point.
Fig. 3
Fig. 3 (a) Uniform sampling of SOPs along a spiral locus around the Poincare sphere, and (b) the normalized intensity for each sampling point.
Fig. 4
Fig. 4 The errors in the estimated Stokes vector due to the retardance errors are plotted with the sampled incident SOPs along the spiral locus around the Poincare sphere for four configurations in (a)-(d). The retardance error of each retarder is 1°, no alignment error and noise are considered in the simulation.
Fig. 5
Fig. 5 The errors in the estimated Stokes vector due to the alignment errors are plotted with the sampled incident SOPs along the spiral locus around the Poincare sphere for four configurations in (a)-(d). The alignment error of each retarder is 0.5°, no alignment error and noise are considered in the simulation.
Fig. 6
Fig. 6 The standard deviations of noise in the estimated Stokes vector due to the noise perturbation are plotted with the sampled incident SOPs along the spiral locus around the Poincare sphere for four configurations in (a)-(d). Assuming the retarder arrays are perfect.
Fig. 7
Fig. 7 The errors in the estimated Stokes vector for the configuration (II). The top row is for P = 0.1 and the bottom row is for P = 0.5. In (a) and (d), the retardance error of each retarder is 1°. In (b) and (e), the alignment error of each retarder is 0.5°. (c) and (f) are the standard deviations of noise on the estimated Stokes vector.
Fig. 8
Fig. 8 The scheme of SSFSIP based on optimized DoAP. Lenses L1, L2 and L3, a retarder array R, a uniform polarizer P, a pyramid prism PP, and an area-array detector.
Fig. 9
Fig. 9 The dependence of the accuracy of estimated Stokes vector on the tolerance of each systematic parameter.
Fig. 10
Fig. 10 The standard deviation of the estimated Stokes vector at different incident SOPs. (a) When the standard deviation of retardance error is 1°, and (b) when the standard deviation of alignment error is 0.45°

Tables (4)

Tables Icon

Table 1 Four optimized configurations in [12], [14], [15], and [21] with different retardance and angular positions of retarders

Tables Icon

Table 2 Figures of merit for the optimized configurations.

Tables Icon

Table 3 The maximum errors of the estimated Stokes vector introduced by the 1° retardance error and 0.5° alignment error respectively in the four configurations.

Tables Icon

Table 4 The tolerance of each systematic parameter for the accuracy of 0.02 in the estimated Stokes parameters.

Equations (25)

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

M= M P (0) M R (δ, θ i ),
M= M P (0) M R 2 ( δ 2i , θ 2i ) M R 1 ( δ 1i , θ 1i ),
S out =M S in .
I=A S in ,
A(δ, θ i )= 1 2 [ 1 cos 2 2 θ 1 + sin 2 2 θ 1 cosδ sin4 θ 1 sin 2 (δ/2) sin2 θ 1 sinδ 1 cos 2 2 θ 2 + sin 2 2 θ 2 cosδ sin4 θ 2 sin 2 (δ/2) sin2 θ 2 sinδ 1 cos 2 2 θ 3 + sin 2 2 θ 3 cosδ sin4 θ 3 sin 2 (δ/2) sin2 θ 3 sinδ 1 cos 2 2 θ 4 + sin 2 2 θ 4 cosδ sin4 θ 4 sin 2 (δ/2) sin2 θ 4 sinδ ].
1 2 [ 1, ( cos 2 2 θ 2i + sin 2 2 θ 2i cos δ 2i )( cos 2 2 θ 1i + sin 2 2 θ 1i cos δ 1i )+ (sin δ 2i /2) 2 sin4 θ 2i (sin δ 1i /2) 2 sin4 θ 1i sin2 θ 2i sin δ 2i sin2 θ 1i sin δ 1i , ( cos 2 2 θ 2i + sin 2 2 θ 2i cos δ 2i ) (sin δ 1i /2) 2 sin4 θ 1i + (sin δ 2i /2) 2 sin4 θ 2i ( sin 2 2 θ 1i + cos 2 2 θ 1i cos δ 1i )+sin2 θ 2i sin δ 2i cos2 θ 1i sin δ 1i , ( cos 2 2 θ 2i + sin 2 2 θ 2i cos δ 2i )sin2 θ 1i sin δ 1i + (sin δ 2i /2) 2 sin4 θ 2i cos2 θ 1i sin δ 1i sin2 θ 2i sin δ 2i cos δ 1i ] T .
S in =BI,
B=[ B 01 B 02 B 03 B 04 B 11 B 12 B 13 B 14 B 21 B 22 B 23 B 24 B 31 B 32 B 33 B 34 ].
S e =B A S in ,
ε S = S e S in =BΔA S in ,
Δ A a = ξ i [ A( θ i + ξ i )A( θ i ) ξ i ]+ ς i [ A(δ+ ς i )A( ς i ) ς i ] = ξ i A(θ) θ | θ i + ς i A(δ) δ | ς i ,
Δ A b = ξ 1i [ A( θ 1i + ξ 1i )A( θ 1i ) ξ 1i ]+ ξ 2i [ A( θ 2i + ξ 2i )A( θ 2i ) ξ 2i ] + ς 1i [ A( δ 1i + ς 1i )A( ς 1i ) ς 1i ]+ ς 2i [ A( δ 2i + ς 2i )A( ς 2i ) ς 2i ] = ξ 1i A( θ 1 ) θ 1 | θ 1i + ξ 2i A( θ 2 ) θ 2 | θ 2i + ς 1i A( δ 1 ) δ 1 | ς 1i + ς 2i A( δ 2 ) δ 2 | ς 2i ,
σ I i = I i + σ G 2 ,
σ S k = i=1 4 ( ( S k ) ( I i ) ) 2 σ I i 2 ,
[ σ S 0 2 σ S 1 2 σ S 2 2 σ S 3 2 ]=[ B 01 2 B 02 2 B 03 2 B 04 2 B 11 2 B 12 2 B 13 2 B 14 2 B 21 2 B 22 2 B 23 2 B 24 2 B 31 2 B 32 2 B 33 2 B 34 2 ][ σ I 1 2 σ I 2 2 σ I 3 2 σ I 4 2 ].
σ S k = i=1 4 B ki 2 σ I i 2 .
S=[ 1 cos2ψcos2χ sin2ψcos2χ sin2χ ],0ψ<π, π 4 χ π 4 ,
S= S U + S P ,
S= [ S 0 S 1 S 2 S 3 ] T ,
S (U) =(1P) S 0 [ 1 0 0 0 ] T ,
S (P) =P S 0 [ 1 S 1 / P S 0 S 2 / P S 0 S 3 / P S 0 ] T ,
P= S 1 2 + S 2 2 + S 3 2 / S 0 ,0P1,
Γ S = σ 2 BC C T B T ,
C ij ς ={ S 1 sin 2 2 θ i sinδ+ S 2 (sin4 θ i sinδ)/2 S 3 sin2 θ i cosδ,i=j 0,ij.
C ij ξ ={ S 1 sin4 θ i (cosδ1) S 2 cos4 θ i (cosδ1) S 3 cos2 θ i sinδ,i=j 0,ij.

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