Abstract

An achromatic snapshot full-Stokes imaging polarimeter (ASSIP) that enables the acquisition of 2D-spatial full Stokes parameters from a single exposure is presented. It is based on the division-of-aperture polarimetry using an array of four-quadrant achromatic elliptical analyzers as polarization state analyzer (PSA). The optimization of PSA is addressed for achieving immunity of Gaussian and Poisson noises. An extended eigenvalue calibration method (ECM) is proposed to calibrate the system, which considers the imperfectness of retarder and polarizer samples and the intensity attenuation of polarizer sample. A compact prototype of ASSIP operating over the waveband of 450-650 nm and an optimized calibration setup are developed. The achromatic performance is evaluated at three bandwidths of 10, 25, and 200 nm, respectively. The results show that the prototype with an uncooled CMOS camera works well at each bandwidth. The instrument matrix determined at the narrower bandwidth is more applicable to the wider one. The uncertainties of the calibrated instrument matrices and reconstructed Stokes parameters are improved by using the extended EMC at each bandwidth. To speed up the acquisition of high-contrast images, wide bandwidth along with short exposure time is preferable. The snapshot capability was verified via capturing dynamic scenes.

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

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References

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2019 (3)

N. A. Rubin, G. D’Aversa, P. Chevalier, Z. Shi, W. T. Chen, and F. Capasso, “Matrix Fourier optics enables a compact full-Stokes polarization camera,” Science 365, eaax1839 (2019).

A. W. Kruse, A. S. Alenin, and J. S. Tyo, “Review of visualization methods for passive polarization imaging,” Opt. Eng. 58(08), 082414 (2019).
[Crossref]

T. Mu, F. Han, D. Bao, C. Zhang, and R. Liang, “Compact snapshot optically replicating and remapping imaging spectrometer (ORRIS) using a focal plane continuous variable filter,” Opt. Lett. 44(5), 1281–1284 (2019).
[Crossref] [PubMed]

2018 (4)

2017 (5)

2016 (7)

2015 (2)

T. Mu, C. Zhang, and R. Liang, “Demonstration of a snapshot full-Stokes division-of-aperture imaging polarimeter using Wollaston prism array,” J. Opt. 17(12), 125708 (2015).
[Crossref]

T. Mu, C. Zhang, Q. Li, and R. Liang, “Error analysis of single-snapshot full-Stokes division-of-aperture imaging polarimeters,” Opt. Express 23(8), 10822–10835 (2015).
[Crossref] [PubMed]

2014 (2)

2013 (1)

2012 (2)

W. Sparks, T. A. Germer, J. W. MacKenty, and F. Snik, “Compact and robust method for full Stokes spectropolarimetry,” Appl. Opt. 51(22), 5495–5511 (2012).
[Crossref] [PubMed]

N. Hagen, R. T. Kester, L. Gao, and T. S. Tkaczyk, “Snapshot advantage: a review of the light collection improvement for parallel high-dimensional measurement systems,” Opt. Eng. 51(11), 111702 (2012).
[Crossref] [PubMed]

2011 (3)

2010 (1)

2009 (3)

2008 (2)

2006 (2)

2005 (1)

J. L. Pezzaniti and D. B. Chenault, “A division of aperture MWIR imaging polarimeter,” Proc. SPIE 5888, 58880V (2005).
[Crossref]

2003 (1)

2000 (3)

1999 (1)

1998 (1)

Alenin, A. S.

Anna, G.

Bai, C.

Bai, Z.

Balakrishnan, K.

Bao, D.

T. Mu, F. Han, D. Bao, C. Zhang, and R. Liang, “Compact snapshot optically replicating and remapping imaging spectrometer (ORRIS) using a focal plane continuous variable filter,” Opt. Lett. 44(5), 1281–1284 (2019).
[Crossref] [PubMed]

T. Mu, D. Bao, C. Zhang, Z. Chen, and J. Song, “Optimal reference polarization states for the calibration of general Stokes polarimeters in the presence of noise,” Opt. Commun. 418, 120–128 (2018).
[Crossref]

Blair, S.

Boffety, M.

Brock, N.

Campos, J.

Capasso, F.

N. A. Rubin, G. D’Aversa, P. Chevalier, Z. Shi, W. T. Chen, and F. Capasso, “Matrix Fourier optics enables a compact full-Stokes polarization camera,” Science 365, eaax1839 (2019).

Chen, W. T.

N. A. Rubin, G. D’Aversa, P. Chevalier, Z. Shi, W. T. Chen, and F. Capasso, “Matrix Fourier optics enables a compact full-Stokes polarization camera,” Science 365, eaax1839 (2019).

Chen, X.

H. Gu, X. Chen, H. Jiang, C. Zhang, and S. Liu, “Optimal broadband Mueller matrix ellipsometer using multi-waveplates with flexibly oriented axes,” J. Opt. 18(2), 025702 (2016).
[Crossref]

Chen, Z.

T. Mu, D. Bao, C. Zhang, Z. Chen, and J. Song, “Optimal reference polarization states for the calibration of general Stokes polarimeters in the presence of noise,” Opt. Commun. 418, 120–128 (2018).
[Crossref]

T. Mu, S. Pacheco, Z. Chen, C. Zhang, and R. Liang, “Snapshot linear-Stokes imaging spectropolarimeter using division-of-focal-plane polarimetry and integral field spectroscopy,” Sci. Rep. 7(1), 42115 (2017).
[Crossref] [PubMed]

T. Mu, Z. Chen, C. Zhang, and R. Liang, “Optimal configurations of full-Stokes polarimeter with immunity to both Poisson and Gaussian noise,” J. Opt. 18(5), 055702 (2016).
[Crossref]

T. Mu, Z. Chen, C. Zhang, and R. Liang, “Optimal design and performance metric of broadband full-Stokes polarimeters with immunity to Poisson and Gaussian noise,” Opt. Express 24(26), 29691–29704 (2016).
[Crossref] [PubMed]

Chenault, D. B.

Chevalier, P.

N. A. Rubin, G. D’Aversa, P. Chevalier, Z. Shi, W. T. Chen, and F. Capasso, “Matrix Fourier optics enables a compact full-Stokes polarization camera,” Science 365, eaax1839 (2019).

Chipman, R. A.

C. F. LaCasse, T. Ririe, R. A. Chipman, and J. S. Tyo, “Spatio-temporal modulated polarimetry,” Proc. SPIE 8160, 81600K (2011).
[Crossref]

Collados, M.

Compain, E.

Cui, N.

D’Aversa, G.

N. A. Rubin, G. D’Aversa, P. Chevalier, Z. Shi, W. T. Chen, and F. Capasso, “Matrix Fourier optics enables a compact full-Stokes polarization camera,” Science 365, eaax1839 (2019).

Davis, T.

De Martino, A.

Dean, P.

J. Mudge, M. Virgena, and P. Dean, “Near-infrared simultaneous Stokes imaging polarimeter,” Proc. SPIE 7461, 74610L (2009).
[Crossref]

del Toro Iniesta, J. C.

Dereniak, E. L.

Descour, M. R.

Drevillon, B.

Drévillon, B.

Engheta, N.

Escuti, M. J.

Fienup, J. R.

Gao, L.

N. Hagen, R. T. Kester, L. Gao, and T. S. Tkaczyk, “Snapshot advantage: a review of the light collection improvement for parallel high-dimensional measurement systems,” Opt. Eng. 51(11), 111702 (2012).
[Crossref] [PubMed]

Garcia, M.

Garcia-Caurel, E.

Germer, T. A.

Goldstein, D. L.

Goudail, F.

F. Goudail and M. Boffety, “Fundamental limits of target detection performance in passive polarization imaging,” J. Opt. Soc. Am. A 34(4), 506–512 (2017).
[Crossref] [PubMed]

F. Goudail and M. Boffety, “Optimal configuration of static polarization imagers for target detection,” J. Opt. Soc. Am. A 33(1), 9–16 (2016).
[Crossref] [PubMed]

F. Goudail and M. Boffety, “Performance comparison of fully adaptive and static passive polarimetric imagers in the presence of intensity and polarization contrast,” J. Opt. Soc. Am. A 33(9), 1880–1886 (2016).
[Crossref] [PubMed]

F. Goudail, “Equalized estimation of Stokes parameters in the presence of Poisson noise for any number of polarization analysis states,” Opt. Lett. 41(24), 5772–5775 (2016).
[Crossref] [PubMed]

M. Boffety, H. Hu, and F. Goudail, “Contrast optimization in broadband passive polarimetric imaging,” Opt. Lett. 39(23), 6759–6762 (2014).
[Crossref] [PubMed]

H. Hu, E. Garcia-Caurel, G. Anna, and F. Goudail, “Maximum likelihood method for calibration of Mueller polarimeters in reflection configuration,” Appl. Opt. 52(25), 6350–6358 (2013).
[Crossref] [PubMed]

F. Goudail and J. S. Tyo, “When is polarimetric imaging preferable to intensity imaging for target detection?” J. Opt. Soc. Am. A 28(1), 46–53 (2011).
[Crossref] [PubMed]

F. Goudail, “Noise minimization and equalization for Stokes polarimeters in the presence of signal-dependent Poisson shot noise,” Opt. Lett. 34(5), 647–649 (2009).
[Crossref] [PubMed]

Gruev, V.

Gu, H.

H. Gu, X. Chen, H. Jiang, C. Zhang, and S. Liu, “Optimal broadband Mueller matrix ellipsometer using multi-waveplates with flexibly oriented axes,” J. Opt. 18(2), 025702 (2016).
[Crossref]

Guizar-Sicairos, M.

Hagen, N.

N. Hagen, R. T. Kester, L. Gao, and T. S. Tkaczyk, “Snapshot advantage: a review of the light collection improvement for parallel high-dimensional measurement systems,” Opt. Eng. 51(11), 111702 (2012).
[Crossref] [PubMed]

Han, F.

He, J.

Hoover, B. G.

Hsu, W. L.

Hu, H.

Ibn-Elhaj, M.

Iemmi, C.

Jiang, H.

H. Gu, X. Chen, H. Jiang, C. Zhang, and S. Liu, “Optimal broadband Mueller matrix ellipsometer using multi-waveplates with flexibly oriented axes,” J. Opt. 18(2), 025702 (2016).
[Crossref]

Ju, H.

Kemme, S. A.

Kester, R. T.

N. Hagen, R. T. Kester, L. Gao, and T. S. Tkaczyk, “Snapshot advantage: a review of the light collection improvement for parallel high-dimensional measurement systems,” Opt. Eng. 51(11), 111702 (2012).
[Crossref] [PubMed]

Kim, Y. K.

Kruse, A. W.

Kudenov, M. W.

LaCasse, C. F.

C. F. LaCasse, T. Ririe, R. A. Chipman, and J. S. Tyo, “Spatio-temporal modulated polarimetry,” Proc. SPIE 8160, 81600K (2011).
[Crossref]

Lara, D.

Laude, B.

Li, J.

Li, Q.

Liang, J.

Liang, R.

T. Mu, F. Han, D. Bao, C. Zhang, and R. Liang, “Compact snapshot optically replicating and remapping imaging spectrometer (ORRIS) using a focal plane continuous variable filter,” Opt. Lett. 44(5), 1281–1284 (2019).
[Crossref] [PubMed]

T. Mu, S. Pacheco, Z. Chen, C. Zhang, and R. Liang, “Snapshot linear-Stokes imaging spectropolarimeter using division-of-focal-plane polarimetry and integral field spectroscopy,” Sci. Rep. 7(1), 42115 (2017).
[Crossref] [PubMed]

T. Mu, Z. Chen, C. Zhang, and R. Liang, “Optimal configurations of full-Stokes polarimeter with immunity to both Poisson and Gaussian noise,” J. Opt. 18(5), 055702 (2016).
[Crossref]

T. Mu, Z. Chen, C. Zhang, and R. Liang, “Optimal design and performance metric of broadband full-Stokes polarimeters with immunity to Poisson and Gaussian noise,” Opt. Express 24(26), 29691–29704 (2016).
[Crossref] [PubMed]

T. Mu, C. Zhang, Q. Li, and R. Liang, “Error analysis of single-snapshot full-Stokes division-of-aperture imaging polarimeters,” Opt. Express 23(8), 10822–10835 (2015).
[Crossref] [PubMed]

T. Mu, C. Zhang, and R. Liang, “Demonstration of a snapshot full-Stokes division-of-aperture imaging polarimeter using Wollaston prism array,” J. Opt. 17(12), 125708 (2015).
[Crossref]

Liu, J.

Liu, Q.

Liu, S.

H. Gu, X. Chen, H. Jiang, C. Zhang, and S. Liu, “Optimal broadband Mueller matrix ellipsometer using multi-waveplates with flexibly oriented axes,” J. Opt. 18(2), 025702 (2016).
[Crossref]

Lizana, A.

MacKenty, J. W.

Mu, T.

T. Mu, F. Han, D. Bao, C. Zhang, and R. Liang, “Compact snapshot optically replicating and remapping imaging spectrometer (ORRIS) using a focal plane continuous variable filter,” Opt. Lett. 44(5), 1281–1284 (2019).
[Crossref] [PubMed]

T. Mu, D. Bao, C. Zhang, Z. Chen, and J. Song, “Optimal reference polarization states for the calibration of general Stokes polarimeters in the presence of noise,” Opt. Commun. 418, 120–128 (2018).
[Crossref]

T. Mu, S. Pacheco, Z. Chen, C. Zhang, and R. Liang, “Snapshot linear-Stokes imaging spectropolarimeter using division-of-focal-plane polarimetry and integral field spectroscopy,” Sci. Rep. 7(1), 42115 (2017).
[Crossref] [PubMed]

T. Mu, Z. Chen, C. Zhang, and R. Liang, “Optimal configurations of full-Stokes polarimeter with immunity to both Poisson and Gaussian noise,” J. Opt. 18(5), 055702 (2016).
[Crossref]

T. Mu, Z. Chen, C. Zhang, and R. Liang, “Optimal design and performance metric of broadband full-Stokes polarimeters with immunity to Poisson and Gaussian noise,” Opt. Express 24(26), 29691–29704 (2016).
[Crossref] [PubMed]

T. Mu, C. Zhang, Q. Li, and R. Liang, “Error analysis of single-snapshot full-Stokes division-of-aperture imaging polarimeters,” Opt. Express 23(8), 10822–10835 (2015).
[Crossref] [PubMed]

T. Mu, C. Zhang, and R. Liang, “Demonstration of a snapshot full-Stokes division-of-aperture imaging polarimeter using Wollaston prism array,” J. Opt. 17(12), 125708 (2015).
[Crossref]

Mudge, J.

J. Mudge, M. Virgena, and P. Dean, “Near-infrared simultaneous Stokes imaging polarimeter,” Proc. SPIE 7461, 74610L (2009).
[Crossref]

Myhre, G.

Oka, K.

Pacheco, S.

T. Mu, S. Pacheco, Z. Chen, C. Zhang, and R. Liang, “Snapshot linear-Stokes imaging spectropolarimeter using division-of-focal-plane polarimetry and integral field spectroscopy,” Sci. Rep. 7(1), 42115 (2017).
[Crossref] [PubMed]

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.

Pugh, E. N.

Qu, E.

Ratliff, B. M.

Ren, L.

Ririe, T.

C. F. LaCasse, T. Ririe, R. A. Chipman, and J. S. Tyo, “Spatio-temporal modulated polarimetry,” Proc. SPIE 8160, 81600K (2011).
[Crossref]

Rubin, N. A.

N. A. Rubin, G. D’Aversa, P. Chevalier, Z. Shi, W. T. Chen, and F. Capasso, “Matrix Fourier optics enables a compact full-Stokes polarization camera,” Science 365, eaax1839 (2019).

Sabatke, D. S.

Shaw, J. A.

Shi, Z.

N. A. Rubin, G. D’Aversa, P. Chevalier, Z. Shi, W. T. Chen, and F. Capasso, “Matrix Fourier optics enables a compact full-Stokes polarization camera,” Science 365, eaax1839 (2019).

Snik, F.

Song, J.

T. Mu, D. Bao, C. Zhang, Z. Chen, and J. Song, “Optimal reference polarization states for the calibration of general Stokes polarimeters in the presence of noise,” Opt. Commun. 418, 120–128 (2018).
[Crossref]

Sparks, W.

Sweatt, W. C.

Tang, Y.

Thurman, S. T.

Tkaczyk, T. S.

N. Hagen, R. T. Kester, L. Gao, and T. S. Tkaczyk, “Snapshot advantage: a review of the light collection improvement for parallel high-dimensional measurement systems,” Opt. Eng. 51(11), 111702 (2012).
[Crossref] [PubMed]

Tyo, J. S.

A. W. Kruse, A. S. Alenin, and J. S. Tyo, “Review of visualization methods for passive polarization imaging,” Opt. Eng. 58(08), 082414 (2019).
[Crossref]

I. J. Vaughn, A. S. Alenin, and J. S. Tyo, “Channeled spatio-temporal Stokes polarimeters,” Opt. Lett. 43(12), 2768–2771 (2018).
[Crossref] [PubMed]

A. W. Kruse, A. S. Alenin, I. J. Vaughn, and J. S. Tyo, “Perceptually uniform color space for visualizing trivariate linear polarization imaging data,” Opt. Lett. 43(11), 2426–2429 (2018).
[Crossref] [PubMed]

A. S. Alenin, I. J. Vaughn, and J. S. Tyo, “Optimal bandwidth micropolarizer arrays,” Opt. Lett. 42(3), 458–461 (2017).
[Crossref] [PubMed]

J. S. Tyo, B. M. Ratliff, and A. S. Alenin, “Adapting the HSV polarization-color mapping for regions with low irradiance and high polarization,” Opt. Lett. 41(20), 4759–4762 (2016).
[Crossref] [PubMed]

F. Goudail and J. S. Tyo, “When is polarimetric imaging preferable to intensity imaging for target detection?” J. Opt. Soc. Am. A 28(1), 46–53 (2011).
[Crossref] [PubMed]

C. F. LaCasse, T. Ririe, R. A. Chipman, and J. S. Tyo, “Spatio-temporal modulated polarimetry,” Proc. SPIE 8160, 81600K (2011).
[Crossref]

J. S. Tyo, “Hybrid division of aperture/division of a focal-plane polarimeter for real-time polarization imagery without an instantaneous field-of-view error,” Opt. Lett. 31(20), 2984–2986 (2006).
[Crossref] [PubMed]

J. S. Tyo, D. L. Goldstein, D. B. Chenault, and J. A. Shaw, “Review of passive imaging polarimetry for remote sensing applications,” Appl. Opt. 45(22), 5453–5469 (2006).
[Crossref] [PubMed]

J. S. Tyo, “Noise equalization in Stokes parameter images obtained by use of variable-retardance polarimeters,” Opt. Lett. 25(16), 1198–1200 (2000).
[Crossref] [PubMed]

J. S. Tyo, E. N. Pugh, and N. Engheta, “Colorimetric representations for use with polarization-difference imaging of objects in scattering media,” J. Opt. Soc. Am. A 15(2), 367–374 (1998).
[Crossref]

Vaughn, I. J.

Vidal, J.

Virgena, M.

J. Mudge, M. Virgena, and P. Dean, “Near-infrared simultaneous Stokes imaging polarimeter,” Proc. SPIE 7461, 74610L (2009).
[Crossref]

Wu, Z.

Zhang, C.

T. Mu, F. Han, D. Bao, C. Zhang, and R. Liang, “Compact snapshot optically replicating and remapping imaging spectrometer (ORRIS) using a focal plane continuous variable filter,” Opt. Lett. 44(5), 1281–1284 (2019).
[Crossref] [PubMed]

T. Mu, D. Bao, C. Zhang, Z. Chen, and J. Song, “Optimal reference polarization states for the calibration of general Stokes polarimeters in the presence of noise,” Opt. Commun. 418, 120–128 (2018).
[Crossref]

T. Mu, S. Pacheco, Z. Chen, C. Zhang, and R. Liang, “Snapshot linear-Stokes imaging spectropolarimeter using division-of-focal-plane polarimetry and integral field spectroscopy,” Sci. Rep. 7(1), 42115 (2017).
[Crossref] [PubMed]

T. Mu, Z. Chen, C. Zhang, and R. Liang, “Optimal configurations of full-Stokes polarimeter with immunity to both Poisson and Gaussian noise,” J. Opt. 18(5), 055702 (2016).
[Crossref]

H. Gu, X. Chen, H. Jiang, C. Zhang, and S. Liu, “Optimal broadband Mueller matrix ellipsometer using multi-waveplates with flexibly oriented axes,” J. Opt. 18(2), 025702 (2016).
[Crossref]

T. Mu, Z. Chen, C. Zhang, and R. Liang, “Optimal design and performance metric of broadband full-Stokes polarimeters with immunity to Poisson and Gaussian noise,” Opt. Express 24(26), 29691–29704 (2016).
[Crossref] [PubMed]

T. Mu, C. Zhang, Q. Li, and R. Liang, “Error analysis of single-snapshot full-Stokes division-of-aperture imaging polarimeters,” Opt. Express 23(8), 10822–10835 (2015).
[Crossref] [PubMed]

T. Mu, C. Zhang, and R. Liang, “Demonstration of a snapshot full-Stokes division-of-aperture imaging polarimeter using Wollaston prism array,” J. Opt. 17(12), 125708 (2015).
[Crossref]

Zhang, W.

Appl. Opt. (7)

J. Opt. (3)

T. Mu, Z. Chen, C. Zhang, and R. Liang, “Optimal configurations of full-Stokes polarimeter with immunity to both Poisson and Gaussian noise,” J. Opt. 18(5), 055702 (2016).
[Crossref]

H. Gu, X. Chen, H. Jiang, C. Zhang, and S. Liu, “Optimal broadband Mueller matrix ellipsometer using multi-waveplates with flexibly oriented axes,” J. Opt. 18(2), 025702 (2016).
[Crossref]

T. Mu, C. Zhang, and R. Liang, “Demonstration of a snapshot full-Stokes division-of-aperture imaging polarimeter using Wollaston prism array,” J. Opt. 17(12), 125708 (2015).
[Crossref]

J. Opt. Soc. Am. A (5)

Opt. Commun. (1)

T. Mu, D. Bao, C. Zhang, Z. Chen, and J. Song, “Optimal reference polarization states for the calibration of general Stokes polarimeters in the presence of noise,” Opt. Commun. 418, 120–128 (2018).
[Crossref]

Opt. Eng. (2)

N. Hagen, R. T. Kester, L. Gao, and T. S. Tkaczyk, “Snapshot advantage: a review of the light collection improvement for parallel high-dimensional measurement systems,” Opt. Eng. 51(11), 111702 (2012).
[Crossref] [PubMed]

A. W. Kruse, A. S. Alenin, and J. S. Tyo, “Review of visualization methods for passive polarization imaging,” Opt. Eng. 58(08), 082414 (2019).
[Crossref]

Opt. Express (7)

Opt. Lett. (13)

F. Goudail, “Noise minimization and equalization for Stokes polarimeters in the presence of signal-dependent Poisson shot noise,” Opt. Lett. 34(5), 647–649 (2009).
[Crossref] [PubMed]

F. Goudail, “Equalized estimation of Stokes parameters in the presence of Poisson noise for any number of polarization analysis states,” Opt. Lett. 41(24), 5772–5775 (2016).
[Crossref] [PubMed]

J. S. Tyo, “Noise equalization in Stokes parameter images obtained by use of variable-retardance polarimeters,” Opt. Lett. 25(16), 1198–1200 (2000).
[Crossref] [PubMed]

D. S. Sabatke, M. R. Descour, E. L. Dereniak, W. C. Sweatt, S. A. Kemme, and G. S. Phipps, “Optimization of retardance for a complete Stokes polarimeter,” Opt. Lett. 25(11), 802–804 (2000).
[Crossref] [PubMed]

T. Mu, F. Han, D. Bao, C. Zhang, and R. Liang, “Compact snapshot optically replicating and remapping imaging spectrometer (ORRIS) using a focal plane continuous variable filter,” Opt. Lett. 44(5), 1281–1284 (2019).
[Crossref] [PubMed]

J. S. Tyo, “Hybrid division of aperture/division of a focal-plane polarimeter for real-time polarization imagery without an instantaneous field-of-view error,” Opt. Lett. 31(20), 2984–2986 (2006).
[Crossref] [PubMed]

A. S. Alenin, I. J. Vaughn, and J. S. Tyo, “Optimal bandwidth micropolarizer arrays,” Opt. Lett. 42(3), 458–461 (2017).
[Crossref] [PubMed]

I. J. Vaughn, A. S. Alenin, and J. S. Tyo, “Channeled spatio-temporal Stokes polarimeters,” Opt. Lett. 43(12), 2768–2771 (2018).
[Crossref] [PubMed]

J. S. Tyo, B. M. Ratliff, and A. S. Alenin, “Adapting the HSV polarization-color mapping for regions with low irradiance and high polarization,” Opt. Lett. 41(20), 4759–4762 (2016).
[Crossref] [PubMed]

A. W. Kruse, A. S. Alenin, I. J. Vaughn, and J. S. Tyo, “Perceptually uniform color space for visualizing trivariate linear polarization imaging data,” Opt. Lett. 43(11), 2426–2429 (2018).
[Crossref] [PubMed]

A. De Martino, Y. K. Kim, E. Garcia-Caurel, B. Laude, and B. Drévillon, “Optimized Mueller polarimeter with liquid crystals,” Opt. Lett. 28(8), 616–618 (2003).
[Crossref] [PubMed]

M. Guizar-Sicairos, S. T. Thurman, and J. R. Fienup, “Efficient subpixel image registration algorithms,” Opt. Lett. 33(2), 156–158 (2008).
[Crossref] [PubMed]

M. Boffety, H. Hu, and F. Goudail, “Contrast optimization in broadband passive polarimetric imaging,” Opt. Lett. 39(23), 6759–6762 (2014).
[Crossref] [PubMed]

Optica (1)

Proc. SPIE (3)

J. Mudge, M. Virgena, and P. Dean, “Near-infrared simultaneous Stokes imaging polarimeter,” Proc. SPIE 7461, 74610L (2009).
[Crossref]

J. L. Pezzaniti and D. B. Chenault, “A division of aperture MWIR imaging polarimeter,” Proc. SPIE 5888, 58880V (2005).
[Crossref]

C. F. LaCasse, T. Ririe, R. A. Chipman, and J. S. Tyo, “Spatio-temporal modulated polarimetry,” Proc. SPIE 8160, 81600K (2011).
[Crossref]

Sci. Rep. (1)

T. Mu, S. Pacheco, Z. Chen, C. Zhang, and R. Liang, “Snapshot linear-Stokes imaging spectropolarimeter using division-of-focal-plane polarimetry and integral field spectroscopy,” Sci. Rep. 7(1), 42115 (2017).
[Crossref] [PubMed]

Science (1)

N. A. Rubin, G. D’Aversa, P. Chevalier, Z. Shi, W. T. Chen, and F. Capasso, “Matrix Fourier optics enables a compact full-Stokes polarization camera,” Science 365, eaax1839 (2019).

Other (1)

H. Bay, T. Tuytelaars, and L. Van Gool, “SURF: speeded up robust features,” in Computer Vision-ECCV 2006 (Springer, 2006), pp. 404–417.

Supplementary Material (3)

NameDescription
» Visualization 1       The video contains the recovered Stokes parameter images of S0, S1, S2 and S3 (left and middle columns); and the polarization-HSV normal color fusion images (right column).
» Visualization 2       The video contains the recovered Stokes parameter images of S0, S1, S2 and S3 (left and middle columns); and the polarization-HSV normal color fusion images (right column).
» Visualization 3       The video contains the polarization-HSV adaptive color fusion images.

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Figures (17)

Fig. 1
Fig. 1 Optical layout of a snapshot full-Stokes imaging polarimeter based on division-of-aperture technique. Abbreviations: OL objective lens, FS field stop, CL collimating lens, RA retarder array, P polarizer, BF bandpass filter, LA lens array, FPA focal plane array.
Fig. 2
Fig. 2 The architecture of the four-quadrant RA. (a) Each sub-aperture consists of a single retarder; (b) each of two sub-apertures consists of a single retarder, and each of the other two sub-apertures consists of two retarders; (c) each sub-aperture consists of two retarders.
Fig. 3
Fig. 3 The tetrahedrons formed by the last three columns of the normalized A within a unit Poincaré sphere and the A is calculated from the optimal set in Table 1. Each trajectory on the sphere represents a retardance δi with the continuously rotated fast-axis azimuth. The vertexes of tetrahedrons correspond to the optimal retardances and optimal fast-axis azimuths.
Fig. 4
Fig. 4 The transmission-limited schematic layout involved in the ECM theory.
Fig. 5
Fig. 5 (a) A photograph of the ASSIP prototype which is assembled on a 60mm cage system. Abbreviations: OL objective lens, FS field stop, CL collimating lens, RA retarder array, P polarizer, LA lens array, AA aperture array. (b) The calibration setup for the ASSIP system.
Fig. 6
Fig. 6 The ray tracing of a compound re-imaging lens modeled using Zemax optics software. (a) The layout and (b) the spot diagrams at different FOVs and wavelengths.
Fig. 7
Fig. 7 The image registration results for a 1951 USAF negative resolution target. The original four sub-images (a), (b), (c), and (d) acquired by the four sub-apertures respectively. The absolute differences of the former three images (a), (b), and (c) from the fourth image (d) are (e), (f), and (g) before registration, and (i), (j), and (k) after registration, respectively. The central part on the fourth image (d) encompassed by yellow rectangle is magnified (h) for clarification. The histogram (l) of (k).
Fig. 8
Fig. 8 The histograms of the measured 16 sub-images with intensified illuminations at 25nm bandwidth for the 0 deg polarizer sample. Each PSG state corresponds to 4 sub-images. While the red solid line represents the Gauss fitting using the statistical mean μ and variance σ2, the blue solid line indicates the Poisson fitting with the mean μ.
Fig. 9
Fig. 9 The histogram of the L2-norm CN2 corresponds to the instrument matrices (A) at each bandwidth. The blue area, the mean μ1, and the STD σ1 for the model #1; the green area, μ2, and σ2 for the model #2; the red area, μ3, and σ3 for the model #3.
Fig. 10
Fig. 10 Upper row: the Stokes parameters of a polarizer’s azimuth angle rotated from 0° to 180° in 10° steps. Middle row: the absolute differences between the measured and theoretical values. Lower row: the STD of each Stokes parameter. Dot markers indicate ASSIP’s data correspond to the instrument matrix of model #1, and solid lines denote theoretical values. The error bar indicates the standard deviation across the FOV.
Fig. 11
Fig. 11 The results correspond to the instrument matrix of model #2.
Fig. 12
Fig. 12 The results correspond to the instrument matrix of model #3.
Fig. 13
Fig. 13 The measured data at the bandwidth of 10 nm with the exposure times of 50 and 150 ms, respectively. (a) and (c) The original sub-image for each sub-aperture, (b) and (d) the reconstructed image for each Stokes parameter. The curves in the third row correspond to the central cross sections of the images along the pink horizontal lines, respectively. The black, red, green, and blue lines correspond to the images of apertures A1-A4 respectively, and the images of S0 - S3 respectively.
Fig. 14
Fig. 14 The measured data at the bandwidth of 200 nm with the two exposure times of 50 and 150 ms, respectively.
Fig. 15
Fig. 15 The recovered images of S0, S1, S2, and S3 (left and middle columns) for a glass window sample with the outer five linear polarizers and the inner left- and right-hand circular polarizers; and the polarization-HSV normal color fusion images (right column) (see Visualization 1).
Fig. 16
Fig. 16 The recovered images of S0, S1, S2, and S3 (left and middle columns) for the automobiles on an urban road; and the polarization-HSV normal color fusion images (right column) (see Visualization 2).
Fig. 17
Fig. 17 The polarization-HSV adaptive color fusion images (see Visualization 3).

Tables (4)

Tables Icon

Table 1 Optimal sets of the fast-axis azimuths θi and retardances δi, determined with the CN2, and the corresponding values of CN2 and BCPN of the instrument matrix A.

Tables Icon

Table 2 The mean value and standard deviation of the calibrated instrument matrices at each bandwidth (10, 25, and 200 nm) corresponding to the models #1, #2, and #3 respectively.

Tables Icon

Table 3 The RMSE between the experimental mean value and theoretical output for all Stokes parameters across the FOV of the ASSIP and the azimuthal angles of the polarizer.

Tables Icon

Table 4 The RMSEs of the cross-validations at different bandwidthsa, and the diagonal elements correspond to the self-validations results in Table 3 at the same bandwidthb.

Equations (21)

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I=AS,
S ^ =BI,
VAR[ S k ] G = i=1 4 B k,i 2 σ 2 .
VAR[ S k ] P = S 0 ( Q k,0 +P q k s ),
k[1,3], Q k,0 =3 Q 0,0 =6/N,andk[0,3], q k =0,
A= 1 2 [ 1 1/ 3 1/ 3 1/ 3 1 1/ 3 +1/ 3 +1/ 3 1 +1/ 3 +1/ 3 1/ 3 1 +1/ 3 1/ 3 +1/ 3 ].
I 0 = η 0 AW,and I i = η i A M i W,
T i = I 0 1 I i =( η i / η 0 ) W 1 M i W.
M P = τ P [ 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 ],and M R = τ R [ 1 0 0 0 0 1 0 0 0 0 cosϕ sinϕ 0 0 sinϕ cosϕ ],
M G = τ G [ 1 a G 0 0 a G 1 0 0 0 0 b G c G 0 0 c G b G ],
τ G =0.5( λ r1 + λ r2 ),
a G =0.5( λ r1 λ r2 )/ τ G ,
b G =0.5( λ c1 + λ c2 )/ τ G ,
c G =imag{ 0.5( λ c1 λ c2 ) }/ τ G ,
I 0 = η 0 AW+n,and I i = η i A M i W+n,
T i = I 0 1 I i ( η i / η 0 ) W 1 M i W.
RMSE= 1 3XYM x=1 X y=1 Y m=1 M k=1 3 [ S k meas ( x,y,m ) S k theo ( m ) ] 2 ,
AoP(x,y)= 1 2 tan 1 [ S 2 (x,y) S 1 (x,y) ],
DoLP(x,y)= S 1 (x,y) 2 + S 2 (x,y) 2 S 0 (x,y) ,
DoCP(x,y)=| S 3 (x,y) S 0 (x,y) |.
max( DoLP ¯ , S 0 ¯ )Vand max( DoCP ¯ , S 0 ¯ )V,

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