Abstract

We present an analysis and test of an image sampling polarimeter based on the concept of Star Test Polarimetry first introduced by Ramkhalawon. The method makes use of a stress engineered optical element (SEO) placed in the pupil plane of an optical system to induce a polarization dependent point spread function (PSF) at the detector. We describe the calibration requirements of the polarimeter and introduce a new algorithm that can robustly extract the Stokes parameters in a single irradiance measurement. By acquiring statistics on the sampled Stokes parameters of a uniformly illuminated pinhole array, we show that a single frame can provide a root mean square angular error of approximately 10 milliradians on the Poincaré sphere.

© 2016 Optical Society of America

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References

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  1. G. Dolgos, J. V. Martins, L. A. Remer, A. L. Correia, M. Tabacniks, and A. R. Lima, “Characterization of aerosol scattering and spectral absorption by unique methods: a Polar/Imaging Nephelometer and spectral reflectance measurements of aerosol samples collected on filters,” Proc. SPIE 7588, 75880E1 (2010).
  2. G. Dolgos and J. V. Martins, “Polarized imaging nephelometer for in situ airborne measurements of aerosol light scattering,” Opt. Express 22(18), 21972–21990 (2014).
    [Crossref] [PubMed]
  3. P. Yang, H. Wei, G. W. Kattawar, Y. X. Hu, D. M. Winker, C. A. Hostetler, and B. A. Baum, “Sensitivity of the backscattering Mueller matrix to particle shape and thermodynamic phase,” Appl. Opt. 42(21), 4389–4395 (2003).
    [Crossref] [PubMed]
  4. S. Firdous and M. Ikram, “Mueller matrix modeling of atmospheric scattering medium through polarized laser beam,” in 2005 Aerospace Conference Proceedings (2005), pp. 1963–1971.
    [Crossref]
  5. R. M. A. Azzam, “Photopolarimetric measurement of the Mueller matrix by Fourier analysis of a single detected signal,” Opt. Lett. 2(6), 148–150 (1978).
    [Crossref] [PubMed]
  6. L. Finzi and D. D. Dunlap, “Polarized Light Microscopy,” in Encyclopedia of Life Sciences (John Wiley and Sons, Ltd., 2001).
  7. R. Oldenbourg, “A new view on polarization microscopy,” Nature 381(6585), 811–812 (1996).
    [Crossref] [PubMed]
  8. 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]
  9. J. Halaijan and H. Hallock, “Principles and techniques of polarimetric mapping,” in Proceedings of the Eighth International Symposium on Remote Sensing of Environment (1972), pp. 523–540.
  10. A. G. Andreau and Z. K. Kalayjian, “Polarization imaging: principles and integrated polarimeters,” IEEE Sens. J. 2(6), 566–576 (2002).
    [Crossref]
  11. R. D. Ramkhalawon, T. G. Brown, and M. A. Alonso, “Imaging the polarization of a light field,” Opt. Express 21(4), 4106–4115 (2013).
    [Crossref] [PubMed]
  12. R. D. Ramkhalawon, A. M. Beckley, and T. G. Brown, “Star test polarimetry using stress-engineered optical elements,” Proc. SPIE 8227, 82270Q (2012).
    [Crossref]
  13. T. G. Brown and A. M. Beckley, “Stress engineering and the applications of inhomogeneously polarized optical fields,” Frontiers Optoelectron. 6(1), 89–96 (2013).
    [Crossref]
  14. B. G. Zimmerman, R. D. Ramkhalawon, M. A. Alonso, and T. G. Brown, “Pinhole array implementation of star test polarimetry,” Proc. SPIE 8949, 894912 (2014).
    [Crossref]
  15. S. Sivankutty, E. R. Andresen, G. Bouwmans, T. G. Brown, M. A. Alonso, and H. Rigneault, “Single-shot polarimetry imaging of multicore fiber,” Opt. Lett. 41(9), 2105–2108 (2016).
    [Crossref] [PubMed]
  16. A. M. Beckley, “Polarimetry and beam apodization using stress-engineered optical elements” Dissertation. The Institute of Optics, University of Rochester, http://hdl.handle.net/1802/24870 (2012).
  17. A. M. Beckley, T. G. Brown, and M. A. Alonso, “Full Poincaré beams,” Opt. Express 18(10), 10777–10785 (2010).
    [Crossref] [PubMed]
  18. B. G. Zimmerman, Polarimetric scatterometry using unconventional polarization states,” Dissertation. The Institute of Optics, University of Rochester, http://hdl.handle.net/1802/30946 (2016).

2016 (1)

2014 (2)

G. Dolgos and J. V. Martins, “Polarized imaging nephelometer for in situ airborne measurements of aerosol light scattering,” Opt. Express 22(18), 21972–21990 (2014).
[Crossref] [PubMed]

B. G. Zimmerman, R. D. Ramkhalawon, M. A. Alonso, and T. G. Brown, “Pinhole array implementation of star test polarimetry,” Proc. SPIE 8949, 894912 (2014).
[Crossref]

2013 (2)

T. G. Brown and A. M. Beckley, “Stress engineering and the applications of inhomogeneously polarized optical fields,” Frontiers Optoelectron. 6(1), 89–96 (2013).
[Crossref]

R. D. Ramkhalawon, T. G. Brown, and M. A. Alonso, “Imaging the polarization of a light field,” Opt. Express 21(4), 4106–4115 (2013).
[Crossref] [PubMed]

2012 (1)

R. D. Ramkhalawon, A. M. Beckley, and T. G. Brown, “Star test polarimetry using stress-engineered optical elements,” Proc. SPIE 8227, 82270Q (2012).
[Crossref]

2010 (1)

2006 (1)

2003 (1)

2002 (1)

A. G. Andreau and Z. K. Kalayjian, “Polarization imaging: principles and integrated polarimeters,” IEEE Sens. J. 2(6), 566–576 (2002).
[Crossref]

1996 (1)

R. Oldenbourg, “A new view on polarization microscopy,” Nature 381(6585), 811–812 (1996).
[Crossref] [PubMed]

1978 (1)

Alonso, M. A.

Andreau, A. G.

A. G. Andreau and Z. K. Kalayjian, “Polarization imaging: principles and integrated polarimeters,” IEEE Sens. J. 2(6), 566–576 (2002).
[Crossref]

Andresen, E. R.

Azzam, R. M. A.

Baum, B. A.

Beckley, A. M.

T. G. Brown and A. M. Beckley, “Stress engineering and the applications of inhomogeneously polarized optical fields,” Frontiers Optoelectron. 6(1), 89–96 (2013).
[Crossref]

R. D. Ramkhalawon, A. M. Beckley, and T. G. Brown, “Star test polarimetry using stress-engineered optical elements,” Proc. SPIE 8227, 82270Q (2012).
[Crossref]

A. M. Beckley, T. G. Brown, and M. A. Alonso, “Full Poincaré beams,” Opt. Express 18(10), 10777–10785 (2010).
[Crossref] [PubMed]

Bouwmans, G.

Brown, T. G.

S. Sivankutty, E. R. Andresen, G. Bouwmans, T. G. Brown, M. A. Alonso, and H. Rigneault, “Single-shot polarimetry imaging of multicore fiber,” Opt. Lett. 41(9), 2105–2108 (2016).
[Crossref] [PubMed]

B. G. Zimmerman, R. D. Ramkhalawon, M. A. Alonso, and T. G. Brown, “Pinhole array implementation of star test polarimetry,” Proc. SPIE 8949, 894912 (2014).
[Crossref]

R. D. Ramkhalawon, T. G. Brown, and M. A. Alonso, “Imaging the polarization of a light field,” Opt. Express 21(4), 4106–4115 (2013).
[Crossref] [PubMed]

T. G. Brown and A. M. Beckley, “Stress engineering and the applications of inhomogeneously polarized optical fields,” Frontiers Optoelectron. 6(1), 89–96 (2013).
[Crossref]

R. D. Ramkhalawon, A. M. Beckley, and T. G. Brown, “Star test polarimetry using stress-engineered optical elements,” Proc. SPIE 8227, 82270Q (2012).
[Crossref]

A. M. Beckley, T. G. Brown, and M. A. Alonso, “Full Poincaré beams,” Opt. Express 18(10), 10777–10785 (2010).
[Crossref] [PubMed]

Chenault, D. B.

Dolgos, G.

Firdous, S.

S. Firdous and M. Ikram, “Mueller matrix modeling of atmospheric scattering medium through polarized laser beam,” in 2005 Aerospace Conference Proceedings (2005), pp. 1963–1971.
[Crossref]

Goldstein, D. L.

Halaijan, J.

J. Halaijan and H. Hallock, “Principles and techniques of polarimetric mapping,” in Proceedings of the Eighth International Symposium on Remote Sensing of Environment (1972), pp. 523–540.

Hallock, H.

J. Halaijan and H. Hallock, “Principles and techniques of polarimetric mapping,” in Proceedings of the Eighth International Symposium on Remote Sensing of Environment (1972), pp. 523–540.

Hostetler, C. A.

Hu, Y. X.

Ikram, M.

S. Firdous and M. Ikram, “Mueller matrix modeling of atmospheric scattering medium through polarized laser beam,” in 2005 Aerospace Conference Proceedings (2005), pp. 1963–1971.
[Crossref]

Kalayjian, Z. K.

A. G. Andreau and Z. K. Kalayjian, “Polarization imaging: principles and integrated polarimeters,” IEEE Sens. J. 2(6), 566–576 (2002).
[Crossref]

Kattawar, G. W.

Martins, J. V.

Oldenbourg, R.

R. Oldenbourg, “A new view on polarization microscopy,” Nature 381(6585), 811–812 (1996).
[Crossref] [PubMed]

Ramkhalawon, R. D.

B. G. Zimmerman, R. D. Ramkhalawon, M. A. Alonso, and T. G. Brown, “Pinhole array implementation of star test polarimetry,” Proc. SPIE 8949, 894912 (2014).
[Crossref]

R. D. Ramkhalawon, T. G. Brown, and M. A. Alonso, “Imaging the polarization of a light field,” Opt. Express 21(4), 4106–4115 (2013).
[Crossref] [PubMed]

R. D. Ramkhalawon, A. M. Beckley, and T. G. Brown, “Star test polarimetry using stress-engineered optical elements,” Proc. SPIE 8227, 82270Q (2012).
[Crossref]

Rigneault, H.

Shaw, J. A.

Sivankutty, S.

Tyo, J. S.

Wei, H.

Winker, D. M.

Yang, P.

Zimmerman, B. G.

B. G. Zimmerman, R. D. Ramkhalawon, M. A. Alonso, and T. G. Brown, “Pinhole array implementation of star test polarimetry,” Proc. SPIE 8949, 894912 (2014).
[Crossref]

Appl. Opt. (2)

Frontiers Optoelectron. (1)

T. G. Brown and A. M. Beckley, “Stress engineering and the applications of inhomogeneously polarized optical fields,” Frontiers Optoelectron. 6(1), 89–96 (2013).
[Crossref]

IEEE Sens. J. (1)

A. G. Andreau and Z. K. Kalayjian, “Polarization imaging: principles and integrated polarimeters,” IEEE Sens. J. 2(6), 566–576 (2002).
[Crossref]

Nature (1)

R. Oldenbourg, “A new view on polarization microscopy,” Nature 381(6585), 811–812 (1996).
[Crossref] [PubMed]

Opt. Express (3)

Opt. Lett. (2)

Proc. SPIE (2)

R. D. Ramkhalawon, A. M. Beckley, and T. G. Brown, “Star test polarimetry using stress-engineered optical elements,” Proc. SPIE 8227, 82270Q (2012).
[Crossref]

B. G. Zimmerman, R. D. Ramkhalawon, M. A. Alonso, and T. G. Brown, “Pinhole array implementation of star test polarimetry,” Proc. SPIE 8949, 894912 (2014).
[Crossref]

Other (6)

A. M. Beckley, “Polarimetry and beam apodization using stress-engineered optical elements” Dissertation. The Institute of Optics, University of Rochester, http://hdl.handle.net/1802/24870 (2012).

B. G. Zimmerman, Polarimetric scatterometry using unconventional polarization states,” Dissertation. The Institute of Optics, University of Rochester, http://hdl.handle.net/1802/30946 (2016).

J. Halaijan and H. Hallock, “Principles and techniques of polarimetric mapping,” in Proceedings of the Eighth International Symposium on Remote Sensing of Environment (1972), pp. 523–540.

G. Dolgos, J. V. Martins, L. A. Remer, A. L. Correia, M. Tabacniks, and A. R. Lima, “Characterization of aerosol scattering and spectral absorption by unique methods: a Polar/Imaging Nephelometer and spectral reflectance measurements of aerosol samples collected on filters,” Proc. SPIE 7588, 75880E1 (2010).

S. Firdous and M. Ikram, “Mueller matrix modeling of atmospheric scattering medium through polarized laser beam,” in 2005 Aerospace Conference Proceedings (2005), pp. 1963–1971.
[Crossref]

L. Finzi and D. D. Dunlap, “Polarized Light Microscopy,” in Encyclopedia of Life Sciences (John Wiley and Sons, Ltd., 2001).

Supplementary Material (2)

NameDescription
» Visualization 1: AVI (2602 KB)      Polarization map of a stressed window illuminated with left hand circular light.
» Visualization 2: AVI (2497 KB)      Mapping of a uniform linear polarizer under rotation.

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Figures (6)

Fig. 1
Fig. 1

Relay system in which an image is sampled by a pinhole array and relayed through an optical system to a CCD. The combination of the SEO element in the pupil and the analyzer produce a polarization dependent point spread function. Typical dimensions: doublet focal length(s) of 100mm, lens diameters of 10mm, aperture stop of 2mm.

Fig. 2
Fig. 2

Top Row: Example experimental point spread functions for horizontal (H), vertical (V), + 45 (P), −45 (M), right hand circular (R) and left hand circular (L) polarization states. Bottom Row: PSF for unpolarized light. The calibration procedure enforces a consistency condition requiring that the sum of the PSFs of any two orthogonal polarizations equal the unpolarized PSF.

Fig. 3
Fig. 3

Example of polarization mapping for uniformly illuminated right-hand circular polarized input beam, with distribution of polarization states shown on the Poincaré sphere, and histogram representation of DoP.

Fig. 4
Fig. 4

Left (Visualization 1): Polarization map of a stressed window. Right (Visualization 2): Polarization map of a uniform linear polarizer under rotation. In each case, the sphere on the left side illustrates the distribution of states on the Poincaré sphere. The upper right inset shows a real time histogram of the degree of polarization.

Fig. 5
Fig. 5

Measurements of the composite polarization error for a white light LED source. Left: Normalized histogram (pdf) of the angular error of the Stokes vectors Right: Normalized histogram (pdf) of the DoP.

Fig. 6
Fig. 6

Left: RMS angular error as a function of signal to noise ratio. Right: RMS angular error as a function of the normalized power in the PSF. The curves are least squares fits to a quadratic function of the normalized fluctuation in S0.

Equations (8)

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I U (x)= 1 2 [ I up (x) S 0 +( I h (x) I v (x)) S 1 +( I p (x) I m (x)) S 2 +( I r (x) I l (x)) S 3 ],
I up (x)= κ 1 I h (x)+ κ 2 I v (x)= κ 3 I p (x)+ κ 4 I m (x)= κ 5 I r (x)+ κ 6 I l (x).
Erro r rms = ( I U (( κ 1 I h + κ 2 I v )+( κ 3 I p + κ 4 I m )+( κ 5 I r + κ 6 I l ))/3 ) 2 .
I U (x)= 1 2 [ I up (x) S 0 +( κ 1 I h (x) κ 2 I v (x)) S 1 +( κ 3 I p (x) κ 4 I m (x)) S 2 +( κ 5 I r (x) κ 6 I l (x)) S 3 ].
P ¯ ¯ S= I U ,
P ¯ ¯ =[ P 0 P 1 P 2 P 3 ],
DoP= S 1 2 + S 2 2 + S 3 2 S 0 :0DoP1.
Δ j = cos 1 ( S S j )

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