Abstract

An imaging Stokes-vector polarimeter using liquid crystal variable retarders (LCVRs) has been built and calibrated. Operating in five bands from 450 to 700  nm, the polarimeter can be changed quickly between narrow (12°) and wide (160°) fields of view. The instrument is designed for studying the effects of differing sky polarization upon the measured polarization of ground-based objects. LCVRs exhibit variations in retardance with ray incidence angle and ray position in the aperture. Therefore LCVR-based Stokes polarimeters exhibit unique calibration challenges not found in other systems. Careful design and calibration of the instrument has achieved errors within ±1.5%. Clear-sky measurements agree well with previously published data and cloudy data provide opportunities to explore spatial and spectral variations in sky polarization.

© 2006 Optical Society of America

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References

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    [PubMed]

2005

2002

2001

I. Pomozi, G. Horvath, and R. Wehner, "How the clear-sky angle of polarization pattern continues underneath clouds: full-sky measurements and implications for animal orientation," J. Exp. Biol. 204, 2933-2942 (2001).
[PubMed]

2000

1997

Barta, A.

Chipman, R.

Coulson, K. L.

K. L. Coulson, Polarization and Intensity of Light in the Atmosphere (Deepak Publishing, 1988).

Dereniak, E. L.

Descour, M. R.

Duggin, M.

Gal, J.

Haiman, O.

Horvath, G.

G. Horvath, A. Barta, J. Gal, B. Suhai, and O. Haiman, "Ground-based full-sky imaging polarimetry of rapidly changing skies and its use for polarimetric cloud detection," Appl. Opt. 41, 543-559 (2002).
[CrossRef] [PubMed]

I. Pomozi, G. Horvath, and R. Wehner, "How the clear-sky angle of polarization pattern continues underneath clouds: full-sky measurements and implications for animal orientation," J. Exp. Biol. 204, 2933-2942 (2001).
[PubMed]

Liu, Y.

North, J.

Pomozi, I.

I. Pomozi, G. Horvath, and R. Wehner, "How the clear-sky angle of polarization pattern continues underneath clouds: full-sky measurements and implications for animal orientation," J. Exp. Biol. 204, 2933-2942 (2001).
[PubMed]

Sabatke, D. S.

Sato, H.

H. Sato, "Fisheye-lens having a short distance compensating function," U.S. Patent 5,434,713 (18 July 1995).

Sato, S.

S. Sato, "Internal focusing type telephoto lens," U.S. Patent 5,757,555 (26 May 1998).

Sugiura, H.

X. Xiao, D. Voelz, and H. Sugiura, "Field of view characteristics of a liquid crystal variable retarder," in Polarization Science and Remote Sensing, J.A.Shaw and J.S.Tyo, eds., Proc. SPIE 5158,142-150 (2003).

Suhai, B.

Suzuki, K.

K. Suzuki, "Lens capable of short distance photographing with vibration reduction function," U.S. Patent 5,751,485 (12 May 1998).

Tyo, J. S.

Voelz, D.

X. Xiao, D. Voelz, and H. Sugiura, "Field of view characteristics of a liquid crystal variable retarder," in Polarization Science and Remote Sensing, J.A.Shaw and J.S.Tyo, eds., Proc. SPIE 5158,142-150 (2003).

Voss, K.

Wehner, R.

I. Pomozi, G. Horvath, and R. Wehner, "How the clear-sky angle of polarization pattern continues underneath clouds: full-sky measurements and implications for animal orientation," J. Exp. Biol. 204, 2933-2942 (2001).
[PubMed]

Xiao, X.

X. Xiao, D. Voelz, and H. Sugiura, "Field of view characteristics of a liquid crystal variable retarder," in Polarization Science and Remote Sensing, J.A.Shaw and J.S.Tyo, eds., Proc. SPIE 5158,142-150 (2003).

Appl. Opt.

J. Exp. Biol.

I. Pomozi, G. Horvath, and R. Wehner, "How the clear-sky angle of polarization pattern continues underneath clouds: full-sky measurements and implications for animal orientation," J. Exp. Biol. 204, 2933-2942 (2001).
[PubMed]

Opt. Lett.

Other

X. Xiao, D. Voelz, and H. Sugiura, "Field of view characteristics of a liquid crystal variable retarder," in Polarization Science and Remote Sensing, J.A.Shaw and J.S.Tyo, eds., Proc. SPIE 5158,142-150 (2003).

K. Suzuki, "Lens capable of short distance photographing with vibration reduction function," U.S. Patent 5,751,485 (12 May 1998).

S. Sato, "Internal focusing type telephoto lens," U.S. Patent 5,757,555 (26 May 1998).

H. Sato, "Fisheye-lens having a short distance compensating function," U.S. Patent 5,434,713 (18 July 1995).

K. L. Coulson, Polarization and Intensity of Light in the Atmosphere (Deepak Publishing, 1988).

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Figures (9)

Fig. 1
Fig. 1

Imaging polarimeter system layout, shown with a telephoto front lens.

Fig. 2
Fig. 2

Example of (left) row–column cross talk in an image with extreme contrast and (right) corrected image.

Fig. 3
Fig. 3

Setup used in the fisheye lens calibration. The luminance standard and the polarizer rotate together in the direction of the arrow for each calibration piece.

Fig. 4
Fig. 4

A discontinuity occurs at the center of the image if all rays with polarization parallel to the horizon are measured as the same polarization angle as shown.

Fig. 5
Fig. 5

Maximum degree of polarization observed in clear sky data (Bozeman, Montana, 17 October 2005) compared with Coulson's data (Ref. 1, p. 285).

Fig. 6
Fig. 6

Reduction of polarization at longer wavelengths when clouds are seen in the sky (Bozeman, Montana, 18 October 2005).

Fig. 7
Fig. 7

Clear-sky polarization at 450   nm (18 October 2005, 2:13 p.m. MDT).

Fig. 8
Fig. 8

Partly cloudy sky polarization at 450   nm (18 October 2005, 3:08 p.m. MDT).

Fig. 9
Fig. 9

Partly cloudy sky polarization at 700   nm (18 October 2005, 3:08 p.m. MDT).

Tables (3)

Tables Icon

Table 1 Retarder Settings for Two-LCVR Polarimeter

Tables Icon

Table 2 Summary of Maximum Errors Without Front Lenses

Tables Icon

Table 3 Measurements of Degree of Polarization Over all f∕#s Using the f∕4.0 Calibration

Equations (8)

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

[ S 0 S 1 S 2 S 3 ] output = [ m 00 m 01 m 02 m 03 m 10 m 11 m 12 m 13 m 20 m 21 m 22 m 23 m 30 m 31 m 32 m 33 ] [ S 0 S 1 S 2 S 3 ] input .
[ S 01 S 02 S 03 S 04 ] = [ a 00 a 01 a 02 a 03 a 10 a 11 a 12 a 13 a 20 a 21 a 22 a 23 a 30 a 31 a 32 a 33 ] [ S 0 S 1 S 2 S 3 ] = A S .
[ S 0 S 1 S 2 S 3 ] = [ m 00 m 01 m 02 m 03 m 10 m 11 m 12 m 13 m 20 m 21 m 22 m 23 m 30 m 31 m 32 m 33 ] [ S 0 ray S 1 ray S 2 ray S 3 ray ] = M 1 S 1 .
[ S 0 total S 1 total S 2 total S 3 total ] = M 1 S 1 + M 2 S 2 + M 3 S 3 + + M N S N ,
[ S 0 total S 1 total S 2 total S 3 total ] = ( M 1 + M 2 + M 3 + + M N ) S ( 1 ) = M S input ,
Image 90 Image 0 Image + 45 Image 45 = 1 a 00 + 1 a 01 + 0 a 02 + 0 a 03 , = 1 a 00 1 a 01 + 0 a 02 + 0 a 03 , = 1 a 00 + 0 a 01 + 1 a 02 + 0 a 03 , = 1 a 00 + 0 a 01 1 a 02 + 0 a 03 .
S 1 ( 0 ) S 1 ( 90 ) S 1 ( + 45 ) S 1 ( 45 ) = 1 m 10 + 1 m 11 + 0 m 12 + 0 m 13 , = 1 m 10 1 m 11 + 0 m 12 + 0 m 13 , = 1 m 10 + 0 m 11 + 1 m 12 + 0 m 13 , = 1 m 10 + 0 m 11 1 m 12 + 0 m 13 .
1.0000 0.0006 0.0018 0.0081 0.0008 1.0083 0.0047 0.0320 0.0009 0.0019 1.0012 0.0089 0.0081 0.0320 0.0089 1.0047 .

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