Abstract

A polarization state generator (PSG) was built to generate light having a degree of linear polarization (DoLP) varying from 0.0005 to 0.4 with 0.0005 uncertainty. The PSG operates by tilting a plane parallel SF11 glass plate in a nearly unpolarized beam. The DoLP of collimated, unpolarized light passing through a plane parallel plate over a defined range of field angles can be calculated from theory, and the PSG was intended to act as a calibration standard based on this calculation. Several effects make the DoLP distribution as a function of field and tilt plate difficult to model to the desired 0.0005 uncertainty: source DoLP and intensity nonuniformity, lens surface diattenuation, and errors in optical alignment. Because of these effects, modeled DoLP was not used as a standard. Instead, DoLP was characterized with repeatability of 0.0005.

© 2011 Optical Society of America

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References

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    [CrossRef]
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2010

2008

2007

2005

D. Diner, R. A. Chipman, N. Beaudry, B. Cairns, L. D. Foo, S. A. Macenka, T. J. Cunningham, S. Seshadri, and C. Keller, “An integrated multiangle, multispectral, and polarimetric imaging concept for aerosol remote sensing from space,” Proc. SPIE 5659, 88–96 (2005).
[CrossRef]

1985

1969

Beaudry, N.

D. Diner, R. A. Chipman, N. Beaudry, B. Cairns, L. D. Foo, S. A. Macenka, T. J. Cunningham, S. Seshadri, and C. Keller, “An integrated multiangle, multispectral, and polarimetric imaging concept for aerosol remote sensing from space,” Proc. SPIE 5659, 88–96 (2005).
[CrossRef]

Beaudry, N. A.

Boulbry, B.

Bull, M.

Cairns, B.

D. J. Diner, A. Davis, B. Hancock, G. Gutt, R. A. Chipman, and B. Cairns, “Dual-photoelastic-modulator-based polarimetric imaging concept for aerosol remote sensing,” Appl. Opt. 46, 8428–8445 (2007).
[CrossRef] [PubMed]

D. Diner, R. A. Chipman, N. Beaudry, B. Cairns, L. D. Foo, S. A. Macenka, T. J. Cunningham, S. Seshadri, and C. Keller, “An integrated multiangle, multispectral, and polarimetric imaging concept for aerosol remote sensing from space,” Proc. SPIE 5659, 88–96 (2005).
[CrossRef]

Chhajed, S.

M. F. Schubert, S. Chhajed, J. K. Kim, E. F. Schubert, and J. Cho, “Polarization of light emission by 460 nm GaInN/GaN light-emitting diodes grown on (0001) oriented sapphire substrates,” Appl. Phys. Lett. 91, 051117 (2007).
[CrossRef]

Chipman, R.

Chipman, R. A.

Cho, J.

M. F. Schubert, S. Chhajed, J. K. Kim, E. F. Schubert, and J. Cho, “Polarization of light emission by 460 nm GaInN/GaN light-emitting diodes grown on (0001) oriented sapphire substrates,” Appl. Phys. Lett. 91, 051117 (2007).
[CrossRef]

Cunningham, T. J.

D. Diner, R. A. Chipman, N. Beaudry, B. Cairns, L. D. Foo, S. A. Macenka, T. J. Cunningham, S. Seshadri, and C. Keller, “An integrated multiangle, multispectral, and polarimetric imaging concept for aerosol remote sensing from space,” Proc. SPIE 5659, 88–96 (2005).
[CrossRef]

Davis, A.

Diner, D.

D. Diner, R. A. Chipman, N. Beaudry, B. Cairns, L. D. Foo, S. A. Macenka, T. J. Cunningham, S. Seshadri, and C. Keller, “An integrated multiangle, multispectral, and polarimetric imaging concept for aerosol remote sensing from space,” Proc. SPIE 5659, 88–96 (2005).
[CrossRef]

Diner, D. J.

Foo, L. D.

D. Diner, R. A. Chipman, N. Beaudry, B. Cairns, L. D. Foo, S. A. Macenka, T. J. Cunningham, S. Seshadri, and C. Keller, “An integrated multiangle, multispectral, and polarimetric imaging concept for aerosol remote sensing from space,” Proc. SPIE 5659, 88–96 (2005).
[CrossRef]

Geier, S.

Germer, T. A.

Goldstein, D. H.

D. H. Goldstein, Polarized Light, 3rd ed. (CRC, 2011).

Gutt, G.

Hancock, B.

Jovanovic, V.

Keller, C.

D. Diner, R. A. Chipman, N. Beaudry, B. Cairns, L. D. Foo, S. A. Macenka, T. J. Cunningham, S. Seshadri, and C. Keller, “An integrated multiangle, multispectral, and polarimetric imaging concept for aerosol remote sensing from space,” Proc. SPIE 5659, 88–96 (2005).
[CrossRef]

Kim, J. K.

M. F. Schubert, S. Chhajed, J. K. Kim, E. F. Schubert, and J. Cho, “Polarization of light emission by 460 nm GaInN/GaN light-emitting diodes grown on (0001) oriented sapphire substrates,” Appl. Phys. Lett. 91, 051117 (2007).
[CrossRef]

Macenka, S. A.

D. Diner, R. A. Chipman, N. Beaudry, B. Cairns, L. D. Foo, S. A. Macenka, T. J. Cunningham, S. Seshadri, and C. Keller, “An integrated multiangle, multispectral, and polarimetric imaging concept for aerosol remote sensing from space,” Proc. SPIE 5659, 88–96 (2005).
[CrossRef]

Mahler, A.

McClain, S. C.

McEldowney, S. C.

Norden, B.

Portigal, D. L.

Ramella-Roman, J. C.

Rheingans, B.

Rider, D. M.

Schubert, E. F.

M. F. Schubert, S. Chhajed, J. K. Kim, E. F. Schubert, and J. Cho, “Polarization of light emission by 460 nm GaInN/GaN light-emitting diodes grown on (0001) oriented sapphire substrates,” Appl. Phys. Lett. 91, 051117 (2007).
[CrossRef]

Schubert, M. F.

M. F. Schubert, S. Chhajed, J. K. Kim, E. F. Schubert, and J. Cho, “Polarization of light emission by 460 nm GaInN/GaN light-emitting diodes grown on (0001) oriented sapphire substrates,” Appl. Phys. Lett. 91, 051117 (2007).
[CrossRef]

Seshadri, S.

D. Diner, R. A. Chipman, N. Beaudry, B. Cairns, L. D. Foo, S. A. Macenka, T. J. Cunningham, S. Seshadri, and C. Keller, “An integrated multiangle, multispectral, and polarimetric imaging concept for aerosol remote sensing from space,” Proc. SPIE 5659, 88–96 (2005).
[CrossRef]

Seth, S.

Shemo, D. M.

Shurcliff, W. A.

W. A. Shurcliff, Polarized Light Production and Use (Harvard University, 1962).

Smith, P. K.

Zalewski, E. F.

E. F. Zalewski, “Radiometry and Photometry,” in Handbook of Optics, (McGraw-Hill, 1995), Vol.  2, Chap. 24.

Zhao, Y.

Appl. Opt.

Appl. Phys. Lett.

M. F. Schubert, S. Chhajed, J. K. Kim, E. F. Schubert, and J. Cho, “Polarization of light emission by 460 nm GaInN/GaN light-emitting diodes grown on (0001) oriented sapphire substrates,” Appl. Phys. Lett. 91, 051117 (2007).
[CrossRef]

Appl. Spectrosc.

J. Opt. Soc. Am. A

Opt. Express

Opt. Lett.

Proc. SPIE

D. Diner, R. A. Chipman, N. Beaudry, B. Cairns, L. D. Foo, S. A. Macenka, T. J. Cunningham, S. Seshadri, and C. Keller, “An integrated multiangle, multispectral, and polarimetric imaging concept for aerosol remote sensing from space,” Proc. SPIE 5659, 88–96 (2005).
[CrossRef]

Other

W. A. Shurcliff, Polarized Light Production and Use (Harvard University, 1962).

D. H. Goldstein, Polarized Light, 3rd ed. (CRC, 2011).

E. F. Zalewski, “Radiometry and Photometry,” in Handbook of Optics, (McGraw-Hill, 1995), Vol.  2, Chap. 24.

R. A. Chipman, “Polarimetry,” in Handbook of Optics (McGraw-Hill, 1995), Vol.  2, Chap. 22.

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Figures (13)

Fig. 2
Fig. 2

PSG layout is shown. The LED source (PSG entrance pupil) is imaged to the MSPI entrance pupil (coincident with the PSG exit pupil). The iris is imaged to the MSPI focal plane.

Fig. 3
Fig. 3

DoLP is shown as a function of tilt angle for an uncoated SF11 plane parallel plate.

Fig. 4
Fig. 4

Upper image shows intensity distribution of an LED encased in a plastic hemispherical lens. Lower image shows intensity distribution of the LED followed by an acrylic light pipe with sanded ends. The light pipe improves intensity uniformity relative to the LED and plastic lens.

Fig. 5
Fig. 5

DOLP magnitude and orientation are shown for the 660 nm LED assembly (top row), the LED assembly followed by the light pipe (middle row), and the LED assembly and light pipe followed by a spatial depolarizer (bottom row).

Fig. 6
Fig. 6

PSG illumination source configuration is shown. An LED with a hemispherical plastic lens is followed by an acrylic light pipe with sanded ends, which is followed by a liquid crystal spatial pseudodepolarizer. The PSG entrance pupil is colocated with the pseudodepolarizer.

Fig. 7
Fig. 7

PSG exit pupil intensity (left), DoLP (center), and DoLP weighted by intensity shown with a circle showing the extent of the MSPI entrance pupil (right).

Fig. 8
Fig. 8

Raytrace of the PSG showing one beam, which includes all rays from the PSG entrance pupil that image the point at the top of the object plane to a point in the MSPI focal plane. If the MSPI entrance pupil (MSPI EP) is misaligned in x or y with respect to the PSG exit pupil (PSG XP), light from a different area of the source plane will be collected. The MSPI EP is shown as an offset slightly in the z direction to differentiate the two apertures.

Fig. 9
Fig. 9

Modeled measurements of DoLP error due to MSPI entrance pupil misalignments in x or y with respect to the PSG exit pupil are shown.

Fig. 10
Fig. 10

If the MSPI entrance pupil (MSPI EP) is misaligned in z with respect to the PSG exit pupil (PSG XP), light from a circle of a different radius will be collected from the source plane.

Fig. 11
Fig. 11

Modeled measurements of DoLP error due to MSPI entrance pupil misalignments in z with respect to the PSG exit pupil are shown.

Fig. 12
Fig. 12

Power measurements (points) were fitted to a function of the form in Eq. (2) (curves).

Fig. 13
Fig. 13

DoLP measurements (points) for the 16 square aperture positions are plotted along with the DoLP calibration curve (mesh) for nine plate angles ( 0 ° , 5 ° , 10 ° , 20 ° , 30 ° , 40 ° , 50 ° , 60 ° , and 70 ° ) for the 865 nm AR coated plate configuration. Some points are not visible because they fall beneath the opaque mesh for the scale shown. Differences between the measured points and the calibration equation are more obvious for smaller plate angles where the range of DoLPs plotted is smaller.

Equations (4)

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DoLP = T s 2 ( 1 / ( 1 R s 2 ) ) T p 2 ( 1 / ( 1 R p 2 ) ) T s 2 ( 1 / ( 1 R s 2 ) ) + T p 2 ( 1 / ( 1 R p 2 ) ) ,
A + B Cos ( χ ) + C Sin ( χ ) + D Cos ( 2 χ ) + E Sin ( 2 χ ) .
DoLP = D 2 + E 2 A .
F ( x , y , θ ) = 0.000302352 0.000682571 x + 0.00125034 x 2 0.000134525 y 0.000125336 x y + 0.000302268 y 2 + 0.0000313441 θ 0.000063499 x θ 0.0000133228 x 2 θ + 4.76609 × 10 6 y θ + 7.41393 × 10 6 x y θ 0.0000541199 y 2 θ + 0.0000186855 θ 2 2.73419 × 10 6 x θ 2 + 1.26416 × 10 7 x 2 θ 2 4.14359 × 10 8 y θ 2 4.76877 × 10 8 x y θ 2 + 5.33246 × 10 7 y 2 θ 2 + 2.03331 × 10 6 θ 3 7.11037 × 10 8 θ 4 + 1.11535 × 10 9 θ 5 5.7677 × 10 12 θ 6 .

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