Abstract

Imaging polarimeters are often designed and optimized by assuming that the polarization properties of the optics are nearly ideal. For example, we often assume that the linear polarizers have infinite extinction ratios. It is also usually assumed that the retarding elements have retardances that do not vary either spatially or with the angle of incidence. We consider the case where the polarization optics used to develop an imaging polarimeter are imperfect. Specifically, we examine the expected performance of a system as the extinction ratio of the diattenuators degrades, as the retardance varies spatially, and as the retardance varies with incidence angle. It is found that the penalty in the signal-to-noise ratio for using diattenuators with low extinction ratios is not severe, as an extinction ratio of 5 causes only a 2.0  dB increase in the noise in the reconstructed Stokes parameter images compared with an ideal diattenuator. Likewise, we find that a system can be optimized in the presence of spatially varying retardance, but that angular positioning error is far more important in rotating retarder imaging polarimeters.

© 2006 Optical Society of America

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  20. N. A. Beaudry, Y. Zhao, and R. Chipman, "Multi-angle generalized ellipsometry of anisotropic optical structures," in Polarizaiton Science and Remote Sensing II, J. A. Shaw and J. S. Tyo, eds., Proc. SPIE 5888, 61-71 (2005).
  21. G. P. Nordin, J. T. Meier, P. C. Deguzman, and M. Jones, "Diffractive optical element for Stokes vector measurement with a focal plane array," in Polarization Measurement, Analysis, and Remote Sensing II, D. H. Goldstein and D. B. Chenault, eds., Proc. SPIE 3754, 169-177 (1999).
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  29. J. S. Tyo, "Noise equalization in Stokes parameter images obtained by use of variable retardance polarimeters," Opt. Lett. 25, 1198-2000 (2000).
  30. M. H. Smith, J. B. Woodruff, and J. D. Howe, "Beam wander considerations in imaging polarimetry," in Polarization Measurement, Analysis, and Remote Sensing II, D. H. Goldstein and D. B. Chenault, eds., Proc. SPIE 3754, 50-54 (1999).
    [CrossRef]
  31. S. H. Sposato, M. P. Fetrow, K. P. Bishop, and T. R. Caudill, "Two long-wave infrared spectral polarimeters for use in remote sensing applications," Opt. Eng. 41, 1055-1064 (2002).
    [CrossRef]

2005 (3)

N. J. Pust and J. A. Shaw, "Dual-field imaging polarimeter for studying the effect of clouds on sky and target polarization," in Polarization Science and Remote Sensing II, J. A. Shaw and J. S. Tyo, eds., Proc. SPIE 5888, 295-303 (2005).

N. A. Beaudry, Y. Zhao, and R. Chipman, "Multi-angle generalized ellipsometry of anisotropic optical structures," in Polarizaiton Science and Remote Sensing II, J. A. Shaw and J. S. Tyo, eds., Proc. SPIE 5888, 61-71 (2005).

J. K. Boger, J. S. Tyo, B. M. Ratliff, M. P. Fetrow, W. Black, and R. Kumar, "Modeling precision and acuracy of a LWIR microgrid array imaging polarimeter," in Polarization Science and Remote Sensing II, J. A. Shaw and J. S. Tyo, eds., Proc. SPIE 5888, 227-238 (2005).

2003 (2)

P. Li and J. S. Tyo, "Experimental measurement of optimal polarimeter systems," in Polarization Science and Remote Sensing, J. A. Shaw and J. S. Tyo, eds., Proc. SPIE 5158, 103-112 (2003).
[CrossRef]

D. C. Dayton, B. G. Hoover, and J. D. Gonglewski, "Full-order Mueller matrix polarimeter using liquid-crystal variable retarders," in Optics in Atmospheric Propagation and Adaptive Systems V, A. Kohnle and J. D. Gonglewski, eds., Proc. SPIE 4884, 40-48 (2003).
[CrossRef]

2002 (5)

C. A. Farlow, D. B. Chenault, K. D. Spradley, M. G. Gulley, M. W. Jones, and C. M. Persons, "Automated registration of polarimetric imagery using fourier transform techniques," in Polarization Measurement, Analysis, and Remote Sensing IV, D. B. Chenault and D. H. Goldstein, eds., Proc. SPIE 4819, 107-117 (2002).
[CrossRef]

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

S. H. Sposato, M. P. Fetrow, K. P. Bishop, and T. R. Caudill, "Two long-wave infrared spectral polarimeters for use in remote sensing applications," Opt. Eng. 41, 1055-1064 (2002).
[CrossRef]

J. S. Tyo, "Design of optimal polarimers: maximization of signal-to-noise ratio and minimization of systematic error," Appl. Opt. 41, 619-630 (2002).

C. K. Harnett and H. G. Craighead, "Liquid-crystal micropolarizer for polarization-difference imaging," Appl. Opt. 41, 1291-1296 (2002).

2001 (1)

2000 (3)

1999 (2)

M. H. Smith, J. B. Woodruff, and J. D. Howe, "Beam wander considerations in imaging polarimetry," in Polarization Measurement, Analysis, and Remote Sensing II, D. H. Goldstein and D. B. Chenault, eds., Proc. SPIE 3754, 50-54 (1999).
[CrossRef]

G. P. Nordin, J. T. Meier, P. C. Deguzman, and M. Jones, "Diffractive optical element for Stokes vector measurement with a focal plane array," in Polarization Measurement, Analysis, and Remote Sensing II, D. H. Goldstein and D. B. Chenault, eds., Proc. SPIE 3754, 169-177 (1999).
[CrossRef]

1998 (1)

1996 (1)

1995 (2)

A. Ambirajan and D. C. Look, "Optimum angles for a polarimeter: part I," Opt. Eng. 34, 1651-1655 (1995).
[CrossRef]

A. Ambirajan and D. C. Look, "Optimum angles for a polarimeter: part II," Opt. Eng. 34, 1656-1659 (1995).
[CrossRef]

1994 (1)

1993 (1)

1991 (2)

L. B. Wolff and T. E. Boult, "Constraining object features using a polarization reflectance model," IEEE Trans. Pattern Anal. Mach. Intell. 13, 635-657 (1991).
[CrossRef]

W. G. Egan, W. R. Johnson, and V. S. Whitehead, "Terrestrial polarization imagery obtained from the space shuttle: characterization and interpretation," Appl. Opt. 30, 435-442 (1991).

1988 (1)

1987 (1)

L. B. Wolff, "Surface orientation from polarization images," in Optics, Illumination, and Image Sensing for Machine Vision II, D. J. Svetkoff, ed., Proc. SPIE 850, 110-121 (1987).

1981 (1)

R. Walraven, "Polarization imagery," Opt. Eng. 20, 14-18 (1981).

1977 (1)

Ambirajan, A.

A. Ambirajan and D. C. Look, "Optimum angles for a polarimeter: part I," Opt. Eng. 34, 1651-1655 (1995).
[CrossRef]

A. Ambirajan and D. C. Look, "Optimum angles for a polarimeter: part II," Opt. Eng. 34, 1656-1659 (1995).
[CrossRef]

Azzam, R. M. A.

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

Beaudry, N. A.

N. A. Beaudry, Y. Zhao, and R. Chipman, "Multi-angle generalized ellipsometry of anisotropic optical structures," in Polarizaiton Science and Remote Sensing II, J. A. Shaw and J. S. Tyo, eds., Proc. SPIE 5888, 61-71 (2005).

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, 973-980 (2002).
[CrossRef]

Bishop, K. P.

S. H. Sposato, M. P. Fetrow, K. P. Bishop, and T. R. Caudill, "Two long-wave infrared spectral polarimeters for use in remote sensing applications," Opt. Eng. 41, 1055-1064 (2002).
[CrossRef]

Black, W.

J. K. Boger, J. S. Tyo, B. M. Ratliff, M. P. Fetrow, W. Black, and R. Kumar, "Modeling precision and acuracy of a LWIR microgrid array imaging polarimeter," in Polarization Science and Remote Sensing II, J. A. Shaw and J. S. Tyo, eds., Proc. SPIE 5888, 227-238 (2005).

Boger, J. K.

J. K. Boger, J. S. Tyo, B. M. Ratliff, M. P. Fetrow, W. Black, and R. Kumar, "Modeling precision and acuracy of a LWIR microgrid array imaging polarimeter," in Polarization Science and Remote Sensing II, J. A. Shaw and J. S. Tyo, eds., Proc. SPIE 5888, 227-238 (2005).

Boult, T. E.

L. B. Wolff and T. E. Boult, "Constraining object features using a polarization reflectance model," IEEE Trans. Pattern Anal. Mach. Intell. 13, 635-657 (1991).
[CrossRef]

Caudill, T. R.

S. H. Sposato, M. P. Fetrow, K. P. Bishop, and T. R. Caudill, "Two long-wave infrared spectral polarimeters for use in remote sensing applications," Opt. Eng. 41, 1055-1064 (2002).
[CrossRef]

Chenault, D. B.

C. A. Farlow, D. B. Chenault, K. D. Spradley, M. G. Gulley, M. W. Jones, and C. M. Persons, "Automated registration of polarimetric imagery using fourier transform techniques," in Polarization Measurement, Analysis, and Remote Sensing IV, D. B. Chenault and D. H. Goldstein, eds., Proc. SPIE 4819, 107-117 (2002).
[CrossRef]

D. B. Chenault and R. A. Chipman, "Infrared birefringence spectra for cadmium sulfide and cadmium selenide," Appl. Opt. 32, 4223-4227 (1993).

Chipman, R.

N. A. Beaudry, Y. Zhao, and R. Chipman, "Multi-angle generalized ellipsometry of anisotropic optical structures," in Polarizaiton Science and Remote Sensing II, J. A. Shaw and J. S. Tyo, eds., Proc. SPIE 5888, 61-71 (2005).

Chipman, R. A.

Craighead, H. G.

Dayton, D. C.

D. C. Dayton, B. G. Hoover, and J. D. Gonglewski, "Full-order Mueller matrix polarimeter using liquid-crystal variable retarders," in Optics in Atmospheric Propagation and Adaptive Systems V, A. Kohnle and J. D. Gonglewski, eds., Proc. SPIE 4884, 40-48 (2003).
[CrossRef]

Deguzman, P. C.

G. P. Nordin, J. T. Meier, P. C. Deguzman, and M. Jones, "Diffractive optical element for Stokes vector measurement with a focal plane array," in Polarization Measurement, Analysis, and Remote Sensing II, D. H. Goldstein and D. B. Chenault, eds., Proc. SPIE 3754, 169-177 (1999).
[CrossRef]

Dereniak, E.

Descour, M. R.

Dlugunovich, V. A.

Egan, W. G.

Elminyawi, I. M.

El-Saba, A. M.

Farlow, C. A.

C. A. Farlow, D. B. Chenault, K. D. Spradley, M. G. Gulley, M. W. Jones, and C. M. Persons, "Automated registration of polarimetric imagery using fourier transform techniques," in Polarization Measurement, Analysis, and Remote Sensing IV, D. B. Chenault and D. H. Goldstein, eds., Proc. SPIE 4819, 107-117 (2002).
[CrossRef]

Fetrow, M. P.

J. K. Boger, J. S. Tyo, B. M. Ratliff, M. P. Fetrow, W. Black, and R. Kumar, "Modeling precision and acuracy of a LWIR microgrid array imaging polarimeter," in Polarization Science and Remote Sensing II, J. A. Shaw and J. S. Tyo, eds., Proc. SPIE 5888, 227-238 (2005).

S. H. Sposato, M. P. Fetrow, K. P. Bishop, and T. R. Caudill, "Two long-wave infrared spectral polarimeters for use in remote sensing applications," Opt. Eng. 41, 1055-1064 (2002).
[CrossRef]

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, 973-980 (2002).
[CrossRef]

Gonglewski, J. D.

D. C. Dayton, B. G. Hoover, and J. D. Gonglewski, "Full-order Mueller matrix polarimeter using liquid-crystal variable retarders," in Optics in Atmospheric Propagation and Adaptive Systems V, A. Kohnle and J. D. Gonglewski, eds., Proc. SPIE 4884, 40-48 (2003).
[CrossRef]

Gulley, M. G.

C. A. Farlow, D. B. Chenault, K. D. Spradley, M. G. Gulley, M. W. Jones, and C. M. Persons, "Automated registration of polarimetric imagery using fourier transform techniques," in Polarization Measurement, Analysis, and Remote Sensing IV, D. B. Chenault and D. H. Goldstein, eds., Proc. SPIE 4819, 107-117 (2002).
[CrossRef]

Harnett, C. K.

Hoover, B. G.

D. C. Dayton, B. G. Hoover, and J. D. Gonglewski, "Full-order Mueller matrix polarimeter using liquid-crystal variable retarders," in Optics in Atmospheric Propagation and Adaptive Systems V, A. Kohnle and J. D. Gonglewski, eds., Proc. SPIE 4884, 40-48 (2003).
[CrossRef]

Howe, J. D.

M. H. Smith, J. B. Woodruff, and J. D. Howe, "Beam wander considerations in imaging polarimetry," in Polarization Measurement, Analysis, and Remote Sensing II, D. H. Goldstein and D. B. Chenault, eds., Proc. SPIE 3754, 50-54 (1999).
[CrossRef]

Jakeman, E.

Johnson, W. R.

Jones, M.

G. P. Nordin, J. T. Meier, P. C. Deguzman, and M. Jones, "Diffractive optical element for Stokes vector measurement with a focal plane array," in Polarization Measurement, Analysis, and Remote Sensing II, D. H. Goldstein and D. B. Chenault, eds., Proc. SPIE 3754, 169-177 (1999).
[CrossRef]

Jones, M. W.

C. A. Farlow, D. B. Chenault, K. D. Spradley, M. G. Gulley, M. W. Jones, and C. M. Persons, "Automated registration of polarimetric imagery using fourier transform techniques," in Polarization Measurement, Analysis, and Remote Sensing IV, D. B. Chenault and D. H. Goldstein, eds., Proc. SPIE 4819, 107-117 (2002).
[CrossRef]

Jordan, D. L.

Kemme, S. A.

Kumar, R.

J. K. Boger, J. S. Tyo, B. M. Ratliff, M. P. Fetrow, W. Black, and R. Kumar, "Modeling precision and acuracy of a LWIR microgrid array imaging polarimeter," in Polarization Science and Remote Sensing II, J. A. Shaw and J. S. Tyo, eds., Proc. SPIE 5888, 227-238 (2005).

Lewis, G. D.

Li, P.

P. Li and J. S. Tyo, "Experimental measurement of optimal polarimeter systems," in Polarization Science and Remote Sensing, J. A. Shaw and J. S. Tyo, eds., Proc. SPIE 5158, 103-112 (2003).
[CrossRef]

Look, D. C.

A. Ambirajan and D. C. Look, "Optimum angles for a polarimeter: part II," Opt. Eng. 34, 1656-1659 (1995).
[CrossRef]

A. Ambirajan and D. C. Look, "Optimum angles for a polarimeter: part I," Opt. Eng. 34, 1651-1655 (1995).
[CrossRef]

Lu, S.-Y.

Meier, J. T.

G. P. Nordin, J. T. Meier, P. C. Deguzman, and M. Jones, "Diffractive optical element for Stokes vector measurement with a focal plane array," in Polarization Measurement, Analysis, and Remote Sensing II, D. H. Goldstein and D. B. Chenault, eds., Proc. SPIE 3754, 169-177 (1999).
[CrossRef]

Nordin, G. P.

G. P. Nordin, J. T. Meier, P. C. Deguzman, and M. Jones, "Diffractive optical element for Stokes vector measurement with a focal plane array," in Polarization Measurement, Analysis, and Remote Sensing II, D. H. Goldstein and D. B. Chenault, eds., Proc. SPIE 3754, 169-177 (1999).
[CrossRef]

Persons, C. M.

C. A. Farlow, D. B. Chenault, K. D. Spradley, M. G. Gulley, M. W. Jones, and C. M. Persons, "Automated registration of polarimetric imagery using fourier transform techniques," in Polarization Measurement, Analysis, and Remote Sensing IV, D. B. Chenault and D. H. Goldstein, eds., Proc. SPIE 4819, 107-117 (2002).
[CrossRef]

Phipps, G. S.

Pust, N. J.

N. J. Pust and J. A. Shaw, "Dual-field imaging polarimeter for studying the effect of clouds on sky and target polarization," in Polarization Science and Remote Sensing II, J. A. Shaw and J. S. Tyo, eds., Proc. SPIE 5888, 295-303 (2005).

Ratliff, B. M.

J. K. Boger, J. S. Tyo, B. M. Ratliff, M. P. Fetrow, W. Black, and R. Kumar, "Modeling precision and acuracy of a LWIR microgrid array imaging polarimeter," in Polarization Science and Remote Sensing II, J. A. Shaw and J. S. Tyo, eds., Proc. SPIE 5888, 227-238 (2005).

Sabatke, D. S.

Shaw, J. A.

N. J. Pust and J. A. Shaw, "Dual-field imaging polarimeter for studying the effect of clouds on sky and target polarization," in Polarization Science and Remote Sensing II, J. A. Shaw and J. S. Tyo, eds., Proc. SPIE 5888, 295-303 (2005).

Smith, M. H.

M. H. Smith, J. B. Woodruff, and J. D. Howe, "Beam wander considerations in imaging polarimetry," in Polarization Measurement, Analysis, and Remote Sensing II, D. H. Goldstein and D. B. Chenault, eds., Proc. SPIE 3754, 50-54 (1999).
[CrossRef]

Snopko, V. N.

Sposato, S. H.

S. H. Sposato, M. P. Fetrow, K. P. Bishop, and T. R. Caudill, "Two long-wave infrared spectral polarimeters for use in remote sensing applications," Opt. Eng. 41, 1055-1064 (2002).
[CrossRef]

Spradley, K. D.

C. A. Farlow, D. B. Chenault, K. D. Spradley, M. G. Gulley, M. W. Jones, and C. M. Persons, "Automated registration of polarimetric imagery using fourier transform techniques," in Polarization Measurement, Analysis, and Remote Sensing IV, D. B. Chenault and D. H. Goldstein, eds., Proc. SPIE 4819, 107-117 (2002).
[CrossRef]

Sweatt, W. C.

Tsaruk, A. V.

Turner, T. S.

Tyo, J. S.

J. K. Boger, J. S. Tyo, B. M. Ratliff, M. P. Fetrow, W. Black, and R. Kumar, "Modeling precision and acuracy of a LWIR microgrid array imaging polarimeter," in Polarization Science and Remote Sensing II, J. A. Shaw and J. S. Tyo, eds., Proc. SPIE 5888, 227-238 (2005).

P. Li and J. S. Tyo, "Experimental measurement of optimal polarimeter systems," in Polarization Science and Remote Sensing, J. A. Shaw and J. S. Tyo, eds., Proc. SPIE 5158, 103-112 (2003).
[CrossRef]

J. S. Tyo, "Design of optimal polarimers: maximization of signal-to-noise ratio and minimization of systematic error," Appl. Opt. 41, 619-630 (2002).

J. S. Tyo and T. S. Turner, "Variable retardance, Fourier transform imaging spectropolarimeters for visible spectrum remote sensing," Appl. Opt. 40, 1450-1458 (2001).

J. S. Tyo, "Noise equalization in Stokes parameter images obtained by use of variable retardance polarimeters," Opt. Lett. 25, 1198-2000 (2000).

Walraven, R.

R. Walraven, "Polarization imagery," Opt. Eng. 20, 14-18 (1981).

Whitehead, V. S.

Wolff, L. B.

L. B. Wolff, "Polarization camera for computer vision with a beam splitter," J. Opt. Soc. Am. A 11, 2935-2945 (1994).

L. B. Wolff and T. E. Boult, "Constraining object features using a polarization reflectance model," IEEE Trans. Pattern Anal. Mach. Intell. 13, 635-657 (1991).
[CrossRef]

L. B. Wolff, "Surface orientation from polarization images," in Optics, Illumination, and Image Sensing for Machine Vision II, D. J. Svetkoff, ed., Proc. SPIE 850, 110-121 (1987).

Woodruff, J. B.

M. H. Smith, J. B. Woodruff, and J. D. Howe, "Beam wander considerations in imaging polarimetry," in Polarization Measurement, Analysis, and Remote Sensing II, D. H. Goldstein and D. B. Chenault, eds., Proc. SPIE 3754, 50-54 (1999).
[CrossRef]

Zhao, Y.

N. A. Beaudry, Y. Zhao, and R. Chipman, "Multi-angle generalized ellipsometry of anisotropic optical structures," in Polarizaiton Science and Remote Sensing II, J. A. Shaw and J. S. Tyo, eds., Proc. SPIE 5888, 61-71 (2005).

Appl. Opt. (6)

IEEE Trans. Pattern Anal. Mach. Intell. (1)

L. B. Wolff and T. E. Boult, "Constraining object features using a polarization reflectance model," IEEE Trans. Pattern Anal. Mach. Intell. 13, 635-657 (1991).
[CrossRef]

J. Opt. Soc. Am. A (3)

J. Opt. Technol. (1)

Opt. Eng. (5)

R. Walraven, "Polarization imagery," Opt. Eng. 20, 14-18 (1981).

A. Ambirajan and D. C. Look, "Optimum angles for a polarimeter: part I," Opt. Eng. 34, 1651-1655 (1995).
[CrossRef]

A. Ambirajan and D. C. Look, "Optimum angles for a polarimeter: part II," Opt. Eng. 34, 1656-1659 (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, 973-980 (2002).
[CrossRef]

S. H. Sposato, M. P. Fetrow, K. P. Bishop, and T. R. Caudill, "Two long-wave infrared spectral polarimeters for use in remote sensing applications," Opt. Eng. 41, 1055-1064 (2002).
[CrossRef]

Opt. Lett. (3)

Proc. (1)

L. B. Wolff, "Surface orientation from polarization images," in Optics, Illumination, and Image Sensing for Machine Vision II, D. J. Svetkoff, ed., Proc. SPIE 850, 110-121 (1987).

Proc. SPIE (8)

P. Li and J. S. Tyo, "Experimental measurement of optimal polarimeter systems," in Polarization Science and Remote Sensing, J. A. Shaw and J. S. Tyo, eds., Proc. SPIE 5158, 103-112 (2003).
[CrossRef]

D. C. Dayton, B. G. Hoover, and J. D. Gonglewski, "Full-order Mueller matrix polarimeter using liquid-crystal variable retarders," in Optics in Atmospheric Propagation and Adaptive Systems V, A. Kohnle and J. D. Gonglewski, eds., Proc. SPIE 4884, 40-48 (2003).
[CrossRef]

M. H. Smith, J. B. Woodruff, and J. D. Howe, "Beam wander considerations in imaging polarimetry," in Polarization Measurement, Analysis, and Remote Sensing II, D. H. Goldstein and D. B. Chenault, eds., Proc. SPIE 3754, 50-54 (1999).
[CrossRef]

N. J. Pust and J. A. Shaw, "Dual-field imaging polarimeter for studying the effect of clouds on sky and target polarization," in Polarization Science and Remote Sensing II, J. A. Shaw and J. S. Tyo, eds., Proc. SPIE 5888, 295-303 (2005).

N. A. Beaudry, Y. Zhao, and R. Chipman, "Multi-angle generalized ellipsometry of anisotropic optical structures," in Polarizaiton Science and Remote Sensing II, J. A. Shaw and J. S. Tyo, eds., Proc. SPIE 5888, 61-71 (2005).

G. P. Nordin, J. T. Meier, P. C. Deguzman, and M. Jones, "Diffractive optical element for Stokes vector measurement with a focal plane array," in Polarization Measurement, Analysis, and Remote Sensing II, D. H. Goldstein and D. B. Chenault, eds., Proc. SPIE 3754, 169-177 (1999).
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J. K. Boger, J. S. Tyo, B. M. Ratliff, M. P. Fetrow, W. Black, and R. Kumar, "Modeling precision and acuracy of a LWIR microgrid array imaging polarimeter," in Polarization Science and Remote Sensing II, J. A. Shaw and J. S. Tyo, eds., Proc. SPIE 5888, 227-238 (2005).

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Other (3)

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

Meadowlark Optics, Boulder, Colo., Liquid Crystal Variable Retarder, http://www.meadowlark.com/.

R. A. Chipman, "Polarimetry," in Handbook of Optics, M.Bass, ed. (McGraw-Hill, 1995), Vol. 2, Chap. 2.

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Figures (4)

Fig. 1
Fig. 1

(Color online) Condition number of the DRM as a function of the extinction ratio of the linear polarization analyzer used in an optimized rotating retarder polarimeter.

Fig. 2
Fig. 2

(Color online) The retarder element is typically located at either (a) an aperture plane or (b) an intermediate field plane in the optical system.

Fig. 3
Fig. 3

(Color online) Mean squared error from Eq. (17) normalized to the length of the input Stokes vector for a rotating retarder polarimeter. The retarder is assumed to be located at a field plane, but with spatially varying retardance with standard deviation σ d with respect to the nominal retardance value. The optimum value of δ 0 is determined to be 0.40 λ .

Fig. 4
Fig. 4

(Color online) Average error in Stokes vector reconstruction for a system with both angular position error and retardance variation as a function of δ 0 . The angular positioning error σ a is assumed to be fixed with a standard deviation of 0.5°, and the angular position error is varied as shown in the figure.

Equations (20)

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S = [ s 0 s 1 s 2 s 3 ] = [ I I 0 I 90 I 45 I 135 I L I R ] ,
X = [ ( S D 1 ) T ( S D 2 ) T ( S D N ) T ] S in = A S in ,
X = A S in + n ,
ϵ = A 1 n .
B = A 1 = [ b 0 T b 1 T b 2 T b 3 T ] ,
n i 2 = b i 2 2 σ 2 ,
S D = [ 1 D T ] T ,
S D = [ 1 q - r q + r cos 2 θ q - r q + r sin 2 θ 0 ] T .
R = q r .
D 2 1 ,
b i 0 2 b 0 2 = 3 .
x i = ( S D i ( x ˜ , y ˜ ) ) T S in ,
Δ = A A d A d | δ = δ 0 ,
( S D i ) T = [ 1 ( cos 4 ϕ i sin 2 δ 0 2 + cos 2 δ 0 2 ) sin 4 ϕ i sin 2 δ 0 2 1 2 sin 2 ϕ i sin δ 0 ] .
Δ i = d S D i δ | δ 0 [ 0 1 2 sin δ 0 ( cos 4 ϕ i 1 ) 1 2 sin δ 0 sin 4 ϕ i 1 2 sin 2 ϕ i cos δ 0 ] .
E [ ϵ 2 2 ] = E [ S ^ - S in 2 2 ] = E [ S in 2 2 ] ,
E [ ϵ 2 2 ] = σ d 2 3 i = 0 3 j = 0 3 B ij 2 k = 0 3 Δ jk 2 .
B F 2 = i = 0 3 j = 0 3 ( B i j ) 2 ,
X = A [ S 1 S 2 ,   , S M ] = A Σ ,
A ^ = Σ 1 X ,

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