Abstract

Channeled spectropolarimetry is a snapshot method of measuring the spectral and polarization content of light. Wave-number domain amplitude modulation is employed to encode all four Stokes component spectra into a single optical power spectrum. We model the channeled spectropolarimeter as a linear operator, which facilitates treatment of nonideal effects and provides a convenient framework for simulations, calibration, and reconstruction. The operator’s singular value decomposition is treated with analytic and computational approaches. This analysis highlights the importance of the choice of object space in constraining and imparting prior knowledge to linear reconstructions of data from underdetermined systems.

© 2005 Optical Society of America

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  1. G. Herzberg, Atomic Spectra and Atomic Structure (Dover, 1945).
  2. D. K. Hore, A. L. Natansohn, P. L. Rochon, “Optical anisotropy as a probe of structural order by Stokes polarimetry,” J. Phys. Chem. B 106, 9004–9012 (2002).
    [CrossRef]
  3. R. M.A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, 1987).
  4. J. Trujillo-Bueno, F. Moreno-Insertis, and F. Sánchez, eds., Astrophysical Spectropolarimetry (Cambridge U. Press, 2002).
  5. P.-Y. Gerligand, M. H. Smith, R. A. Chipman, “Polarimetric images of a cone,” Opt. Express 4, 420–430 (1999).
    [CrossRef] [PubMed]
  6. F. Cremer, W. de Jong, K. Schutte, “Infrared polarization measurements and modeling applied to surface-laid antipersonnel landmines,” Opt. Eng. (Bellingham) 41, 1021–1032 (2002).
    [CrossRef]
  7. B. K. Ford, M. R. Descour, R. M. Lynch, “Large-image-format computed tomography imaging spectrometer for fluorescence microscopy,” Opt. Express 9, 444–453 (2001).
    [CrossRef] [PubMed]
  8. C. Bowd, L. M. Zangwill, E. Z. Blumenthal, C. Vasile, A. G. Boehm, P. A. Gokhale, K. Mohammadi, P. Amini, T. M. Sankary, R. N. Weinreb, “Imaging of the optic disc and retinal nerve fiber layer: the effects of age, optic disc area, refractive error, and gender,” J. Opt. Soc. Am. A 19, 197–207 (2002).
    [CrossRef]
  9. J. W. Dally, Experimental Stress Analysis, 3rd ed. (McGraw-Hill, 1991).
  10. B. Henderson, “Optical spectrometers,” in Handbook of Optics, 2nd ed., M. Bass, ed. (McGraw-Hill, 1995), Vol. 2, pp. 20.1–20.32.
  11. B. Henderson, “Spectroscopic measurements,” in Handbook of Optics, 2nd ed., M. Bass, ed. (McGraw-Hill, 1995), pp. 28.1–28.27.
  12. J. M. Bennett, “Polarizers,” in Handbook of Optics, 2nd ed., M. Bass, ed. (McGraw-Hill, 1995), pp. 3.1–3.70.
  13. R. A. Chipman, “Polarimetry,” in Handbook of Optics, 2nd ed., M. Bass, ed. (McGraw-Hill, 1995), pp. 22.1–22.37.
  14. R. M.A. Azzam, “Ellipsometry,” in Handbook of Optics, 2nd ed., M. Bass, ed. (McGraw-Hill, 1995), pp. 27.1–27.27.
  15. D. S. Sabatke, A. M. Locke, E. L. Dereniak, R. W. McMillan, “Linear calibration and reconstruction techniques for channeled spectropolarimetry,” Opt. Express 11, 2940–2952 (2003).
    [CrossRef] [PubMed]
  16. T. Kato, K. Oka, T. Tanaka, Y. Otsuka, “Measurement of the spectral distribution of polarization based on frequency domain interferometry,” in Proceedings of the Hokkaido Branch of the Japan Society of Applied Physics Vol. 34, p. 41 (1998) (in Japanese).
  17. F. J. Iannarilli, S. H. Jones, H. E. Scott, P. Kebabian, “Polarimetric-spectral intensity modulation (P-SIM): enabling simultaneous hyperspectral and polarimetric imaging,” in Infrared Technology and Applications XXV, B. F. Andresen and M. Strojnik, eds., Proc. SPIE3698, 474–481 (1999).
    [CrossRef]
  18. F. J. Iannarilli, J. A. Shaw, S. H. Jones, H. E. Scott, “Snapshot LWIR hyperspectral polarimetric imager for ocean surface sensing,” in Polarization Analysis, Measurement, and Remote Sensing III, D. B. Chenault, M. J. Duggin, W. G. Egan, and D. H. Goldstein, eds., Proc. SPIE4133, 270–283 (2000).
  19. K. Oka, T. Kato, “Spectroscopic polarimetry with a channeled spectrum,” Opt. Lett. 24, 1475–1477 (1999).
    [CrossRef]
  20. D. S. Sabatke, A. M. Locke, M. R. Descour, E. L. Dereniak, J. P. Garcia, T. K. Hamilton, R. W. McMillan, “Analysis of channeled spectropolarimetry using singular value decomposition,” in Polarization Analysis, Measurement, and Remote Sensing IV, D. H. Goldstein, D. B. Chenault, W. G. Egan, and M. J. Duggin, eds., Proc. SPIE4481, 73–80 (2001).
  21. D. Sabatke, A. Locke, E. L. Dereniak, M. Descour, J. Garcia, T. Hamilton, R. W. McMillan, “Snapshot imaging spectropolarimeter,” Opt. Eng. (Bellingham) 41, 1048–1054 (2002).
    [CrossRef]
  22. D. S. Sabatke, “Snapshot spectropolarimetry,” Ph.D. dissertation (University of Arizona, Tucson, 2002), available from UMI Dissertation Services, Ann Arbor, Michigan.
  23. H. H. Barrett, K. J. Meyers, Foundations of Image Science (Wiley, 2004).
  24. G. H. Golub, C. F. Van Loan, Matrix Computations, 3rd ed. (Johns Hopkins U. Press, 1996).
  25. J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, 1978).
  26. W. J. Tropf, M. E. Thomas, T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics, 2nd ed., M. Bass, ed. (McGraw-Hill, 1995), pp. 33.1–33.101.
  27. G. Strang, Linear Algebra and Its Applications, 3rd ed. (Saunders, 1988).
  28. J. S. Tyo, “Design of optimal polarimeters: maximization of signal-to-noise ratio and minimization of systematic error,” Appl. Opt. 41, 619–630 (2002).
    [CrossRef] [PubMed]

2003 (1)

2002 (5)

C. Bowd, L. M. Zangwill, E. Z. Blumenthal, C. Vasile, A. G. Boehm, P. A. Gokhale, K. Mohammadi, P. Amini, T. M. Sankary, R. N. Weinreb, “Imaging of the optic disc and retinal nerve fiber layer: the effects of age, optic disc area, refractive error, and gender,” J. Opt. Soc. Am. A 19, 197–207 (2002).
[CrossRef]

J. S. Tyo, “Design of optimal polarimeters: maximization of signal-to-noise ratio and minimization of systematic error,” Appl. Opt. 41, 619–630 (2002).
[CrossRef] [PubMed]

F. Cremer, W. de Jong, K. Schutte, “Infrared polarization measurements and modeling applied to surface-laid antipersonnel landmines,” Opt. Eng. (Bellingham) 41, 1021–1032 (2002).
[CrossRef]

D. K. Hore, A. L. Natansohn, P. L. Rochon, “Optical anisotropy as a probe of structural order by Stokes polarimetry,” J. Phys. Chem. B 106, 9004–9012 (2002).
[CrossRef]

D. Sabatke, A. Locke, E. L. Dereniak, M. Descour, J. Garcia, T. Hamilton, R. W. McMillan, “Snapshot imaging spectropolarimeter,” Opt. Eng. (Bellingham) 41, 1048–1054 (2002).
[CrossRef]

2001 (1)

1999 (2)

Amini, P.

Azzam, R. M.A.

R. M.A. Azzam, “Ellipsometry,” in Handbook of Optics, 2nd ed., M. Bass, ed. (McGraw-Hill, 1995), pp. 27.1–27.27.

R. M.A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, 1987).

Barrett, H. H.

H. H. Barrett, K. J. Meyers, Foundations of Image Science (Wiley, 2004).

Bashara, N. M.

R. M.A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, 1987).

Bennett, J. M.

J. M. Bennett, “Polarizers,” in Handbook of Optics, 2nd ed., M. Bass, ed. (McGraw-Hill, 1995), pp. 3.1–3.70.

Blumenthal, E. Z.

Boehm, A. G.

Bowd, C.

Chipman, R. A.

P.-Y. Gerligand, M. H. Smith, R. A. Chipman, “Polarimetric images of a cone,” Opt. Express 4, 420–430 (1999).
[CrossRef] [PubMed]

R. A. Chipman, “Polarimetry,” in Handbook of Optics, 2nd ed., M. Bass, ed. (McGraw-Hill, 1995), pp. 22.1–22.37.

Cremer, F.

F. Cremer, W. de Jong, K. Schutte, “Infrared polarization measurements and modeling applied to surface-laid antipersonnel landmines,” Opt. Eng. (Bellingham) 41, 1021–1032 (2002).
[CrossRef]

Dally, J. W.

J. W. Dally, Experimental Stress Analysis, 3rd ed. (McGraw-Hill, 1991).

de Jong, W.

F. Cremer, W. de Jong, K. Schutte, “Infrared polarization measurements and modeling applied to surface-laid antipersonnel landmines,” Opt. Eng. (Bellingham) 41, 1021–1032 (2002).
[CrossRef]

Dereniak, E. L.

D. S. Sabatke, A. M. Locke, E. L. Dereniak, R. W. McMillan, “Linear calibration and reconstruction techniques for channeled spectropolarimetry,” Opt. Express 11, 2940–2952 (2003).
[CrossRef] [PubMed]

D. Sabatke, A. Locke, E. L. Dereniak, M. Descour, J. Garcia, T. Hamilton, R. W. McMillan, “Snapshot imaging spectropolarimeter,” Opt. Eng. (Bellingham) 41, 1048–1054 (2002).
[CrossRef]

D. S. Sabatke, A. M. Locke, M. R. Descour, E. L. Dereniak, J. P. Garcia, T. K. Hamilton, R. W. McMillan, “Analysis of channeled spectropolarimetry using singular value decomposition,” in Polarization Analysis, Measurement, and Remote Sensing IV, D. H. Goldstein, D. B. Chenault, W. G. Egan, and M. J. Duggin, eds., Proc. SPIE4481, 73–80 (2001).

Descour, M.

D. Sabatke, A. Locke, E. L. Dereniak, M. Descour, J. Garcia, T. Hamilton, R. W. McMillan, “Snapshot imaging spectropolarimeter,” Opt. Eng. (Bellingham) 41, 1048–1054 (2002).
[CrossRef]

Descour, M. R.

B. K. Ford, M. R. Descour, R. M. Lynch, “Large-image-format computed tomography imaging spectrometer for fluorescence microscopy,” Opt. Express 9, 444–453 (2001).
[CrossRef] [PubMed]

D. S. Sabatke, A. M. Locke, M. R. Descour, E. L. Dereniak, J. P. Garcia, T. K. Hamilton, R. W. McMillan, “Analysis of channeled spectropolarimetry using singular value decomposition,” in Polarization Analysis, Measurement, and Remote Sensing IV, D. H. Goldstein, D. B. Chenault, W. G. Egan, and M. J. Duggin, eds., Proc. SPIE4481, 73–80 (2001).

Ford, B. K.

Garcia, J.

D. Sabatke, A. Locke, E. L. Dereniak, M. Descour, J. Garcia, T. Hamilton, R. W. McMillan, “Snapshot imaging spectropolarimeter,” Opt. Eng. (Bellingham) 41, 1048–1054 (2002).
[CrossRef]

Garcia, J. P.

D. S. Sabatke, A. M. Locke, M. R. Descour, E. L. Dereniak, J. P. Garcia, T. K. Hamilton, R. W. McMillan, “Analysis of channeled spectropolarimetry using singular value decomposition,” in Polarization Analysis, Measurement, and Remote Sensing IV, D. H. Goldstein, D. B. Chenault, W. G. Egan, and M. J. Duggin, eds., Proc. SPIE4481, 73–80 (2001).

Gaskill, J. D.

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, 1978).

Gerligand, P.-Y.

Gokhale, P. A.

Golub, G. H.

G. H. Golub, C. F. Van Loan, Matrix Computations, 3rd ed. (Johns Hopkins U. Press, 1996).

Hamilton, T.

D. Sabatke, A. Locke, E. L. Dereniak, M. Descour, J. Garcia, T. Hamilton, R. W. McMillan, “Snapshot imaging spectropolarimeter,” Opt. Eng. (Bellingham) 41, 1048–1054 (2002).
[CrossRef]

Hamilton, T. K.

D. S. Sabatke, A. M. Locke, M. R. Descour, E. L. Dereniak, J. P. Garcia, T. K. Hamilton, R. W. McMillan, “Analysis of channeled spectropolarimetry using singular value decomposition,” in Polarization Analysis, Measurement, and Remote Sensing IV, D. H. Goldstein, D. B. Chenault, W. G. Egan, and M. J. Duggin, eds., Proc. SPIE4481, 73–80 (2001).

Harris, T. J.

W. J. Tropf, M. E. Thomas, T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics, 2nd ed., M. Bass, ed. (McGraw-Hill, 1995), pp. 33.1–33.101.

Henderson, B.

B. Henderson, “Optical spectrometers,” in Handbook of Optics, 2nd ed., M. Bass, ed. (McGraw-Hill, 1995), Vol. 2, pp. 20.1–20.32.

B. Henderson, “Spectroscopic measurements,” in Handbook of Optics, 2nd ed., M. Bass, ed. (McGraw-Hill, 1995), pp. 28.1–28.27.

Herzberg, G.

G. Herzberg, Atomic Spectra and Atomic Structure (Dover, 1945).

Hore, D. K.

D. K. Hore, A. L. Natansohn, P. L. Rochon, “Optical anisotropy as a probe of structural order by Stokes polarimetry,” J. Phys. Chem. B 106, 9004–9012 (2002).
[CrossRef]

Iannarilli, F. J.

F. J. Iannarilli, S. H. Jones, H. E. Scott, P. Kebabian, “Polarimetric-spectral intensity modulation (P-SIM): enabling simultaneous hyperspectral and polarimetric imaging,” in Infrared Technology and Applications XXV, B. F. Andresen and M. Strojnik, eds., Proc. SPIE3698, 474–481 (1999).
[CrossRef]

F. J. Iannarilli, J. A. Shaw, S. H. Jones, H. E. Scott, “Snapshot LWIR hyperspectral polarimetric imager for ocean surface sensing,” in Polarization Analysis, Measurement, and Remote Sensing III, D. B. Chenault, M. J. Duggin, W. G. Egan, and D. H. Goldstein, eds., Proc. SPIE4133, 270–283 (2000).

Jones, S. H.

F. J. Iannarilli, J. A. Shaw, S. H. Jones, H. E. Scott, “Snapshot LWIR hyperspectral polarimetric imager for ocean surface sensing,” in Polarization Analysis, Measurement, and Remote Sensing III, D. B. Chenault, M. J. Duggin, W. G. Egan, and D. H. Goldstein, eds., Proc. SPIE4133, 270–283 (2000).

F. J. Iannarilli, S. H. Jones, H. E. Scott, P. Kebabian, “Polarimetric-spectral intensity modulation (P-SIM): enabling simultaneous hyperspectral and polarimetric imaging,” in Infrared Technology and Applications XXV, B. F. Andresen and M. Strojnik, eds., Proc. SPIE3698, 474–481 (1999).
[CrossRef]

Kato, T.

K. Oka, T. Kato, “Spectroscopic polarimetry with a channeled spectrum,” Opt. Lett. 24, 1475–1477 (1999).
[CrossRef]

T. Kato, K. Oka, T. Tanaka, Y. Otsuka, “Measurement of the spectral distribution of polarization based on frequency domain interferometry,” in Proceedings of the Hokkaido Branch of the Japan Society of Applied Physics Vol. 34, p. 41 (1998) (in Japanese).

Kebabian, P.

F. J. Iannarilli, S. H. Jones, H. E. Scott, P. Kebabian, “Polarimetric-spectral intensity modulation (P-SIM): enabling simultaneous hyperspectral and polarimetric imaging,” in Infrared Technology and Applications XXV, B. F. Andresen and M. Strojnik, eds., Proc. SPIE3698, 474–481 (1999).
[CrossRef]

Locke, A.

D. Sabatke, A. Locke, E. L. Dereniak, M. Descour, J. Garcia, T. Hamilton, R. W. McMillan, “Snapshot imaging spectropolarimeter,” Opt. Eng. (Bellingham) 41, 1048–1054 (2002).
[CrossRef]

Locke, A. M.

D. S. Sabatke, A. M. Locke, E. L. Dereniak, R. W. McMillan, “Linear calibration and reconstruction techniques for channeled spectropolarimetry,” Opt. Express 11, 2940–2952 (2003).
[CrossRef] [PubMed]

D. S. Sabatke, A. M. Locke, M. R. Descour, E. L. Dereniak, J. P. Garcia, T. K. Hamilton, R. W. McMillan, “Analysis of channeled spectropolarimetry using singular value decomposition,” in Polarization Analysis, Measurement, and Remote Sensing IV, D. H. Goldstein, D. B. Chenault, W. G. Egan, and M. J. Duggin, eds., Proc. SPIE4481, 73–80 (2001).

Lynch, R. M.

McMillan, R. W.

D. S. Sabatke, A. M. Locke, E. L. Dereniak, R. W. McMillan, “Linear calibration and reconstruction techniques for channeled spectropolarimetry,” Opt. Express 11, 2940–2952 (2003).
[CrossRef] [PubMed]

D. Sabatke, A. Locke, E. L. Dereniak, M. Descour, J. Garcia, T. Hamilton, R. W. McMillan, “Snapshot imaging spectropolarimeter,” Opt. Eng. (Bellingham) 41, 1048–1054 (2002).
[CrossRef]

D. S. Sabatke, A. M. Locke, M. R. Descour, E. L. Dereniak, J. P. Garcia, T. K. Hamilton, R. W. McMillan, “Analysis of channeled spectropolarimetry using singular value decomposition,” in Polarization Analysis, Measurement, and Remote Sensing IV, D. H. Goldstein, D. B. Chenault, W. G. Egan, and M. J. Duggin, eds., Proc. SPIE4481, 73–80 (2001).

Meyers, K. J.

H. H. Barrett, K. J. Meyers, Foundations of Image Science (Wiley, 2004).

Mohammadi, K.

Natansohn, A. L.

D. K. Hore, A. L. Natansohn, P. L. Rochon, “Optical anisotropy as a probe of structural order by Stokes polarimetry,” J. Phys. Chem. B 106, 9004–9012 (2002).
[CrossRef]

Oka, K.

K. Oka, T. Kato, “Spectroscopic polarimetry with a channeled spectrum,” Opt. Lett. 24, 1475–1477 (1999).
[CrossRef]

T. Kato, K. Oka, T. Tanaka, Y. Otsuka, “Measurement of the spectral distribution of polarization based on frequency domain interferometry,” in Proceedings of the Hokkaido Branch of the Japan Society of Applied Physics Vol. 34, p. 41 (1998) (in Japanese).

Otsuka, Y.

T. Kato, K. Oka, T. Tanaka, Y. Otsuka, “Measurement of the spectral distribution of polarization based on frequency domain interferometry,” in Proceedings of the Hokkaido Branch of the Japan Society of Applied Physics Vol. 34, p. 41 (1998) (in Japanese).

Rochon, P. L.

D. K. Hore, A. L. Natansohn, P. L. Rochon, “Optical anisotropy as a probe of structural order by Stokes polarimetry,” J. Phys. Chem. B 106, 9004–9012 (2002).
[CrossRef]

Sabatke, D.

D. Sabatke, A. Locke, E. L. Dereniak, M. Descour, J. Garcia, T. Hamilton, R. W. McMillan, “Snapshot imaging spectropolarimeter,” Opt. Eng. (Bellingham) 41, 1048–1054 (2002).
[CrossRef]

Sabatke, D. S.

D. S. Sabatke, A. M. Locke, E. L. Dereniak, R. W. McMillan, “Linear calibration and reconstruction techniques for channeled spectropolarimetry,” Opt. Express 11, 2940–2952 (2003).
[CrossRef] [PubMed]

D. S. Sabatke, A. M. Locke, M. R. Descour, E. L. Dereniak, J. P. Garcia, T. K. Hamilton, R. W. McMillan, “Analysis of channeled spectropolarimetry using singular value decomposition,” in Polarization Analysis, Measurement, and Remote Sensing IV, D. H. Goldstein, D. B. Chenault, W. G. Egan, and M. J. Duggin, eds., Proc. SPIE4481, 73–80 (2001).

D. S. Sabatke, “Snapshot spectropolarimetry,” Ph.D. dissertation (University of Arizona, Tucson, 2002), available from UMI Dissertation Services, Ann Arbor, Michigan.

Sankary, T. M.

Schutte, K.

F. Cremer, W. de Jong, K. Schutte, “Infrared polarization measurements and modeling applied to surface-laid antipersonnel landmines,” Opt. Eng. (Bellingham) 41, 1021–1032 (2002).
[CrossRef]

Scott, H. E.

F. J. Iannarilli, S. H. Jones, H. E. Scott, P. Kebabian, “Polarimetric-spectral intensity modulation (P-SIM): enabling simultaneous hyperspectral and polarimetric imaging,” in Infrared Technology and Applications XXV, B. F. Andresen and M. Strojnik, eds., Proc. SPIE3698, 474–481 (1999).
[CrossRef]

F. J. Iannarilli, J. A. Shaw, S. H. Jones, H. E. Scott, “Snapshot LWIR hyperspectral polarimetric imager for ocean surface sensing,” in Polarization Analysis, Measurement, and Remote Sensing III, D. B. Chenault, M. J. Duggin, W. G. Egan, and D. H. Goldstein, eds., Proc. SPIE4133, 270–283 (2000).

Shaw, J. A.

F. J. Iannarilli, J. A. Shaw, S. H. Jones, H. E. Scott, “Snapshot LWIR hyperspectral polarimetric imager for ocean surface sensing,” in Polarization Analysis, Measurement, and Remote Sensing III, D. B. Chenault, M. J. Duggin, W. G. Egan, and D. H. Goldstein, eds., Proc. SPIE4133, 270–283 (2000).

Smith, M. H.

Strang, G.

G. Strang, Linear Algebra and Its Applications, 3rd ed. (Saunders, 1988).

Tanaka, T.

T. Kato, K. Oka, T. Tanaka, Y. Otsuka, “Measurement of the spectral distribution of polarization based on frequency domain interferometry,” in Proceedings of the Hokkaido Branch of the Japan Society of Applied Physics Vol. 34, p. 41 (1998) (in Japanese).

Thomas, M. E.

W. J. Tropf, M. E. Thomas, T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics, 2nd ed., M. Bass, ed. (McGraw-Hill, 1995), pp. 33.1–33.101.

Tropf, W. J.

W. J. Tropf, M. E. Thomas, T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics, 2nd ed., M. Bass, ed. (McGraw-Hill, 1995), pp. 33.1–33.101.

Tyo, J. S.

Van Loan, C. F.

G. H. Golub, C. F. Van Loan, Matrix Computations, 3rd ed. (Johns Hopkins U. Press, 1996).

Vasile, C.

Weinreb, R. N.

Zangwill, L. M.

Appl. Opt. (1)

J. Opt. Soc. Am. A (1)

J. Phys. Chem. B (1)

D. K. Hore, A. L. Natansohn, P. L. Rochon, “Optical anisotropy as a probe of structural order by Stokes polarimetry,” J. Phys. Chem. B 106, 9004–9012 (2002).
[CrossRef]

Opt. Eng. (Bellingham) (2)

D. Sabatke, A. Locke, E. L. Dereniak, M. Descour, J. Garcia, T. Hamilton, R. W. McMillan, “Snapshot imaging spectropolarimeter,” Opt. Eng. (Bellingham) 41, 1048–1054 (2002).
[CrossRef]

F. Cremer, W. de Jong, K. Schutte, “Infrared polarization measurements and modeling applied to surface-laid antipersonnel landmines,” Opt. Eng. (Bellingham) 41, 1021–1032 (2002).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Other (19)

G. Herzberg, Atomic Spectra and Atomic Structure (Dover, 1945).

D. S. Sabatke, “Snapshot spectropolarimetry,” Ph.D. dissertation (University of Arizona, Tucson, 2002), available from UMI Dissertation Services, Ann Arbor, Michigan.

H. H. Barrett, K. J. Meyers, Foundations of Image Science (Wiley, 2004).

G. H. Golub, C. F. Van Loan, Matrix Computations, 3rd ed. (Johns Hopkins U. Press, 1996).

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, 1978).

W. J. Tropf, M. E. Thomas, T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics, 2nd ed., M. Bass, ed. (McGraw-Hill, 1995), pp. 33.1–33.101.

G. Strang, Linear Algebra and Its Applications, 3rd ed. (Saunders, 1988).

T. Kato, K. Oka, T. Tanaka, Y. Otsuka, “Measurement of the spectral distribution of polarization based on frequency domain interferometry,” in Proceedings of the Hokkaido Branch of the Japan Society of Applied Physics Vol. 34, p. 41 (1998) (in Japanese).

F. J. Iannarilli, S. H. Jones, H. E. Scott, P. Kebabian, “Polarimetric-spectral intensity modulation (P-SIM): enabling simultaneous hyperspectral and polarimetric imaging,” in Infrared Technology and Applications XXV, B. F. Andresen and M. Strojnik, eds., Proc. SPIE3698, 474–481 (1999).
[CrossRef]

F. J. Iannarilli, J. A. Shaw, S. H. Jones, H. E. Scott, “Snapshot LWIR hyperspectral polarimetric imager for ocean surface sensing,” in Polarization Analysis, Measurement, and Remote Sensing III, D. B. Chenault, M. J. Duggin, W. G. Egan, and D. H. Goldstein, eds., Proc. SPIE4133, 270–283 (2000).

R. M.A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, 1987).

J. Trujillo-Bueno, F. Moreno-Insertis, and F. Sánchez, eds., Astrophysical Spectropolarimetry (Cambridge U. Press, 2002).

J. W. Dally, Experimental Stress Analysis, 3rd ed. (McGraw-Hill, 1991).

B. Henderson, “Optical spectrometers,” in Handbook of Optics, 2nd ed., M. Bass, ed. (McGraw-Hill, 1995), Vol. 2, pp. 20.1–20.32.

B. Henderson, “Spectroscopic measurements,” in Handbook of Optics, 2nd ed., M. Bass, ed. (McGraw-Hill, 1995), pp. 28.1–28.27.

J. M. Bennett, “Polarizers,” in Handbook of Optics, 2nd ed., M. Bass, ed. (McGraw-Hill, 1995), pp. 3.1–3.70.

R. A. Chipman, “Polarimetry,” in Handbook of Optics, 2nd ed., M. Bass, ed. (McGraw-Hill, 1995), pp. 22.1–22.37.

R. M.A. Azzam, “Ellipsometry,” in Handbook of Optics, 2nd ed., M. Bass, ed. (McGraw-Hill, 1995), pp. 27.1–27.27.

D. S. Sabatke, A. M. Locke, M. R. Descour, E. L. Dereniak, J. P. Garcia, T. K. Hamilton, R. W. McMillan, “Analysis of channeled spectropolarimetry using singular value decomposition,” in Polarization Analysis, Measurement, and Remote Sensing IV, D. H. Goldstein, D. B. Chenault, W. G. Egan, and M. J. Duggin, eds., Proc. SPIE4481, 73–80 (2001).

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Fig. 1
Fig. 1

Channeled spectropolarimeter (after Oka and Kato[19]). The complicated spectrum recorded at the output of the polarization optics is formed by a superposition of the Stokes component spectra modulating carriers. With proper choice of carrier frequencies, the Stokes components can be isolated in the Fourier domain.

Fig. 2
Fig. 2

Arrangement of channels in a channeled spectropolarimeter is controlled by the choice of OPDs for the retarders. The illustrated h-domain spectrum corresponds to a 1 : 2 ratio in OPDs.

Fig. 3
Fig. 3

Channeled spectropolarimeter, described as the composition of two operators.

Fig. 4
Fig. 4

Sample object space singular vector u k ( σ ) . The vector consists of a portion of the carrier waves, windowed off by the corresponding band-sensitivity function (here assumed to be constant within its support).

Fig. 5
Fig. 5

Singular values obtained by numerical computation of the SVD.

Fig. 6
Fig. 6

Selection of the object space singular vectors u ̱ k ( σ ) obtained by numerical computation of the SVD.

Fig. 7
Fig. 7

Eliminating a basis vector from object space can reduce the dimensions of the null space, even though the eliminated vector does not belong to the null space.

Equations (23)

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g = H f .
( f ̱ 1 , f ̱ 2 ) = f ̱ 1 t ( σ ) f ̱ 2 ( σ ) d σ in L 2 4 .
( g , A f ) = ( A g , f ) for all f U and g V .
f 1 f 2 = ( f 1 , f 2 ) .
X = x ̱ t ( σ ) = 1 2 ( 1 cos δ 2 sin δ 1 sin δ 2 cos δ 1 sin δ 2 ) t .
[ D I ] k = ϕ k ( σ ) I ( σ ) d σ or D = d σ ϕ ̱ ( σ ) ,
H = k = 1 R α k v k u k .
H H v k = μ k v k .
u k = 1 μ k H v k = 1 α k H v k .
H + = k = 1 R 1 α k u k v k .
X = x ̱ ( σ ) = 1 2 ( 1 cos δ 2 sin δ 1 sin δ 2 cos δ 1 sin δ 2 ) for X : L 2 4 L 2 ,
D = ϕ ̱ ( σ ) t for D : L 2 R N .
H H = D X X D = d σ ϕ ̱ x ̱ t x ̱ ϕ ̱ t ,
x ( σ ) t x ( σ ) = 1 2 .
[ H H ] j k = 1 2 ϕ j ( σ ) ϕ k ( σ ) d σ .
α k = [ 1 2 ϕ k 2 ( σ ) d σ ] 1 2 .
u k = 1 α k H v k = 1 α k X D v k = 1 α k x ̱ ( σ ) ϕ k ( σ ) .
X = B γ x ̱ ( σ ) for X : B γ 4 B Γ ,
D = B Γ ϕ ̱ ( σ ) t for D : B Γ R N .
H H = D X X D = d σ ϕ ̱ x ̱ t B γ x ̱ B Γ ϕ ̱ t .
f 1 ( σ ) f 2 ( σ ) d σ ( f ̂ 1 δ σ ̱ ) ( f ̂ 2 δ σ ̱ ) .
s ̱ ( σ ) k α k s ̱ k ( σ ) ,
0 s 1 2 + s 2 2 + s 3 2 s 0 .

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