Abstract

Channeled spectropolarimetry is a novel method of measuring the spectral and polarization content of light. It employs amplitude modulation to encode all four Stokes component spectra into a single optical power spectrum. We describe a practical approach to system calibration and object reconstruction, which is able to account for important non-ideal effects. These include dispersion in retarder materials and limited spectral resolution in the incorporated spectrometer. The spectropolarimeter is modeled as a linear operator, represented in practice by a matrix. The matrix is estimated in the calibration, and pseudoinverted subject to a constraint on object space for reconstructions. Experimental results are shown and compared with reference measurements. An example is given of the technique’s application to the characterization of time-varying, stress-induced birefringence.

© 2003 Optical Society of America

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References

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  16. F. J. Iannarilli, S. H. Jones, H. E. Scott, and 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).
  17. F. J. Iannarilli, J. A. Shaw, S. H. Jones, and 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).
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    [Crossref]
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    [Crossref]
  24. P. R. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1992), 2 edn.
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    [Crossref]
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    [Crossref]

2002 (5)

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

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

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

R. Chipman and R. Kinnera, “High-order polarization mode dispersion emulator,” Opt. Eng. 41, 932–937 (2002).
[Crossref]

C. Bowd and L. M. Zangwillet al., “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]

2001 (1)

2000 (1)

1999 (2)

1996 (1)

1995 (2)

A. Ambirajan and D. C. Look, Jr., “Optimum angles for a polarimeter: part I,”  34, 1651–1655 (1995).

A. Ambirajan and D. C. Look, Jr., “Optimum angles for a polarimeter: part II,”  34, 1656–1658 (1995).

1993 (1)

1988 (1)

Ambirajan, A.

A. Ambirajan and D. C. Look, Jr., “Optimum angles for a polarimeter: part I,”  34, 1651–1655 (1995).

A. Ambirajan and D. C. Look, Jr., “Optimum angles for a polarimeter: part II,”  34, 1656–1658 (1995).

Azzam, R. M. A.

R. M. A. Azzam, I. M. Elminyawi, and A. M. El-Saba, “General analysis and optimization of the four-detector photopolarimeter,” J. Opt. Soc. Am. A 5, 681–689 (1988).
[Crossref]

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

R. M. A. Azzam, “Ellipsometry,” in Handbook of Optics, M. Bass, ed., (McGraw-Hill, New York, 1995), 2 edn., vol. 2.

Barrett, H. H.

H. H. Barrett and K. Meyers, Foundations of Image Science (Wiley, New York, 2003).

Bashara, N. M.

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

Bennett, J. M.

J. M. Bennett, “Polarizers,” in Handbook of Optics, M. Bass, ed., (McGraw-Hill, New York, 1995), 2 edn., vol. 2.

Bevington, P. R.

P. R. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1992), 2 edn.

Bowd, C.

Chenault, D. B.

Chipman, R.

R. Chipman and R. Kinnera, “High-order polarization mode dispersion emulator,” Opt. Eng. 41, 932–937 (2002).
[Crossref]

Chipman, R. A.

Cremer, F.

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

Dally, J. W.

J. W. Dally, Experimental Stress Analysis (McGraw-Hill, New York, 1991), 3 edn.

de Jong, W.

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

Dereniak, E. L.

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

D. S. Sabatke, M. R. Descour, E. L. Dereniak, W. C. Sweatt, S. A. Kemme, and G. S. Phipps, “Optimization of retardance for a complete Stokes polarimeter,” Opt. Lett. 25, 802–804 (2000).
[Crossref]

N. A. Hagen, D. S. Sabatke, J. F. Scholl, P. A. Jansson, and E. L. Dereniak, “Compact methods for measuring stress birefringence,” to be published in Polarization Science and Remote sensing, J. A. Shaw and J. S. Tyo, eds., Proc. SPIE5158 (2003).

D. S. Sabatke, Ball Aerospace & Technologies Corporation, PO Box 1062, Boulder, CO 80306, A. M. Locke, E. L. Dereniak, and R. W. McMillan are preparing a manuscript to be called “Linear operator theory of channeled spectropolarimetry.”

Descour, M.

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

Descour, M. R.

Elminyawi, I. M.

El-Saba, A. M.

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge U.P., Cambridge, 1995), 2 edn, http://www.nr.com/

Ford, B. K.

Garcia, J.

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

Gaskill, J. D.

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

Gdoutos, E. E.

P. S. Theocaris and E. E. Gdoutos, Matrix Theory of Photoelasticity (Springer-Verlag, Berlin, 1979).

Gerligand, P.-Y.

Hagen, N. A.

N. A. Hagen, D. S. Sabatke, J. F. Scholl, P. A. Jansson, and E. L. Dereniak, “Compact methods for measuring stress birefringence,” to be published in Polarization Science and Remote sensing, J. A. Shaw and J. S. Tyo, eds., Proc. SPIE5158 (2003).

Hamilton, T.

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

Henderson, B.

B. Henderson, “Spectroscopic measurements,” in Handbook of Optics, M. Bass, ed., (McGraw-Hill, New York, 1995), 2 edn., vol. 2.

B. Henderson, “Optical spectrometers,” in Handbook of Optics, M. Bass, ed., (McGraw-Hill, New York, 1995), 2 edn., vol. 2.

Herzberg, G.

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

Hore, D. K.

D. K. Hore, A. L. Natansohn, and 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, J. A. Shaw, S. H. Jones, and 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, and 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).

Jansson, P. A.

N. A. Hagen, D. S. Sabatke, J. F. Scholl, P. A. Jansson, and E. L. Dereniak, “Compact methods for measuring stress birefringence,” to be published in Polarization Science and Remote sensing, J. A. Shaw and J. S. Tyo, eds., Proc. SPIE5158 (2003).

Jones, S. H.

F. J. Iannarilli, S. H. Jones, H. E. Scott, and 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).

F. J. Iannarilli, J. A. Shaw, S. H. Jones, and 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).

Kato, T.

Kebabian, P.

F. J. Iannarilli, S. H. Jones, H. E. Scott, and 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).

Kemme, S. A.

Kinnera, R.

R. Chipman and R. Kinnera, “High-order polarization mode dispersion emulator,” Opt. Eng. 41, 932–937 (2002).
[Crossref]

Locke, A.

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

Locke, A. M.

D. S. Sabatke, Ball Aerospace & Technologies Corporation, PO Box 1062, Boulder, CO 80306, A. M. Locke, E. L. Dereniak, and R. W. McMillan are preparing a manuscript to be called “Linear operator theory of channeled spectropolarimetry.”

Look, Jr., D. C.

A. Ambirajan and D. C. Look, Jr., “Optimum angles for a polarimeter: part II,”  34, 1656–1658 (1995).

A. Ambirajan and D. C. Look, Jr., “Optimum angles for a polarimeter: part I,”  34, 1651–1655 (1995).

Lu, S.-Y.

Lynch, R. M.

McMillan, R. W.

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

D. S. Sabatke, Ball Aerospace & Technologies Corporation, PO Box 1062, Boulder, CO 80306, A. M. Locke, E. L. Dereniak, and R. W. McMillan are preparing a manuscript to be called “Linear operator theory of channeled spectropolarimetry.”

Meyers, K.

H. H. Barrett and K. Meyers, Foundations of Image Science (Wiley, New York, 2003).

Natansohn, A. L.

D. K. Hore, A. L. Natansohn, and 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.

Phipps, G. S.

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge U.P., Cambridge, 1995), 2 edn, http://www.nr.com/

Robinson, D. K.

P. R. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1992), 2 edn.

Rochon, P. L.

D. K. Hore, A. L. Natansohn, and 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, and R. W. McMillan, “Snapshot imaging spectropolarimeter,” Opt. Eng. 41, 1048–1054 (2002).
[Crossref]

Sabatke, D. S.

D. S. Sabatke, M. R. Descour, E. L. Dereniak, W. C. Sweatt, S. A. Kemme, and G. S. Phipps, “Optimization of retardance for a complete Stokes polarimeter,” Opt. Lett. 25, 802–804 (2000).
[Crossref]

D. S. Sabatke, Ball Aerospace & Technologies Corporation, PO Box 1062, Boulder, CO 80306, A. M. Locke, E. L. Dereniak, and R. W. McMillan are preparing a manuscript to be called “Linear operator theory of channeled spectropolarimetry.”

N. A. Hagen, D. S. Sabatke, J. F. Scholl, P. A. Jansson, and E. L. Dereniak, “Compact methods for measuring stress birefringence,” to be published in Polarization Science and Remote sensing, J. A. Shaw and J. S. Tyo, eds., Proc. SPIE5158 (2003).

D. S. Sabatke, Snapshot spectropolarimetry, Ph.D. dissertation, University of Arizona, Tucson, Arizona (2002). Available from UMI Dissertation Services, Ann Arbor, MI.

Scholl, J. F.

N. A. Hagen, D. S. Sabatke, J. F. Scholl, P. A. Jansson, and E. L. Dereniak, “Compact methods for measuring stress birefringence,” to be published in Polarization Science and Remote sensing, J. A. Shaw and J. S. Tyo, eds., Proc. SPIE5158 (2003).

Schutte, K.

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

Scott, H. E.

F. J. Iannarilli, J. A. Shaw, S. H. Jones, and 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, and 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).

Shaw, J. A.

F. J. Iannarilli, J. A. Shaw, S. H. Jones, and 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.

Sweatt, W. C.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge U.P., Cambridge, 1995), 2 edn, http://www.nr.com/

Theocaris, P. S.

P. S. Theocaris and E. E. Gdoutos, Matrix Theory of Photoelasticity (Springer-Verlag, Berlin, 1979).

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge U.P., Cambridge, 1995), 2 edn, http://www.nr.com/

Zangwill, L. M.

Appl. Opt. (1)

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

J. Phys. Chem. B (1)

D. K. Hore, A. L. Natansohn, and 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. (3)

R. Chipman and R. Kinnera, “High-order polarization mode dispersion emulator,” Opt. Eng. 41, 932–937 (2002).
[Crossref]

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

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

Opt. Express (2)

Opt. Lett. (2)

Other (21)

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

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

D. S. Sabatke, Ball Aerospace & Technologies Corporation, PO Box 1062, Boulder, CO 80306, A. M. Locke, E. L. Dereniak, and R. W. McMillan are preparing a manuscript to be called “Linear operator theory of channeled spectropolarimetry.”

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

P. R. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1992), 2 edn.

H. H. Barrett and K. Meyers, Foundations of Image Science (Wiley, New York, 2003).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge U.P., Cambridge, 1995), 2 edn, http://www.nr.com/

A. Ambirajan and D. C. Look, Jr., “Optimum angles for a polarimeter: part I,”  34, 1651–1655 (1995).

A. Ambirajan and D. C. Look, Jr., “Optimum angles for a polarimeter: part II,”  34, 1656–1658 (1995).

D. S. Sabatke, Snapshot spectropolarimetry, Ph.D. dissertation, University of Arizona, Tucson, Arizona (2002). Available from UMI Dissertation Services, Ann Arbor, MI.

N. A. Hagen, D. S. Sabatke, J. F. Scholl, P. A. Jansson, and E. L. Dereniak, “Compact methods for measuring stress birefringence,” to be published in Polarization Science and Remote sensing, J. A. Shaw and J. S. Tyo, eds., Proc. SPIE5158 (2003).

P. S. Theocaris and E. E. Gdoutos, Matrix Theory of Photoelasticity (Springer-Verlag, Berlin, 1979).

J. W. Dally, Experimental Stress Analysis (McGraw-Hill, New York, 1991), 3 edn.

B. Henderson, “Optical spectrometers,” in Handbook of Optics, M. Bass, ed., (McGraw-Hill, New York, 1995), 2 edn., vol. 2.

B. Henderson, “Spectroscopic measurements,” in Handbook of Optics, M. Bass, ed., (McGraw-Hill, New York, 1995), 2 edn., vol. 2.

J. M. Bennett, “Polarizers,” in Handbook of Optics, M. Bass, ed., (McGraw-Hill, New York, 1995), 2 edn., vol. 2.

R. A. Chipman, “Polarimetry,” in Handbook of Optics, M. Bass, ed., (McGraw-Hill, New York, 1995), 2 edn., vol. 2.

R. M. A. Azzam, “Ellipsometry,” in Handbook of Optics, M. Bass, ed., (McGraw-Hill, New York, 1995), 2 edn., vol. 2.

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