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

Full Article  |  PDF Article

References

  • View by:
  • |

  1. G. Herzberg, Atomic Spectra and Atomic Structure (Dover, New York, 1945).
  2. 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]
  3. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, Amsterdam, 1987).
  4. J. Trujillo-Bueno, F. Moreno-Insertis, and F. Sánchez, eds. Astrophysical Spectropolarimetry (Cambridge U.P., Cambridge, 2002).
  5. P.-Y. Gerligand, M. H. Smith, and R. A. Chipman, �??Polarimetric images of a cone,�?? Opt. Express 4, 420�??430 (1999), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-4-10-420">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-4-10-420<a/>.
    [CrossRef] [PubMed]
  6. 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]
  7. B. K. Ford, M. R. Descour, and R. M. Lynch, �??Large-image-format computed tomography imaging spectrometer for fluorescence microscopy,�?? Opt. Express 9, 444�??453 (2001), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-9-444">"http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-9-444</a>.
    [CrossRef] [PubMed]
  8. C. Bowd, L. M. Zangwill, et 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]
  9. P. S. Theocaris and E. E. Gdoutos, Matrix Theory of Photoelasticity (Springer-Verlag, Berlin, 1979).
  10. J. W. Dally, Experimental Stress Analysis (McGraw-Hill, New York, 1991), 3 edn.
  11. B. Henderson, �??Optical spectrometers,�?? in Handbook of Optics, M. Bass, ed., (McGraw-Hill, New York, 1995), 2 edn., vol. 2.
  12. B. Henderson, �??Spectroscopic measurements,�?? in Handbook of Optics, M. Bass, ed., (McGraw-Hill, New York, 1995), 2 edn., vol. 2.
  13. J. M. Bennett, �??Polarizers,�?? in Handbook of Optics, M. Bass, ed., (McGraw-Hill, New York, 1995), 2 edn., vol. 2.
  14. R. A. Chipman, �??Polarimetry,�?? in Handbook of Optics, M. Bass, ed., (McGraw-Hill, New York, 1995), 2 edn., vol. 2.
  15. R. M. A. Azzam, �??Ellipsometry,�?? in Handbook of Optics, M. Bass, ed., (McGraw-Hill, New York, 1995), 2 edn., vol. 2.
  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. SPIE 3698, 474�??481 (1999).
    [CrossRef]
  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. SPIE 4133, 270�??283 (2000).
    [CrossRef]
  18. K. Oka and T. Kato, �??Spectroscopic polarimetry with a channeled spectrum,�?? Opt. Lett. 24, 1475�??1477 (1999).
    [CrossRef]
  19. 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]
  20. 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.�??
  21. J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).
  22. D. B. Chenault and R. A. Chipman, �??Measurement of linear diattenuation and linear retardance spectra with a rotating sample spectropolarimeter,�?? Appl. Opt. 32, 3513�??3519 (1993).
    [CrossRef] [PubMed]
  23. 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]
  24. P. R. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1992), 2 edn.
  25. H. H. Barrett and K. Meyers, Foundations of Image Science (Wiley, New York, 2003).
  26. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge U.P., Cambridge, 1995), 2 edn, <a href="http://www.nr.com/">http://www.nr.com/</a>
  27. 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]
  28. A. Ambirajan and D. C. Look, Jr., �??Optimum angles for a polarimeter: part I,�?? 34, 1651�??1655 (1995).
  29. A. Ambirajan and D. C. Look, Jr., �??Optimum angles for a polarimeter: part II,�?? 34, 1656�??1658 (1995).
  30. D. S. Sabatke, Snapshot spectropolarimetry, Ph.D. dissertation, University of Arizona, Tucson, Arizona (2002). Available from UMI Dissertation Services, Ann Arbor, MI.
  31. N. A. Hagen, D. S. Sabatke, J. F. Scholl, P. A. Jansson, 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. SPIE 5158 (2003).
    [CrossRef]
  32. R. Chipman and R. Kinnera, �??High-order polarization mode dispersion emulator,�?? Opt. Eng. 41, 932�??937 (2002).
    [CrossRef]
  33. S.-Y. Lu and R. A. Chipman, �??Interpretation of Mueller matrices based on polar decomposition,�?? J. Opt. Soc. Am. A 13, 1106�??1113 (1996).
    [CrossRef]

Appl. Opt. (1)

Handbook of Optics (5)

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.

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)

Proc. SPIE (3)

N. A. Hagen, D. S. Sabatke, J. F. Scholl, P. A. Jansson, 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. SPIE 5158 (2003).
[CrossRef]

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. SPIE 3698, 474�??481 (1999).
[CrossRef]

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. SPIE 4133, 270�??283 (2000).
[CrossRef]

Other (13)

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

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, <a href="http://www.nr.com/">http://www.nr.com/</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).

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

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).

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.

Supplementary Material (2)

» Media 1: GIF (106 KB)     
» Media 2: GIF (113 KB)     

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1.
Fig. 1.

The channeled spectropolarimeter (after Oka and Kato [18]). 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.

Retarder characterization system.

Fig. 3.
Fig. 3.

Measurements of a spectral polarization state generated with light from a yellow LED in the state generator. The overall normalization is determined so that the s0 curve has unit area.

Fig. 4.
Fig. 4.

Measurements of a spectral polarization state generated with white light in the state generator. The overall normalization is determined so that the s0 curve has unit area. Note that each vertical axis has a different scale.

Fig. 5.
Fig. 5.

(116 KB) Measurements of a spectral polarization state generated by linearly polarizing light from a white LED and passing it through plastic with stress-induced birefringence. Time variation of the state (contained in the animation) was introduced by varying the stress. The overall normalization is determined on the basis of total optical power.

Fig. 6.
Fig. 6.

(108 KB) Animation of the time-varying spectral polarization state plotted on the Poincaré sphere.

Fig. 7.
Fig. 7.

The Stokes snake for the channeled SP data from the stress-induced bire-fringence experiment corresponds to a circular arc on the Poincaré sphere.

Equations (5)

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

s ( σ ) = ( s 0 ( σ ) s 1 ( σ ) s 2 ( σ ) s 3 ( σ ) ) .
g = H s ( σ ) .
G = H Q
H ̂ = G Q +
s ̂ = H + g .

Metrics