Abstract

Scenes from a Mueller matrix movie of a brass cone are shown. From the Mueller matrix image, a variety of polarization measures are calculated and displayed. These polarization images reveal considerable details about the geometry of the cone despite the fact that the images are taken from a single vantage point, i. e. they are “flat images”. As the cone rotates, the orientation of the diattenuation and retardance follow the shape of the cone, providing a clear indication of its shape.

© 1999 Optical Society of America

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References

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  1. J. L. Pezzaniti and R. A. Chipman, “Mueller Matrix Imaging Polarimetry,” Opt. Eng. 34, 1558–1568 (1995).
    [Crossref]
  2. R. A. Chipman, “Polarimetry,” in the Handbook of Optics, (McGraw-Hill, New-York, 1994) Chap. 22.
  3. G. Videen, J.-Y. Hsu, W. S. Bickel, and W. L. Wolfe, “Polarized light scattering from rough surfaces,” J. Opt. Soc. Am. A 9, 1111–1118 (1992).
    [Crossref]
  4. W. S. Bickel, R. R. Zito, and V. J. Iafelice, “Polarized light scattering from metal surfaces,” J. Appl. Phys. 61, 5392–5398 (1987).
    [Crossref]
  5. M. W. Williams, “Depolarization and cross polarization in Ellipsometry of rough surfaces,” Appl. Opt 25, 3616–3622 (1986).
    [Crossref] [PubMed]
  6. J. L. Pezzaniti and R. A. Chipman, “Angular dependence of polarizing beam splitter cubes,” Appl. Opt. 33, 1916–1929 (1994).
    [Crossref]
  7. J. L. Pezzaniti and R. A. Chipman, “Mueller matrix scatter polarimetry of a diamond-turned mirror,” Opt. Eng. 34, 1593–1598 (1995).
    [Crossref]
  8. J. L. Pezzaniti, S. C. McClain, R. A Chipman, and S.-Y. Lu, “Depolarization in a liquid crystal TV’s,” Opt. Lett. 18, 2071–2073 (1993).
    [Crossref] [PubMed]
  9. E. A. Sornsin and R. A. Chipman, “Mueller matrix polarimetry of PLZT electro-optic modulators,” Proc. SPIE 2873196–201 (1996).
    [Crossref]
  10. M. H. Smith, E. A. Sornsin, and R. A. Chipman, “Polarization characterization of self-imaging GaAs/AlGaAs,” in Physics and Simulation of Optoelectronic Devices V, M. Osinski and W. W. Chow, ed., Proc. SPIE2994 (1997).
  11. D. H Goldstein and R. A. Chipman, “Error analysis of a Mueller matrix polarimeter,” J. Opt. Soc. Am. A 7, 693–700 (1990).
    [Crossref]
  12. S. Y. Lu and R. A. Chipman, “Interpretation of Mueller matrices based on polar decomposition,” J. Opt. Soc. Am. A,  13, 1–8 (1996).
    [Crossref]
  13. J. J Gil and E. Bernabeu, “Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from the polar decomposition of its Mueller matrix,” Optik,  76, 67–71 (1987).
  14. D. M. G. Anderson and R. Barakat, “Necessary and sufficient conditions for a Mueller matrix to be derivable from a Jones matrix,” J. Opt. Soc. Am. A 11, 2305–2319 (1994).
    [Crossref]
  15. R. Simon, “Mueller matrices and depolarization criteria”, J. of Modern Opt.,  34(4), 569–575 (1987).
    [Crossref]
  16. A. B. Kostinski, C. R. Given, and J. M. Kwiatkowski, “Constraints on Mueller matrices of polarization optics,” Appl. Opt. 32, 1646–1651 (1993).
    [Crossref] [PubMed]
  17. J. J. Gil and E. Bernabeu, “Depolarization and polarization indices of an optical system,” Opt. Acta,  33, 185–189 (1986).
    [Crossref]

1996 (2)

E. A. Sornsin and R. A. Chipman, “Mueller matrix polarimetry of PLZT electro-optic modulators,” Proc. SPIE 2873196–201 (1996).
[Crossref]

S. Y. Lu and R. A. Chipman, “Interpretation of Mueller matrices based on polar decomposition,” J. Opt. Soc. Am. A,  13, 1–8 (1996).
[Crossref]

1995 (2)

J. L. Pezzaniti and R. A. Chipman, “Mueller matrix scatter polarimetry of a diamond-turned mirror,” Opt. Eng. 34, 1593–1598 (1995).
[Crossref]

J. L. Pezzaniti and R. A. Chipman, “Mueller Matrix Imaging Polarimetry,” Opt. Eng. 34, 1558–1568 (1995).
[Crossref]

1994 (2)

1993 (2)

1992 (1)

1990 (1)

1987 (3)

W. S. Bickel, R. R. Zito, and V. J. Iafelice, “Polarized light scattering from metal surfaces,” J. Appl. Phys. 61, 5392–5398 (1987).
[Crossref]

R. Simon, “Mueller matrices and depolarization criteria”, J. of Modern Opt.,  34(4), 569–575 (1987).
[Crossref]

J. J Gil and E. Bernabeu, “Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from the polar decomposition of its Mueller matrix,” Optik,  76, 67–71 (1987).

1986 (2)

J. J. Gil and E. Bernabeu, “Depolarization and polarization indices of an optical system,” Opt. Acta,  33, 185–189 (1986).
[Crossref]

M. W. Williams, “Depolarization and cross polarization in Ellipsometry of rough surfaces,” Appl. Opt 25, 3616–3622 (1986).
[Crossref] [PubMed]

Anderson, D. M. G.

Barakat, R.

Bernabeu, E.

J. J Gil and E. Bernabeu, “Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from the polar decomposition of its Mueller matrix,” Optik,  76, 67–71 (1987).

J. J. Gil and E. Bernabeu, “Depolarization and polarization indices of an optical system,” Opt. Acta,  33, 185–189 (1986).
[Crossref]

Bickel, W. S.

G. Videen, J.-Y. Hsu, W. S. Bickel, and W. L. Wolfe, “Polarized light scattering from rough surfaces,” J. Opt. Soc. Am. A 9, 1111–1118 (1992).
[Crossref]

W. S. Bickel, R. R. Zito, and V. J. Iafelice, “Polarized light scattering from metal surfaces,” J. Appl. Phys. 61, 5392–5398 (1987).
[Crossref]

Chipman, R. A

Chipman, R. A.

E. A. Sornsin and R. A. Chipman, “Mueller matrix polarimetry of PLZT electro-optic modulators,” Proc. SPIE 2873196–201 (1996).
[Crossref]

S. Y. Lu and R. A. Chipman, “Interpretation of Mueller matrices based on polar decomposition,” J. Opt. Soc. Am. A,  13, 1–8 (1996).
[Crossref]

J. L. Pezzaniti and R. A. Chipman, “Mueller matrix scatter polarimetry of a diamond-turned mirror,” Opt. Eng. 34, 1593–1598 (1995).
[Crossref]

J. L. Pezzaniti and R. A. Chipman, “Mueller Matrix Imaging Polarimetry,” Opt. Eng. 34, 1558–1568 (1995).
[Crossref]

J. L. Pezzaniti and R. A. Chipman, “Angular dependence of polarizing beam splitter cubes,” Appl. Opt. 33, 1916–1929 (1994).
[Crossref]

D. H Goldstein and R. A. Chipman, “Error analysis of a Mueller matrix polarimeter,” J. Opt. Soc. Am. A 7, 693–700 (1990).
[Crossref]

R. A. Chipman, “Polarimetry,” in the Handbook of Optics, (McGraw-Hill, New-York, 1994) Chap. 22.

M. H. Smith, E. A. Sornsin, and R. A. Chipman, “Polarization characterization of self-imaging GaAs/AlGaAs,” in Physics and Simulation of Optoelectronic Devices V, M. Osinski and W. W. Chow, ed., Proc. SPIE2994 (1997).

Gil, J. J

J. J Gil and E. Bernabeu, “Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from the polar decomposition of its Mueller matrix,” Optik,  76, 67–71 (1987).

Gil, J. J.

J. J. Gil and E. Bernabeu, “Depolarization and polarization indices of an optical system,” Opt. Acta,  33, 185–189 (1986).
[Crossref]

Given, C. R.

Goldstein, D. H

Hsu, J.-Y.

Iafelice, V. J.

W. S. Bickel, R. R. Zito, and V. J. Iafelice, “Polarized light scattering from metal surfaces,” J. Appl. Phys. 61, 5392–5398 (1987).
[Crossref]

Kostinski, A. B.

Kwiatkowski, J. M.

Lu, S. Y.

S. Y. Lu and R. A. Chipman, “Interpretation of Mueller matrices based on polar decomposition,” J. Opt. Soc. Am. A,  13, 1–8 (1996).
[Crossref]

Lu, S.-Y.

McClain, S. C.

Pezzaniti, J. L.

J. L. Pezzaniti and R. A. Chipman, “Mueller Matrix Imaging Polarimetry,” Opt. Eng. 34, 1558–1568 (1995).
[Crossref]

J. L. Pezzaniti and R. A. Chipman, “Mueller matrix scatter polarimetry of a diamond-turned mirror,” Opt. Eng. 34, 1593–1598 (1995).
[Crossref]

J. L. Pezzaniti and R. A. Chipman, “Angular dependence of polarizing beam splitter cubes,” Appl. Opt. 33, 1916–1929 (1994).
[Crossref]

J. L. Pezzaniti, S. C. McClain, R. A Chipman, and S.-Y. Lu, “Depolarization in a liquid crystal TV’s,” Opt. Lett. 18, 2071–2073 (1993).
[Crossref] [PubMed]

Simon, R.

R. Simon, “Mueller matrices and depolarization criteria”, J. of Modern Opt.,  34(4), 569–575 (1987).
[Crossref]

Smith, M. H.

M. H. Smith, E. A. Sornsin, and R. A. Chipman, “Polarization characterization of self-imaging GaAs/AlGaAs,” in Physics and Simulation of Optoelectronic Devices V, M. Osinski and W. W. Chow, ed., Proc. SPIE2994 (1997).

Sornsin, E. A.

E. A. Sornsin and R. A. Chipman, “Mueller matrix polarimetry of PLZT electro-optic modulators,” Proc. SPIE 2873196–201 (1996).
[Crossref]

M. H. Smith, E. A. Sornsin, and R. A. Chipman, “Polarization characterization of self-imaging GaAs/AlGaAs,” in Physics and Simulation of Optoelectronic Devices V, M. Osinski and W. W. Chow, ed., Proc. SPIE2994 (1997).

Videen, G.

Williams, M. W.

M. W. Williams, “Depolarization and cross polarization in Ellipsometry of rough surfaces,” Appl. Opt 25, 3616–3622 (1986).
[Crossref] [PubMed]

Wolfe, W. L.

Zito, R. R.

W. S. Bickel, R. R. Zito, and V. J. Iafelice, “Polarized light scattering from metal surfaces,” J. Appl. Phys. 61, 5392–5398 (1987).
[Crossref]

Appl. Opt (1)

M. W. Williams, “Depolarization and cross polarization in Ellipsometry of rough surfaces,” Appl. Opt 25, 3616–3622 (1986).
[Crossref] [PubMed]

Appl. Opt. (2)

J. Appl. Phys. (1)

W. S. Bickel, R. R. Zito, and V. J. Iafelice, “Polarized light scattering from metal surfaces,” J. Appl. Phys. 61, 5392–5398 (1987).
[Crossref]

J. of Modern Opt. (1)

R. Simon, “Mueller matrices and depolarization criteria”, J. of Modern Opt.,  34(4), 569–575 (1987).
[Crossref]

J. Opt. Soc. Am. A (4)

Opt. Acta (1)

J. J. Gil and E. Bernabeu, “Depolarization and polarization indices of an optical system,” Opt. Acta,  33, 185–189 (1986).
[Crossref]

Opt. Eng. (2)

J. L. Pezzaniti and R. A. Chipman, “Mueller Matrix Imaging Polarimetry,” Opt. Eng. 34, 1558–1568 (1995).
[Crossref]

J. L. Pezzaniti and R. A. Chipman, “Mueller matrix scatter polarimetry of a diamond-turned mirror,” Opt. Eng. 34, 1593–1598 (1995).
[Crossref]

Opt. Lett. (1)

Optik (1)

J. J Gil and E. Bernabeu, “Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from the polar decomposition of its Mueller matrix,” Optik,  76, 67–71 (1987).

Proc. SPIE (1)

E. A. Sornsin and R. A. Chipman, “Mueller matrix polarimetry of PLZT electro-optic modulators,” Proc. SPIE 2873196–201 (1996).
[Crossref]

Other (2)

M. H. Smith, E. A. Sornsin, and R. A. Chipman, “Polarization characterization of self-imaging GaAs/AlGaAs,” in Physics and Simulation of Optoelectronic Devices V, M. Osinski and W. W. Chow, ed., Proc. SPIE2994 (1997).

R. A. Chipman, “Polarimetry,” in the Handbook of Optics, (McGraw-Hill, New-York, 1994) Chap. 22.

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Figures (7)

Fig. 1.
Fig. 1.

Mueller matrix imaging polarimeter configured for scattering measurement

Fig. 2.
Fig. 2.

16-dimensional Mueller matrix space

Fig. 3.
Fig. 3.

Mueller matrix images of the brass cone

Fig. 4.
Fig. 4.

Magnitude and orientation images of the diattenuation for different orientations of the brass cone (0°, 30°, 60°, 90°, 120°, and 150°)

Fig. 5.
Fig. 5.

Magnitude and orientation images of the retardance for different orientations of the brass cone (0°, 30°, 60°, 90°, 120°, and 150°)

Fig.6.
Fig.6.

Polarization crosstalk images for different orientations of the brass cone (0°, 30°, 60°, 90°, 120°, and 150°)

Fig. 7.
Fig. 7.

Polarizance and depolarization index images for different orientations of the brass cone (0°, 30°, 60°, 90°, 120°, and 150°)

Equations (2)

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M = Dep . R . D
Dep ( M ) = 1 ( i , j m ij 2 ) m 00 2 3 m 00 2

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