Abstract

This paper reports on the design and implementation of a liquid crystal variable retarder based overdetermined spectroscopic Mueller matrix polarimeter, with parallel processing of all wavelengths. The system was designed using a modified version of a recently developed genetic algorithm [Letnes et al. Opt. Express 18, 22, 23095 (2010)]. A generalization of the eigenvalue calibration method is reported that allows the calibration of such overdetermined polarimetric systems. Out of several possible designs, one of the designs was experimentally implemented and calibrated. It is reported that the instrument demonstrated good performance, with a measurement accuracy in the range of 0.1% for the measurement of air.

© 2013 OSA

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  1. P. G. Ellingsen, M. B. Lilledahl, L. M. S. Aas, C. d. L. Davies, and M. Kildemo, “Quantitative characterization of articular cartilage using Mueller matrix imaging and multiphoton microscopy,” J. Biomed. Opt.16, 116002 (2011).
    [CrossRef] [PubMed]
  2. M. H. Smith, P. D. Burke, A. Lompado, E. A. Tanner, and L. W. Hillman, “Mueller matrix imaging polarimetry in dermatology,” Proc. SPIE3911, 210–216 (2000).
    [CrossRef]
  3. R. N. Weinreb, S. Shakiba, and L. Zangwill, “Scanning laser polarimetry to measure the nerve fiber layer of normal and glaucomatous eyes,” Am. J. Ophthalmol.119, 627–636 (1995).
    [PubMed]
  4. J. D. Howe, M. A. Miller, R. V. Blumer, T. E. Petty, M. A. Stevens, D. M. Teale, and M. H. Smith, “Polarization sensing for target acquisition and mine detection,” Proc. SPIE4133, 202–213 (2000).
    [CrossRef]
  5. A. Alvarez-Herrero, V. Martínez-Pillet, J. del Toro Iniesta, and V. Domingo, “The IMaX polarimeter for the solar telescope SUNRISE of the NASA long duration balloon program,” in API’09, (2010), pp. 05002.
  6. R. Azzam and N. Bashara, Ellipsometry and Polarized light (North-Holland, 1977).
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    [CrossRef]
  8. H. Tompkins and E. A. Irene, Handbook of Ellipsometry (William Andrew, 2005).
    [CrossRef]
  9. M. Foldyna, A. D. Martino, R. Ossikovski, E. Garcia-Caurel, and C. Licitra, “Characterization of grating structures by Mueller polarimetry in presence of strong depolarization due to finite spot size,” Opt. Commun.282, 735–741 (2009).
    [CrossRef]
  10. D. Schmidt, A. C. Kjerstad, T. Hofmann, R. Skomski, E. Schubert, and M. Schubert, “Optical, structural, and magnetic properties of cobalt nanostructure thin films,” J. Appl. Phys.105, 113508 (2009).
    [CrossRef]
  11. L. M. S. Aas, M. Kildemo, Y. Cohin, and E. Søndergård, “Determination of small tilt angles of short gasb nanopillars using uv-visible mueller matrix ellipsometry,” Thin Solid Films (2012).
    [CrossRef]
  12. I. S. Nerbø, S. Le Roy, M. Foldyna, M. Kildemo, and E. Søndergård, “Characterization of inclined GaSb nanopillars by Mueller matrix ellipsometry,” J. Appl. Phys.108, 014307 (2010).
    [CrossRef]
  13. T. Oates, H. Wormeester, and H. Arwin, “Characterization of plasmonic effects in thin films and metamaterials using spectroscopic ellipsometry,” Prog. Surf. Sci.86, 328–376 (2011).
    [CrossRef]
  14. B. Gallas, K. Robbie, R. Abdeddaïm, G. Guida, J. Yang, J. Rivory, and a. Priou, “Silver square nanospirals mimic optical properties of U-shaped metamaterials.” Opt. Express18, 16335–16344 (2010).
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  19. F. Stabo-Eeg, M. Kildemo, I. Nerbø, and M. Lindgren, “Well-conditioned multiple laser Mueller matrix ellipsometer,” Opt. Eng.47, 073604 (2008).
    [CrossRef]
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  23. E. Garcia-Caurel, A. D. Martino, and B. Drevillon, “Spectroscopic Mueller polarimeter based on liquid crystal devices,” Thin Solid Films455, 120–123 (2004).
    [CrossRef]
  24. L. Aas, P. Ellingsen, and M. Kildemo, “Near infra-red Mueller matrix imaging system and application to retardance imaging of strain,” Thin Solid Films519, 2737–2741 (2010).
    [CrossRef]
  25. P. Letnes, I. Nerbø, L. Aas, P. Ellingsen, and M. Kildemo, “Fast and optimal broad-band Stokes/Mueller polarimeter design by the use of a genetic algorithm,” Opt. Express18, 23095–23103 (2010).
    [CrossRef] [PubMed]
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    [CrossRef]
  29. S. B. Hatit, M. Foldyna, A. De Martino, and B. Drévillon, “Angle-resolved Mueller polarimeter using a microscope objective,” Phys. Stat. Sol. (a)205, 743–747 (2008).
    [CrossRef]
  30. A. Ben-Israel and T. N. E. Greville, Generalized Inverses: Theory and Applications (Springer-Verlag, 2003).
  31. R. Hagen, S. Roch, and B. Silbermann, C* Algebras Numerical Analysis (Marcel Dekker, 2001).
  32. L. Aas, P. Ellingsen, M. Kildemo, and M. Lindgren, “Dynamic Response of a fast near infra-red Mueller matrix ellipsometer,” J. Mod. Opt.57, 1603–1610 (2010).
    [CrossRef]
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2012

L. M. S. Aas, M. Kildemo, Y. Cohin, and E. Søndergård, “Determination of small tilt angles of short gasb nanopillars using uv-visible mueller matrix ellipsometry,” Thin Solid Films (2012).
[CrossRef]

Ø. Svensen, M. Kildemo, J. Maria, J. J. Stamnes, and O. Frette, “Mueller matrix measurements and modeling pertaining to Spectralon white reflectance standards.” Opt. Express20, 15045–15053 (2012).
[CrossRef] [PubMed]

O. Arteaga, J. Freudenthal, B. Wang, and B. Kahr, “Mueller matrix polarimetry with four photoelastic modulators: theory and calibration.” Appl. Optics51, 6805–6817 (2012).
[CrossRef]

2011

P. G. Ellingsen, M. B. Lilledahl, L. M. S. Aas, C. d. L. Davies, and M. Kildemo, “Quantitative characterization of articular cartilage using Mueller matrix imaging and multiphoton microscopy,” J. Biomed. Opt.16, 116002 (2011).
[CrossRef] [PubMed]

T. Oates, H. Wormeester, and H. Arwin, “Characterization of plasmonic effects in thin films and metamaterials using spectroscopic ellipsometry,” Prog. Surf. Sci.86, 328–376 (2011).
[CrossRef]

2010

B. Gallas, K. Robbie, R. Abdeddaïm, G. Guida, J. Yang, J. Rivory, and a. Priou, “Silver square nanospirals mimic optical properties of U-shaped metamaterials.” Opt. Express18, 16335–16344 (2010).
[CrossRef] [PubMed]

I. S. Nerbø, S. Le Roy, M. Foldyna, M. Kildemo, and E. Søndergård, “Characterization of inclined GaSb nanopillars by Mueller matrix ellipsometry,” J. Appl. Phys.108, 014307 (2010).
[CrossRef]

L. Aas, P. Ellingsen, and M. Kildemo, “Near infra-red Mueller matrix imaging system and application to retardance imaging of strain,” Thin Solid Films519, 2737–2741 (2010).
[CrossRef]

P. Letnes, I. Nerbø, L. Aas, P. Ellingsen, and M. Kildemo, “Fast and optimal broad-band Stokes/Mueller polarimeter design by the use of a genetic algorithm,” Opt. Express18, 23095–23103 (2010).
[CrossRef] [PubMed]

L. Aas, P. Ellingsen, M. Kildemo, and M. Lindgren, “Dynamic Response of a fast near infra-red Mueller matrix ellipsometer,” J. Mod. Opt.57, 1603–1610 (2010).
[CrossRef]

2009

M. Foldyna, A. D. Martino, R. Ossikovski, E. Garcia-Caurel, and C. Licitra, “Characterization of grating structures by Mueller polarimetry in presence of strong depolarization due to finite spot size,” Opt. Commun.282, 735–741 (2009).
[CrossRef]

D. Schmidt, A. C. Kjerstad, T. Hofmann, R. Skomski, E. Schubert, and M. Schubert, “Optical, structural, and magnetic properties of cobalt nanostructure thin films,” J. Appl. Phys.105, 113508 (2009).
[CrossRef]

2008

F. Stabo-Eeg, M. Kildemo, I. Nerbø, and M. Lindgren, “Well-conditioned multiple laser Mueller matrix ellipsometer,” Opt. Eng.47, 073604 (2008).
[CrossRef]

S. B. Hatit, M. Foldyna, A. De Martino, and B. Drévillon, “Angle-resolved Mueller polarimeter using a microscope objective,” Phys. Stat. Sol. (a)205, 743–747 (2008).
[CrossRef]

2004

E. Garcia-Caurel, A. D. Martino, and B. Drevillon, “Spectroscopic Mueller polarimeter based on liquid crystal devices,” Thin Solid Films455, 120–123 (2004).
[CrossRef]

2001

2000

T. Germer, “Measurement of roughness of two interfaces of a dielectric film by scattering ellipsometry,” Phys. Rev. Lett.85, 349–352 (2000).
[CrossRef] [PubMed]

M. H. Smith, P. D. Burke, A. Lompado, E. A. Tanner, and L. W. Hillman, “Mueller matrix imaging polarimetry in dermatology,” Proc. SPIE3911, 210–216 (2000).
[CrossRef]

J. D. Howe, M. A. Miller, R. V. Blumer, T. E. Petty, M. A. Stevens, D. M. Teale, and M. H. Smith, “Polarization sensing for target acquisition and mine detection,” Proc. SPIE4133, 202–213 (2000).
[CrossRef]

1999

E. Compain, S. Poirier, and B. Drevillon, “General and self-consistent method for the calibration of polarization modulators, polarimeters, and mueller-matrix ellipsometers.” Appl. Optics38, 3490–3502 (1999).
[CrossRef]

1997

E. Compain and B. Drevillon, “Complete high-frequency measurement of Mueller matrices based on a new coupled-phase modulator,” Rev. Sci. Instrum.68, 2671 (1997).
[CrossRef]

1995

R. N. Weinreb, S. Shakiba, and L. Zangwill, “Scanning laser polarimetry to measure the nerve fiber layer of normal and glaucomatous eyes,” Am. J. Ophthalmol.119, 627–636 (1995).
[PubMed]

1992

J. H. Holland, “Genetic algorithms,” Sci. Am.267, 44–50 (1992).
[CrossRef]

1990

G. E. Jellison and F. a. Modine, “Two-channel polarization modulation ellipsometer.” Appl. Optics29, 959–974 (1990).
[CrossRef]

Aas, L.

L. Aas, P. Ellingsen, and M. Kildemo, “Near infra-red Mueller matrix imaging system and application to retardance imaging of strain,” Thin Solid Films519, 2737–2741 (2010).
[CrossRef]

P. Letnes, I. Nerbø, L. Aas, P. Ellingsen, and M. Kildemo, “Fast and optimal broad-band Stokes/Mueller polarimeter design by the use of a genetic algorithm,” Opt. Express18, 23095–23103 (2010).
[CrossRef] [PubMed]

L. Aas, P. Ellingsen, M. Kildemo, and M. Lindgren, “Dynamic Response of a fast near infra-red Mueller matrix ellipsometer,” J. Mod. Opt.57, 1603–1610 (2010).
[CrossRef]

Aas, L. M. S.

L. M. S. Aas, M. Kildemo, Y. Cohin, and E. Søndergård, “Determination of small tilt angles of short gasb nanopillars using uv-visible mueller matrix ellipsometry,” Thin Solid Films (2012).
[CrossRef]

P. G. Ellingsen, M. B. Lilledahl, L. M. S. Aas, C. d. L. Davies, and M. Kildemo, “Quantitative characterization of articular cartilage using Mueller matrix imaging and multiphoton microscopy,” J. Biomed. Opt.16, 116002 (2011).
[CrossRef] [PubMed]

Abdeddaïm, R.

Alvarez-Herrero, A.

A. Alvarez-Herrero, V. Martínez-Pillet, J. del Toro Iniesta, and V. Domingo, “The IMaX polarimeter for the solar telescope SUNRISE of the NASA long duration balloon program,” in API’09, (2010), pp. 05002.

Arteaga, O.

O. Arteaga, J. Freudenthal, B. Wang, and B. Kahr, “Mueller matrix polarimetry with four photoelastic modulators: theory and calibration.” Appl. Optics51, 6805–6817 (2012).
[CrossRef]

Arwin, H.

T. Oates, H. Wormeester, and H. Arwin, “Characterization of plasmonic effects in thin films and metamaterials using spectroscopic ellipsometry,” Prog. Surf. Sci.86, 328–376 (2011).
[CrossRef]

Azzam, R.

R. Azzam and N. Bashara, Ellipsometry and Polarized light (North-Holland, 1977).

Azzam, R. M. A.

J. M. Bennet, R. Chipman, and R. M. A. Azzam, “Polarized light,” in Handbook of Optics, M. Bass and V. Mahajan, eds. (McGraw-Hill, Inc., 2010), pp. 12.3–16.21.

Bashara, N.

R. Azzam and N. Bashara, Ellipsometry and Polarized light (North-Holland, 1977).

Ben-Israel, A.

A. Ben-Israel and T. N. E. Greville, Generalized Inverses: Theory and Applications (Springer-Verlag, 2003).

Bennet, J. M.

J. M. Bennet, R. Chipman, and R. M. A. Azzam, “Polarized light,” in Handbook of Optics, M. Bass and V. Mahajan, eds. (McGraw-Hill, Inc., 2010), pp. 12.3–16.21.

Blumer, R. V.

J. D. Howe, M. A. Miller, R. V. Blumer, T. E. Petty, M. A. Stevens, D. M. Teale, and M. H. Smith, “Polarization sensing for target acquisition and mine detection,” Proc. SPIE4133, 202–213 (2000).
[CrossRef]

Burke, P. D.

M. H. Smith, P. D. Burke, A. Lompado, E. A. Tanner, and L. W. Hillman, “Mueller matrix imaging polarimetry in dermatology,” Proc. SPIE3911, 210–216 (2000).
[CrossRef]

Chipman, R.

J. M. Bennet, R. Chipman, and R. M. A. Azzam, “Polarized light,” in Handbook of Optics, M. Bass and V. Mahajan, eds. (McGraw-Hill, Inc., 2010), pp. 12.3–16.21.

Cohin, Y.

L. M. S. Aas, M. Kildemo, Y. Cohin, and E. Søndergård, “Determination of small tilt angles of short gasb nanopillars using uv-visible mueller matrix ellipsometry,” Thin Solid Films (2012).
[CrossRef]

Compain, E.

E. Compain, S. Poirier, and B. Drevillon, “General and self-consistent method for the calibration of polarization modulators, polarimeters, and mueller-matrix ellipsometers.” Appl. Optics38, 3490–3502 (1999).
[CrossRef]

E. Compain and B. Drevillon, “Complete high-frequency measurement of Mueller matrices based on a new coupled-phase modulator,” Rev. Sci. Instrum.68, 2671 (1997).
[CrossRef]

Davies, C. d. L.

P. G. Ellingsen, M. B. Lilledahl, L. M. S. Aas, C. d. L. Davies, and M. Kildemo, “Quantitative characterization of articular cartilage using Mueller matrix imaging and multiphoton microscopy,” J. Biomed. Opt.16, 116002 (2011).
[CrossRef] [PubMed]

De Martino, A.

S. B. Hatit, M. Foldyna, A. De Martino, and B. Drévillon, “Angle-resolved Mueller polarimeter using a microscope objective,” Phys. Stat. Sol. (a)205, 743–747 (2008).
[CrossRef]

del Toro Iniesta, J.

A. Alvarez-Herrero, V. Martínez-Pillet, J. del Toro Iniesta, and V. Domingo, “The IMaX polarimeter for the solar telescope SUNRISE of the NASA long duration balloon program,” in API’09, (2010), pp. 05002.

Domingo, V.

A. Alvarez-Herrero, V. Martínez-Pillet, J. del Toro Iniesta, and V. Domingo, “The IMaX polarimeter for the solar telescope SUNRISE of the NASA long duration balloon program,” in API’09, (2010), pp. 05002.

Drevillon, B.

E. Garcia-Caurel, A. D. Martino, and B. Drevillon, “Spectroscopic Mueller polarimeter based on liquid crystal devices,” Thin Solid Films455, 120–123 (2004).
[CrossRef]

E. Compain, S. Poirier, and B. Drevillon, “General and self-consistent method for the calibration of polarization modulators, polarimeters, and mueller-matrix ellipsometers.” Appl. Optics38, 3490–3502 (1999).
[CrossRef]

E. Compain and B. Drevillon, “Complete high-frequency measurement of Mueller matrices based on a new coupled-phase modulator,” Rev. Sci. Instrum.68, 2671 (1997).
[CrossRef]

Drévillon, B.

S. B. Hatit, M. Foldyna, A. De Martino, and B. Drévillon, “Angle-resolved Mueller polarimeter using a microscope objective,” Phys. Stat. Sol. (a)205, 743–747 (2008).
[CrossRef]

Ellingsen, P.

P. Letnes, I. Nerbø, L. Aas, P. Ellingsen, and M. Kildemo, “Fast and optimal broad-band Stokes/Mueller polarimeter design by the use of a genetic algorithm,” Opt. Express18, 23095–23103 (2010).
[CrossRef] [PubMed]

L. Aas, P. Ellingsen, and M. Kildemo, “Near infra-red Mueller matrix imaging system and application to retardance imaging of strain,” Thin Solid Films519, 2737–2741 (2010).
[CrossRef]

L. Aas, P. Ellingsen, M. Kildemo, and M. Lindgren, “Dynamic Response of a fast near infra-red Mueller matrix ellipsometer,” J. Mod. Opt.57, 1603–1610 (2010).
[CrossRef]

Ellingsen, P. G.

P. G. Ellingsen, M. B. Lilledahl, L. M. S. Aas, C. d. L. Davies, and M. Kildemo, “Quantitative characterization of articular cartilage using Mueller matrix imaging and multiphoton microscopy,” J. Biomed. Opt.16, 116002 (2011).
[CrossRef] [PubMed]

Floreano, D.

D. Floreano and C. Mattiussi, Bio-Inspired Artificial Intelligence: Theories, Methods, and Technologies (The MIT Press, 2008).

Foldyna, M.

I. S. Nerbø, S. Le Roy, M. Foldyna, M. Kildemo, and E. Søndergård, “Characterization of inclined GaSb nanopillars by Mueller matrix ellipsometry,” J. Appl. Phys.108, 014307 (2010).
[CrossRef]

M. Foldyna, A. D. Martino, R. Ossikovski, E. Garcia-Caurel, and C. Licitra, “Characterization of grating structures by Mueller polarimetry in presence of strong depolarization due to finite spot size,” Opt. Commun.282, 735–741 (2009).
[CrossRef]

S. B. Hatit, M. Foldyna, A. De Martino, and B. Drévillon, “Angle-resolved Mueller polarimeter using a microscope objective,” Phys. Stat. Sol. (a)205, 743–747 (2008).
[CrossRef]

Frette, O.

Freudenthal, J.

O. Arteaga, J. Freudenthal, B. Wang, and B. Kahr, “Mueller matrix polarimetry with four photoelastic modulators: theory and calibration.” Appl. Optics51, 6805–6817 (2012).
[CrossRef]

Fujiwara, H.

H. Fujiwara, Spectroscopic Ellipsometry: Principles and Applications (John Wiley & Sons, Chichester, England; Hoboken, NJ, 2007).
[CrossRef]

Gallas, B.

Garcia-Caurel, E.

M. Foldyna, A. D. Martino, R. Ossikovski, E. Garcia-Caurel, and C. Licitra, “Characterization of grating structures by Mueller polarimetry in presence of strong depolarization due to finite spot size,” Opt. Commun.282, 735–741 (2009).
[CrossRef]

E. Garcia-Caurel, A. D. Martino, and B. Drevillon, “Spectroscopic Mueller polarimeter based on liquid crystal devices,” Thin Solid Films455, 120–123 (2004).
[CrossRef]

Germer, T.

T. Germer, “Measurement of roughness of two interfaces of a dielectric film by scattering ellipsometry,” Phys. Rev. Lett.85, 349–352 (2000).
[CrossRef] [PubMed]

Germer, T. A.

Greville, T. N. E.

A. Ben-Israel and T. N. E. Greville, Generalized Inverses: Theory and Applications (Springer-Verlag, 2003).

Guida, G.

Hagen, R.

R. Hagen, S. Roch, and B. Silbermann, C* Algebras Numerical Analysis (Marcel Dekker, 2001).

Hatit, S. B.

S. B. Hatit, M. Foldyna, A. De Martino, and B. Drévillon, “Angle-resolved Mueller polarimeter using a microscope objective,” Phys. Stat. Sol. (a)205, 743–747 (2008).
[CrossRef]

Hillman, L. W.

M. H. Smith, P. D. Burke, A. Lompado, E. A. Tanner, and L. W. Hillman, “Mueller matrix imaging polarimetry in dermatology,” Proc. SPIE3911, 210–216 (2000).
[CrossRef]

Hofmann, T.

D. Schmidt, A. C. Kjerstad, T. Hofmann, R. Skomski, E. Schubert, and M. Schubert, “Optical, structural, and magnetic properties of cobalt nanostructure thin films,” J. Appl. Phys.105, 113508 (2009).
[CrossRef]

Holland, J. H.

J. H. Holland, “Genetic algorithms,” Sci. Am.267, 44–50 (1992).
[CrossRef]

Howe, J. D.

J. D. Howe, M. A. Miller, R. V. Blumer, T. E. Petty, M. A. Stevens, D. M. Teale, and M. H. Smith, “Polarization sensing for target acquisition and mine detection,” Proc. SPIE4133, 202–213 (2000).
[CrossRef]

Irene, E. A.

H. Tompkins and E. A. Irene, Handbook of Ellipsometry (William Andrew, 2005).
[CrossRef]

Jellison, G. E.

G. E. Jellison and F. a. Modine, “Two-channel polarization modulation ellipsometer.” Appl. Optics29, 959–974 (1990).
[CrossRef]

Kahr, B.

O. Arteaga, J. Freudenthal, B. Wang, and B. Kahr, “Mueller matrix polarimetry with four photoelastic modulators: theory and calibration.” Appl. Optics51, 6805–6817 (2012).
[CrossRef]

Kildemo, M.

L. M. S. Aas, M. Kildemo, Y. Cohin, and E. Søndergård, “Determination of small tilt angles of short gasb nanopillars using uv-visible mueller matrix ellipsometry,” Thin Solid Films (2012).
[CrossRef]

Ø. Svensen, M. Kildemo, J. Maria, J. J. Stamnes, and O. Frette, “Mueller matrix measurements and modeling pertaining to Spectralon white reflectance standards.” Opt. Express20, 15045–15053 (2012).
[CrossRef] [PubMed]

P. G. Ellingsen, M. B. Lilledahl, L. M. S. Aas, C. d. L. Davies, and M. Kildemo, “Quantitative characterization of articular cartilage using Mueller matrix imaging and multiphoton microscopy,” J. Biomed. Opt.16, 116002 (2011).
[CrossRef] [PubMed]

I. S. Nerbø, S. Le Roy, M. Foldyna, M. Kildemo, and E. Søndergård, “Characterization of inclined GaSb nanopillars by Mueller matrix ellipsometry,” J. Appl. Phys.108, 014307 (2010).
[CrossRef]

L. Aas, P. Ellingsen, and M. Kildemo, “Near infra-red Mueller matrix imaging system and application to retardance imaging of strain,” Thin Solid Films519, 2737–2741 (2010).
[CrossRef]

P. Letnes, I. Nerbø, L. Aas, P. Ellingsen, and M. Kildemo, “Fast and optimal broad-band Stokes/Mueller polarimeter design by the use of a genetic algorithm,” Opt. Express18, 23095–23103 (2010).
[CrossRef] [PubMed]

L. Aas, P. Ellingsen, M. Kildemo, and M. Lindgren, “Dynamic Response of a fast near infra-red Mueller matrix ellipsometer,” J. Mod. Opt.57, 1603–1610 (2010).
[CrossRef]

F. Stabo-Eeg, M. Kildemo, I. Nerbø, and M. Lindgren, “Well-conditioned multiple laser Mueller matrix ellipsometer,” Opt. Eng.47, 073604 (2008).
[CrossRef]

Kjerstad, A. C.

D. Schmidt, A. C. Kjerstad, T. Hofmann, R. Skomski, E. Schubert, and M. Schubert, “Optical, structural, and magnetic properties of cobalt nanostructure thin films,” J. Appl. Phys.105, 113508 (2009).
[CrossRef]

Le Roy, S.

I. S. Nerbø, S. Le Roy, M. Foldyna, M. Kildemo, and E. Søndergård, “Characterization of inclined GaSb nanopillars by Mueller matrix ellipsometry,” J. Appl. Phys.108, 014307 (2010).
[CrossRef]

Letnes, P.

Licitra, C.

M. Foldyna, A. D. Martino, R. Ossikovski, E. Garcia-Caurel, and C. Licitra, “Characterization of grating structures by Mueller polarimetry in presence of strong depolarization due to finite spot size,” Opt. Commun.282, 735–741 (2009).
[CrossRef]

Lilledahl, M. B.

P. G. Ellingsen, M. B. Lilledahl, L. M. S. Aas, C. d. L. Davies, and M. Kildemo, “Quantitative characterization of articular cartilage using Mueller matrix imaging and multiphoton microscopy,” J. Biomed. Opt.16, 116002 (2011).
[CrossRef] [PubMed]

Lindgren, M.

L. Aas, P. Ellingsen, M. Kildemo, and M. Lindgren, “Dynamic Response of a fast near infra-red Mueller matrix ellipsometer,” J. Mod. Opt.57, 1603–1610 (2010).
[CrossRef]

F. Stabo-Eeg, M. Kildemo, I. Nerbø, and M. Lindgren, “Well-conditioned multiple laser Mueller matrix ellipsometer,” Opt. Eng.47, 073604 (2008).
[CrossRef]

Lompado, A.

M. H. Smith, P. D. Burke, A. Lompado, E. A. Tanner, and L. W. Hillman, “Mueller matrix imaging polarimetry in dermatology,” Proc. SPIE3911, 210–216 (2000).
[CrossRef]

Maria, J.

Martínez-Pillet, V.

A. Alvarez-Herrero, V. Martínez-Pillet, J. del Toro Iniesta, and V. Domingo, “The IMaX polarimeter for the solar telescope SUNRISE of the NASA long duration balloon program,” in API’09, (2010), pp. 05002.

Martino, A. D.

M. Foldyna, A. D. Martino, R. Ossikovski, E. Garcia-Caurel, and C. Licitra, “Characterization of grating structures by Mueller polarimetry in presence of strong depolarization due to finite spot size,” Opt. Commun.282, 735–741 (2009).
[CrossRef]

E. Garcia-Caurel, A. D. Martino, and B. Drevillon, “Spectroscopic Mueller polarimeter based on liquid crystal devices,” Thin Solid Films455, 120–123 (2004).
[CrossRef]

Mattiussi, C.

D. Floreano and C. Mattiussi, Bio-Inspired Artificial Intelligence: Theories, Methods, and Technologies (The MIT Press, 2008).

Miller, M. A.

J. D. Howe, M. A. Miller, R. V. Blumer, T. E. Petty, M. A. Stevens, D. M. Teale, and M. H. Smith, “Polarization sensing for target acquisition and mine detection,” Proc. SPIE4133, 202–213 (2000).
[CrossRef]

Modine, F. a.

G. E. Jellison and F. a. Modine, “Two-channel polarization modulation ellipsometer.” Appl. Optics29, 959–974 (1990).
[CrossRef]

Nerbø, I.

Nerbø, I. S.

I. S. Nerbø, S. Le Roy, M. Foldyna, M. Kildemo, and E. Søndergård, “Characterization of inclined GaSb nanopillars by Mueller matrix ellipsometry,” J. Appl. Phys.108, 014307 (2010).
[CrossRef]

Oates, T.

T. Oates, H. Wormeester, and H. Arwin, “Characterization of plasmonic effects in thin films and metamaterials using spectroscopic ellipsometry,” Prog. Surf. Sci.86, 328–376 (2011).
[CrossRef]

Ossikovski, R.

M. Foldyna, A. D. Martino, R. Ossikovski, E. Garcia-Caurel, and C. Licitra, “Characterization of grating structures by Mueller polarimetry in presence of strong depolarization due to finite spot size,” Opt. Commun.282, 735–741 (2009).
[CrossRef]

Petty, T. E.

J. D. Howe, M. A. Miller, R. V. Blumer, T. E. Petty, M. A. Stevens, D. M. Teale, and M. H. Smith, “Polarization sensing for target acquisition and mine detection,” Proc. SPIE4133, 202–213 (2000).
[CrossRef]

Poirier, S.

E. Compain, S. Poirier, and B. Drevillon, “General and self-consistent method for the calibration of polarization modulators, polarimeters, and mueller-matrix ellipsometers.” Appl. Optics38, 3490–3502 (1999).
[CrossRef]

Priou, a.

Rivory, J.

Robbie, K.

Roch, S.

R. Hagen, S. Roch, and B. Silbermann, C* Algebras Numerical Analysis (Marcel Dekker, 2001).

Schmidt, D.

D. Schmidt, A. C. Kjerstad, T. Hofmann, R. Skomski, E. Schubert, and M. Schubert, “Optical, structural, and magnetic properties of cobalt nanostructure thin films,” J. Appl. Phys.105, 113508 (2009).
[CrossRef]

Schubert, E.

D. Schmidt, A. C. Kjerstad, T. Hofmann, R. Skomski, E. Schubert, and M. Schubert, “Optical, structural, and magnetic properties of cobalt nanostructure thin films,” J. Appl. Phys.105, 113508 (2009).
[CrossRef]

Schubert, M.

D. Schmidt, A. C. Kjerstad, T. Hofmann, R. Skomski, E. Schubert, and M. Schubert, “Optical, structural, and magnetic properties of cobalt nanostructure thin films,” J. Appl. Phys.105, 113508 (2009).
[CrossRef]

Shakiba, S.

R. N. Weinreb, S. Shakiba, and L. Zangwill, “Scanning laser polarimetry to measure the nerve fiber layer of normal and glaucomatous eyes,” Am. J. Ophthalmol.119, 627–636 (1995).
[PubMed]

Silbermann, B.

R. Hagen, S. Roch, and B. Silbermann, C* Algebras Numerical Analysis (Marcel Dekker, 2001).

Skomski, R.

D. Schmidt, A. C. Kjerstad, T. Hofmann, R. Skomski, E. Schubert, and M. Schubert, “Optical, structural, and magnetic properties of cobalt nanostructure thin films,” J. Appl. Phys.105, 113508 (2009).
[CrossRef]

Smith, M. H.

M. H. Smith, P. D. Burke, A. Lompado, E. A. Tanner, and L. W. Hillman, “Mueller matrix imaging polarimetry in dermatology,” Proc. SPIE3911, 210–216 (2000).
[CrossRef]

J. D. Howe, M. A. Miller, R. V. Blumer, T. E. Petty, M. A. Stevens, D. M. Teale, and M. H. Smith, “Polarization sensing for target acquisition and mine detection,” Proc. SPIE4133, 202–213 (2000).
[CrossRef]

Søndergård, E.

L. M. S. Aas, M. Kildemo, Y. Cohin, and E. Søndergård, “Determination of small tilt angles of short gasb nanopillars using uv-visible mueller matrix ellipsometry,” Thin Solid Films (2012).
[CrossRef]

I. S. Nerbø, S. Le Roy, M. Foldyna, M. Kildemo, and E. Søndergård, “Characterization of inclined GaSb nanopillars by Mueller matrix ellipsometry,” J. Appl. Phys.108, 014307 (2010).
[CrossRef]

Stabo-Eeg, F.

F. Stabo-Eeg, M. Kildemo, I. Nerbø, and M. Lindgren, “Well-conditioned multiple laser Mueller matrix ellipsometer,” Opt. Eng.47, 073604 (2008).
[CrossRef]

Stamnes, J. J.

Stevens, M. A.

J. D. Howe, M. A. Miller, R. V. Blumer, T. E. Petty, M. A. Stevens, D. M. Teale, and M. H. Smith, “Polarization sensing for target acquisition and mine detection,” Proc. SPIE4133, 202–213 (2000).
[CrossRef]

Svensen, Ø.

Tanner, E. A.

M. H. Smith, P. D. Burke, A. Lompado, E. A. Tanner, and L. W. Hillman, “Mueller matrix imaging polarimetry in dermatology,” Proc. SPIE3911, 210–216 (2000).
[CrossRef]

Teale, D. M.

J. D. Howe, M. A. Miller, R. V. Blumer, T. E. Petty, M. A. Stevens, D. M. Teale, and M. H. Smith, “Polarization sensing for target acquisition and mine detection,” Proc. SPIE4133, 202–213 (2000).
[CrossRef]

Tompkins, H.

H. Tompkins and E. A. Irene, Handbook of Ellipsometry (William Andrew, 2005).
[CrossRef]

Wang, B.

O. Arteaga, J. Freudenthal, B. Wang, and B. Kahr, “Mueller matrix polarimetry with four photoelastic modulators: theory and calibration.” Appl. Optics51, 6805–6817 (2012).
[CrossRef]

Weinreb, R. N.

R. N. Weinreb, S. Shakiba, and L. Zangwill, “Scanning laser polarimetry to measure the nerve fiber layer of normal and glaucomatous eyes,” Am. J. Ophthalmol.119, 627–636 (1995).
[PubMed]

Wormeester, H.

T. Oates, H. Wormeester, and H. Arwin, “Characterization of plasmonic effects in thin films and metamaterials using spectroscopic ellipsometry,” Prog. Surf. Sci.86, 328–376 (2011).
[CrossRef]

Yang, J.

Zangwill, L.

R. N. Weinreb, S. Shakiba, and L. Zangwill, “Scanning laser polarimetry to measure the nerve fiber layer of normal and glaucomatous eyes,” Am. J. Ophthalmol.119, 627–636 (1995).
[PubMed]

Am. J. Ophthalmol.

R. N. Weinreb, S. Shakiba, and L. Zangwill, “Scanning laser polarimetry to measure the nerve fiber layer of normal and glaucomatous eyes,” Am. J. Ophthalmol.119, 627–636 (1995).
[PubMed]

Appl. Optics

O. Arteaga, J. Freudenthal, B. Wang, and B. Kahr, “Mueller matrix polarimetry with four photoelastic modulators: theory and calibration.” Appl. Optics51, 6805–6817 (2012).
[CrossRef]

G. E. Jellison and F. a. Modine, “Two-channel polarization modulation ellipsometer.” Appl. Optics29, 959–974 (1990).
[CrossRef]

E. Compain, S. Poirier, and B. Drevillon, “General and self-consistent method for the calibration of polarization modulators, polarimeters, and mueller-matrix ellipsometers.” Appl. Optics38, 3490–3502 (1999).
[CrossRef]

J. Appl. Phys.

D. Schmidt, A. C. Kjerstad, T. Hofmann, R. Skomski, E. Schubert, and M. Schubert, “Optical, structural, and magnetic properties of cobalt nanostructure thin films,” J. Appl. Phys.105, 113508 (2009).
[CrossRef]

I. S. Nerbø, S. Le Roy, M. Foldyna, M. Kildemo, and E. Søndergård, “Characterization of inclined GaSb nanopillars by Mueller matrix ellipsometry,” J. Appl. Phys.108, 014307 (2010).
[CrossRef]

J. Biomed. Opt.

P. G. Ellingsen, M. B. Lilledahl, L. M. S. Aas, C. d. L. Davies, and M. Kildemo, “Quantitative characterization of articular cartilage using Mueller matrix imaging and multiphoton microscopy,” J. Biomed. Opt.16, 116002 (2011).
[CrossRef] [PubMed]

J. Mod. Opt.

L. Aas, P. Ellingsen, M. Kildemo, and M. Lindgren, “Dynamic Response of a fast near infra-red Mueller matrix ellipsometer,” J. Mod. Opt.57, 1603–1610 (2010).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

M. Foldyna, A. D. Martino, R. Ossikovski, E. Garcia-Caurel, and C. Licitra, “Characterization of grating structures by Mueller polarimetry in presence of strong depolarization due to finite spot size,” Opt. Commun.282, 735–741 (2009).
[CrossRef]

Opt. Eng.

F. Stabo-Eeg, M. Kildemo, I. Nerbø, and M. Lindgren, “Well-conditioned multiple laser Mueller matrix ellipsometer,” Opt. Eng.47, 073604 (2008).
[CrossRef]

Opt. Express

Phys. Rev. Lett.

T. Germer, “Measurement of roughness of two interfaces of a dielectric film by scattering ellipsometry,” Phys. Rev. Lett.85, 349–352 (2000).
[CrossRef] [PubMed]

Phys. Stat. Sol. (a)

S. B. Hatit, M. Foldyna, A. De Martino, and B. Drévillon, “Angle-resolved Mueller polarimeter using a microscope objective,” Phys. Stat. Sol. (a)205, 743–747 (2008).
[CrossRef]

Proc. SPIE

M. H. Smith, P. D. Burke, A. Lompado, E. A. Tanner, and L. W. Hillman, “Mueller matrix imaging polarimetry in dermatology,” Proc. SPIE3911, 210–216 (2000).
[CrossRef]

J. D. Howe, M. A. Miller, R. V. Blumer, T. E. Petty, M. A. Stevens, D. M. Teale, and M. H. Smith, “Polarization sensing for target acquisition and mine detection,” Proc. SPIE4133, 202–213 (2000).
[CrossRef]

Prog. Surf. Sci.

T. Oates, H. Wormeester, and H. Arwin, “Characterization of plasmonic effects in thin films and metamaterials using spectroscopic ellipsometry,” Prog. Surf. Sci.86, 328–376 (2011).
[CrossRef]

Rev. Sci. Instrum.

E. Compain and B. Drevillon, “Complete high-frequency measurement of Mueller matrices based on a new coupled-phase modulator,” Rev. Sci. Instrum.68, 2671 (1997).
[CrossRef]

Sci. Am.

J. H. Holland, “Genetic algorithms,” Sci. Am.267, 44–50 (1992).
[CrossRef]

Thin Solid Films

E. Garcia-Caurel, A. D. Martino, and B. Drevillon, “Spectroscopic Mueller polarimeter based on liquid crystal devices,” Thin Solid Films455, 120–123 (2004).
[CrossRef]

L. Aas, P. Ellingsen, and M. Kildemo, “Near infra-red Mueller matrix imaging system and application to retardance imaging of strain,” Thin Solid Films519, 2737–2741 (2010).
[CrossRef]

L. M. S. Aas, M. Kildemo, Y. Cohin, and E. Søndergård, “Determination of small tilt angles of short gasb nanopillars using uv-visible mueller matrix ellipsometry,” Thin Solid Films (2012).
[CrossRef]

Other

A. Alvarez-Herrero, V. Martínez-Pillet, J. del Toro Iniesta, and V. Domingo, “The IMaX polarimeter for the solar telescope SUNRISE of the NASA long duration balloon program,” in API’09, (2010), pp. 05002.

R. Azzam and N. Bashara, Ellipsometry and Polarized light (North-Holland, 1977).

H. Fujiwara, Spectroscopic Ellipsometry: Principles and Applications (John Wiley & Sons, Chichester, England; Hoboken, NJ, 2007).
[CrossRef]

H. Tompkins and E. A. Irene, Handbook of Ellipsometry (William Andrew, 2005).
[CrossRef]

J. M. Bennet, R. Chipman, and R. M. A. Azzam, “Polarized light,” in Handbook of Optics, M. Bass and V. Mahajan, eds. (McGraw-Hill, Inc., 2010), pp. 12.3–16.21.

D. Floreano and C. Mattiussi, Bio-Inspired Artificial Intelligence: Theories, Methods, and Technologies (The MIT Press, 2008).

A. Ben-Israel and T. N. E. Greville, Generalized Inverses: Theory and Applications (Springer-Verlag, 2003).

R. Hagen, S. Roch, and B. Silbermann, C* Algebras Numerical Analysis (Marcel Dekker, 2001).

C. S. Perone, “Pyevolve,” http://pyevolve.sourceforge.net/ .

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Figures (4)

Fig. 1
Fig. 1

(a) The measured retardance of a LCVR as a function of wavelength and the voltage applied. (b) The retardance of the LCVR measured at 0 V with the temperature stabilized at 26°C, 28°C and 30°C. The figure shows the relative difference to the LCVR retardance at 24°C.

Fig. 2
Fig. 2

Schematic drawing of a typical spectroscopic Mueller matrix polarimeter using liquid crystal variable retarders (LCVR), a broad band light source and spectrometer.

Fig. 3
Fig. 3

The inverse of the generalized condition number of W as a function of wavelength. Figure (a) shows the comparison between the best designs for a 2 × 2, 2 × 3 and 2 × 4 states system, where the systems are presented in terms of the number of retardance (voltage) states for each of the two LCVRs making up the PSG or the PSA. Figure (b) shows both the simulated, measured and calibrated inverse condition number of the experimentally realized polarimeter with 2 × 3 states.

Fig. 4
Fig. 4

The measured spectroscopic Mueller matrix of air normalized to the m11 element.

Tables (2)

Tables Icon

Table 1 General settings for the genetic optimization

Tables Icon

Table 2 Configuration of the optimal polarimeters

Equations (7)

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

S = [ s 1 s 2 s 3 s 4 ] = [ E x ( t ) 2 + E y ( t ) 2 E x ( t ) 2 E y ( t ) 2 2 E x ( t ) E y ( t ) cos δ ( t ) 2 E x ( t ) E y ( t ) sin δ ( t ) ] ,
W = [ S W 1 , S W 2 , S W 3 , S W 4 , S W 5 , S W 6 ] , A = [ S A 1 , S A 2 , S A 3 , S A 4 , S A 5 , S A 6 ] T .
B i = A M i W .
C i = B 0 B i = W M i W and C i = B i B 0 = A M i A ,
Δ M M κ W κ A Δ B B + κ A Δ A A + κ W Δ W W ,
f = 1 e ,
e = n = 1 N λ ( 1 3 1 κ ( λ n ) ) 4 .

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