Abstract

A fast multichannel Stokes/Mueller polarimeter with no mechanically moving parts has been designed to have close to optimal performance from 430 – 2000 nm by applying a genetic algorithm. Stokes (Mueller) polarimeters are characterized by their ability to analyze the full Stokes (Mueller) vector (matrix) of the incident light (sample). This ability is characterized by the condition number, κ, which directly influences the measurement noise in polarimetric measurements. Due to the spectral dependence of the retardance in birefringent materials, it is not trivial to design a polarimeter using dispersive components. We present here both a method to do this optimization using a genetic algorithm, as well as simulation results. Our results include fast, broad-band polarimeter designs for spectrographic use, based on 2 and 3 Ferroelectric Liquid Crystals, whose material properties are taken from measured values. The results promise to reduce the measurement noise significantly over previous designs, up to a factor of 4.5 for a Mueller polarimeter, in addition to extending the spectral range.

© 2010 Optical Society of America

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References

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  1. A. M. Gandorfer, "Ferroelectric retarders as an alternative to piezoelastic modulators for use in solar Stokes vector polarimetry," Opt. Eng. 38, 1402-1408 (1999).
    [CrossRef]
  2. P. Collins, R. Redfern, and B. Sheehan, "Design, construction and calibration of the Galway astronomical Stokes polarimeter (GASP)," in AIP Conference Proceedings, D. Phelan, O. Ryan, and A. Shearer, eds. (AIP, Edinburgh (Scotland), 2008), vol. 984, p. 241.
    [CrossRef]
  3. 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 Proceedings of API’09, E. Garcia-Caurel, ed. (EPJ Web of Conferences, 2010), vol. 5, p. 05002.
  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," 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, 202-213 (2000).
  5. M. H. Smith, P. D. Burke, A. Lompado, E. A. Tanner, and L. W. Hillman, "Mueller matrix imaging polarimetry in dermatology," in Biomedical Diagnostic, Guidance, and Surgical-Assist Systems II, T. Vo-Dinh, W. S. Grundfest, and D. A. Benaron, eds., Proc. SPIE 3911, 210-216 (2000).
  6. 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]
  7. 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]
  8. 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]
  9. L. Jin, M. Kasahara, B. Gelloz, and K. Takizawa, "Polarization properties of scattered light from macrorough surfaces," Opt. Lett. 35, 595-597 (2010).
    [CrossRef] [PubMed]
  10. T. A. Germer, "Polarized light scattering by microroughness and small defects in dielectric layers," J. Opt. Soc. Am. A 18, 1279-1288 (2001).
    [CrossRef]
  11. T. Germer, "Measurement of roughness of two interfaces of a dielectric film by scattering ellipsometry," Phys. Rev. Lett. 85, 349-352 (2000).
    [CrossRef] [PubMed]
  12. F. Stabo-Eeg, M. Kildemo, I. Nerbø, and M. Lindgren, "Well-conditioned multiple laser Mueller matrix ellipsometer," Opt. Eng. 47, 073604 (2008).
    [CrossRef]
  13. J. S. Tyo, "Noise equalization in Stokes parameter images obtained by use of variable-retardance polarimeters," Opt. Lett. 25, 1198-1200 (2000).
    [CrossRef]
  14. 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]
  15. R. M. A. Azzam, and A. De, "Optimal beam splitters for the division-of-amplitude photopolarimeter," J. Opt. Soc. Am. A 20, 955-958 (2003).
    [CrossRef]
  16. R. M. A. Azzam, "Photopolarimetric measurement of the Mueller matrix by Fourier analysis of a single detected signal," Opt. Lett. 2, 148 (1978).
    [CrossRef] [PubMed]
  17. J. M. Bueno, "Polarimetry using liquid-crystal variable retarders: theory and calibration," J. Opt. A, Pure Appl. Opt. 2, 216-222 (2000).
    [CrossRef]
  18. E. Garcia-Caurel, A. D. Martino, and B. Drévillon, "Spectroscopic Mueller polarimeter based on liquid crystal devices," Thin Solid Films 455-456, 120-123 (2004).
    [CrossRef]
  19. J. Ladstein, M. Kildemo, G. Svendsen, I. Nerbø, and F. Stabo-Eeg, "Characterisation of liquid crystals for broadband optimal design of Mueller matrix ellipsometers," in Liquid Crystals and Applications in Optics, M. Glogarova, P. Palffy-Muhoray, and M. Copic, eds. Proc. SPIE 6587, 65870D (2007).
  20. L. M. S. Aas, P. G. Ellingsen, M. Kildemo, and M. Lindgren, "Dynamic Response of a fast near infra-red Mueller matrix ellipsometer," J. Mod. Opt. (accepted).
    [CrossRef]
  21. D. Cattelan, E. Garcia-Caurel, A. De Martino, and B. Drevillon, "Device and method for taking spectroscopic polarimetric measurements in the visible and near-infrared ranges," Patent application 2937732, France (2010).
  22. J. H. Holland, "Genetic algorithms," Sci. Am. 267, 44-50 (1992).
  23. D. Floreano, and C. Mattiussi, Bio-Inspired Artificial Intelligence: Theories, Methods, and Technologies (The MIT Press, 2008).
  24. A. Kudla, "Application of the genetic algorithms in spectroscopic ellipsometry," Thin Solid Films 455-456, 804-808 (2004).
    [CrossRef]
  25. G. Cormier, and R. Boudreau, "Genetic algorithm for ellipsometric data inversion of absorbing layers," J. Opt. Soc. Am. A 17, 129-134 (2000).
    [CrossRef]
  26. V. R. Fernandes, C. M. S. Vicente, N. Wada, P. S. André, and R. A. S. Ferreira, "Multi-objective genetic algorithm applied to spectroscopic ellipsometry of organic-inorganic hybrid planar waveguides," Opt. Express 18, 16580-16586 (2010).
    [CrossRef] [PubMed]
  27. F. Stabo-Eeg, M. Kildemo, E. Garcia-Caurel, and M. Lindgren, "Design and characterization of achromatic 132◦ retarders in CaF2 and fused silica," J. Mod. Opt. 55, 2203-2214 (2008).
    [CrossRef]
  28. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing (Cambridge University Press, 2007).
  29. E. Compain, S. Poirier, and B. Drevillon, "General and self-consistent method for the calibration of polarization modulators, polarimeters, and Mueller-matrix ellipsometers," Appl. Opt. 38, 3490-3502 (1999).
    [CrossRef]
  30. J. Ladstein, F. Stabo-Eeg, E. Garcia-Caurel, and M. Kildemo, "Fast near-infra-red spectroscopic Mueller matrix ellipsometer based on ferroelectric liquid crystal retarders," Phys. Status Solidi C 5, 1097-1100 (2008).
    [CrossRef]

2010 (3)

2009 (1)

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]

2008 (3)

F. Stabo-Eeg, M. Kildemo, E. Garcia-Caurel, and M. Lindgren, "Design and characterization of achromatic 132◦ retarders in CaF2 and fused silica," J. Mod. Opt. 55, 2203-2214 (2008).
[CrossRef]

J. Ladstein, F. Stabo-Eeg, E. Garcia-Caurel, and M. Kildemo, "Fast near-infra-red spectroscopic Mueller matrix ellipsometer based on ferroelectric liquid crystal retarders," Phys. Status Solidi C 5, 1097-1100 (2008).
[CrossRef]

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

2004 (2)

E. Garcia-Caurel, A. D. Martino, and B. Drévillon, "Spectroscopic Mueller polarimeter based on liquid crystal devices," Thin Solid Films 455-456, 120-123 (2004).
[CrossRef]

A. Kudla, "Application of the genetic algorithms in spectroscopic ellipsometry," Thin Solid Films 455-456, 804-808 (2004).
[CrossRef]

2003 (1)

2001 (1)

2000 (5)

1999 (2)

A. M. Gandorfer, "Ferroelectric retarders as an alternative to piezoelastic modulators for use in solar Stokes vector polarimetry," Opt. Eng. 38, 1402-1408 (1999).
[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. Opt. 38, 3490-3502 (1999).
[CrossRef]

1995 (1)

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 (1)

J. H. Holland, "Genetic algorithms," Sci. Am. 267, 44-50 (1992).

1978 (1)

Aas, L. M. S.

L. M. S. Aas, P. G. Ellingsen, M. Kildemo, and M. Lindgren, "Dynamic Response of a fast near infra-red Mueller matrix ellipsometer," J. Mod. Opt. (accepted).
[CrossRef]

André, P. S.

Azzam, R. M. A.

Boudreau, R.

Bueno, J. M.

J. M. Bueno, "Polarimetry using liquid-crystal variable retarders: theory and calibration," J. Opt. A, Pure Appl. Opt. 2, 216-222 (2000).
[CrossRef]

Compain, E.

Cormier, G.

De, A.

Dereniak, E. L.

Descour, M. R.

Drevillon, B.

Drévillon, B.

E. Garcia-Caurel, A. D. Martino, and B. Drévillon, "Spectroscopic Mueller polarimeter based on liquid crystal devices," Thin Solid Films 455-456, 120-123 (2004).
[CrossRef]

Ellingsen, P. G.

L. M. S. Aas, P. G. Ellingsen, M. Kildemo, and M. Lindgren, "Dynamic Response of a fast near infra-red Mueller matrix ellipsometer," J. Mod. Opt. (accepted).
[CrossRef]

Fernandes, V. R.

Ferreira, R. A. S.

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]

Gandorfer, A. M.

A. M. Gandorfer, "Ferroelectric retarders as an alternative to piezoelastic modulators for use in solar Stokes vector polarimetry," Opt. Eng. 38, 1402-1408 (1999).
[CrossRef]

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]

F. Stabo-Eeg, M. Kildemo, E. Garcia-Caurel, and M. Lindgren, "Design and characterization of achromatic 132◦ retarders in CaF2 and fused silica," J. Mod. Opt. 55, 2203-2214 (2008).
[CrossRef]

J. Ladstein, F. Stabo-Eeg, E. Garcia-Caurel, and M. Kildemo, "Fast near-infra-red spectroscopic Mueller matrix ellipsometer based on ferroelectric liquid crystal retarders," Phys. Status Solidi C 5, 1097-1100 (2008).
[CrossRef]

E. Garcia-Caurel, A. D. Martino, and B. Drévillon, "Spectroscopic Mueller polarimeter based on liquid crystal devices," Thin Solid Films 455-456, 120-123 (2004).
[CrossRef]

Gelloz, B.

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.

Holland, J. H.

J. H. Holland, "Genetic algorithms," Sci. Am. 267, 44-50 (1992).

Jin, L.

Kasahara, M.

Kemme, S. A.

Kildemo, 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]

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

J. Ladstein, F. Stabo-Eeg, E. Garcia-Caurel, and M. Kildemo, "Fast near-infra-red spectroscopic Mueller matrix ellipsometer based on ferroelectric liquid crystal retarders," Phys. Status Solidi C 5, 1097-1100 (2008).
[CrossRef]

F. Stabo-Eeg, M. Kildemo, E. Garcia-Caurel, and M. Lindgren, "Design and characterization of achromatic 132◦ retarders in CaF2 and fused silica," J. Mod. Opt. 55, 2203-2214 (2008).
[CrossRef]

L. M. S. Aas, P. G. Ellingsen, M. Kildemo, and M. Lindgren, "Dynamic Response of a fast near infra-red Mueller matrix ellipsometer," J. Mod. Opt. (accepted).
[CrossRef]

Kudla, A.

A. Kudla, "Application of the genetic algorithms in spectroscopic ellipsometry," Thin Solid Films 455-456, 804-808 (2004).
[CrossRef]

Ladstein, J.

J. Ladstein, F. Stabo-Eeg, E. Garcia-Caurel, and M. Kildemo, "Fast near-infra-red spectroscopic Mueller matrix ellipsometer based on ferroelectric liquid crystal retarders," Phys. Status Solidi C 5, 1097-1100 (2008).
[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]

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]

Lindgren, M.

F. Stabo-Eeg, M. Kildemo, E. Garcia-Caurel, and M. Lindgren, "Design and characterization of achromatic 132◦ retarders in CaF2 and fused silica," J. Mod. Opt. 55, 2203-2214 (2008).
[CrossRef]

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

L. M. S. Aas, P. G. Ellingsen, M. Kildemo, and M. Lindgren, "Dynamic Response of a fast near infra-red Mueller matrix ellipsometer," J. Mod. Opt. (accepted).
[CrossRef]

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. Drévillon, "Spectroscopic Mueller polarimeter based on liquid crystal devices," Thin Solid Films 455-456, 120-123 (2004).
[CrossRef]

Nerbø, I.

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

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]

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]

Phipps, G. S.

Poirier, S.

Sabatke, D. S.

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]

Søndergård, E.

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]

F. Stabo-Eeg, M. Kildemo, E. Garcia-Caurel, and M. Lindgren, "Design and characterization of achromatic 132◦ retarders in CaF2 and fused silica," J. Mod. Opt. 55, 2203-2214 (2008).
[CrossRef]

J. Ladstein, F. Stabo-Eeg, E. Garcia-Caurel, and M. Kildemo, "Fast near-infra-red spectroscopic Mueller matrix ellipsometer based on ferroelectric liquid crystal retarders," Phys. Status Solidi C 5, 1097-1100 (2008).
[CrossRef]

Sweatt, W. C.

Takizawa, K.

Tyo, J. S.

Vicente, C. M. S.

Wada, N.

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]

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. (1)

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. Opt. (1)

J. Appl. Phys. (1)

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. Mod. Opt. (2)

L. M. S. Aas, P. G. Ellingsen, M. Kildemo, and M. Lindgren, "Dynamic Response of a fast near infra-red Mueller matrix ellipsometer," J. Mod. Opt. (accepted).
[CrossRef]

F. Stabo-Eeg, M. Kildemo, E. Garcia-Caurel, and M. Lindgren, "Design and characterization of achromatic 132◦ retarders in CaF2 and fused silica," J. Mod. Opt. 55, 2203-2214 (2008).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

J. M. Bueno, "Polarimetry using liquid-crystal variable retarders: theory and calibration," J. Opt. A, Pure Appl. Opt. 2, 216-222 (2000).
[CrossRef]

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

Opt. Commun. (1)

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. (2)

A. M. Gandorfer, "Ferroelectric retarders as an alternative to piezoelastic modulators for use in solar Stokes vector polarimetry," Opt. Eng. 38, 1402-1408 (1999).
[CrossRef]

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 (1)

Opt. Lett. (4)

Phys. Rev. Lett. (1)

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. Status Solidi C (1)

J. Ladstein, F. Stabo-Eeg, E. Garcia-Caurel, and M. Kildemo, "Fast near-infra-red spectroscopic Mueller matrix ellipsometer based on ferroelectric liquid crystal retarders," Phys. Status Solidi C 5, 1097-1100 (2008).
[CrossRef]

Sci. Am. (1)

J. H. Holland, "Genetic algorithms," Sci. Am. 267, 44-50 (1992).

Thin Solid Films (2)

A. Kudla, "Application of the genetic algorithms in spectroscopic ellipsometry," Thin Solid Films 455-456, 804-808 (2004).
[CrossRef]

E. Garcia-Caurel, A. D. Martino, and B. Drévillon, "Spectroscopic Mueller polarimeter based on liquid crystal devices," Thin Solid Films 455-456, 120-123 (2004).
[CrossRef]

Other (8)

J. Ladstein, M. Kildemo, G. Svendsen, I. Nerbø, and F. Stabo-Eeg, "Characterisation of liquid crystals for broadband optimal design of Mueller matrix ellipsometers," in Liquid Crystals and Applications in Optics, M. Glogarova, P. Palffy-Muhoray, and M. Copic, eds. Proc. SPIE 6587, 65870D (2007).

P. Collins, R. Redfern, and B. Sheehan, "Design, construction and calibration of the Galway astronomical Stokes polarimeter (GASP)," in AIP Conference Proceedings, D. Phelan, O. Ryan, and A. Shearer, eds. (AIP, Edinburgh (Scotland), 2008), vol. 984, p. 241.
[CrossRef]

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 Proceedings of API’09, E. Garcia-Caurel, ed. (EPJ Web of Conferences, 2010), vol. 5, p. 05002.

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," 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, 202-213 (2000).

M. H. Smith, P. D. Burke, A. Lompado, E. A. Tanner, and L. W. Hillman, "Mueller matrix imaging polarimetry in dermatology," in Biomedical Diagnostic, Guidance, and Surgical-Assist Systems II, T. Vo-Dinh, W. S. Grundfest, and D. A. Benaron, eds., Proc. SPIE 3911, 210-216 (2000).

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

D. Cattelan, E. Garcia-Caurel, A. De Martino, and B. Drevillon, "Device and method for taking spectroscopic polarimetric measurements in the visible and near-infrared ranges," Patent application 2937732, France (2010).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing (Cambridge University Press, 2007).

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Figures (6)

Fig. 1
Fig. 1

(a) A Stokes polarimeter measures the polarization state of an arbitrary light source using a Polarization State Analyzer (PSA). (b) A Mueller polarimeter measures how the polarization state of light, generated by with a Polarization State Generator (PSG), is changed by a sample.

Fig. 2
Fig. 2

Sketch of a PSA consisting of 3 FLC’s, 3 waveplates (WP), each with a retardance δ and an orientation θ relative to the transmission axis of a polarizer.

Fig. 3
Fig. 3

The four essential processes in a genetic algorithm are shown above. Sexual reproduction is performed by multi-point genetic crossover, giving rise to the next generation of individuals. Mutation can be simulated with simple bit negation (e.g. 0 → 1 and vice versa). Development is the process where a genotype is interpreted into its phenotype, i.e. the binary genome is interpreted as a polarimeter design. In the mating contest, one evaluates the fitness of each individual’s phenotype, and let the more fit individuals reproduce with higher probability than the less fit individuals.

Fig. 4
Fig. 4

Inverse condition number for the best GA-generated 3-FLC design. For comparison, we show the inverse condition number of the patented 3-FLC design [21].

Fig. 5
Fig. 5

Convergence of fitness as a function of generation number. μ and σ refer to the average and standard deviation of the population’s fitness, respectively. The best result from this simulation is the one shown in Fig. 4.

Fig. 6
Fig. 6

Condition number for two designs using 2 FLC retarders and 2 waveplates. By optimizing κ(λ) over a narrower part of the spectrum, we can design good polarimeters with fewer components. The polarimeter designs labeled “Visible” and “IR” show our two designs, optimized for 430 nm < λ < 1100 nm and 800 nm < λ < 1700 nm, respectively. For comparison with our “NIR” design, we show the previous simulated design from Ref. [30]. The curve labeled “Commercial” shows the measured condition number of a commercial instrument (MM16, Horiba, 2006) based on the same (FLC) technology.

Tables (3)

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Table 2 Genetic Algorithm parameters. The “crossover rate” is the probability for two parents to undergo sexual reproduction (the alternative being asexual reproduction). The parameter “crossover points” refer to the number of points where we cut the genome during crossover (sexual reproduction). “Mutation rate” is the probability for any given individual to undergo one or several bit flip mutations in one generation

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Table 1 Orientation angles, θ, and normalized thicknesses L, of the components of the best 3-FLC polarimeter. (WP = (fixed) waveplate)

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Table 3 Orientation angle, θ, and normalized thickness, L, of the 2-FLC polarimeters shown in Fig. 6

Equations (4)

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Δ M M κ W κ A Δ B B + κ A Δ A A + κ W Δ W W .
e = 1 N λ n = 1 N λ ( κ 1 ( λ n ) 1 / 3 ) 4 .
f = 1 e .
δ 2 π L [ A UV ( λ 2 λ UV 2 ) 1 / 2 A IR ( λ IR 2 λ 2 ) 1 / 2 ] ,

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