Abstract

Decomposition methods have been applied to in-plane Mueller matrix ellipsometric scattering data of the Spectralon reflectance standard. Data were measured at the wavelengths 532 nm and 1500 nm, using an achromatic optimal Mueller matrix scatterometer applying a photomultiplier tube and a high gain InGaAs detector for the two wavelengths. A parametric model with physical significance was deduced through analysis of the product decomposed matrices. It is found that when the data are analyzed as a function of the scattering angle, similar to particle scattering, the matrix elements are largely independent of incidence angle. To the first order, we propose that a Guassian lineshape is appropriate to describe the polarization index, while the decomposed diagonal elements of the retardance matrix have a form resembling Rayleigh single scattering. New models are proposed for the off diagonal elements of the measured Mueller matrix.

© 2013 OSA

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  1. Ø. Svensen, M. Kildemo, J. Maria, J. J. Stamnes, and Ø. Frette, “Mueller matrix measurements and modeling pertaining to spectralon white reflectance standards,” Opt. Express20, 15045–15053 (2012).
    [CrossRef] [PubMed]
  2. T. A. Germer and H. J. Patrick, “Mueller matrix bidirectional reflectance distribution function measurements and modeling of diffuse reflectance standards,” Proc. SPIE8160, 81600D (2011).
    [CrossRef]
  3. D. A. Haner, B. T. McGuckin, and C. J. Bruegge, “Polarization characteristics of spectralon illuminated by coherent light,” Appl. Opt.38, 6350–6356 (1999).
    [CrossRef]
  4. A. Bhandari, B. Hamre, Ø. Frette, L. Zhao, J. J. Stamnes, and M. Kildemo, “Bidirectional reflectance distribution function of spectralon white reflectance standard illuminated by incoherent unpolarized and plane-polarized light,” Appl. Opt.50, 2431–2442 (2011).
    [CrossRef] [PubMed]
  5. T. A. Leskova, P. A. Letnes, A. A. Maradudin, T. Nordam, and I. Simonsen, “The scattering of light from two-dimensional randomly rough surfaces,” Proc. SPIE8172, 817208 (2011).
  6. I. Simonsen, A. A. Maradudin, and T. A. Leskova, “Scattering of electromagnetic waves from two-dimensional randomly rough penetrable surfaces,” Phys. Rev. Lett.104, 223904 (2010).
    [CrossRef] [PubMed]
  7. I. Simonsen, A. A. Maradudin, and T. A. Leskova, “Scattering of electromagnetic waves from two-dimensional randomly rough perfectly conducting surfaces: The full angular intensity distribution,” Phys. Rev. A81, 013806 (2010).
    [CrossRef]
  8. N. Ghosh, J. Soni, M. Wood, M. Wallenberg, and I. Vitkin, “Mueller matrix polarimetry for the characterization of complex random medium like biological tissues,” Pramana75, 1071–1086 (2010).
    [CrossRef]
  9. N. Ghosh and I. A. Vitkin, “Tissue polarimetry: concepts, challenges, applications, and outlook,” J. Biomed. Opt.16, 110801 (2011).
    [CrossRef] [PubMed]
  10. A. Pierangelo, S. Manhas, A. Benali, M. R. Antonelli, T. Novikova, P. Validire, B. Gayet, and A. De Martino, “Use of mueller polarimetric imaging for the staging of human colon cancer,” Proc. SPIE7895, 78950E (2011).
    [CrossRef]
  11. V. V. Tuchin, L. V. Wang, and D. A. Zimnyakov, Optical Polarization in Biomedical Applications (Berlin Heidelberg, 2006).
  12. S. Kumar, H. Purwar, R. Ossikovski, I. A. Vitkin, and N. Ghosh, “Comparative study of differential matrix and extended polar decomposition formalisms for polarimetric characterization of complex tissue-like turbid media,” Journal of Biomedical Optics17, 105006–105006 (2012).
    [CrossRef] [PubMed]
  13. R. Ossikovski, A. D. Martino, and S. Guyot, “Forward and reverse product decompositions of depolarizing mueller matrices,” Opt. Lett.32, 689–691 (2007).
    [CrossRef] [PubMed]
  14. R. Ossikovski, M. Anastasiadou, S. Ben Hatit, E. Garcia-Caurel, and A. De Martino, “Depolarizing mueller matrices: how to decompose them?” Phys. Status Solidi (a)205, 720–727 (2008).
    [CrossRef]
  15. R. Ossikovski, “Analysis of depolarizing mueller matrices through a symmetric decomposition,” J. Opt. Soc. Am. A26, 1109–1118 (2009).
    [CrossRef]
  16. R. Ossikovski, “Differential matrix formalism for depolarizing anisotropic media,” Opt. Lett.36, 2330–2332 (2011).
    [CrossRef] [PubMed]
  17. S.-Y. Lu and R. A. Chipman, “Interpretation of mueller matrices based on polar decomposition,” J. Opt. Soc. Am. A13, 1106–1113 (1996).
    [CrossRef]
  18. S. Manhas, M. K. Swami, P. Buddhiwant, N. Ghosh, P. K. Gupta, and J. Singh, “Mueller matrix approach for determination of optical rotation in chiral turbid media in backscattering geometry,” Opt. Express14, 190–202 (2006).
    [CrossRef] [PubMed]
  19. N. Ortega-Quijano and J. L. Arce-Diego, “Mueller matrix differential decomposition.” Opt. lett.36, 1942–4 (2011).
    [CrossRef] [PubMed]
  20. H. D. Noble and R. a. Chipman, “Mueller matrix roots algorithm and computational considerations.” Opt. Express20, 17–31 (2012).
    [CrossRef] [PubMed]
  21. H. Noble, S. McClain, and R. Chipman, “Mueller matrix roots depolarization parameters,” Appl. Optics51, 735–744 (2012).
    [CrossRef]
  22. C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles Interscience (J. Wiley & Sons, New York, 1983).
  23. P. Hauge, R. Muller, and C. Smith, “Conventions and formulas for using the mueller-stokes calculus in ellipsometry,” Surf. Sci.96, 81–107 (1980).
    [CrossRef]
  24. R. Azzam and N. Bashara, Ellipsometry and Polarized Light (North Holland, 1977).
  25. J. J. Gil and E. Bernabeu, “A depolarization criterion in mueller matrices,” Opt. Acta32, 259–261 (1985).
    [CrossRef]
  26. S. R. Cloude, “Conditions for the physical realisability of matrix operators in polarimetry,” Proc. SPIE1166, 177–185 (1989).
    [CrossRef]
  27. F. Stabo-Eeg, M. Kildemo, I. S. Nerbø, and M. Lindgren, “Well-conditioned multiple laser mueller matrix ellipsometer,” Opt. Eng.47, 073604–073604–9 (2008).
    [CrossRef]
  28. R. Ossikovski, M. Anastasiadou, and A. D. Martino, “Product decompositions of depolarizing mueller matrices with negative determinants,” Opt. Commun.281, 2406–2410 (2008).
    [CrossRef]
  29. R. L. White, “Polarization in reflection nebulae. I - Scattering properties of interstellar grains,” Astrophys. J.229, 954–961 (1979).
    [CrossRef]
  30. A. Erbe, K. Tauer, and R. Sigel, “Ellipsometric light scattering for the characterization of thin layers on dispersed colloidal particles,” Phys. Rev. E73, 031406 (2006).
    [CrossRef]

2012 (4)

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

S. Kumar, H. Purwar, R. Ossikovski, I. A. Vitkin, and N. Ghosh, “Comparative study of differential matrix and extended polar decomposition formalisms for polarimetric characterization of complex tissue-like turbid media,” Journal of Biomedical Optics17, 105006–105006 (2012).
[CrossRef] [PubMed]

H. D. Noble and R. a. Chipman, “Mueller matrix roots algorithm and computational considerations.” Opt. Express20, 17–31 (2012).
[CrossRef] [PubMed]

H. Noble, S. McClain, and R. Chipman, “Mueller matrix roots depolarization parameters,” Appl. Optics51, 735–744 (2012).
[CrossRef]

2011 (7)

R. Ossikovski, “Differential matrix formalism for depolarizing anisotropic media,” Opt. Lett.36, 2330–2332 (2011).
[CrossRef] [PubMed]

N. Ortega-Quijano and J. L. Arce-Diego, “Mueller matrix differential decomposition.” Opt. lett.36, 1942–4 (2011).
[CrossRef] [PubMed]

T. A. Germer and H. J. Patrick, “Mueller matrix bidirectional reflectance distribution function measurements and modeling of diffuse reflectance standards,” Proc. SPIE8160, 81600D (2011).
[CrossRef]

N. Ghosh and I. A. Vitkin, “Tissue polarimetry: concepts, challenges, applications, and outlook,” J. Biomed. Opt.16, 110801 (2011).
[CrossRef] [PubMed]

A. Pierangelo, S. Manhas, A. Benali, M. R. Antonelli, T. Novikova, P. Validire, B. Gayet, and A. De Martino, “Use of mueller polarimetric imaging for the staging of human colon cancer,” Proc. SPIE7895, 78950E (2011).
[CrossRef]

A. Bhandari, B. Hamre, Ø. Frette, L. Zhao, J. J. Stamnes, and M. Kildemo, “Bidirectional reflectance distribution function of spectralon white reflectance standard illuminated by incoherent unpolarized and plane-polarized light,” Appl. Opt.50, 2431–2442 (2011).
[CrossRef] [PubMed]

T. A. Leskova, P. A. Letnes, A. A. Maradudin, T. Nordam, and I. Simonsen, “The scattering of light from two-dimensional randomly rough surfaces,” Proc. SPIE8172, 817208 (2011).

2010 (3)

I. Simonsen, A. A. Maradudin, and T. A. Leskova, “Scattering of electromagnetic waves from two-dimensional randomly rough penetrable surfaces,” Phys. Rev. Lett.104, 223904 (2010).
[CrossRef] [PubMed]

I. Simonsen, A. A. Maradudin, and T. A. Leskova, “Scattering of electromagnetic waves from two-dimensional randomly rough perfectly conducting surfaces: The full angular intensity distribution,” Phys. Rev. A81, 013806 (2010).
[CrossRef]

N. Ghosh, J. Soni, M. Wood, M. Wallenberg, and I. Vitkin, “Mueller matrix polarimetry for the characterization of complex random medium like biological tissues,” Pramana75, 1071–1086 (2010).
[CrossRef]

2009 (1)

2008 (3)

R. Ossikovski, M. Anastasiadou, S. Ben Hatit, E. Garcia-Caurel, and A. De Martino, “Depolarizing mueller matrices: how to decompose them?” Phys. Status Solidi (a)205, 720–727 (2008).
[CrossRef]

F. Stabo-Eeg, M. Kildemo, I. S. Nerbø, and M. Lindgren, “Well-conditioned multiple laser mueller matrix ellipsometer,” Opt. Eng.47, 073604–073604–9 (2008).
[CrossRef]

R. Ossikovski, M. Anastasiadou, and A. D. Martino, “Product decompositions of depolarizing mueller matrices with negative determinants,” Opt. Commun.281, 2406–2410 (2008).
[CrossRef]

2007 (1)

2006 (2)

S. Manhas, M. K. Swami, P. Buddhiwant, N. Ghosh, P. K. Gupta, and J. Singh, “Mueller matrix approach for determination of optical rotation in chiral turbid media in backscattering geometry,” Opt. Express14, 190–202 (2006).
[CrossRef] [PubMed]

A. Erbe, K. Tauer, and R. Sigel, “Ellipsometric light scattering for the characterization of thin layers on dispersed colloidal particles,” Phys. Rev. E73, 031406 (2006).
[CrossRef]

1999 (1)

1996 (1)

1989 (1)

S. R. Cloude, “Conditions for the physical realisability of matrix operators in polarimetry,” Proc. SPIE1166, 177–185 (1989).
[CrossRef]

1985 (1)

J. J. Gil and E. Bernabeu, “A depolarization criterion in mueller matrices,” Opt. Acta32, 259–261 (1985).
[CrossRef]

1980 (1)

P. Hauge, R. Muller, and C. Smith, “Conventions and formulas for using the mueller-stokes calculus in ellipsometry,” Surf. Sci.96, 81–107 (1980).
[CrossRef]

1979 (1)

R. L. White, “Polarization in reflection nebulae. I - Scattering properties of interstellar grains,” Astrophys. J.229, 954–961 (1979).
[CrossRef]

Anastasiadou, M.

R. Ossikovski, M. Anastasiadou, S. Ben Hatit, E. Garcia-Caurel, and A. De Martino, “Depolarizing mueller matrices: how to decompose them?” Phys. Status Solidi (a)205, 720–727 (2008).
[CrossRef]

R. Ossikovski, M. Anastasiadou, and A. D. Martino, “Product decompositions of depolarizing mueller matrices with negative determinants,” Opt. Commun.281, 2406–2410 (2008).
[CrossRef]

Antonelli, M. R.

A. Pierangelo, S. Manhas, A. Benali, M. R. Antonelli, T. Novikova, P. Validire, B. Gayet, and A. De Martino, “Use of mueller polarimetric imaging for the staging of human colon cancer,” Proc. SPIE7895, 78950E (2011).
[CrossRef]

Arce-Diego, J. L.

Azzam, R.

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

Bashara, N.

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

Ben Hatit, S.

R. Ossikovski, M. Anastasiadou, S. Ben Hatit, E. Garcia-Caurel, and A. De Martino, “Depolarizing mueller matrices: how to decompose them?” Phys. Status Solidi (a)205, 720–727 (2008).
[CrossRef]

Benali, A.

A. Pierangelo, S. Manhas, A. Benali, M. R. Antonelli, T. Novikova, P. Validire, B. Gayet, and A. De Martino, “Use of mueller polarimetric imaging for the staging of human colon cancer,” Proc. SPIE7895, 78950E (2011).
[CrossRef]

Bernabeu, E.

J. J. Gil and E. Bernabeu, “A depolarization criterion in mueller matrices,” Opt. Acta32, 259–261 (1985).
[CrossRef]

Bhandari, A.

Bohren, C.

C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles Interscience (J. Wiley & Sons, New York, 1983).

Bruegge, C. J.

Buddhiwant, P.

Chipman, R.

H. Noble, S. McClain, and R. Chipman, “Mueller matrix roots depolarization parameters,” Appl. Optics51, 735–744 (2012).
[CrossRef]

Chipman, R. a.

Cloude, S. R.

S. R. Cloude, “Conditions for the physical realisability of matrix operators in polarimetry,” Proc. SPIE1166, 177–185 (1989).
[CrossRef]

De Martino, A.

A. Pierangelo, S. Manhas, A. Benali, M. R. Antonelli, T. Novikova, P. Validire, B. Gayet, and A. De Martino, “Use of mueller polarimetric imaging for the staging of human colon cancer,” Proc. SPIE7895, 78950E (2011).
[CrossRef]

R. Ossikovski, M. Anastasiadou, S. Ben Hatit, E. Garcia-Caurel, and A. De Martino, “Depolarizing mueller matrices: how to decompose them?” Phys. Status Solidi (a)205, 720–727 (2008).
[CrossRef]

Erbe, A.

A. Erbe, K. Tauer, and R. Sigel, “Ellipsometric light scattering for the characterization of thin layers on dispersed colloidal particles,” Phys. Rev. E73, 031406 (2006).
[CrossRef]

Frette, Ø.

Garcia-Caurel, E.

R. Ossikovski, M. Anastasiadou, S. Ben Hatit, E. Garcia-Caurel, and A. De Martino, “Depolarizing mueller matrices: how to decompose them?” Phys. Status Solidi (a)205, 720–727 (2008).
[CrossRef]

Gayet, B.

A. Pierangelo, S. Manhas, A. Benali, M. R. Antonelli, T. Novikova, P. Validire, B. Gayet, and A. De Martino, “Use of mueller polarimetric imaging for the staging of human colon cancer,” Proc. SPIE7895, 78950E (2011).
[CrossRef]

Germer, T. A.

T. A. Germer and H. J. Patrick, “Mueller matrix bidirectional reflectance distribution function measurements and modeling of diffuse reflectance standards,” Proc. SPIE8160, 81600D (2011).
[CrossRef]

Ghosh, N.

S. Kumar, H. Purwar, R. Ossikovski, I. A. Vitkin, and N. Ghosh, “Comparative study of differential matrix and extended polar decomposition formalisms for polarimetric characterization of complex tissue-like turbid media,” Journal of Biomedical Optics17, 105006–105006 (2012).
[CrossRef] [PubMed]

N. Ghosh and I. A. Vitkin, “Tissue polarimetry: concepts, challenges, applications, and outlook,” J. Biomed. Opt.16, 110801 (2011).
[CrossRef] [PubMed]

N. Ghosh, J. Soni, M. Wood, M. Wallenberg, and I. Vitkin, “Mueller matrix polarimetry for the characterization of complex random medium like biological tissues,” Pramana75, 1071–1086 (2010).
[CrossRef]

S. Manhas, M. K. Swami, P. Buddhiwant, N. Ghosh, P. K. Gupta, and J. Singh, “Mueller matrix approach for determination of optical rotation in chiral turbid media in backscattering geometry,” Opt. Express14, 190–202 (2006).
[CrossRef] [PubMed]

Gil, J. J.

J. J. Gil and E. Bernabeu, “A depolarization criterion in mueller matrices,” Opt. Acta32, 259–261 (1985).
[CrossRef]

Gupta, P. K.

Guyot, S.

Hamre, B.

Haner, D. A.

Hauge, P.

P. Hauge, R. Muller, and C. Smith, “Conventions and formulas for using the mueller-stokes calculus in ellipsometry,” Surf. Sci.96, 81–107 (1980).
[CrossRef]

Huffman, D.

C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles Interscience (J. Wiley & Sons, New York, 1983).

Kildemo, M.

Kumar, S.

S. Kumar, H. Purwar, R. Ossikovski, I. A. Vitkin, and N. Ghosh, “Comparative study of differential matrix and extended polar decomposition formalisms for polarimetric characterization of complex tissue-like turbid media,” Journal of Biomedical Optics17, 105006–105006 (2012).
[CrossRef] [PubMed]

Leskova, T. A.

T. A. Leskova, P. A. Letnes, A. A. Maradudin, T. Nordam, and I. Simonsen, “The scattering of light from two-dimensional randomly rough surfaces,” Proc. SPIE8172, 817208 (2011).

I. Simonsen, A. A. Maradudin, and T. A. Leskova, “Scattering of electromagnetic waves from two-dimensional randomly rough penetrable surfaces,” Phys. Rev. Lett.104, 223904 (2010).
[CrossRef] [PubMed]

I. Simonsen, A. A. Maradudin, and T. A. Leskova, “Scattering of electromagnetic waves from two-dimensional randomly rough perfectly conducting surfaces: The full angular intensity distribution,” Phys. Rev. A81, 013806 (2010).
[CrossRef]

Letnes, P. A.

T. A. Leskova, P. A. Letnes, A. A. Maradudin, T. Nordam, and I. Simonsen, “The scattering of light from two-dimensional randomly rough surfaces,” Proc. SPIE8172, 817208 (2011).

Lindgren, M.

F. Stabo-Eeg, M. Kildemo, I. S. Nerbø, and M. Lindgren, “Well-conditioned multiple laser mueller matrix ellipsometer,” Opt. Eng.47, 073604–073604–9 (2008).
[CrossRef]

Lu, S.-Y.

Manhas, S.

A. Pierangelo, S. Manhas, A. Benali, M. R. Antonelli, T. Novikova, P. Validire, B. Gayet, and A. De Martino, “Use of mueller polarimetric imaging for the staging of human colon cancer,” Proc. SPIE7895, 78950E (2011).
[CrossRef]

S. Manhas, M. K. Swami, P. Buddhiwant, N. Ghosh, P. K. Gupta, and J. Singh, “Mueller matrix approach for determination of optical rotation in chiral turbid media in backscattering geometry,” Opt. Express14, 190–202 (2006).
[CrossRef] [PubMed]

Maradudin, A. A.

T. A. Leskova, P. A. Letnes, A. A. Maradudin, T. Nordam, and I. Simonsen, “The scattering of light from two-dimensional randomly rough surfaces,” Proc. SPIE8172, 817208 (2011).

I. Simonsen, A. A. Maradudin, and T. A. Leskova, “Scattering of electromagnetic waves from two-dimensional randomly rough penetrable surfaces,” Phys. Rev. Lett.104, 223904 (2010).
[CrossRef] [PubMed]

I. Simonsen, A. A. Maradudin, and T. A. Leskova, “Scattering of electromagnetic waves from two-dimensional randomly rough perfectly conducting surfaces: The full angular intensity distribution,” Phys. Rev. A81, 013806 (2010).
[CrossRef]

Maria, J.

Martino, A. D.

R. Ossikovski, M. Anastasiadou, and A. D. Martino, “Product decompositions of depolarizing mueller matrices with negative determinants,” Opt. Commun.281, 2406–2410 (2008).
[CrossRef]

R. Ossikovski, A. D. Martino, and S. Guyot, “Forward and reverse product decompositions of depolarizing mueller matrices,” Opt. Lett.32, 689–691 (2007).
[CrossRef] [PubMed]

McClain, S.

H. Noble, S. McClain, and R. Chipman, “Mueller matrix roots depolarization parameters,” Appl. Optics51, 735–744 (2012).
[CrossRef]

McGuckin, B. T.

Muller, R.

P. Hauge, R. Muller, and C. Smith, “Conventions and formulas for using the mueller-stokes calculus in ellipsometry,” Surf. Sci.96, 81–107 (1980).
[CrossRef]

Nerbø, I. S.

F. Stabo-Eeg, M. Kildemo, I. S. Nerbø, and M. Lindgren, “Well-conditioned multiple laser mueller matrix ellipsometer,” Opt. Eng.47, 073604–073604–9 (2008).
[CrossRef]

Noble, H.

H. Noble, S. McClain, and R. Chipman, “Mueller matrix roots depolarization parameters,” Appl. Optics51, 735–744 (2012).
[CrossRef]

Noble, H. D.

Nordam, T.

T. A. Leskova, P. A. Letnes, A. A. Maradudin, T. Nordam, and I. Simonsen, “The scattering of light from two-dimensional randomly rough surfaces,” Proc. SPIE8172, 817208 (2011).

Novikova, T.

A. Pierangelo, S. Manhas, A. Benali, M. R. Antonelli, T. Novikova, P. Validire, B. Gayet, and A. De Martino, “Use of mueller polarimetric imaging for the staging of human colon cancer,” Proc. SPIE7895, 78950E (2011).
[CrossRef]

Ortega-Quijano, N.

Ossikovski, R.

S. Kumar, H. Purwar, R. Ossikovski, I. A. Vitkin, and N. Ghosh, “Comparative study of differential matrix and extended polar decomposition formalisms for polarimetric characterization of complex tissue-like turbid media,” Journal of Biomedical Optics17, 105006–105006 (2012).
[CrossRef] [PubMed]

R. Ossikovski, “Differential matrix formalism for depolarizing anisotropic media,” Opt. Lett.36, 2330–2332 (2011).
[CrossRef] [PubMed]

R. Ossikovski, “Analysis of depolarizing mueller matrices through a symmetric decomposition,” J. Opt. Soc. Am. A26, 1109–1118 (2009).
[CrossRef]

R. Ossikovski, M. Anastasiadou, S. Ben Hatit, E. Garcia-Caurel, and A. De Martino, “Depolarizing mueller matrices: how to decompose them?” Phys. Status Solidi (a)205, 720–727 (2008).
[CrossRef]

R. Ossikovski, M. Anastasiadou, and A. D. Martino, “Product decompositions of depolarizing mueller matrices with negative determinants,” Opt. Commun.281, 2406–2410 (2008).
[CrossRef]

R. Ossikovski, A. D. Martino, and S. Guyot, “Forward and reverse product decompositions of depolarizing mueller matrices,” Opt. Lett.32, 689–691 (2007).
[CrossRef] [PubMed]

Patrick, H. J.

T. A. Germer and H. J. Patrick, “Mueller matrix bidirectional reflectance distribution function measurements and modeling of diffuse reflectance standards,” Proc. SPIE8160, 81600D (2011).
[CrossRef]

Pierangelo, A.

A. Pierangelo, S. Manhas, A. Benali, M. R. Antonelli, T. Novikova, P. Validire, B. Gayet, and A. De Martino, “Use of mueller polarimetric imaging for the staging of human colon cancer,” Proc. SPIE7895, 78950E (2011).
[CrossRef]

Purwar, H.

S. Kumar, H. Purwar, R. Ossikovski, I. A. Vitkin, and N. Ghosh, “Comparative study of differential matrix and extended polar decomposition formalisms for polarimetric characterization of complex tissue-like turbid media,” Journal of Biomedical Optics17, 105006–105006 (2012).
[CrossRef] [PubMed]

Sigel, R.

A. Erbe, K. Tauer, and R. Sigel, “Ellipsometric light scattering for the characterization of thin layers on dispersed colloidal particles,” Phys. Rev. E73, 031406 (2006).
[CrossRef]

Simonsen, I.

T. A. Leskova, P. A. Letnes, A. A. Maradudin, T. Nordam, and I. Simonsen, “The scattering of light from two-dimensional randomly rough surfaces,” Proc. SPIE8172, 817208 (2011).

I. Simonsen, A. A. Maradudin, and T. A. Leskova, “Scattering of electromagnetic waves from two-dimensional randomly rough penetrable surfaces,” Phys. Rev. Lett.104, 223904 (2010).
[CrossRef] [PubMed]

I. Simonsen, A. A. Maradudin, and T. A. Leskova, “Scattering of electromagnetic waves from two-dimensional randomly rough perfectly conducting surfaces: The full angular intensity distribution,” Phys. Rev. A81, 013806 (2010).
[CrossRef]

Singh, J.

Smith, C.

P. Hauge, R. Muller, and C. Smith, “Conventions and formulas for using the mueller-stokes calculus in ellipsometry,” Surf. Sci.96, 81–107 (1980).
[CrossRef]

Soni, J.

N. Ghosh, J. Soni, M. Wood, M. Wallenberg, and I. Vitkin, “Mueller matrix polarimetry for the characterization of complex random medium like biological tissues,” Pramana75, 1071–1086 (2010).
[CrossRef]

Stabo-Eeg, F.

F. Stabo-Eeg, M. Kildemo, I. S. Nerbø, and M. Lindgren, “Well-conditioned multiple laser mueller matrix ellipsometer,” Opt. Eng.47, 073604–073604–9 (2008).
[CrossRef]

Stamnes, J. J.

Svensen, Ø.

Swami, M. K.

Tauer, K.

A. Erbe, K. Tauer, and R. Sigel, “Ellipsometric light scattering for the characterization of thin layers on dispersed colloidal particles,” Phys. Rev. E73, 031406 (2006).
[CrossRef]

Tuchin, V. V.

V. V. Tuchin, L. V. Wang, and D. A. Zimnyakov, Optical Polarization in Biomedical Applications (Berlin Heidelberg, 2006).

Validire, P.

A. Pierangelo, S. Manhas, A. Benali, M. R. Antonelli, T. Novikova, P. Validire, B. Gayet, and A. De Martino, “Use of mueller polarimetric imaging for the staging of human colon cancer,” Proc. SPIE7895, 78950E (2011).
[CrossRef]

Vitkin, I.

N. Ghosh, J. Soni, M. Wood, M. Wallenberg, and I. Vitkin, “Mueller matrix polarimetry for the characterization of complex random medium like biological tissues,” Pramana75, 1071–1086 (2010).
[CrossRef]

Vitkin, I. A.

S. Kumar, H. Purwar, R. Ossikovski, I. A. Vitkin, and N. Ghosh, “Comparative study of differential matrix and extended polar decomposition formalisms for polarimetric characterization of complex tissue-like turbid media,” Journal of Biomedical Optics17, 105006–105006 (2012).
[CrossRef] [PubMed]

N. Ghosh and I. A. Vitkin, “Tissue polarimetry: concepts, challenges, applications, and outlook,” J. Biomed. Opt.16, 110801 (2011).
[CrossRef] [PubMed]

Wallenberg, M.

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Figures (8)

Fig. 1
Fig. 1

Geometry for the scattering experiment, defining the incidence angle θi, the Rayleigh scattering angle θR and the Rayleigh scattering angle θS used in [1]. The figure also shows the right handed coordinate system {, ŷ, } used in the paper, where = − , ŷ =ŝ with reference to the right handed system {ŝ, , }. The arrows define positive direction.

Fig. 2
Fig. 2

The measured Mueller matrix data from the Spectralon surface with illumination at incidence angles θi of 0° (green x marks), 30° (purple crosses), 45° (blue circles), 60° (red stars), 75° (cyan squares) plotted as a function of the Rayleigh scattering angle θR. The full curves show the fitted parametric model in Eq. (19). All elements, except M11, are normalized to M11.

Fig. 3
Fig. 3

The difference of the off-diagonal elements (m24m42), Δm33m33 − 〈m33〉 and Δ(m34m43) ≡ (m34 − 〈 m34〉) − (m43 − 〈 m43〉), where 〈mij〉 are the averages upon a full 360 degrees rotation, at 532 nm. The data are plotted against the azimuthal angle of the Spectralon for incidence angle 75° and Rayleigh scattering angle 35°.

Fig. 4
Fig. 4

Measured Mueller matrix data from the Spectralon surface with illumination at an incidence angle of θi = 75° and wavelengths 532 nm (red triangles) and 1500 nm (blue crosses) plotted against the Rayleigh scattering angle θR. The full curve shows the fitted parametric model at 1500 nm in Eq. (19). All elements are normalized to M11.

Fig. 5
Fig. 5

Figures (a) and (b) show the depolarization index pD (a) and the depolarization factors α, β and γ (b) determined from forward product decomposition for five different incidence angles (θi = 0°, 30°, 45°, 60°, 75°) at λ =532 nm plotted against the Rayleigh scattering angle θR. Tentative fits are shown using the model in Eq. (11) and the parameters in Table 1. Figures (c) and (d) show the depolarization index pD (c) and the depolarization factor γ (d) determined from the forward product decomposition for two different incidence angles (θi = 30°, 75°) at λ = 1500 nm plotted against θR. The full and dotted lines in (c) show the fitted models for pD to the data at λ = 1500 nm (see Table 2) and λ = 532 nm, respectively. The full and dotted lines in (d) shows the fitted model for γ in Eq. (13) with the parameters in Table 2 for λ = 1500 nm and the model for λ = 532 nm, respectively.

Fig. 6
Fig. 6

Retardance (given by Eq. (4)) at 532 nm (full squares) and 1500 nm (hollow triangles) with incident angle θi = 75° plotted as a function of the Rayleigh scattering angle θR. The two vertical lines indicate when the retardance crosses 90°. Note that θB (i.e. vertical lines) were determined from Fig. 7. The Figure also shows the function R ≈ arccos(C) (blue dotted line), with θB ≈ 7°.

Fig. 7
Fig. 7

Figures (a) at 532 nm and (c) at 1500 nm show the mR33 and mR44 elements from the retardance matrix MR plotted against the Rayleigh scattering angle θR. The simulated curve is given by Rayleigh scattering theory (see Eq. (14)). Figs. (b) at 532 nm and (d) at 1500 nm show the mR34 and mR43 elements from the retardance matrix MR plotted against θR. The simulated curve shows ±S (see Eq. (15)). The left Figs. (a) and (b) are data at 532 nm, with incident angles θi = 30°, 45°, 60°, 75°. The simulated data at 532 nm (full and dotted lines) use θB ≈ 7°. Figs. (c) and (d) are data at 1500 nm, with incidence angles θi = 30° and 75°, and simulated data with θB ≈ 15°. The vertical lines indicate the location of θB.

Fig. 8
Fig. 8

The experimental retardance sub-matrix mR (symbols) and the simulated mR (full lines), both plotted against the Rayleigh scattering angle θR. The experimental data are at 532 nm, with incident angles θi = 30°, 45°, 60° and 75°. The simulated data use θB ≈ 7°, and the basis functions N, C and S in addition to p0. The notation mRij refers to the retardance matrix MR.

Tables (2)

Tables Icon

Table 1 Fitted parameters for the polarization index (pD) and the depolarization factors, using Eq. (11) at 532 nm. The fitted data are shown in Figs. 5(a) and 5(b).

Tables Icon

Table 2 Fitted parameters for the depolarization factors α and β using Eq. (11) and γ using Eq. (13), at 1500 nm. The fits to pD and γ are shown in Fig. 5.

Equations (21)

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M = M Δ M R M D ,
M Δ = M 11 [ 1 0 T p m Δ ] , M D = [ 1 d T d m D ] , M R = [ 1 0 T 0 m R ] .
p C = 1 3 ( α + β + γ ) .
R = cos 1 ( Tr ( M R ) 1 2 ) .
M D R = M 11 [ 1 m 12 0 0 m 21 1 0 0 0 0 m 33 m 34 0 0 m 43 m 44 ] .
m 12 = m 21 = cos ( 2 Ψ ) , m 33 = m 44 = sin ( 2 Ψ ) cos Δ , m 34 = m 43 = sin ( 2 Ψ ) sin Δ .
m 12 = m 21 = sin 2 ( θ R ) 1 + cos 2 ( θ R ) , m 33 = m 44 = 2 cos ( θ R ) 1 + cos 2 ( θ R ) , m 34 = m 43 = 0.
p D = ( Tr ( M T M ) M 11 2 3 M 11 2 ) 1 / 2 = ( i , j = 1 4 M i j 2 M 11 2 3 M 11 2 ) 1 / 2 .
S = [ I x ^ + I y ^ I x ^ I y ^ I x ^ + y ^ I x ^ y ^ I R C I L C ] .
p D = | ( θ S + θ i ) 3 22 | = | ( 180 θ R ) 3 22 | .
p D ( θ R ) = p 0 + ( 1 p 0 p B S ) exp ( 0.5 ( θ R θ F w F ) 2 ) + p B S ( θ R ) ,
p B S ( θ R ) = A B S exp ( 0.5 ( | θ R | 180 w B ) 2 ) .
p 0 + ( 1 p 0 ) [ 1 + ( θ R θ F w F ) 2 ] 1 .
C = m R 33 = m R 44 = 2 cos ( θ R θ B ) 1 + cos 2 ( θ R θ B ) ,
S = m R 34 = m R 43 = sin ( θ R θ B ) 1 + cos 2 ( θ R θ B ) ,
m 12 + p 0 / 2 4 p D 2 sin 2 ( θ R θ B ) 1 + cos 2 ( θ R θ B ) = N .
M M 11 [ 1 1 2 p 0 4 α 2 N 0 0 1 2 p 0 4 α 2 N α 0 0 0 0 β C β S 0 0 γ S γ C ] ,
m R [ 1 1 3 p 0 + R 6 1 3 p 0 1 2 N sin χ 1 3 p 0 + R 6 C S 1 3 p 0 + 1 2 N sin χ S C ] ,
M = M 11 [ 1 1 2 p 0 4 α 2 N 1 2 p 0 2 α 2 N 1 3 p 0 1 2 p 0 4 α 2 N α α ( 1 3 p 0 1 6 R ) α ( 1 3 p 0 1 2 N sin χ ) 1 3 p 0 γ ( 1 3 p 0 + 1 2 N sin χ ) 1 4 p 0 γ S γ C ] .
M = M 11 [ 1 4 p D 2 N 2 p D 2 N 0 4 p D 2 N p D p D 1 6 R p D 1 2 N sin χ 2 p D 2 N p D 1 6 R p D C p D S 0 p D 1 2 N sin χ p D S p D C ] ,
M = M 11 ( ( 1 p D ) diag ( 1 , 0 , 0 , 0 ) + p D [ 1 4 p D N 2 p D N 0 4 p D N 1 1 6 R 1 2 N sin χ 2 p D N 1 6 R C S 0 1 2 N sin χ S C ] ) ,

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