Abstract

Dual photoelastic modulator polarimeter systems are widely used for the measurement of light beam polarization, most often described by Stokes vectors, that carry information about an interrogated sample. The sample polarization properties can be described more thoroughly through its Mueller matrix, which can be derived from judiciously chosen input polarization Stokes vectors and correspondingly measured output Stokes vectors. However, several sources of error complicate the construction of a Mueller matrix from the measured Stokes vectors. Here we present a general formalism to examine these sources of error and their effects on the derived Mueller matrix, and identify the optimal input polarization states to minimize their effects in a dual photoelastic modulator polarimeter configuration. The input Stokes vector states leading to the most robust Mueller matrix determination are shown to form Platonic solids in the Poincaré sphere space; we also identify the optimal 3D orientation of these solids for error minimization.

© 2012 OSA

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    [CrossRef] [PubMed]
  7. X. Guo, M. F. G. Wood, and I. A. Vitkin, “Angular measurements of light scattered by turbid chiral media using linear Stokes polarimeter,” J. Biomed. Opt.11, 041105 (2006).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2010 (1)

2009 (1)

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophoton.2, 145–156 (2009).
[CrossRef]

2008 (3)

2006 (2)

X. Guo, M. F. G. Wood, and I. A. Vitkin, “Angular measurements of light scattered by turbid chiral media using linear Stokes polarimeter,” J. Biomed. Opt.11, 041105 (2006).
[CrossRef] [PubMed]

J. Zallat, S. Aïnouz, and M. P. Stoll, “Optimal configurations for imaging polarimeters: impact of image noise and systematic errors,” J. Opt. A, Pure Appl. Opt.8, 807–814 (2006).
[CrossRef]

2004 (3)

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

A. D. Martino, E. Garcia-Caurel, B. Laude, and B. Drévillon, “General methods for optimized design and calibration of Mueller polarimeters,” Thin Solid Films455, 112–119 (2004).
[CrossRef]

D. Côté and I. A. Vitkin, “Balanced detection for low-noise precision polarimetric measurements of optically active, multiply scattering tissue phantoms,” J. Biomed. Opt.9, 213–220 (2004).
[CrossRef] [PubMed]

2003 (2)

2002 (3)

2000 (2)

1995 (2)

A. Ambirajan and D. C. Look, “Optimum angles for a polarimeter: part 2,” Opt. Eng.34, 1656–1658 (1995).
[CrossRef]

A. Ambirajan and D. C. Look, “Optimum angles for a polarimeter: part 1,” Opt. Eng.34, 1651–1655 (1995).
[CrossRef]

1988 (1)

1973 (1)

G. H. Golub and V. Pereyra, “The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate,” SIAM J. Numer. Anal.10, 413–432 (1973).
[CrossRef]

1852 (1)

G. G. Stokes, “On the composition and resolution of streams of polarized light from different sources,” Trans. Cambridge Phil. Soc.9, 399–416 (1852).

Aas, L. M. S.

Aïnouz, S.

J. Zallat, S. Aïnouz, and M. P. Stoll, “Optimal configurations for imaging polarimeters: impact of image noise and systematic errors,” J. Opt. A, Pure Appl. Opt.8, 807–814 (2006).
[CrossRef]

Ambirajan, A.

A. Ambirajan and D. C. Look, “Optimum angles for a polarimeter: part 1,” Opt. Eng.34, 1651–1655 (1995).
[CrossRef]

A. Ambirajan and D. C. Look, “Optimum angles for a polarimeter: part 2,” Opt. Eng.34, 1656–1658 (1995).
[CrossRef]

Arya, A. P.

A. P. Arya, Introduction to Classical Mechanics, 2nd ed. (Prentice-Hall, 1998).

Atiyah, M.

M. Atiyah and P. Sutcliffe, “Polyhedra in physics, chemistry and geometry,” Milan J. Math.71, 33–58 (2003).
[CrossRef]

Azzam, R. M. A.

Chipman, R. A.

Collett, E.

E. Collett, Field Guide to Polarization (SPIE Press, 2005).

Côté, D.

D. Côté and I. A. Vitkin, “Balanced detection for low-noise precision polarimetric measurements of optically active, multiply scattering tissue phantoms,” J. Biomed. Opt.9, 213–220 (2004).
[CrossRef] [PubMed]

Dattorro, J.

J. Dattorro, Convex Optimization & Euclidean Distance Geometry (Meboo Publishing USA, 2005).

Dereniak, E. L.

Descour, M. R.

Drévillon, B.

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

A. D. Martino, E. Garcia-Caurel, B. Laude, and B. Drévillon, “General methods for optimized design and calibration of Mueller polarimeters,” Thin Solid Films455, 112–119 (2004).
[CrossRef]

A. D. Martino, Y.-K. Kim, E. Garcia-Caurel, B. Laude, and B. Drévillon, “Optimized Mueller polarimeter with liquid crystals,” Opt. Lett.28, 616–618 (2003).
[CrossRef] [PubMed]

Ellingsen, P. G.

Elminyawi, I. M.

El-Saba, A. M.

Friedberg, S. H.

S. H. Friedberg, A. J. Insel, and L. E. Spence, Linear Algebra, 2nd ed. (Prentice-Hall, 1989).

Garcia-Caurel, E.

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

A. D. Martino, E. Garcia-Caurel, B. Laude, and B. Drévillon, “General methods for optimized design and calibration of Mueller polarimeters,” Thin Solid Films455, 112–119 (2004).
[CrossRef]

A. D. Martino, Y.-K. Kim, E. Garcia-Caurel, B. Laude, and B. Drévillon, “Optimized Mueller polarimeter with liquid crystals,” Opt. Lett.28, 616–618 (2003).
[CrossRef] [PubMed]

Ghosh, N.

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophoton.2, 145–156 (2009).
[CrossRef]

Golub, G. H.

G. H. Golub and V. Pereyra, “The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate,” SIAM J. Numer. Anal.10, 413–432 (1973).
[CrossRef]

G. H. Golub and C. F. V. Loan, Matrix Computations, 3rd ed. (The Johns Hopkins University Press, 1996).

Guan, W.

W. Guan, G. A. Jones, Y. Liu, and T. H. Shen, “The measurement of the Stokes parameters: a generalized methodology using a dual photoelastic modulator system,” J. Appl. Phys.103, 043104 (2008).
[CrossRef]

Guo, X.

X. Guo, M. F. G. Wood, and I. A. Vitkin, “Angular measurements of light scattered by turbid chiral media using linear Stokes polarimeter,” J. Biomed. Opt.11, 041105 (2006).
[CrossRef] [PubMed]

Hoover, B. G.

Insel, A. J.

S. H. Friedberg, A. J. Insel, and L. E. Spence, Linear Algebra, 2nd ed. (Prentice-Hall, 1989).

Jones, G. A.

W. Guan, G. A. Jones, Y. Liu, and T. H. Shen, “The measurement of the Stokes parameters: a generalized methodology using a dual photoelastic modulator system,” J. Appl. Phys.103, 043104 (2008).
[CrossRef]

Kemme, S. A.

Kildemo, M.

Kim, Y.-K.

Laude, B.

A. D. Martino, E. Garcia-Caurel, B. Laude, and B. Drévillon, “General methods for optimized design and calibration of Mueller polarimeters,” Thin Solid Films455, 112–119 (2004).
[CrossRef]

A. D. Martino, Y.-K. Kim, E. Garcia-Caurel, B. Laude, and B. Drévillon, “Optimized Mueller polarimeter with liquid crystals,” Opt. Lett.28, 616–618 (2003).
[CrossRef] [PubMed]

Letnes, P. A.

Li, R.-K.

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophoton.2, 145–156 (2009).
[CrossRef]

Li, S.

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophoton.2, 145–156 (2009).
[CrossRef]

Liu, Y.

W. Guan, G. A. Jones, Y. Liu, and T. H. Shen, “The measurement of the Stokes parameters: a generalized methodology using a dual photoelastic modulator system,” J. Appl. Phys.103, 043104 (2008).
[CrossRef]

Loan, C. F. V.

G. H. Golub and C. F. V. Loan, Matrix Computations, 3rd ed. (The Johns Hopkins University Press, 1996).

Look, D. C.

A. Ambirajan and D. C. Look, “Optimum angles for a polarimeter: part 2,” Opt. Eng.34, 1656–1658 (1995).
[CrossRef]

A. Ambirajan and D. C. Look, “Optimum angles for a polarimeter: part 1,” Opt. Eng.34, 1651–1655 (1995).
[CrossRef]

Martino, A. D.

A. D. Martino, E. Garcia-Caurel, B. Laude, and B. Drévillon, “General methods for optimized design and calibration of Mueller polarimeters,” Thin Solid Films455, 112–119 (2004).
[CrossRef]

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

A. D. Martino, Y.-K. Kim, E. Garcia-Caurel, B. Laude, and B. Drévillon, “Optimized Mueller polarimeter with liquid crystals,” Opt. Lett.28, 616–618 (2003).
[CrossRef] [PubMed]

Mueller, H.

H. Mueller, “Memorandum on the polarization optics of the photoelastic shutter,” Report No. 2 of the OSRD project OEMsr-576, (1943).

Nerbø, I. S.

Pereyra, V.

G. H. Golub and V. Pereyra, “The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate,” SIAM J. Numer. Anal.10, 413–432 (1973).
[CrossRef]

Phipps, G. S.

Poincaré, H.

H. Poincaré, Théorie mathématique de la lumière (Gauthiers-Villars, 1892).

Sabatke, D. S.

Savenkov, S. N.

S. N. Savenkov, “Optimization and structuring of the instrument matrix for polarimetric measurements,” Opt. Eng.41, 965–972 (2002).
[CrossRef]

Shen, T. H.

W. Guan, G. A. Jones, Y. Liu, and T. H. Shen, “The measurement of the Stokes parameters: a generalized methodology using a dual photoelastic modulator system,” J. Appl. Phys.103, 043104 (2008).
[CrossRef]

Smith, M. H.

Spence, L. E.

S. H. Friedberg, A. J. Insel, and L. E. Spence, Linear Algebra, 2nd ed. (Prentice-Hall, 1989).

Stewart, J.

J. Stewart, Calculus Early Transcendentals, 6th ed. (Thompson Brooks/Cole, 2008).

Stokes, G. G.

G. G. Stokes, “On the composition and resolution of streams of polarized light from different sources,” Trans. Cambridge Phil. Soc.9, 399–416 (1852).

Stoll, M. P.

J. Zallat, S. Aïnouz, and M. P. Stoll, “Optimal configurations for imaging polarimeters: impact of image noise and systematic errors,” J. Opt. A, Pure Appl. Opt.8, 807–814 (2006).
[CrossRef]

Sutcliffe, P.

M. Atiyah and P. Sutcliffe, “Polyhedra in physics, chemistry and geometry,” Milan J. Math.71, 33–58 (2003).
[CrossRef]

Sweatt, W. C.

Twietmeyer, K. M.

Tyo, J. S.

Vaughn, I. J.

Vitkin, I. A.

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophoton.2, 145–156 (2009).
[CrossRef]

X. Guo, M. F. G. Wood, and I. A. Vitkin, “Angular measurements of light scattered by turbid chiral media using linear Stokes polarimeter,” J. Biomed. Opt.11, 041105 (2006).
[CrossRef] [PubMed]

D. Côté and I. A. Vitkin, “Balanced detection for low-noise precision polarimetric measurements of optically active, multiply scattering tissue phantoms,” J. Biomed. Opt.9, 213–220 (2004).
[CrossRef] [PubMed]

Weisel, R. D.

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophoton.2, 145–156 (2009).
[CrossRef]

Wilson, B. C.

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophoton.2, 145–156 (2009).
[CrossRef]

Wood, M. F. G.

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophoton.2, 145–156 (2009).
[CrossRef]

X. Guo, M. F. G. Wood, and I. A. Vitkin, “Angular measurements of light scattered by turbid chiral media using linear Stokes polarimeter,” J. Biomed. Opt.11, 041105 (2006).
[CrossRef] [PubMed]

Zallat, J.

J. Zallat, S. Aïnouz, and M. P. Stoll, “Optimal configurations for imaging polarimeters: impact of image noise and systematic errors,” J. Opt. A, Pure Appl. Opt.8, 807–814 (2006).
[CrossRef]

Appl. Opt. (2)

J. Appl. Phys. (1)

W. Guan, G. A. Jones, Y. Liu, and T. H. Shen, “The measurement of the Stokes parameters: a generalized methodology using a dual photoelastic modulator system,” J. Appl. Phys.103, 043104 (2008).
[CrossRef]

J. Biomed. Opt. (2)

D. Côté and I. A. Vitkin, “Balanced detection for low-noise precision polarimetric measurements of optically active, multiply scattering tissue phantoms,” J. Biomed. Opt.9, 213–220 (2004).
[CrossRef] [PubMed]

X. Guo, M. F. G. Wood, and I. A. Vitkin, “Angular measurements of light scattered by turbid chiral media using linear Stokes polarimeter,” J. Biomed. Opt.11, 041105 (2006).
[CrossRef] [PubMed]

J. Biophoton. (1)

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J. Biophoton.2, 145–156 (2009).
[CrossRef]

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

J. Zallat, S. Aïnouz, and M. P. Stoll, “Optimal configurations for imaging polarimeters: impact of image noise and systematic errors,” J. Opt. A, Pure Appl. Opt.8, 807–814 (2006).
[CrossRef]

J. Opt. Soc. Am. A (1)

Milan J. Math. (1)

M. Atiyah and P. Sutcliffe, “Polyhedra in physics, chemistry and geometry,” Milan J. Math.71, 33–58 (2003).
[CrossRef]

Opt. Eng. (3)

A. Ambirajan and D. C. Look, “Optimum angles for a polarimeter: part 2,” Opt. Eng.34, 1656–1658 (1995).
[CrossRef]

S. N. Savenkov, “Optimization and structuring of the instrument matrix for polarimetric measurements,” Opt. Eng.41, 965–972 (2002).
[CrossRef]

A. Ambirajan and D. C. Look, “Optimum angles for a polarimeter: part 1,” Opt. Eng.34, 1651–1655 (1995).
[CrossRef]

Opt. Express (3)

Opt. Lett. (3)

SIAM J. Numer. Anal. (1)

G. H. Golub and V. Pereyra, “The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate,” SIAM J. Numer. Anal.10, 413–432 (1973).
[CrossRef]

Thin Solid Films (2)

A. D. Martino, E. Garcia-Caurel, B. Laude, and B. Drévillon, “General methods for optimized design and calibration of Mueller polarimeters,” Thin Solid Films455, 112–119 (2004).
[CrossRef]

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

Trans. Cambridge Phil. Soc. (1)

G. G. Stokes, “On the composition and resolution of streams of polarized light from different sources,” Trans. Cambridge Phil. Soc.9, 399–416 (1852).

Other (8)

E. Collett, Field Guide to Polarization (SPIE Press, 2005).

H. Poincaré, Théorie mathématique de la lumière (Gauthiers-Villars, 1892).

H. Mueller, “Memorandum on the polarization optics of the photoelastic shutter,” Report No. 2 of the OSRD project OEMsr-576, (1943).

S. H. Friedberg, A. J. Insel, and L. E. Spence, Linear Algebra, 2nd ed. (Prentice-Hall, 1989).

J. Dattorro, Convex Optimization & Euclidean Distance Geometry (Meboo Publishing USA, 2005).

J. Stewart, Calculus Early Transcendentals, 6th ed. (Thompson Brooks/Cole, 2008).

G. H. Golub and C. F. V. Loan, Matrix Computations, 3rd ed. (The Johns Hopkins University Press, 1996).

A. P. Arya, Introduction to Classical Mechanics, 2nd ed. (Prentice-Hall, 1998).

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