Abstract

An optimized Mueller-matrix polarimeter is simulated. The polarimeter is optimized by finding the configurations of the polarization state generator and polarization state analyzer that give the minimum condition number. Noise is included in the measurement of the polarimeter intensities, and the eigenvalue calibration procedure is used to reduce the errors in the final Mueller matrix. Controlled errors are introduced to the polarimeter configuration, and the error in the final measured Mueller matrix is calculated as a function of these configuration errors. It is found that the alignment of the retarder axes in the polarimeter is much more important than the use of the ideal, optimized retardance values. In particular, the misalignment of the retarders farthest from the sample is the error source with the highest impact in the precision of the polarimeter.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2016 (1)

2014 (1)

2012 (1)

2011 (1)

G. Martínez-Ponce, C. Solano, and C. Pérez Barrios, “Hybrid complete Mueller polarimeter based on phase modulators,” Opt. Lasers Eng. 49(6), 723–728 (2011).
[Crossref]

2008 (1)

2006 (1)

2003 (1)

2002 (2)

1999 (2)

1992 (1)

1985 (1)

W. S. Bickel and W. M. Bailey, “Stokes vectors, Mueller matrices and polarized scattered light,” Am. J. Phys. 53(5), 468–478 (1985).
[Crossref]

1980 (1)

Artal, P.

Bailey, W. M.

W. S. Bickel and W. M. Bailey, “Stokes vectors, Mueller matrices and polarized scattered light,” Am. J. Phys. 53(5), 468–478 (1985).
[Crossref]

Bickel, W. S.

W. S. Bickel and W. M. Bailey, “Stokes vectors, Mueller matrices and polarized scattered light,” Am. J. Phys. 53(5), 468–478 (1985).
[Crossref]

Bottiger, J. R.

Bruce, N. C.

Bueno, J. M.

Chipman, R. A.

Compain, E.

De Martino, A.

Drevillon, B.

Drévillon, B.

Fry, E. S.

García-Caurel, E.

Goldstein, D. H.

Kim, Y.-K.

Laude, B.

Layden, D.

López-Téllez, J. M.

Martínez-Ponce, G.

G. Martínez-Ponce, C. Solano, and C. Pérez Barrios, “Hybrid complete Mueller polarimeter based on phase modulators,” Opt. Lasers Eng. 49(6), 723–728 (2011).
[Crossref]

Pérez Barrios, C.

G. Martínez-Ponce, C. Solano, and C. Pérez Barrios, “Hybrid complete Mueller polarimeter based on phase modulators,” Opt. Lasers Eng. 49(6), 723–728 (2011).
[Crossref]

Poirier, S.

Rodríguez-Herrera, O. G.

Smith, M. H.

Solano, C.

G. Martínez-Ponce, C. Solano, and C. Pérez Barrios, “Hybrid complete Mueller polarimeter based on phase modulators,” Opt. Lasers Eng. 49(6), 723–728 (2011).
[Crossref]

Thompson, R. C.

Twietmeyer, K. M.

Tyo, J. S.

Vitkin, I. A.

Wei, H.

Wood, M. F. G.

Am. J. Phys. (1)

W. S. Bickel and W. M. Bailey, “Stokes vectors, Mueller matrices and polarized scattered light,” Am. J. Phys. 53(5), 468–478 (1985).
[Crossref]

Appl. Opt. (8)

Opt. Express (2)

Opt. Lasers Eng. (1)

G. Martínez-Ponce, C. Solano, and C. Pérez Barrios, “Hybrid complete Mueller polarimeter based on phase modulators,” Opt. Lasers Eng. 49(6), 723–728 (2011).
[Crossref]

Opt. Lett. (2)

Other (4)

D. Goldstein, Polarized Light, 2nd ed. (CRC, Boca Raton, 2003).

R. A. Chipman, Polarimetry, in Handbook of Optics, M. Bass editor, McGraw-Hill, Columbus, (1995). Chapter 22.

D. Lara-Saucedo, Three-dimensional complete polarisation sensitive imaging using a confocal Mueller matrix polarimeter, PhD thesis, Imperial College, London, (2005).

O. G. Rodríguez-Herrera, Far-field method for the characterization of three-dimensional fields: vector polarimetry, PhD thesis, National University of Ireland, Galway, (2009).

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Figures (6)

Fig. 1
Fig. 1 Experimental setup for a Mueller-matrix polarimeter. The angles associated with each component refer to the relative angle of the optical axis of that component with respect to the horizontal plane.
Fig. 2
Fig. 2 Values of the total rms error after the data-extraction and calibration process for polarimeters with errors and noise, for noise levels of 0.5% (top graph), 1.5% (middle graph) and 5% (bottom graph). Each point on a graph represents the simulation results for a particular configuration of the polarimeter with errors. The gray lines show the limiting values of condition number for given values of the total rms error.
Fig. 3
Fig. 3 Graph of the estimated limiting condition number for different values of the error level in the measured intensity data, and for different levels of the desired limiting total rms level in the final Mueller matrix.
Fig. 4
Fig. 4 The distribution of values of each of the four polarimeter parameters from the simulation for two values of the limiting condition number: δ 1,4 , filled squares; δ 2,3 , open circles; θ 1,4 , filled upward triangles, and θ 2,3 , open downward triangles. The points are the frequency values calculated from the simulation results, and the lines are fits of Gaussian functions to these frequency values.
Fig. 5
Fig. 5 The 1/e width of the frequency distributions of the acceptable polarimeter parameter errors as a function of condition number from a Gaussian fit to the simulation data for each limiting condition number
Fig. 6
Fig. 6 Permitted polarimeter parameter errors, in each of the four polarimeter parameters, as a function of the percentage errors in the intensity measurements for given required total rms errors in the final, calibrated Mueller matrix

Equations (18)

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P inc =( S inc1 S inc2 S incN )
P det =( S det1 S det2 S detN )
S out = M PSA M S M PSG S in ,
M PSG = M R2 M R1 M P1 ,
M PSA = M P2 M R4 M R3 ,
θ 1 = θ 4 =27.4°,
θ 2 = θ 3 =72.4°,
( δ 1 , δ 2 , δ 3 , δ 4 )=( Δ 1 , Δ 1 , Δ 1 , Δ 1 ),( Δ 1 , Δ 1 , Δ 1 , Δ 2 ), ( Δ 1 , Δ 1 , Δ 2 , Δ 1 ),( Δ 1 , Δ 1 , Δ 2 , Δ 2 ), ( Δ 1 , Δ 2 , Δ 1 , Δ 1 ),( Δ 1 , Δ 2 , Δ 1 , Δ 2 ), ( Δ 1 , Δ 2 , Δ 2 , Δ 1 ),( Δ 1 , Δ 2 , Δ 2 , Δ 2 ), ( Δ 2 , Δ 1 , Δ 1 , Δ 1 ),( Δ 2 , Δ 1 , Δ 1 , Δ 2 ), ( Δ 2 , Δ 1 , Δ 2 , Δ 1 ),( Δ 2 , Δ 1 , Δ 2 , Δ 2 ), ( Δ 2 , Δ 2 , Δ 1 , Δ 1 ),( Δ 2 , Δ 2 , Δ 1 , Δ 2 ), ( Δ 2 , Δ 2 , Δ 2 , Δ 1 ),( Δ 2 , Δ 2 , Δ 2 , Δ 2 )
S 1 out = i=1 4 j=1 4 M 1i PSA M j1 PSG M ij S ,
M S = ( M 11 S M 12 S M 13 S M 14 S M 21 S M 44 S ) T ,
W 1 =( M 11 PSA M 11 PSG M 11 PSA M 21 PSG M 11 PSA M 31 PSG M 11 PSA M 41 PSG M 12 PSA M 11 PSG M 12 PSA M 21 PSG M 14 PSA M 41 PSG ),
S 1 out1 = W 1 M S .
( S 1 out1 S 1 out2 S 1 out3 S 1 out16 )=( W 1 W 2 W 3 W 16 ) M S ,
I=W M S ,
I=( S 1 out1 S 1 out2 S 1 out3 S 1 out16 ),
W=( W 1 W 2 W 3 W 16 ).
M S = W 1 I.
rms= 1 64 N=1 4 i=1 4 j=1 4 ( M ijN S M ijN theoryS ) 2 ,

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