Abstract

Systematic errors specific to a snapshot Mueller matrix polarimeter are studied. Their origins and effects are highlighted, and solutions for correction and stabilization are proposed. The different effects induced by them are evidenced by experimental results acquired with a given setup and theoretical simulations carried out for more general cases. We distinguish the errors linked to some imperfection of elements in the experimental setup from those linked to the sample under study.

© 2009 Optical Society of America

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References

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  1. B. Boulbry, B. Le Jeune, F. Pellen, J. Cariou, and J. Lotrian, “Error analysis and calibration of a spectroscopic Mueller matrix polarimeter using a short-pulse laser source,” Meas. Sci. Technol. 13, 1563-1573 (2002).
    [CrossRef]
  2. D. H. Goldstein and R. A. Chipman, “Error analysis of a Mueller matrix polarimeter,” J. Opt. Soc. Am. A 7, 693-700 (1990).
    [CrossRef]
  3. L. Broch, A. En Naciri, and L. Johann, “Systematic errors for a Mueller matrix dual rotating compensator ellipsometer,” Opt. Express 16, 8814-8824 (2008).
    [CrossRef] [PubMed]
  4. M. Dubreuil, S. Rivet, B. Le Jeune, and J. Cariou, “Snapshot Mueller matrix polarimeter by wavelength polarization coding,” Opt. Express 15, 13660-13668 (2007).
    [CrossRef] [PubMed]
  5. K. Oka and T. Kato, “Spectroscopic polarimetry with a channeled spectrum,” Opt. Lett. 24, 1475-1477 (1999).
    [CrossRef]
  6. N. Hagen, K. Oka, and E. L. Dereniak, “Snapshot Mueller matrix spectropolarimeter,” Opt. Lett. 32, 2100-2102 (2007).
    [CrossRef] [PubMed]
  7. P. Lemaillet, S. Rivet, and B. Le Jeune, “Optimization of a snapshot Mueller matrix polarimeter,” Opt. Lett. 33, 144-146(2008).
    [CrossRef] [PubMed]
  8. J. J. Gil and E. Bernabeu, “Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from polar decomposition of its Mueller matrix,” Optik (Stuttgart) 76, 67-71 (1987).
  9. D. G. M. Anderson and R. Barakat, “Necessary and sufficient conditions for a Mueller matrix to be derivable from a Jones matrix,” J. Opt. Soc. Am. A 11, 2305-2319 (1994).
    [CrossRef]

2008 (2)

2007 (2)

2002 (1)

B. Boulbry, B. Le Jeune, F. Pellen, J. Cariou, and J. Lotrian, “Error analysis and calibration of a spectroscopic Mueller matrix polarimeter using a short-pulse laser source,” Meas. Sci. Technol. 13, 1563-1573 (2002).
[CrossRef]

1999 (1)

1994 (1)

1990 (1)

1987 (1)

J. J. Gil and E. Bernabeu, “Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from polar decomposition of its Mueller matrix,” Optik (Stuttgart) 76, 67-71 (1987).

Anderson, D. G. M.

Barakat, R.

Bernabeu, E.

J. J. Gil and E. Bernabeu, “Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from polar decomposition of its Mueller matrix,” Optik (Stuttgart) 76, 67-71 (1987).

Boulbry, B.

B. Boulbry, B. Le Jeune, F. Pellen, J. Cariou, and J. Lotrian, “Error analysis and calibration of a spectroscopic Mueller matrix polarimeter using a short-pulse laser source,” Meas. Sci. Technol. 13, 1563-1573 (2002).
[CrossRef]

Broch, L.

Cariou, J.

M. Dubreuil, S. Rivet, B. Le Jeune, and J. Cariou, “Snapshot Mueller matrix polarimeter by wavelength polarization coding,” Opt. Express 15, 13660-13668 (2007).
[CrossRef] [PubMed]

B. Boulbry, B. Le Jeune, F. Pellen, J. Cariou, and J. Lotrian, “Error analysis and calibration of a spectroscopic Mueller matrix polarimeter using a short-pulse laser source,” Meas. Sci. Technol. 13, 1563-1573 (2002).
[CrossRef]

Chipman, R. A.

Dereniak, E. L.

Dubreuil, M.

En Naciri, A.

Gil, J. J.

J. J. Gil and E. Bernabeu, “Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from polar decomposition of its Mueller matrix,” Optik (Stuttgart) 76, 67-71 (1987).

Goldstein, D. H.

Hagen, N.

Johann, L.

Kato, T.

Le Jeune, B.

Lemaillet, P.

Lotrian, J.

B. Boulbry, B. Le Jeune, F. Pellen, J. Cariou, and J. Lotrian, “Error analysis and calibration of a spectroscopic Mueller matrix polarimeter using a short-pulse laser source,” Meas. Sci. Technol. 13, 1563-1573 (2002).
[CrossRef]

Oka, K.

Pellen, F.

B. Boulbry, B. Le Jeune, F. Pellen, J. Cariou, and J. Lotrian, “Error analysis and calibration of a spectroscopic Mueller matrix polarimeter using a short-pulse laser source,” Meas. Sci. Technol. 13, 1563-1573 (2002).
[CrossRef]

Rivet, S.

J. Opt. Soc. Am. A (2)

Meas. Sci. Technol. (1)

B. Boulbry, B. Le Jeune, F. Pellen, J. Cariou, and J. Lotrian, “Error analysis and calibration of a spectroscopic Mueller matrix polarimeter using a short-pulse laser source,” Meas. Sci. Technol. 13, 1563-1573 (2002).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Optik (Stuttgart) (1)

J. J. Gil and E. Bernabeu, “Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from polar decomposition of its Mueller matrix,” Optik (Stuttgart) 76, 67-71 (1987).

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Figures (5)

Fig. 1
Fig. 1

Experimental setup for an SMMP in the configuration ( e , e , 5 e , 5 e ) , where e is the reference thickness of the first retarder.

Fig. 2
Fig. 2

Evolution of the argument ( ϕ w ) of the peak at 5 f 0 given by a signal of one calcite retarder of thickness 5 e set between crossed polarizers versus temperature.

Fig. 3
Fig. 3

Evolution of phases ϕ w , ϕ 2 + ϕ 3 , and ϕ 4 calculated with a no-sample measurement versus temperature. Phases were adapted so as to be null at t = 0 .

Fig. 4
Fig. 4

Evolution of the Mueller coefficients of a no-sample measurement (vacuum) versus temperature over the first 15 min of the experiment of Fig. 3. Solid curves represent Mueller coefficients with no correction, and dashed curves show them after correction by ϕ w .

Fig. 5
Fig. 5

Intensity spectrum T FP ( λ ) of the quartz wave plate (circular birefringent) between crossed polarizers.

Tables (7)

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Table 1 Relationships between Magnitudes of the Peaks—Real Part ( g n ) and Imaginary Part ( h n )—and Mueller Coefficients ( m i j ) in the Fourier Domain for the Ideal Configuration ( e , e , 5 e , 5 e )

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Table 2 Relationships between Magnitudes of Peaks—Real Part ( g n ) and Imaginary Part ( h n )—and the Mueller Coefficients ( m i j ) in the Fourier Domain for the True Configuration ( e , e + Δ e 2 , 5 e + Δ e 3 , 5 e + Δ e 4 )

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Table 3 Influence of Phases ϕ w , ϕ 2 , ϕ 3 , and ϕ 4 on the Mueller Matrix for Vacuum and a Linear Polarizer at 30 ° a

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Table 4 Experimental Mueller Matrix Given by the SMMP for Vacuum and a Linear Partial Polarizer at 30 ° : Theoretical, without Corrections by ϕ w , ϕ 2 , ϕ 3 , and ϕ 4 and with Corrections by ϕ w , ϕ 2 , ϕ 3 and ϕ 4 a

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Table 5 Simulation of the Influence of the Misalignment Errors Δ θ 1 , Δ θ 2 , Δ θ 3 , Δ θ 4 and Δ θ pol on the Mueller Matrix for Vacuum

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Table 6 Simulation of a Quarter-Wave Plate ( R = 90 ° , α = 20 ° ) at Different Orders a

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Table 7 Experimental Mueller Matrix for the Quartz Wave Plate

Equations (6)

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I ( λ ) = s ( λ ) Re [ g 0 + n = 1 12 ( g n + i h n ) e i ( n f 0 λ ) ] ,
I ( λ ) = s ( λ ) Re [ g 0 + n = 1 12 e i φ n ( g n + i h n ) e i n ( f 0 λ + ϕ w ) ] ,
16 I vacuum ( λ ) = 3 + cos [ 2 ( ϕ w + f 0 λ ) + ϕ 2 + ϕ 3 ϕ 4 ] 2 cos [ 4 ( ϕ w + f 0 λ ) + ϕ 4 ] 2 cos [ 6 ( ϕ w + f 0 λ ) + ϕ 4 ] + cos [ 10 ( ϕ w + f 0 λ ) + ϕ 2 + ϕ 3 + ϕ 4 ] cos [ 12 ( ϕ w + f 0 λ ) + ϕ 2 + ϕ 3 + ϕ 4 ] .
( 1 0 0 0 0 0.914 0.407 0 0 0.407 0.914 0 0 0 0 1 )
( 1 0.056 0.018 0.006 0.019 0.926 0.386 0.012 0.021 0.464 0.911 0.03 0.019 0.147 0.032 1.013 )
( 1 0.023 0.022 0.009 0.005 0.919 0.399 0.006 0.010 0.379 0.907 0.016 0.01 0.014 0.017 1.004 )

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