Abstract

We report on the optimization of a snapshot Mueller matrix polarimeter performed by using singular-value decomposition. The snapshot technique relies on wavelength polarization coding by four wave plates. The statistical noise on Mueller components is minimized through adjustment of the thickness of each plate. The spectrometer response and its cutoff frequency were considered to find the optimal configurations described here.

© 2008 Optical Society of America

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References

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    [CrossRef]
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2007 (3)

2005 (1)

F. Boulvert, B. Boulbry, G. Le Brun, B. Le Jeune, S. Rivet, and J. Cariou, J. Opt. A, Pure Appl. Opt. 7, 21 (2005).
[CrossRef]

2000 (2)

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

F. Boulvert, B. Boulbry, G. Le Brun, B. Le Jeune, S. Rivet, and J. Cariou, J. Opt. A, Pure Appl. Opt. 7, 21 (2005).
[CrossRef]

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

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. E (1)

C. Baravian, J. Dillet, and J. P. Decruppe, Phys. Rev. E 75, 032502 (2007).
[CrossRef]

Other (3)

M. Stchakovsky, C. Caillaud, M. Foldyna, R. Ossikovski, and E. Garcia-Caurel, Thin Solid Films (to be published).

G. Golub and C. V. Loan, Matrix Computations, 3rd ed. (Johns Hopkins U. Press, 1996).

J. Delmas, Introduction aux probabilités (Ellipses, 1993).

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Figures (3)

Fig. 1
Fig. 1

Snapshot Mueller polarimeter in the ( k e , l e , m e , n e ) configuration. The coding device is made of a vertical linear polarizer and of two wave plates with optical axes set at 45° and 0°. The decoding device consists of two wave plates with optical axes set at 0° and 45° and is followed with a horizontal linear polarizer. All wave plates are made of the same crystalline material.

Fig. 2
Fig. 2

EWV versus coding- and decoding-plate thickness, respectively n × e and m × e , for various cutoff frequencies, f c .

Fig. 3
Fig. 3

EWV versus cutoff frequencies for optimal ( k e , l e , m e , n e ) configurations. For f c = , EWV is 964 for both ( e , 4 e , 2 e , 9 e ) and ( 2 e , e , 7 e , 14 e ) against 1097 and 3524 for ( 3 e , 2 e , e , 8 e ) and ( e , e , 5 e , 5 e ) , respectively.

Tables (2)

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Table 1 Magnitudes of Fourier Peaks versus Mueller Components for the ( e , e , 5 e , 5 e ) Configuration a

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Table 2 Specifications of ( k e , l e , m e , n e ) Configurations

Equations (7)

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I ( λ ) = i = 1 s g i cos ( p i f 0 λ ) + h i sin ( p i f 0 λ ) + g 0 ,
m = ( P ̃ T P ̃ ) 1 P ̃ T v = P ̃ + v ,
Cov ( m ) = P ̃ + Cov ( v ) P ̃ + T .
Var ( m ) i = j = 1 N Var ( v ) j ( P ̃ + ) i j 2 ,
Var ( m ) i = α ( P ̃ + ) i 2 2 ,
EWV = 1 α i = 1 16 Var ( m ) i .
EWV = i = 1 16 j = 1 N ( P ̃ + ) i j 2 = Tr [ ( P ̃ + ) T P ̃ + ] = i = 1 16 1 μ i 2 ,

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