Abstract

We address calibration of Mueller polarimeters in transmission configuration and in the presence of noise. By comparing the maximum likelihood (ML) method and the extended eigenvalue calibration method, it is found that the ML method yields higher precision in the presence of noise. Moreover, we show that by employing the ML method together with simple constraints on the calibration matrices, it is possible to perform the calibration without using a retarder, and with only polarizers. This result is of great interest for the calibration of multispectral polarimeters.

© 2014 Optical Society of America

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References

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  1. E. Compain, S. Poirier, and B. Drévillon, Appl. Opt. 38, 3490 (1999).
    [CrossRef]
  2. A. D. Martino, E. Garcia-Caurel, B. Laude, and B. Drévillon, Thin Solid Films 455–456, 112 (2004).
    [CrossRef]
  3. C. Macias-Romero and P. Torok, J. Eur. Opt. Soc. Rapid Pub. 7, 12004 (2012).
    [CrossRef]
  4. R. M. A. Azzam and A. G. Lopez, J. Opt. Soc. Am. A 6, 1513 (1989).
    [CrossRef]
  5. P. S. Hauge, J. Opt. Soc. Am. 68, 1519 (1978).
    [CrossRef]
  6. R. C. Thompson, J. R. Bottiger, and E. S. Fry, Appl. Opt. 19, 1323 (1980).
    [CrossRef]
  7. H. Hu, E. Garcia-Caurel, G. Anna, and F. Goudail, Appl. Opt. 52, 6350 (2013).
    [CrossRef]
  8. A. Mahler and R. Chipman, Appl. Opt. 50, 1726 (2011).
    [CrossRef]
  9. M. Romerein, J. Philippson, R. Brooks, and R. Shiell, Appl. Opt. 50, 5382 (2011).
    [CrossRef]
  10. J. Sanz, C. Extremiana, and J. Saiz, Appl. Opt. 52, 6051 (2013).
    [CrossRef]
  11. O. Arteaga, J. Freudenthal, B. Wang, and B. Kahr, Appl. Opt. 51, 6805 (2012).
    [CrossRef]
  12. A. D. Martino, Y.-K. Kim, E. Garcia-Caurel, B. Laude, and B. Drévillon, Opt. Lett. 28, 616 (2003).
    [CrossRef]
  13. P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization (Academic, 1981).
  14. S. M. Kay, Fundamentals of Statistical Signal Processing—Volume I: Estimation Theory (Prentice-Hall, 1993).
  15. F. Goudail and J. S. Tyo, J. Opt. Soc. Am. A 28, 46 (2011).
    [CrossRef]

2013 (2)

2012 (2)

O. Arteaga, J. Freudenthal, B. Wang, and B. Kahr, Appl. Opt. 51, 6805 (2012).
[CrossRef]

C. Macias-Romero and P. Torok, J. Eur. Opt. Soc. Rapid Pub. 7, 12004 (2012).
[CrossRef]

2011 (3)

2004 (1)

A. D. Martino, E. Garcia-Caurel, B. Laude, and B. Drévillon, Thin Solid Films 455–456, 112 (2004).
[CrossRef]

2003 (1)

1999 (1)

1989 (1)

1980 (1)

1978 (1)

Anna, G.

Arteaga, O.

Azzam, R. M. A.

Bottiger, J. R.

Brooks, R.

Chipman, R.

Compain, E.

Drévillon, B.

Extremiana, C.

Freudenthal, J.

Fry, E. S.

Garcia-Caurel, E.

Gill, P. E.

P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization (Academic, 1981).

Goudail, F.

Hauge, P. S.

Hu, H.

Kahr, B.

Kay, S. M.

S. M. Kay, Fundamentals of Statistical Signal Processing—Volume I: Estimation Theory (Prentice-Hall, 1993).

Kim, Y.-K.

Laude, B.

A. D. Martino, E. Garcia-Caurel, B. Laude, and B. Drévillon, Thin Solid Films 455–456, 112 (2004).
[CrossRef]

A. D. Martino, Y.-K. Kim, E. Garcia-Caurel, B. Laude, and B. Drévillon, Opt. Lett. 28, 616 (2003).
[CrossRef]

Lopez, A. G.

Macias-Romero, C.

C. Macias-Romero and P. Torok, J. Eur. Opt. Soc. Rapid Pub. 7, 12004 (2012).
[CrossRef]

Mahler, A.

Martino, A. D.

A. D. Martino, E. Garcia-Caurel, B. Laude, and B. Drévillon, Thin Solid Films 455–456, 112 (2004).
[CrossRef]

A. D. Martino, Y.-K. Kim, E. Garcia-Caurel, B. Laude, and B. Drévillon, Opt. Lett. 28, 616 (2003).
[CrossRef]

Murray, W.

P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization (Academic, 1981).

Philippson, J.

Poirier, S.

Romerein, M.

Saiz, J.

Sanz, J.

Shiell, R.

Thompson, R. C.

Torok, P.

C. Macias-Romero and P. Torok, J. Eur. Opt. Soc. Rapid Pub. 7, 12004 (2012).
[CrossRef]

Tyo, J. S.

Wang, B.

Wright, M. H.

P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization (Academic, 1981).

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Figures (5)

Fig. 1.
Fig. 1.

Scheme of transmission configuration for calibration.

Fig. 2.
Fig. 2.

(a) Intensity of light source and (b) phase delay of the wave plate as a function of wavelength.

Fig. 3.
Fig. 3.

RMSE of Q^ for extended ECM and ML methods at different wavelengths with two different noise levels. For the ML method, we perform the calibrations with two sets of reference samples: two polarizers at 0° and 90° together with the wave plate (denoted by “2P+R” configuration); three polarizers at 0°, 45°, and 90° (denoted by “3P” configuration). The sampling interval is 5 nm. The SNR in (b) is 10 times that in (a).

Fig. 4.
Fig. 4.

Average value of DOP for the Stokes vectors in W and A as a function of wavelength.

Fig. 5.
Fig. 5.

RMSE of Q^ for extended the ECM and ML method at different wavelengths at different noise levels. The DOP of each Stokes vector in W^ is set to be 0.995, while that in A^ is set to be 0.99. The sampling interval is 5 nm. The SNR in (b) is 10 times that in (a).

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

M(θ,a,b,c)=J(θ)[1a00a10000bc00cb]J(θ),
Ik=βkAMkW,
{ξ^m,ξ^W,ξ^A}=argmaxξm,ξW,ξA{L(ξm,ξW,ξA)},
L(ξm,ξW,ξA)=k([ik]TQmk)2Qmk2,
Fm,k=E[lnL(i|x)xmlnL(i|x)xk],mN,kN,
RMSE=i,j=015(Q^ijQij0)2,

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