Abstract

Imaging polarimeters infer the spatial distribution of the polarization state of the optical field as a function of time and/or wavelength. A polarimeter indirectly determines the polarization state by first modulating the intensity of the light field and then demodulating the measured data to infer the polarization parameters. This Letter considers passive Stokes parameter polarimeters and their inversion methods. The most widely used method is the data reduction matrix (DRM), which builds up a matrix equation that can be inverted to find the polarization state from a set of intensity measurements. An alternate strategy uses linear system formulations that allow band limited reconstruction through a filtering perspective. Here we compare these two strategies for overdetermined polarimeters and find that design of the null space of the inversion operator provides degrees of freedom to optimize the trade off between accuracy and signal-to-noise ratio. We further describe adaptive filtering techniques that could optimize the reconstruction for a particular experimental configuration. This Letter considers time-varying Stokes parameters, but the methods apply equally to polarimeters that are modulated in space or in wavelength.

© 2012 Optical Society of America

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References

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  1. C. F. LaCasse, R. A. Chipman, and J. S. Tyo, Opt. Express 19, 14976 (2011).
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  2. R. A. Chipman, in Handbook of Optics, Vol. 2, M. Bass, ed. (McGraw-Hill, 1995).
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    [CrossRef]
  5. M. P. Silverman and W. Strange, Opt. Commun. 144, 7 (1997).
    [CrossRef]
  6. D. J. Diner, A. Davis, B. Hancock, G. Gutt, R. A. Chipman, and B. Cairns, Appl. Opt. 46, 8428 (2007).
    [CrossRef]
  7. J. S. Tyo, C. F. LaCasse, and B. M. Ratliff, Opt. Lett. 34, 3187 (2009).
    [CrossRef]
  8. R. A. Chipman, Proc. SPIE 1317, 223 (1990).
    [CrossRef]
  9. D. J. Diner, A. Davis, B. Hancock, S. Geier, B. Rheingans, V. Jovanovic, M. Bull, D. M. R. R. A. Chipman, A.-B. Mahler, and S. C. McClain, Appl. Opt. 49, 2929 (2010).
    [CrossRef]
  10. C. F. LaCasse, J. S. Tyo, and R. A. Chipman, in Proceedings of IEEE Aerospace Conference (IEEE, to be published).
  11. B. M. Ratliff, C. F. LaCasse, and J. S. Tyo, in Proceedings of IEEE Aerospace Conference (IEEE, 2011).
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    [CrossRef]
  13. C. F. LaCasse, T. Ririe, R. A. Chipman, and J. S. Tyo, Proc. SPIE 8160, 81600K (2011).
    [CrossRef]

2011

C. F. LaCasse, T. Ririe, R. A. Chipman, and J. S. Tyo, Proc. SPIE 8160, 81600K (2011).
[CrossRef]

C. F. LaCasse, R. A. Chipman, and J. S. Tyo, Opt. Express 19, 14976 (2011).
[CrossRef]

2010

2009

2008

2007

2001

1997

M. P. Silverman and W. Strange, Opt. Commun. 144, 7 (1997).
[CrossRef]

1990

R. A. Chipman, Proc. SPIE 1317, 223 (1990).
[CrossRef]

1977

Azzam, R. M. A.

Bull, M.

Cairns, B.

Chipman, D. M. R. R. A.

Chipman, R. A.

C. F. LaCasse, T. Ririe, R. A. Chipman, and J. S. Tyo, Proc. SPIE 8160, 81600K (2011).
[CrossRef]

C. F. LaCasse, R. A. Chipman, and J. S. Tyo, Opt. Express 19, 14976 (2011).
[CrossRef]

D. J. Diner, A. Davis, B. Hancock, G. Gutt, R. A. Chipman, and B. Cairns, Appl. Opt. 46, 8428 (2007).
[CrossRef]

R. A. Chipman, Proc. SPIE 1317, 223 (1990).
[CrossRef]

C. F. LaCasse, J. S. Tyo, and R. A. Chipman, in Proceedings of IEEE Aerospace Conference (IEEE, to be published).

R. A. Chipman, in Handbook of Optics, Vol. 2, M. Bass, ed. (McGraw-Hill, 1995).

Davis, A.

Dereniak, E. L.

Diner, D. J.

Geier, S.

Gerhart, G. R.

Gutt, G.

Hancock, B.

Jovanovic, V.

Kudenov, M. W.

LaCasse, C. F.

C. F. LaCasse, T. Ririe, R. A. Chipman, and J. S. Tyo, Proc. SPIE 8160, 81600K (2011).
[CrossRef]

C. F. LaCasse, R. A. Chipman, and J. S. Tyo, Opt. Express 19, 14976 (2011).
[CrossRef]

J. S. Tyo, C. F. LaCasse, and B. M. Ratliff, Opt. Lett. 34, 3187 (2009).
[CrossRef]

C. F. LaCasse, J. S. Tyo, and R. A. Chipman, in Proceedings of IEEE Aerospace Conference (IEEE, to be published).

B. M. Ratliff, C. F. LaCasse, and J. S. Tyo, in Proceedings of IEEE Aerospace Conference (IEEE, 2011).

Mahler, A.-B.

McClain, S. C.

Pezzaniti, L.

Ratliff, B. M.

J. S. Tyo, C. F. LaCasse, and B. M. Ratliff, Opt. Lett. 34, 3187 (2009).
[CrossRef]

B. M. Ratliff, C. F. LaCasse, and J. S. Tyo, in Proceedings of IEEE Aerospace Conference (IEEE, 2011).

Rheingans, B.

Ririe, T.

C. F. LaCasse, T. Ririe, R. A. Chipman, and J. S. Tyo, Proc. SPIE 8160, 81600K (2011).
[CrossRef]

Silverman, M. P.

M. P. Silverman and W. Strange, Opt. Commun. 144, 7 (1997).
[CrossRef]

Strange, W.

M. P. Silverman and W. Strange, Opt. Commun. 144, 7 (1997).
[CrossRef]

Turner, T. S.

Tyo, J. S.

C. F. LaCasse, R. A. Chipman, and J. S. Tyo, Opt. Express 19, 14976 (2011).
[CrossRef]

C. F. LaCasse, T. Ririe, R. A. Chipman, and J. S. Tyo, Proc. SPIE 8160, 81600K (2011).
[CrossRef]

J. S. Tyo, C. F. LaCasse, and B. M. Ratliff, Opt. Lett. 34, 3187 (2009).
[CrossRef]

J. S. Tyo and T. S. Turner, Appl. Opt. 40, 1450 (2001).
[CrossRef]

C. F. LaCasse, J. S. Tyo, and R. A. Chipman, in Proceedings of IEEE Aerospace Conference (IEEE, to be published).

B. M. Ratliff, C. F. LaCasse, and J. S. Tyo, in Proceedings of IEEE Aerospace Conference (IEEE, 2011).

Appl. Opt.

Opt. Commun.

M. P. Silverman and W. Strange, Opt. Commun. 144, 7 (1997).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. SPIE

R. A. Chipman, Proc. SPIE 1317, 223 (1990).
[CrossRef]

C. F. LaCasse, T. Ririe, R. A. Chipman, and J. S. Tyo, Proc. SPIE 8160, 81600K (2011).
[CrossRef]

Other

R. A. Chipman, in Handbook of Optics, Vol. 2, M. Bass, ed. (McGraw-Hill, 1995).

C. F. LaCasse, J. S. Tyo, and R. A. Chipman, in Proceedings of IEEE Aerospace Conference (IEEE, to be published).

B. M. Ratliff, C. F. LaCasse, and J. S. Tyo, in Proceedings of IEEE Aerospace Conference (IEEE, 2011).

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Figures (2)

Fig. 1.
Fig. 1.

The frequency domain representation of the space spanned by each of the modulators in Eq. (12) as for an RR polarimeter. In this particular case, the DC component contributes to s0 and s1, the 2f0 component contributes to s3, and the in-phase and quadrature components at 4f0 contribute to s1 and s2, respectively. All other frequencies are rejected.

Fig. 2.
Fig. 2.

The space spanned by the BLR operator for each of the Stokes parameters. Each band of frequencies is dedicated to a particular set of Stokes parameters, and there is no attenuation in the band.

Equations (13)

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

Sin(t)=[s0(t)s1(t)s2(t)s3(t)]T,
A(t)=[a0(t)a1(t)a2(t)a3(t)]T,
I(t)=[a0(t)s0(t)+a1(t)s1(t)+a2(t)s2(t)+a3(t)s3(t).
I=[I1IN]=[A1AN]Sin=W̲̲Sin.
S^=W̲̲1I,
S^(no)=n=0N1w[nn0]Z̲̲1[n]A[n]I[n],
Z̲̲[n]=w[n]*A[n]AT[n].
Zij=1Nn=1Nai[n]aj[n].
S^[no=0]=n=0N1w[n]Z̲̲1A[n]I[n].
S^[no=0]=w˜[f]*Z̲̲1A˜(f)*I˜(f)|f=0,
S^[no=0]=Z̲̲1A˜(f)I˜*(f)df.
A(t)=[a0(t)a1(t)a2(t)a3(t)]=[11+cosδ2+(1cosδ2)cos(2π4f0t)(1cosδ2)sin(2π4f0t)sinδsin(2π2f0t)].
w˜(f)=rect(f/(2fo)).

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