Abstract

An imaging variable retardance polarimeter was developed and tested by Tyo and Turner [Proc. SPIE 3753, 214 (1999)]. The signal-to-noise ratio (SNR) in the reconstructed polarization images obtained with this system varied for the four Stokes parameters. The difference in SNR is determined to be due to differences in the Euclidean lengths of the rows of the synthesis matrix used to reconstruct the Stokes parameters from the measured intensity data. I equalize (and minimize) the lengths of the rows of this matrix by minimizing the condition number of the synthesis matrix, thereby maximizing the relative importance of each of the polarimeter measurements. The performance of the optimized system is demonstrated with simulated data, and the SNR is shown to increase from a worst case of -3.1 dB for the original settings to a worst case of +5.0 dB for the optimized system.

© 2000 Optical Society of America

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References

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  1. L. J. Cheng, J. C. Mahoney, and G. Reyes, Proc. SPIE 2237, 251 (1994).
    [CrossRef]
  2. J. S. Tyo, M. P. Rowe, E. N. Pugh, and N. Engheta, Appl. Opt. 35, 1855 (1996).
    [CrossRef] [PubMed]
  3. M. P. Silverman and W. Strange, Opt. Commun. 144, 7 (1997).
    [CrossRef]
  4. J. S. Tyo and T. S. Turner, Proc. SPIE 3753, 214 (1999).
    [CrossRef]
  5. G. H. Golub and C. F. van Loan, Matrix Computations (Johns Hopkins U. Press, Baltimore, Md., 1983), Chap. 2, pp. 11–29.
  6. A. Ambirajan and D. C. Look, Opt. Eng. 34, 1651, 1656 (1995).
  7. D. S. Sabatke, M. R. Descour, E. Dereniak, W. C. Sweatt, S. A. Kemme, and G. S. Phipps, Opt. Lett. 25, 802 (2000).
    [CrossRef]
  8. J. S. Tyo, J. Opt. Soc. Am. A 15, 359 (1998).
    [CrossRef]

2000 (1)

1999 (1)

J. S. Tyo and T. S. Turner, Proc. SPIE 3753, 214 (1999).
[CrossRef]

1998 (1)

1997 (1)

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

1996 (1)

1995 (1)

A. Ambirajan and D. C. Look, Opt. Eng. 34, 1651, 1656 (1995).

1994 (1)

L. J. Cheng, J. C. Mahoney, and G. Reyes, Proc. SPIE 2237, 251 (1994).
[CrossRef]

Ambirajan, A.

A. Ambirajan and D. C. Look, Opt. Eng. 34, 1651, 1656 (1995).

Cheng, L. J.

L. J. Cheng, J. C. Mahoney, and G. Reyes, Proc. SPIE 2237, 251 (1994).
[CrossRef]

Dereniak, E.

Descour, M. R.

Engheta, N.

Golub, G. H.

G. H. Golub and C. F. van Loan, Matrix Computations (Johns Hopkins U. Press, Baltimore, Md., 1983), Chap. 2, pp. 11–29.

Kemme, S. A.

Look, D. C.

A. Ambirajan and D. C. Look, Opt. Eng. 34, 1651, 1656 (1995).

Mahoney, J. C.

L. J. Cheng, J. C. Mahoney, and G. Reyes, Proc. SPIE 2237, 251 (1994).
[CrossRef]

Phipps, G. S.

Pugh, E. N.

Reyes, G.

L. J. Cheng, J. C. Mahoney, and G. Reyes, Proc. SPIE 2237, 251 (1994).
[CrossRef]

Rowe, M. P.

Sabatke, D. S.

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]

Sweatt, W. C.

Turner, T. S.

J. S. Tyo and T. S. Turner, Proc. SPIE 3753, 214 (1999).
[CrossRef]

Tyo, J. S.

van Loan, C. F.

G. H. Golub and C. F. van Loan, Matrix Computations (Johns Hopkins U. Press, Baltimore, Md., 1983), Chap. 2, pp. 11–29.

Appl. Opt. (1)

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

Opt. Commun. (1)

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

Opt. Eng. (1)

A. Ambirajan and D. C. Look, Opt. Eng. 34, 1651, 1656 (1995).

Opt. Lett. (1)

Proc. SPIE (2)

L. J. Cheng, J. C. Mahoney, and G. Reyes, Proc. SPIE 2237, 251 (1994).
[CrossRef]

J. S. Tyo and T. S. Turner, Proc. SPIE 3753, 214 (1999).
[CrossRef]

Other (1)

G. H. Golub and C. F. van Loan, Matrix Computations (Johns Hopkins U. Press, Baltimore, Md., 1983), Chap. 2, pp. 11–29.

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Figures (3)

Fig. 1
Fig. 1

Simulated noisy data from the VR parameter settings of Ref. 4. The actual image distribution has a Stokes vector of 3 1 1 1T in the central region and of 0 outside. The gray-scale axes are stretched to maximize the dynamic range. For A s0, the gray-scale range corresponds to reconstructed values from -2.93 to 4.13; for B, C, and D (s1, s2, and s3), the range is from -5.70 to 5.53.

Fig. 2
Fig. 2

Simulated data for the optimized settings given in this study. Actual image distributions are the same as in Fig. 1. The gray-scale ranges maximize dynamic range and are different from those in Fig. 1. The gray-scale range corresponds to reconstructed values from -0.96 to 2.79. For B, C, and D (s1, s2, and s3) the range is from -2.04 to 2.98. The optimization is not restricted to this particular Stokes vector, as the system condition is independent of the input.

Fig. 3
Fig. 3

Regions accessible by the VR polarimeter with ϕ1=22.5° and ϕ2=45°. These are polar projections with left- and right-elliptically polarized (LEP and REP) states in the north and south hemispheres, respectively. The straight lines actually form coaxial circles on the Poincaré sphere. The common axis bisects the angle between the s1 and s2 axes. The points form inscribed regular tetrahedrons and are optimal configurations. Crosses, 158°,50.6°, 127°,-178°, 47.0°,-16.9°, and 0.659°,126°. Circles, 160°,50.1°, -10.1°,144°, 89.8°,-144°, and 57.4°,-12.9°. Triangles, values in the text.

Equations (3)

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Is0,out=M11s0+M12s1+M12s2+M11s3.
varsi=σ2Bi+122,
Ap=supxDAAxp/xp,  xpp=ixip,

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