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Stokes polarimeter optimization in the presence of shot and Gaussian noise.

Lara D, Paterson C - Opt Express (2009)

Bottom Line: The expectation of the Stokes vector variance is used as a performance measure.This measure is compared with the condition number of a polarization state analyzer matrix that is commonly used as a figure of merit.The approach is used to optimize existing prism based polarimeters giving improvements in the performance when shot-noise cannot be neglected.

View Article: PubMed Central - PubMed

Affiliation: The Blackett Laboratory, Imperial College London, SW7 2BW, UK. d.lara@imperial.ac.uk

ABSTRACT
An error minimization method is presented for Stokes polarimeters applicable when the detected signals are affected by a combination of shot and Gaussian noise. The expectation of the Stokes vector variance is used as a performance measure. This measure is compared with the condition number of a polarization state analyzer matrix that is commonly used as a figure of merit. We show that a polarimeter with the minimum condition number is not necessarily optimal. The approach is used to optimize existing prism based polarimeters giving improvements in the performance when shot-noise cannot be neglected.

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Sampling of states of polarization represented on the surface of the Poincaré sphere. Uniformly distributed samples are taken along a right-handed spiral locus that starts at the south pole and finishes at the north pole, with 128 samples per revolution (For clarity the figure shows only 24 revolutions, though 128 were used in the numerical evaluation). Parameters u and θ are uniformly distributed within the intervals shown.
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fig02: Sampling of states of polarization represented on the surface of the Poincaré sphere. Uniformly distributed samples are taken along a right-handed spiral locus that starts at the south pole and finishes at the north pole, with 128 samples per revolution (For clarity the figure shows only 24 revolutions, though 128 were used in the numerical evaluation). Parameters u and θ are uniformly distributed within the intervals shown.

Mentions: In this paper the cost function is evaluated numerically. The particular method we choose is to sample the states of polarization along a spiral locus around the Poincaré sphere with the spiral locus and azimuthal sampling chosen to give approximately uniform distribution of samples over the sphere (Fig. 2). By mapping samples to a one-parameter locus this method also makes it straightforward to show the behavior over the whole sphere on a simple plot, as will be seen later in Figs. 3–5.


Stokes polarimeter optimization in the presence of shot and Gaussian noise.

Lara D, Paterson C - Opt Express (2009)

Sampling of states of polarization represented on the surface of the Poincaré sphere. Uniformly distributed samples are taken along a right-handed spiral locus that starts at the south pole and finishes at the north pole, with 128 samples per revolution (For clarity the figure shows only 24 revolutions, though 128 were used in the numerical evaluation). Parameters u and θ are uniformly distributed within the intervals shown.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3369578&req=5

fig02: Sampling of states of polarization represented on the surface of the Poincaré sphere. Uniformly distributed samples are taken along a right-handed spiral locus that starts at the south pole and finishes at the north pole, with 128 samples per revolution (For clarity the figure shows only 24 revolutions, though 128 were used in the numerical evaluation). Parameters u and θ are uniformly distributed within the intervals shown.
Mentions: In this paper the cost function is evaluated numerically. The particular method we choose is to sample the states of polarization along a spiral locus around the Poincaré sphere with the spiral locus and azimuthal sampling chosen to give approximately uniform distribution of samples over the sphere (Fig. 2). By mapping samples to a one-parameter locus this method also makes it straightforward to show the behavior over the whole sphere on a simple plot, as will be seen later in Figs. 3–5.

Bottom Line: The expectation of the Stokes vector variance is used as a performance measure.This measure is compared with the condition number of a polarization state analyzer matrix that is commonly used as a figure of merit.The approach is used to optimize existing prism based polarimeters giving improvements in the performance when shot-noise cannot be neglected.

View Article: PubMed Central - PubMed

Affiliation: The Blackett Laboratory, Imperial College London, SW7 2BW, UK. d.lara@imperial.ac.uk

ABSTRACT
An error minimization method is presented for Stokes polarimeters applicable when the detected signals are affected by a combination of shot and Gaussian noise. The expectation of the Stokes vector variance is used as a performance measure. This measure is compared with the condition number of a polarization state analyzer matrix that is commonly used as a figure of merit. We show that a polarimeter with the minimum condition number is not necessarily optimal. The approach is used to optimize existing prism based polarimeters giving improvements in the performance when shot-noise cannot be neglected.

Show MeSH
Related in: MedlinePlus