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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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Shape parameters for the optimized polarimeter.
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fig06: Shape parameters for the optimized polarimeter.

Mentions: The optimization method we present is used to improve the performance of the original Compain prism. We allowed the PSA prism’s shape to vary without constraining it to be a parallelepiped. The parameters that defined the model of the prism were the material (refractive index and absorption), the three shape angles ϕ1, ϕ2, and ϕ3 illustrated in Fig. 6, and the angle of incidence of the beam (ϕ0) on the prism. As in the Compain PSA, an ideal polarizing beam-splitter was placed at each exit port A and B, shown in Fig. 6. The orientations of these last beam-splitters were initially left as free parameters, but the optimization always returned 45° for both beam-splitters. The path length inside the prism was fixed at 10 cm to allow fair comparison between materials of different absorption. We performed optimizations for three different types of glass that resulted in three different prism geometries. The cost functions of the optimized prisms are shown in Table 1, together with those for the three PSAs compared in Section 4.1. The first optimized prism (Optim1) uses the same glass parameters as the Compain prism: Corning glass E00-046 (refractive index (RI)=1.812, absorption constant α=1.123 m-1). The noise cost function was reduced despite the new prism having a slightly larger condition number than the Compain prism (see Table 1). The second prism (Optim2) uses a different glass, Shott SF57HHT (RI=1.872, α=0.548 m-1), which resulted in a even smaller cost function. Finally, we included the refractive index of the material as a free parameter, with an ideal zero absorption constant (Optim3). Note that reducing the overall pathlength inside the prism reduces the impact of absorption, although the extent to which this is possible depends on the required optical geometry. By including these material effects in the optimization, the method presented can be used to evaluate the suitability of different materials for a PSA. For the sake of comparison, Figure 7 shows the noise on the Stokes parameters calculated for the Optim3 prism. The resulting parameters for the optimized prism are: RI=2.11, ϕ0=81.19°, ϕ1=78.53°, ϕ2=52.85°, and ϕ3=53.54°. The instrument matrix for this optimized polarimeter is


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

Lara D, Paterson C - Opt Express (2009)

Shape parameters for the optimized polarimeter.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig06: Shape parameters for the optimized polarimeter.
Mentions: The optimization method we present is used to improve the performance of the original Compain prism. We allowed the PSA prism’s shape to vary without constraining it to be a parallelepiped. The parameters that defined the model of the prism were the material (refractive index and absorption), the three shape angles ϕ1, ϕ2, and ϕ3 illustrated in Fig. 6, and the angle of incidence of the beam (ϕ0) on the prism. As in the Compain PSA, an ideal polarizing beam-splitter was placed at each exit port A and B, shown in Fig. 6. The orientations of these last beam-splitters were initially left as free parameters, but the optimization always returned 45° for both beam-splitters. The path length inside the prism was fixed at 10 cm to allow fair comparison between materials of different absorption. We performed optimizations for three different types of glass that resulted in three different prism geometries. The cost functions of the optimized prisms are shown in Table 1, together with those for the three PSAs compared in Section 4.1. The first optimized prism (Optim1) uses the same glass parameters as the Compain prism: Corning glass E00-046 (refractive index (RI)=1.812, absorption constant α=1.123 m-1). The noise cost function was reduced despite the new prism having a slightly larger condition number than the Compain prism (see Table 1). The second prism (Optim2) uses a different glass, Shott SF57HHT (RI=1.872, α=0.548 m-1), which resulted in a even smaller cost function. Finally, we included the refractive index of the material as a free parameter, with an ideal zero absorption constant (Optim3). Note that reducing the overall pathlength inside the prism reduces the impact of absorption, although the extent to which this is possible depends on the required optical geometry. By including these material effects in the optimization, the method presented can be used to evaluate the suitability of different materials for a PSA. For the sake of comparison, Figure 7 shows the noise on the Stokes parameters calculated for the Optim3 prism. The resulting parameters for the optimized prism are: RI=2.11, ϕ0=81.19°, ϕ1=78.53°, ϕ2=52.85°, and ϕ3=53.54°. The instrument matrix for this optimized polarimeter is

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