Limits...
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.

Show MeSH

Related in: MedlinePlus

Signal to noise ratio of an APD and transimpedance amplifier combination operating at 8MHz sampling rate and with 5 nW of optical power falling on the detector. Realistic model of APD Perkin Elmer C30902E and a transimpedance amplifier with noise current of 3pA/Hz1/2.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC3369578&req=5

fig01: Signal to noise ratio of an APD and transimpedance amplifier combination operating at 8MHz sampling rate and with 5 nW of optical power falling on the detector. Realistic model of APD Perkin Elmer C30902E and a transimpedance amplifier with noise current of 3pA/Hz1/2.

Mentions: Stringent illumination conditions make the avalanche photodiode (APD) a suitable detector for a laser scanning ophthalmoscope. APDs have three main sources of noise [13, 14]: 1) fluctuations in the dark surface current, 2) fluctuations in the dark leakage current which are amplified by the gain of the APD, and 3) excess (shot) noise due to the statistical nature of the avalanche multiplication process. This last type of noise depends on the optical signal strength and the gain of the APD, and can be much higher than the other two, which results in shot noise limited operation of the APD. After the avalanche multiplication the current produced by the APD is typically fed to a transimpedance amplifier and therefore is affected by the amplifier’s thermal (Gaussian) noise. The exact mechanism of the production of noise in a APD-amplifier module falls beyond the scope of this paper, but it is well understood and documented [13–15]. We may note, however, that the combination of all these sources of noise results in a strong dependence of the overall signal to noise ratio (SNR) on the gain of the APD. This SNR reaches an optimum value approximately when the shot noise equals the thermal noise [13], hence neither should be neglected. Figure 1 shows the SNR as a function of the APD gain in a realistic detector suitable for a scanning laser ophthalmoscope.


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

Lara D, Paterson C - Opt Express (2009)

Signal to noise ratio of an APD and transimpedance amplifier combination operating at 8MHz sampling rate and with 5 nW of optical power falling on the detector. Realistic model of APD Perkin Elmer C30902E and a transimpedance amplifier with noise current of 3pA/Hz1/2.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig01: Signal to noise ratio of an APD and transimpedance amplifier combination operating at 8MHz sampling rate and with 5 nW of optical power falling on the detector. Realistic model of APD Perkin Elmer C30902E and a transimpedance amplifier with noise current of 3pA/Hz1/2.
Mentions: Stringent illumination conditions make the avalanche photodiode (APD) a suitable detector for a laser scanning ophthalmoscope. APDs have three main sources of noise [13, 14]: 1) fluctuations in the dark surface current, 2) fluctuations in the dark leakage current which are amplified by the gain of the APD, and 3) excess (shot) noise due to the statistical nature of the avalanche multiplication process. This last type of noise depends on the optical signal strength and the gain of the APD, and can be much higher than the other two, which results in shot noise limited operation of the APD. After the avalanche multiplication the current produced by the APD is typically fed to a transimpedance amplifier and therefore is affected by the amplifier’s thermal (Gaussian) noise. The exact mechanism of the production of noise in a APD-amplifier module falls beyond the scope of this paper, but it is well understood and documented [13–15]. We may note, however, that the combination of all these sources of noise results in a strong dependence of the overall signal to noise ratio (SNR) on the gain of the APD. This SNR reaches an optimum value approximately when the shot noise equals the thermal noise [13], hence neither should be neglected. Figure 1 shows the SNR as a function of the APD gain in a realistic detector suitable for a scanning laser ophthalmoscope.

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