<title>Performance limitations of a four-channel polarimeter in the presence of detection noise</title>

Abstract

We examine the performance limitations of a four-channel polarimeter in the presence of detection noise for arbitrary light levels. We treat the case where the light exiting the polarimeter is detected by a photon counting sensor at each of the four channels. Specifically, we theoretically describe the propagation of detection noise through the polarimeter calibration matrix. The variances in the four estimated Stokes vector components, both orthogonal intensities and mutual phase delay are theoretically predicted for photon counting noise following Poison statistics, and additive Gaussian detection noise. The variances of these parameters depend on the average number of photons incident on the polarimeter, the root-mean-square read noise, and the polarimeter calibration matrix. This methodology allows for including fixed errors in the polarimeter calibration matrix. Various polarimeter designs, whose calibration matrices are known exactly, are examined for high, low and very low light levels. Theoretical performance curves are shown for various sensor parameters and light levels. The theoretically predicted values are compared to simulated results. Excellent agreement between theory and simulation is shown. The simulation also validates the use of the Gaussian probability density function for the parallel (in-phase) and normal components of the phase fluctuations. and results in an accurate theoretical prediction of phase delay fluctuations for arbitrary light levels. The phase delay noise cloud is illustrated for several cases.

Optimization and performance criteria of a Stokes polarimeter based on two variable retarders

“…In order to diminish the effect of noise in the final measurements, some studies have been carried out [7,[13][14][15][16][17]. For instance, different indicators as the condition number (CN) [18] or the equally weighted variance (EWV) [7] have been used in optimization procedures.…”

Target detection in active polarization images perturbed with additive noise and illumination nonuniformity

“…The problem of OSC estimation has been widely addressed with different types of noise, such as for example speckle noise, coupled photon and speckle noise, and detector noise [12][13][14]. More recently, we addressed the case of additive and signal-dependent photon noise [15], which presents great similarities with the case of additive Gaussian noise [16].…”