Performance limitations of a four channel polarimeter in the presence of detection

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 exciting 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.