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

The performance limitations of an imperfectly calibrated four- channel polarimeter in the presence of photon-counting detection noise is examined for arbitrary light levels. The theory described here provides a framework for developing polarimeter designs with minimal noise sen- sitivity and to evaluate the noise performance of existing designs. The polarimeter decomposes the input field into four channels, each of which is detected by the photon-counting sensor. We theoretically describe the propagation of detection noise through the polarimeter calibration matrix. The variances of both the mutual phase delay and the orthogonal inten- sities are given for photon-counting noise following Poisson statistics, and additive Gaussian detection noise. The variances of these param- eters depend on the average number of photons incident on the polar- imeter, the detector read noise, and errors in the polarimeter calibration matrix. A particular polarimeter design, whose calibration matrix is known exactly, is examined for moderate, low, and very low light levels. Theo- retical performance curves are shown for various sensor parameters and light levels, and are compared to simulated results. Very good agree- ment between theory and simulation is shown. The simulation validates the use of the Gaussian probability density function for the parallel (in- phase) and normal components of the phase fluctuations, and provides an accurate theoretical prediction of phase delay fluctuations for arbitrary light levels. The phase-delay noise cloud is illustrated for several cases.