Optical EngineeringPerformance limitations of a four-channel polarimeter in the presence of detection noise
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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 sensitivity 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 intensities are given for photon-counting noise following Poisson statistics, and additive Gaussian detection noise. The variances of these parameters depend on the average number of photons incident on the polarimeter, 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. Theoretical performance curves are shown for various sensor parameters and light levels, and are compared to simulated results. Very good agreement between theory and simulation is shown. The simulation validates the use of the Gaussian probability density function for the parallel (inphase) 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.