Estimation of the Stokes vector is based on projecting the input light on a number of polarization analysis states. We address the optimization of the distribution of these analysis states on the Poincaré sphere in the presence of signal-dependent Poisson shot noise for an arbitrary value of . We show that if this distribution forms a spherical 3 design, the Stokes vector is estimated with minimal equally weighted variance and with estimation variances of the last three Stokes parameters equal and independent of the input Stokes vector. We also demonstrate that in the presence of Poisson shot noise, the estimation signal to noise ratio is independent of , whereas in the presence of signal independent additive noise, it is proportional to , which means that there is a precision loss in increasing the number of measurements.
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