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High precision polarization measurements open new opportunities for the studyof the magnetic field structure as traced by polarimetric measurements of theinterstellar dust emission. Polarization parameters suffer from bias in thepresence of measurement noise. It is critical to take into account all theinformation available in the data in order to accurately derive theseparameters. The goal of this paper is to characterize the bias on thepolarization angle dispersion function that is used to study the spatialcoherence of the polarization angle. We characterize, for the first time, thebias on the conventional estimator of the polarization angle dispersionfunction (S hereafter) and show that it can be positive or negative dependingon the true value. Monte Carlo simulations are performed in order to explorethe impact of the noise properties of the polarization data, as well as theimpact of the distribution of the true polarization angles on the bias. We showthat in the case where the ellipticity of the noise in (Q, U) varies by lessthan 10 percent, one can use simplified, diagonal approximation of the noisecovariance matrix. In other cases, the shape of the noise covariance matrixshould be taken into account in the estimation of S. We also study newestimators such as the dichotomic and the polynomial estimators. Though thedichotomic estimator cannot be directly used to estimate S, we show that, onthe one hand, it can serve as an indicator of the accuracy of the conventionalestimator and, on the other hand, it can be used for deriving the polynomialestimator. We propose a method for determining the upper limit of the bias onthe conventional estimator of S. The method is applicable to any linearpolarization data set for which the noise covariance matrices are known.

Polarization measurement analysis III. Analysis of the polarization angle dispersion function with high precision polarization data