Unbiased centroiding of point targets close to the Cramer Rao limit
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This paper focuses on the achievable accuracy of center-of-gravity (CoG) centroiding with respect to the ultimate limits defined by the Cramer Rao lower variance bounds. In a practical scenario, systematic centroiding errors occur through coarse sampling of the points-spread-function (PSF) as well as signal truncation errors at the boundaries of the region-of-interest (ROI). While previous studies focused on sampling errors alone, this paper derives and analyzes the full systematic error, as truncation error become increasingly important for small ROIs where the effect of random pixel noise may be more efficiently suppressed than for large ROIs. Unbiased estimators are introduced and analytical expressions derived for their variance, detailing the effects of photon shot noise, pixel random noise and residual systematic error. Analytical results are verified by Monte Carlo simulations and the performances compared to those of other algorithms, such as Iteratively Weighted CoG, Thresholded CoG, and Least Squares Fits. The unbiased estimators allow achieving centroiding errors very close to the Cramer Rao Lower Bound (CRLB), for low and high photon number, at significantly lower computational effort than other algorithms. Additionally, optimal configurations in relation to PSF radius and ROI size and other specific parameters, are determined for all other algorithms, and their normalized centroid error assessed with respect to the CRLB.
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