Unbiased centroiding of point targets close to the Cramer Rao limit

Systematic errors affecting center-of-gravity (CoG) measurements may occur from coarse sampling of the point-spread-function (PSF) or from signal truncation at the boundaries of the region-of-interest (ROI). For small ROI and PSF widths, these effects are shown to become dominant, but this can be mitigated by introducing novel unbiased estimators that are largely free of systematic error and perform particularly well for low photon number. Analytical expressions for the estimator variances, comprising contributions from photon shot noise, random pixel noise and residual systematic error, are derived and verified by Monte Carlo simulations. The accuracy and computational speed of the unbiased estimators is compared to those of other common estimators, including iteratively weighted CoG, thresholded CoG, iterative least squares fitting, and two-dimensional Gaussian regression. Each estimator is optimized with respect to ROI size and PSF radius and its error compared to the theoretical limit defined by the Cramer Rao lower bound (CRLB). The unbiased estimator with full systematic error correction operating on a small ROI [3x3] emerges as one of the most accurate estimators while requiring significantly less computing effort than alternative algorithms.