Unbiased centroiding of point targets close to the Cramer Rao limit

TL;DR

This paper introduces novel unbiased estimators for centroiding point targets that significantly reduce systematic errors near the Cramer Rao limit, especially for small regions and low photon counts, outperforming traditional methods.

Contribution

The authors develop and validate new unbiased centroid estimators that minimize systematic errors and improve accuracy and speed compared to existing methods.

Findings

Unbiased estimators outperform traditional methods near the CRLB.

Full systematic error correction with small ROI [3x3] achieves high accuracy.

Estimators are computationally efficient and robust for low photon numbers.

Abstract

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.