Minimum variance unbiased subpixel centroid estimation of point image limited by photon shot noise

Abstract

An unbiased subpixel centroid estimation algorithm of point image is proposed through the compensation of the systematic error of the center of mass method. The Cramér-Rao lower bound on centroid estimation variances is derived under the photon shot noise condition and is utilized to evaluate the proposed algorithm. Numerical analysis shows that the proposed centroid estimator attains the required lower bound; thus the proposed algorithm can be asserted as a minimum variance estimator. Simulation results indicate that the centroid accuracy is maximized when the Gaussian width of the signal spot is 0.2-0.3 pixel and the estimator can attain subpixel accuracy close to 1/100 pixel when 1000 photons are detected.