The Estimation of the "Center of Gravity" of a Photon Density Profile in Noise

A model for an optical position estimation system is developed employing the photon Poisson process theory. The position estimate is based upon the definition of a center of gravity (CG) of the power density profile of the optical source on the focal plane. An estimator structure is derived using maximum likelihood estimates of the image profile. The resulting estimate of the CG is shown to be unbiased and its variance is obtained. The variance is shown to depend upon the signal energy and noise level as well as upon the distance of the center from the initial counting point. Thus, a composite estimation system is presented which reduces the variance and yet yields a simple structure. Studies on star estimation have yielded position accuracies better than 0.1 seconds of arc for a 2.5 visual magnitude star in a background of equivalent intensity.