The Cramer-Rao lower bound and stellar photometry with aberrated HST images

Abstract

The Cramer-Rao lower bound theorem of statistics is applied to the problem of extracting 2D stellar photometry from aberrated Hubble Space Telescope camera images. The theorem is used to derive a simple and general expression for the best possible photometric precision that can be derived from a given image, regardless of what image processing or deconvolution techniques are applied to the data. This hard limit, which reflects the underlying photon statistics of the overlapping stellar images, is quite universal in nature and valid for arbitrary point spread function and any degree of crowding. The form of the expression is also such that it can be used to estimate a minimum statistical photometric error directly from the raw data once the positions of the stars in the image are known. As a specific example, the Cramer-Rao lower bound is used to quantify the irrecoverable loss in sensitivity introduced by the HST spherical aberration in the case of the Faint Object Camera.