The accuracy of locating weak photographic star images is described from a theoretical viewpoint. The objective is to determine the accuracy limitations imposed by the granular nature of the photographic image, by background radiation, and by image size and shape. After selecting models for both saturated and unsaturated images, lower bounds are derived for the rms location errors. These relationships are based on results developed for photoelectric images. The bounds apply to every method of interrogating the photographic images, and thus represent intrinsic limitations. For unsaturated images, the bound is a monotone function of the image “spread” σ; it is approximately proportional to σ(<i>c</i>-lnσ)<sup>-½</sup> where <i>c</i> is a constant. For saturated images, the bound is not necessarily a monotone function of the image spread. The bound may <i>decrease</i> as the image spread <i>increases</i>. The error bounds are compared to experimental errors. For an eighteenth-magnitude star, the bound is 70% of the experimental errors observed with plates from the 48-in. Schmidt telescope on Palomar.
EDWARD J. FARRELL, "Intrinsic Limitations in Locating Photographic Star Images," J. Opt. Soc. Am. 56, 1385-1389 (1966)