Introduction

Astronomical images are commonly taken with the intent of making photometric measurements of objects in the field. For pre-COSTAR HST images, the question then arises: should these measurements be made on the original or on the restored image? When the objects of interest are stellar, we might intuitively expect that higher accuracy will be achieved using the restored image. The reason for this is that the sharpening of point sources should allow the photometry to be carried out with a smaller aperture, thus reducing contamination by light from nearby sources and from the background.

Unfortunately, two effects have hindered the realization of this expected gain in accuracy. The first arises when the stars to be measured are superposed on an extended background source - nebular emission or numerous unresolved stars. In this circumstance, non-linear restoration techniques - e.g., Richardson-Lucy (R-L) or Maximum Entropy (ME) - give rise to Gibbs oscillations or ``ringing'' as they attempt the impossible task of recovering delta functions. Because of this effect, image restoration does not necessarily increase the rate at which a photometric measurement of a stellar object converges with increasing aperture.

The second effect is statistical bias and is of particular concern for ME restorations. When entropy is defined relative to a uniform prior (or default) image, the restored ME image departs from uniformity because of real structure in the observed image, but only by the amount required by the adopted goodness-of-fit criterion. Accordingly, the restored ME image is biased in favor of uniformity (flatness), and this implies that the highest intensity peaks are underestimated.

For stellar photometry, these problems have led to the suggestion that the restored HST image be used merely to identify and locate point sources, with the actual photometric measurements being then made on the original image. Here, however, the possibility is explored of developing more powerful restoration procedures that eliminate the above difficulties. Some years ago already, Frieden and Wells (1978) implemented a scheme that effectively solved the first of the above problems. Their scheme comprised the following discrete steps: 1) a model of the slowly varying background is constructed; 2) this model is subtracted from the original image and the resulting residual image is deconvolved; 3) the background model is added to the deconvolved residual image to obtain the final restored image. In this paper, a somewhat related procedure is described, leading to a hierarchy of fully automatic codes of increasing sophistication which yield restorations of high photometric precision for both stars and distributed emission. The performance of these codes is tested and illustrated in Paper II (Hook &Lucy 1994).