Introduction

The HST Medium Deep Survey (MDS) Key Project (Griffiths et al. 1992, 1994) includes observations of a large number of random WFC fields. They are taken in parallel mode, when another detector is being used on a primary target at a single pointing extending over two or more orbits. Most of the objects detected are faint galaxy images. For statistical analysis of the large scale structure of the universe, the survey is generating a catalog of galaxy magnitudes, colors, half light radii, axis ratios and morphology. In order for this catalog to be well-defined despite the relatively long span over which the observations have been obtained, and to ensure uniformity in the processing, we need reliable error estimates for all evaluated parameters to combine information from different fields, with different integrated exposure times.

In the traditional approach to image analysis, CCD observations are first calibrated to subtract the bias and dark current and eliminate variations in the detector sensitivity. Bright cosmic rays are then removed, by stacking multiple observations if available, otherwise by using one of several algorithms that identify cosmic ray events in the image. Defective pixels may be removed by interpolation. For HST, the brighter images are then deconvolved to restore the images to the high resolution of the core of the PSF.

This approach can be very successful when dealing with bright (high signal-to-noise) images. The result is a cosmetically clean image on which morphological classification and other measurements can be carried out in a non-parametric, model-independent way. However, this procedure does have some drawbacks when applied to a large sample of galaxies. Some quantities, such as magnitudes, are very difficult to measure accurately and without bias on deconvolved images; even for those quantities that can be measured, the error distribution is distorted and probably non-Gaussian. Intercomparison of galaxy properties does require, implicitly or explicitly, the adoption of a model. The primary disadvantage is that deconvolution of faint images is likely to be unstable (Schade and Elson 1993).

In the alternative approach described below we assume a simple parametrized model for the galaxy image and transform it to the observed domain. Parameters used in the model definition are then estimated by maximizing the likelihood function, which is the probability of obtaining each observed image for any set of galaxy parameters. Tests of the procedure on simulated galaxy images show that derived model parameters and their error estimates are unbiased. The likelihood ratio between fits to different types of models can be used for a coarse morphological classification.