We have developed a method for the linear reconstruction of an image from undersampled, dithered data, which has been sued to create the distributed, combined Hubble Deep Field images - the deepest optical images yet taken of the universe. The algorithm known as variable-pixel linear reconstruction, preserves photometry and resolution, can weight input images according to the statistical significance of each pixel, and removes the effects of geometric distortion both on image shape and photometry. In this paper, the algorithm and its implementation are described, and measurements of the photometric accuracy and image fidelity are presented. In addition, we describe the use drizzling to combine dithered images in the presence of cosmic rays.© (1997) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.