  We have developed a method for the linear reconstruction of an image from
undersampled, dithered data, which has been used 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 (or
informally as "drizzling"), 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 of drizzling to combine dithered images in the
presence of cosmic rays.
