  We consider the inverse problem of in-line holography, applied to
minimally-destructive imaging of cold atom clouds. Absorption imaging
near-resonance provides a simple, but destructive measurement of atom column
density. Imaging off resonance greatly reduces heating, and sequential images
may be taken. Under the conditions required for off-resonant imaging, the
generally-intractable inverse problem may be linearized. A
minimally-destructive, quantitative and high-resolution image of the atom cloud
column density is then retrieved from a single diffraction pattern.
