This paper presents a formal solution to the problem of object restoration in a one-dimensional, diffraction-limited imaging system. It is found that if the illumination in the object space is confined to a finite region, then the imaging equation can be solved for the object in terms of the image. The solution can be expressed as a series expansion on the eigenfunctions of the imaging operator.
CASPER W. BARNES, "Object Restoration in a Diffraction-Limited Imaging System," J. Opt. Soc. Am. 56, 575-578 (1966)