A relatively simple theory for reconstructing self-luminous objects from their diffraction images is presented for thin object disks that have axial symmetry and for thin, long objects whose radiance varies only along the width. Availability of a priori information about the variation of the radiance is assumed. With these simple objects the complete spatial-frequency spectrum of the object function can be deduced in a direct manner from considerations of the Fourier transform of the measured irradiance in an image having negligible noise. Objects having constant radiance are treated in detail and are found to be advantageous for use in experiments designed to test the validity and practicality of the principles of object reconstruction.
HAROLD OSTERBERG, "Reconstruction of Objects from their Diffraction Images," J. Opt. Soc. Am. 56, 723-726 (1966)