Apodizations with decreasing transmissions and with central obstructions transmute the point spread functions in image size and in the distribution of image irradiance. The distributions are characterized by the envelope functions which are exponential functions descending with variable exponents. At high apodization levels and lower central obstruction (<0.1) new extended radial zones in the outer part of the central ring groups are formed. Such transmutations of the image functions are of more than theoretical interest, particularly if the irradiance levels in the outer ring zones are to be compared to background irradiance levels.
Hubert F. A. Tschunko, "Imaging performance of annular apertures. 4: Apodization and point spread functions," Appl. Opt. 22, 133-136 (1983)