A slightly modified version of the Head equations are used to describe an aplanatic grazing incidence microscope with possible application in the field of controlled fusion research. The improved theoretical blur circle radius of the aplanatic microscope is presented and compared to the theoretical blur circle radius of the corresponding ellipsoid-hyperboloid microscope. The results show that the improvement is important for high resolution instruments having grazing angles greater than about 2°.
Richard C. Chase, "Aplanatic grazing incidence x-ray microscopes: design and performance," Appl. Opt. 15, 3094-3097 (1976)