Focusing from a plane grating can be accomplished by using convergent radiation incident on the grating in such a manner that any incident angle αn, the resulting diffraction angle βn, will be on the same side of the grating normal. The theory for the focal properties is developed by applying Fermat’s principle of least time to selected terms resulting from a finite series expansion of the system’s distance function. Derivations are given for finding the focal curve equation, astigmatism, and coma, of the most usable configuration of the optical components. Discussions of the aberrations disclose methods for eliminating the astigmatism and reducing the coma.
James T. Hall, "Focal Properties of a Plane Grating in a Convergent Beam," Appl. Opt. 5, 1051-1055 (1966)