Aplanatic grazing incidence diffraction grating: a new optical element

We present the theory of a grazing incidence reflection grating capable of imaging at submicron resolution. The optic is mechanically ruled on a spherical or cylindrical surface with varied groove spacings, delivering diffraction-limited response and a wide field of view at a selected wavelength. Geometrical aberrations are calculated on the basis of Fermat’s principle, revealing significant improvements over a grazing incidence mirror. Aplanatic and quasi-aplanatic versions of the grating have applications in both imaging and scanning microscopes, microprobes, collimators, and telescopes. A 2-D crossed system of such gratings, similar to the grazing incidence mirror geometry of Kirkpatrick and Baez, could potentially provide spatial resolutions of ~200 Å.