Astigmatism-corrected gratings for plane grating–spherical mirror spectrographs

In order to take full advantage of modern, multiple-element detectors, the astigmatism in traditional plane grating instrument designs must be significantly reduced. Slight cylindrical distortions of the plane grating are shown to correct astigmatism near the plane of dispersion without significantly altering spectral resolution. Basic geometrical theory for all in-plane systems is presented. Extensions to other slight distortions such as anticlastic or toroidal surfaces are given. Limitations imposed by image degradation away from the plane of dispersion are discussed. Ray traces of a representative system are explored. Results and images from a test system that incorporates a cylindrical grating made from a plane master grating are presented.