Deformed ellipsoidal gratings for far-ultraviolet spectrographs - Analytic optimization

Analytic formulas are developed for the semiaxes and for the deformation coefficients of a deformed ellipsoidal grating that minimize aberrations over a given spectral range. These include the Rowland circle mount and quasi-Rowland circle mounts, as required for systems that combine spectra from multiple gratings on a common detector. It is also shown that the necessary condition for a holographic grating to give a better performance over a conventional grating is the use of a convergent beam and a divergent beam for the recording. Examples applicable to the Far-Ultraviolet Spectroscopic Explorer are given. The light-path function for a deformed ellipsoidal holographic grating is also presented.