Theory and computation of three cosmic origin spectrograph aspheric gratings recorded with a multimode deformable mirror.

The theory of three Cosmic Origin Spectrograph holographic gratings recorded with a deformable plane mirror is presented. Their working conditions are severe, since they have to correct the strong spherical aberration and the field astigmatism of the Hubble Space Telescope. Recorded on aspherized substrates, the gratings produce images that are diffraction limited with regard to spectral resolution.