Aberrations of a facet-type transmission grating for cosmic x-ray and XUV spectroscopy.

The aberrations of various types of curved constant-period transmission gratings are discussed, using Fermat's principle. We show that optimal performance is achieved with a grating assembled from individual facets which form a nonclosed surface. For this geometry, primary coma and astigmatism are proportional to the facet size and, hence, may be adapted to the angular resolution of a Wolter-type telescope.