The focal length of grazing incidence x-ray telescopes, in particular the type-I Wolter (1952), is fixed by the mirror diameter and the angles of grazing incidence on the surfaces. Often this focal length is too short to give adequate plate scale for imaging, the resulting low f/No. also makes it difficult to match a spectrometer to the output of the telescope, and high resolution spectroscopy is therefore impossible. Both these problems can be alleviated through the use of grazing incidence relay optics (GIRO) systems. These are analogous to secondary optical systems such as Barlow lenses used in visible light optics, serving to magnify the primary image and decrease the divergence of the beam. GIROs can be made with one or more elements; we first discuss single-element GIROS which are useful for spectroscopy. For imaging, two-element systems are required; we discuss a variety of different configurations giving analytical equations for the surfaces. The systems have been studied by ray tracing, and results on resolution and overall system collecting area are shown. Finally we show how the results for resolution can be approximated by simple empirical formulas.
R. C. Chase, A. S. Krieger, and J. H. Underwood, "Grazing incidence relay optics," Appl. Opt. 21, 4446-4452 (1982)