The wavefront aberration polynomial and transverse ray aberration expansions will be derived for grazing incidence two-mirror Wolter telescopes including all paraboloid-hyperboloid and paraboloid-ellipsoid combinations. The reference sphere is determined with the help of the principal surface of the telescope, and the aberration polynomials will be given as functions of the coordinates of the ray intersection with the reference sphere. Third, and some of the fifth- and seventh-order aberration terms will be analyzed. Also, the well-known relationship between wavefront aberration polynomial and transverse ray aberration polynomials will be verified.
Timo T. Saha, Timo T. Saha,
"Aberrations For Grazing Incidence Telescopes", Proc. SPIE 0830, Grazing Incidence Optics for Astronomical and Laboratory Applications, (9 August 1988); doi: 10.1117/12.942190; https://doi.org/10.1117/12.942190