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.

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F is the effective focal length, z_{p} is the distance from the exit pupil to the image plane, R_{1} and R_{2} are axial radii of curvature for the primary and secondary, respectively.

F is the effective focal length (cm), L is the physical length (cm), R1max and R2max are the maximum radii of the primary and secondary (cm), R1min and R2min are the minimum radii of the primary and secondary (cm), R_{1} and R_{2} are the vertex radii of curvature of the primary and secondary (cm), and e is the eccentricity of the secondary.

Table III

Comparison of the rms Spot Radius and rms OPD Values Calculated from Exact Ray Tracing Results and TRA and OPD Polynomials

F is the effective focal length, z_{p} is the distance from the exit pupil to the image plane, R_{1} and R_{2} are axial radii of curvature for the primary and secondary, respectively.

F is the effective focal length (cm), L is the physical length (cm), R1max and R2max are the maximum radii of the primary and secondary (cm), R1min and R2min are the minimum radii of the primary and secondary (cm), R_{1} and R_{2} are the vertex radii of curvature of the primary and secondary (cm), and e is the eccentricity of the secondary.

Table III

Comparison of the rms Spot Radius and rms OPD Values Calculated from Exact Ray Tracing Results and TRA and OPD Polynomials