Design of a tilted two-mirror system

Abstract

Formulae have been derived for eliminating main aberrations on the center of field of the tilted two-mirror system (TTS). The spherical aberration may be eliminated by considering the TTS as a co-axial system. The coma on the center of field will be reduced by conserving certain relationships between the tilting angles of the primary mirror and the secondary. In order to cancel the astigmatism on the center of field, one of the two mirrors must have bi-curvature at the vertex of the mirror. Ray tracing shows that the TTS solved by the given equations produces quite good image quality within a small field of view. In order to increase the useful field of view, the bi-curvature mirror with the shape 0L an inverse ellipsoid must have high order terms in its surface equation.