Mathematical solutions to the problem of creating basic decenter optical mirror models from the coma and astigmatism correction conditions

Abstract

 A serious drawback of reflective optics is a center without central screening that degrades the image quality. To eliminate it, rotations or displacements of mirrors are introduced, but there appear even-order non-elementary aberrations that must be corrected. The creation of compositions with decentered catoptric elements requires further development of the calculation and methodological base. The exact formulas are obtained for calculation of real rays from the astigmatism and coma correction conditions for the given angles of incidence of the main ray on the mirror surfaces and the “oblique” thickness d, that determines their mutual position. Based on the proposed formulas, a new method for parametric calculation of decentered mirror systems has been created, which allows one to compose algorithms and to design both basic models and complex mirror systems from off-axis mirrors. The development of new algorithms for two- and three-mirror off-center lenses will increase the accumulated potential of computational optics. The scope of the proposed technique can be expanded in terms of the number of components.