Optical system of an aplanatic telescope with a spherical primary mirror

The subject of study is the optical system of a telescope with a primary spherical mirror and a mirror corrector of field aberrations. The aim of the study is to describe the method of analytical design for a telescope system with a primary spherical mirror and a two-mirror aplanatic corrector of spherical mirror aberrations. The method involves analyzing the application of Fermat's principle and the Abbe sine condition in a system consisting of a combination of a spherical surface and conical surfaces. The main results include proposed mathematical equations for the mirror surfaces of the aplanatic system with a spherical primary mirror and a two-element corrector of field aberrations. The corrector consists of two concave hyperbolic mirrors placed near the paraxial focus of the spherical mirror. The focal length of the telescope is equal to the paraxial focal length of the primary mirror. The results of the calculation show two variants of the optical schemes of the telescope with the following values for the diameter of the entrance pupil, aperture f-number, and angular field: 1) D=6000mm, F-no.=4, and 2w=0.12(degrees) and 2) D=500mm, F-no.=2, and 2w=0.57(degrees). Practical significance. The use of a spherical mirror in telescopes enhances the accuracy of optical metrology of the surface shape of telescope segments during manufacturing and operation. The compact all-mirror corrector provides operation in a wide spectral range, correcting spherical aberration and coma, thereby increasing the system's relative aperture, angular field, and image quality. (c) 2024 Optica Publishing Group