Study of higher order aberrations of an on-axis three-mirror telescope with an off-axis field of view

Currently, numerous projects for the study of both outer space and the Earth's surface use mirror optical systems, since they allow working in a wide spectral range. As a rule, three-mirror anastigmats (TMA) are used, however, it is possible to correct four aberrations in some configurations of three-mirror systems without an intermediate image. In order to avoid obscuration, such schemes in a configuration with an off-axis field may be used. In the case of very compact systems, it is necessary to apply fast mirrors, so aspherical surfaces are used. To select the optimal position of an aspherical surface and an equation for describing higher-order and free-form aspherical surfaces, a study is made of higher-order aberrations in systems with various parameters, empirical dependencies are derived that allow one to evaluate the correction capabilities of the schemes. Examples of system designs with an off-axis field are presented.