The theoretical basis for the mirror high-aperture optical system synthesis, based on the properties of the reflecting surface accepted as the base having a shape of a paraboloid of rotation are considered in the work Design parameters and residual aberrations tables of the few design solutions for considered optical systems are presented. From the analysis of aberration correction of the image formed by the considered optical system, it follows that the angular value image space is limited, primarily, the image surface curvature. To compensate for curvature of the image surface can be applied Smith lens. The additional condition that determines a high aperture ratio of the optical system of the considered lens as a whole was introduced, but it complicates the process of correcting the aberrations of a wide beam of rays. It is shown that the use of afocal Mersenne system with known anaberration properties, allows you to build a series of compact and SLR mirror-lens systems with aplanatic, anastigmatic and plananastigmatic aberration correction formed the image, at the same time the length of the system is about four times smaller than the diameter of its entrance pupil. Importantly, when applying the lens for using in a long wavelength range emission, the requirements for aberration correction image formed by the lens are reduced, and accordingly, manufacturability are increases.