In this paper, an optical design is presented for an anastigmatic telescope with back focal length corrected with exact ray tracing to eliminate spherical, coma, and astigmatism aberrations. The telescope is formed of three conical mirrors, two of them polished on the same substratum. The optical design is divided into three stages: we began the design obtaining the Gaussian parameters in a first-order solution; posteriorly, were obtained analytically the three mirrors’ asphericity in a third-order design. The final design stage consists of the implementation of the Fermat’s principle, the Abbe sine condition, and the Coddingtonequations for the exact correction for the three aforementioned aberrations. © 2011 Optical Society of America