The design of a two-mirror telescope using a free-form surface for the primary mirror, to obtain a compensation of thespherical and coma aberrations, in the entire pupil of the telescope is proposed. In this design, the conic constant ( _1) ofthe primary mirror is a function of the heights, measure from the center to the edge of primary mirror. In this method, weuse the exact ray tracing to find the optical path length (OPL) for each ray that intersect the primary mirror at differentdistances measured from the center of the primary mirror. The OPL is calculated with the sum of the distances that eachray travels until reaching the plane of the image, and the sum of the distances for a paraxial axial ray. From the opticalpath difference (OPD) of a set of rays, we obtain a set of values of the conic constant that guarantees that the OPD has avalue of zero for each incident ray height. With the set of values of the conic constant it is possible to obtain the shape ofthe surface of the primary mirror.
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