Aix Marseille Univ, CNRS, LAM, Laboratoire d'Astrophysique de Marseille, 38, rue Joliot-Curie, Marseille, France, Kazan National Research Technical, University named after A.N. Tupolev –KAI, 10 K. Marx, Kazan, Russian Federation, Univ. Grenoble Alpes, CEA, LETI, Minatec campus, Grenoble, France

In the recent years a significant progress was achieved in the field of design and fabrication of optical systems based on freeform optical surfaces. They provide a possibility to build fast, wide-angle and high-resolution systems, which are very compact and free of obscuration. However, the field of freeform surfaces design techniques still remains underexplored. In the present paper we use the mathematical apparatus of orthogonal polynomials defined over a square aperture, which was developed before for the tasks of wavefront reconstruction, to describe shape of a mirror surface. Two cases, namely Legendre polynomials and generalization of the Zernike polynomials on a square, are considered. The potential advantages of these polynomials sets are demonstrated on example of a three-mirror unobscured telescope with F/# = 2.5 and FoV = 7.2x7.2°. In addition, we discuss possibility of use of curved detectors in such a design. © 2017 Optical Society of America

Adaptive optics, Mirrors, High-resolution systems, Legendre polynomials, Mathematical apparatus, Orthogonal polynomial, Polynomial approach, Wave front reconstruction, Wide field imaging, Zernike polynomials, Polynomials