  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{\deg}. In addition, we discuss possibility of use of curved
detectors in such a design.
