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In the recent years a significant progress was achieved in the field ofdesign and fabrication of optical systems based on freeform optical surfaces.They provide a possibility to build fast, wide-angle and high-resolutionsystems, which are very compact and free of obscuration. However, the field offreeform surfaces design techniques still remains underexplored. In the presentpaper we use the mathematical apparatus of orthogonal polynomials defined overa square aperture, which was developed before for the tasks of wavefrontreconstruction, to describe shape of a mirror surface. Two cases, namelyLegendre polynomials and generalization of the Zernike polynomials on a square,are considered. The potential advantages of these polynomials sets aredemonstrated on example of a three-mirror unobscured telescope with F/#=2.5 andFoV=7.2x7.2{\deg}. In addition, we discuss possibility of use of curveddetectors in such a design.

Combining freeform optics and curved detectors for wide field imaging: a polynomial approach over squared aperture