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

## TL;DR

This paper explores using orthogonal polynomial-based freeform mirror surfaces and curved detectors to design compact, wide-field optical systems, demonstrated through a three-mirror unobscured telescope example.

## Contribution

It introduces a polynomial approach over a squared aperture for freeform mirror design and discusses integrating curved detectors in wide-field optical systems.

## Key findings

- Polynomial surface descriptions improve freeform mirror design.
- Curved detectors enable more compact wide-field systems.
- Demonstrated design achieves a 7.2x7.2° field of view.

## Abstract

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.

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Source: https://tomesphere.com/paper/1706.05520