Nowadays, miniature satellites carrying simple optical payloads are capable of relevant space observation. But designing a lens with a satisfactory angular resolution in small volumes with a given form factor is a challenge and adapting a conventional system to CubeSat can often only be done by significantly degrading optical performance. At the same time, a new type of optics, freeform optics, is gaining interest. These are optics without centers or axes of symmetry. By freeing themselves from the geometrical constraints of classical optics, they increase significantly the degrees of freedom available to design an optical system. By using these freeform surfaces, these additional degrees of freedom can be used to find new solutions that outperform conventional solutions by offering, for example, better angular resolution. Freeform surfaces complicate however drastically the design processes because the usual difficulties that one encounters in symmetric designs are exacerbated. Many unobscured catoptric designs have been revisited with freeform mirrors. However, an important common point is that all these systems keep a coplanar configuration, maybe to ease the optimization process with commercial software. The purpose of this thesis will therefore be to study radically freeform and non-coplanar optical systems that fully exploit modern manufacturing capabilities and to demonstrate the benefits of this approach. Non-coplanar optical systems are optical systems where the path of the parabasal optical ray is not contained in a plane. They expand the degrees of freedom of catoptric freeform system to answer harsh geometrical constraints and ONERA has discovered in a first example that they are not more difficult to manufacture. New strategies to find a good starting point have to be developed as well, for example by directly constructing the surfaces by resolving a system of differential equations from a parabasal ray.
