Notes on the design of free-form optics

Compared to conventional, rotationally-symmetric optics, free-form optics provide additional degrees of freedom that enable special geometrical and performance features. For instance, in AR and VR, some approaches based on free-forms have shown their ability to reduce the display to pupil distance (total track length, or TTL), to increase the Field of view (FOV) or to improve the apparent resolution of the VR scene. This work will discuss different forms to treat design problems with free-forms, ranging from the direct calculation of point-clouds using the so-called SMS method (followed by a NURBS representation of results) to the combination of direct calculation + optimization. In the latter approach, different types of polynomial descriptions of the free-form surfaces will be considered, with special emphasis on the importance of using a basis that is orthogonal, either with a sag metric or a gradient one.