Freeform geometrical optics II: from parametric representation to CAD/CAM

Freeform optical surfaces are of great importance because of two main properties. The first is their ability to enhance the image quality of image-forming optical systems; the second is their inherent reduction in the number of surfaces in image and nonimage-forming optical systems. However, the main characteristic of freeform surfaces is that they lack symmetry about any spatial axis. This attribute allows describing freeform surfaces with a mathematical parametric representation. Unfortunately, parametric representation can be extremely extended. On the other hand, when describing freeform surfaces, the explicit representation is commonly preferred because of its compactness and CAD-format exportable easiness. Parametrically represented freeform surfaces can nonetheless be exported to a CAD format, with no significant departure of surface shape, as shown here. The vector method presented here guarantees that the surface's sampling density be proportional to the irradiance on the surface.