Freeform optics: Evolution? No, revolution!

After over 125 years of design, polishing, and testing lens elements with rotationally symmetric, often spherical surfaces placed in round tubes—including single-lens-reflex cameras and microscope objective lenses—computer control has come along to interject advances that are rapidly changing the field. In the 1990s (the late) Harvey Pollicove founded and led the Rochester Center for Optics Manufacturing to automate fabrication of spherical and rotationally symmetric aspheric surfaces under computer numerical control (CNC). Now, this technology is moving forward to fabricate surfaces without rotational symmetry, or more generally freeform surfaces. These advances are bringing a new paradigm in our millennium. Previously, most optical imaging systems were constrained to spherical surfaces for economic reasons. In such a system, a typical lens element contributes to up to 15 aberrations, or ways to lose, each with individual characteristics. Using a more complicated (freeform) shape for the surface offers an opportunity to introduce innovative 3D packages while simultaneously correcting more directly the limiting aberrations. CNC machines now produce freeform surfaces that depart from rotational symmetry for use at wavelengths as short as one micron. This is revolutionary. Today, the optical design, fabrication, and testing communities are scrambling to develop a self-consistent structure for describing freeform surfaces through their respective processes. In 2006, Greg Forbes, a leading industry mathematician, sounded the alarm when he showed definitively that the formulation of rotationally symmetric surfaces introduced by Abbe in his 1902 patent was failing dramatically, as optical designers added more and more terms in a misguided effort to achieve a lower value for the optimization merit function. This shortcoming led to the introduction in the optical design environment of so-called Q-polynomial surfaces,1 whose effectiveness in reducing assembly sensitivity we have demonstrated.2 This Figure 1. Left to right: A design with three freeform surfaces and three full-field displays showing new field dependencies for astigmatism in systems with freeform surfaces and asymmetric configurations. Field binodal (left), field linear, field asymmetric (also seen in unobscured three-mirror anastigmats, like the James Webb Space Telescope) (middle), and the latest discovery, field linear, field conjugate astigmatism of freeform surfaces (right), all predicted from nodal aberration theory.5