Roland V. Shack’s discovery of nodal aberration theory, the expansion into the aberrations of freeform optics, and impact in optical design

Freeform optics is poised to revolutionize the optical systems of our collective future, including high precision imaging systems. In this tribute paper to Roland Victor Shack, we tell the story of how Nodal Aberration Theory (NAT), invented by Shack and developed to 5th order by Kevin Paul Thompson, took on an incredible journey to become the foundation for the aberrations of freeform optics. Nodal Aberration Theory was conceived initially to understand the aberrations of misaligned optical systems. Nodal aberration theory is beautiful, as is any mathematical construct that reduces complex problems into simple formulations. The impact of moving from 100 years of design with rotationally symmetric surfaces (or sections of) into freeform optics is tremendous and opens the design space towards higher performance, more aggressive specifications in the field of view and F/#, more compact solutions, broadband solutions, and distortion-free or distortion-tailored designs.