Fall 2011 GRASP Seminar - R. Andrew Hicks, Drexel University, "The Geometry of Optical Design"

Abstract: The first photograph was created in 1827 by Joseph Nicephore Niepce. In 1828, William Rowan Hamilton's founding papers on geometric optics began to appear. This seems to be a remarkable coincidence and one would think that the two siblings, photography and geometric optics, would each contribute to the growth of the other. But this never happened. Optical design in the 19th century was largely empirical, and today design is mostly performed by optimizing a cost function which is defined via ray tracing. It is instructive to observer Hamilton's name appears no where in Rudolf Kinglslake's classic 1978 book "Lens Design Fundamentals".

Recent advances in machining, such as 5-axis raster grinding, have now made it possible to make high quality freeform optical surfaces, i.e. surfaces that do not have rotational symmetry. This opens up a whole new realm of design possibilities for illumination and imaging applications, but little theory exists for the design of such surfaces. I will describe methods that I have developed for this problem, based on differential geometry and partial differential equations. For some optical design problems, the surfaces may be modeled as integrals of distributions in Euclidean space. Hints of connections between Hamiltonian optics and these methods appear, but the full story remains unclear. During my lecture prototypes will be available for examination by the audience.

Presenter's biography

R. Andrew Hicks graduated from Queens College CUNY in with a BA in mathematics in 1988. He received his Ph.D. in 1995 in Mathematics from the University of Pennsylvania, in the field of Differential Geometry. He was enrolled in the CIS Masters program at Penn from 1995-96. From 1996-99 he was a postdoc at the GRASP laboratory of UPenn under Ruzena Bajcsy. He is currently professor of mathematics at Drexel University. His research interests include optical design, numerical analysis and computing.