Distributions for Optical Design

Drexel University, Philadelphia PA

Investigators

Abstract

Hicks DMS-0908299 Until approximately ten years ago, it was only possible to machine optical quality mirrors and lenses that were surfaces of revolution. Due to advances in optical machining technology it is now possible to essentially machine a surface of any shape. This increase in design possibilities calls for new design techniques. Traditionally, partial differential equations and differential geometry did not play a role in optical design because of the restrictions of what surfaces could actually be made. Now, using these methods, and in particular the viewpoint of exterior differential systems, we have a framework to attack these complex problems. Additionally, new models for optical systems are developed based on functional differential equations. In recent years a plethora of difficult new optical design problems have appeared. Energy conservation has become a problem of global concern, and in particular the problem of efficient lighting. Significant advances are currently taking place in illumination technology, due to the rise of the light emitting diode. Yet the design problem for illumination systems has proven to be notoriously difficult, and is currently more of an art than a science. The investigator and his colleague develop new mathematical methods to deal with these challenges in optical design. The project provides a framework for illumination design. Another application is to automotive safety. The principal investigator has already designed a driver-side mirror without a blind spot, that has no distortion. The problem of designing a similar mirror for the passenger side of a car is more complex, and is pursued in this project. Finally, the investigators disseminate this work through interactive exhibits based on the project that are hosted by The Franklin Institute, a major US science museum located in Philadelphia, Pennsylvania, which is visited every year by over 750,000 people.