Distributions for Optical Design

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HicksDMS-0908299 Until approximately ten years ago, it was only possible tomachine optical quality mirrors and lenses that were surfaces ofrevolution. Due to advances in optical machining technology itis now possible to essentially machine a surface of any shape. This increase in design possibilities calls for new designtechniques. Traditionally, partial differential equations anddifferential geometry did not play a role in optical designbecause of the restrictions of what surfaces could actually bemade. Now, using these methods, and in particular the viewpointof exterior differential systems, we have a framework to attackthese complex problems. Additionally, new models for opticalsystems are developed based on functional differential equations. In recent years a plethora of difficult new optical designproblems have appeared. Energy conservation has become a problemof global concern, and in particular the problem of efficientlighting. Significant advances are currently taking place inillumination technology, due to the rise of the light emittingdiode. Yet the design problem for illumination systems hasproven to be notoriously difficult, and is currently more of anart than a science. The investigator and his colleague developnew mathematical methods to deal with these challenges in opticaldesign. The project provides a framework for illuminationdesign. Another application is to automotive safety. Theprincipal investigator has already designed a driver-side mirrorwithout a blind spot, that has no distortion. The problem ofdesigning a similar mirror for the passenger side of a car ismore complex, and is pursued in this project. Finally, theinvestigators disseminate this work through interactive exhibitsbased on the project that are hosted by The Franklin Institute, amajor US science museum located in Philadelphia, Pennsylvania,which is visited every year by over 750,000 people.