Distributions for Optical Design

光学设计分布

• 批准号: 0908299
• 负责人: Robert Hicks
• 金额: $ 26.4万
• 依托单位: Drexel University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-08-15 至 2013-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0908299&HistoricalAwards=false
• 关键词: Distributions; Optical; Design

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.

直到大约十年前，人们才有可能制造出具有光学质量的镜面和透镜。由于光学加工技术的进步，现在基本上可以加工任何形状的表面。这种设计可能性的增加需要新的设计技术。传统上，偏微分方程和微分几何在光学设计中没有发挥作用，因为实际可以制作的表面受到限制。现在，利用这些方法，特别是外部微分系统的观点，我们有了一个框架来解决这些复杂的问题。此外，还建立了基于泛函微分方程的光学系统新模型。近年来出现了大量新的光学设计难题。节能已成为全球关注的问题，尤其是高效照明问题。由于发光二极管的兴起，目前照明技术正在取得重大进展。然而，照明系统的设计问题已被证明是出了名的困难，目前更多的是一门艺术而不是一门科学。研究者和他的同事开发了新的数学方法来处理光学设计中的这些挑战。该项目为照明设计提供了一个框架。另一个应用是汽车安全。首席研究员已经设计了一种无盲点、无失真的驾驶侧后视镜。为汽车的乘客侧设计一个类似的后视镜的问题更为复杂，这是本项目所追求的。最后，研究人员通过富兰克林研究所主办的项目互动展览来传播这项工作，富兰克林研究所是位于宾夕法尼亚州费城的美国主要科学博物馆，每年有超过75万人参观。