Dissertation
Vector fields, eigensurfaces, and prescribed curvature in optical design
Doctor of Philosophy (Ph.D.), Drexel University
Jun 2017
DOI:
https://doi.org/10.17918/etd-7345
Abstract
In this thesis, we will consider the general problem of optical design in the field of geometric optics. A specific problem of interest is that of finding a passenger side mirror for a motor vehicle that has a wider field of view than a flat mirror, but less distortion than a spherical mirror. The goal here is to eliminate the well-known blind spot that most drivers experience. First, we show how to construct a vector field to mathematically model certain design problems in geometric optics. Second, we demonstrate how to use the vector field to determine whether or not the optical design problem is well-posed, and, in particular, if it has an exact solution. In the case where there is no exact solution, such as the case for a wide-angle, non-distorting passenger side mirror, we will show two constructions for an approximate solution. The first construction comes from the concept of an eigensurface, a surface that is invariant under the transformation of a curved reflector. The second construction comes from the solution of the Euler-Lagrange equation resulting from a cost functional that measures the difference between the desired vector field and the normal vectors to a potential solution. We show how this method relates to the prescribed curvature problem. Finally, we apply these methods to the passenger side blind spot problem.
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Details
- Title
- Vector fields, eigensurfaces, and prescribed curvature in optical design
- Creators
- Sarah G. Rody - DU
- Contributors
- R. Andrew Hicks (Advisor) - Drexel University (1970-)
- Awarding Institution
- Drexel University
- Degree Awarded
- Doctor of Philosophy (Ph.D.)
- Publisher
- Drexel University; Philadelphia, Pennsylvania
- Number of pages
- ix, 108 pages
- Resource Type
- Dissertation
- Language
- English
- Academic Unit
- College of Arts and Sciences; Drexel University; Mathematics
- Other Identifier
- 7345; 991014632600504721