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Dissertation
Catadioptric sensors
Doctor of Philosophy (Ph.D.), Drexel University
Jul 2009
DOI:
https://doi.org/10.17918/etd-3068
Abstract
In this thesis we present two different catadioptric sensor designs. First one is a folded catadioptric system which is rectifying. The sensor consists of an orthographic or perspective camera coupled with two rotationally symmetric mirrors. The primary mirror is chosen to be a conic section or a cone because of their reflective properties. The rectifying property enforces that the transformation between the image plane and the object plane be linear. The equations describing the secondary mirror are determined by the projection induced by the primary mirror and the rectifying property of the sensor. By solving the resulting ordinary differential equation, we obtain the cross section of the secondary mirror. These systems are designed to image a distant plane without distortion. The second system we present consists of a micromirror array, a conventional asymmetric mirror and an orthographic camera. The main problem of catadioptric sensor design is constructing a mirror for a given projection which generically does not have a solution. We overcome limitations of single-mirror catadioptric sensors by designing the camera projection as well as the mirror surface. This construction allows us to exactly achieve any desired projection, not only orthographic or perspective. The key in finding the mirror surface and the camera projection is, constructing a vector field normal to the sought-after surface. For the surface to exist, the normal vector field has to be integrable. The integrability condition for the vector field is provided by Frobenius integration theorem for differential forms, since a 1-form corresponds to a vector field in R3. The integrability condition yields a system of first order quasilinear partial differential equaitons, whose numerical solution is the camera projection. Computing the mirror surface is done by numerically integrating the normal vector field. We present our results for four different systems where error for both projection and mirror surface are very promising.
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Details
- Title
- Catadioptric sensors
- Creators
- Emek Kose Can - DU
- Contributors
- Ronald K. Perline (Advisor) - Drexel University (1970-)
- Awarding Institution
- Drexel University
- Degree Awarded
- Doctor of Philosophy (Ph.D.)
- Publisher
- Drexel University; Philadelphia, Pennsylvania
- Resource Type
- Dissertation
- Language
- English
- Academic Unit
- College of Arts and Sciences; Drexel University; Mathematics
- Other Identifier
- 3068; 991014632679204721