21 September 2007 Direct methods for freeform surface design
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Optical design in the 19th century was largely empirical, and today design in the geometric realm is often performed by optimizing a cost function which is defined via ray tracing. A natural question to ask then, is how to perform optical design using a more direct method, such as solving partial differential equations or variational problems. We consider the problem of writing down equations to model a single surface (mirror or lens) to completely control a single bundle of rays. When this is done, with high probability the solution surface will not be rotationally symmetric, but freeform. Although a bundle may not be completely controllable with a single surface, approximate solution can be sometimes have applications. In particular, we will show how to compute the shape of a driver-side mirror that has no blind-spot or distortion.
© (2007) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
R. Andrew Hicks, "Direct methods for freeform surface design", Proc. SPIE 6668, Novel Optical Systems Design and Optimization X, 666802 (21 September 2007); doi: 10.1117/12.731453; https://doi.org/10.1117/12.731453


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