21 September 2007 Direct methods for freeform surface design
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Abstract
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.
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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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