Direct methods for freeform surface design - art. no. 666802

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.