Fast robust non-sequential optical ray-tracing with implicit algebraic surfaces

Abstract

The fastest, most robust, general technique for non-sequentially ray-tracing a large class of imaging and non-imaging optical systems is by geometric modeling with algebraic (i.e. polynomial) implicit surfaces. The basic theory of these surfaces with special attention to optimizing their precise intersection with a ray (even at grazing incidence) is outlined for an admittedly limited software implementation. On a couple of “tame” examples, a 64-bit Windows 7 version is significantly faster than the fastest commercial design software (all multi-threaded). Non-sequential ray-surface interactions approaching 30M/sec are achieved on a 12-core 2.67 GHz Mac Pro desktop computer. For a more exotic example of a 6th degree Wood’s horn beam dump (light trap), a 32-bit Windows single thread version traces rays nearly 4 times faster than the commercial ASAP software’s implicit algebraic surface and over 13 times faster than its equivalent NURBS surface. However, implicit surfaces are foreign to most CAD systems and thus unfortunately, don’t easily fit into a modern workflow.