A Geometric Optics Approach to Simulating Light Wave Phenomena in Computer Graphics

Abstract

In this work an introduction to the Wigner Distribution function (WDF) is provided using geometric optics principles. The WDF provides a useful model of wave{ elds, allowing simulation of di raction and interference e ects. These Fourier optics concepts are explained to computer graphics researchers by clarifying the relationship between the WDF and position{ angle representations. A novel method for simulating wave e ects in graphics using ray{based renderers is presented with a new function: the Wave BSDF (Bidirectional Scattering Distribution Function). Re ections from neighboring surface patches represented by local BSDFs are mutually independent. However, in many surfaces with wavelength{scale micro structures, interference and di raction requires a joint analysis of re ected wave fronts from neighboring patches. A simple method is demonstrated to compute the BSDF for the entire micro structure, which can be used independently for each patch. This allows using traditional ray{based rendering pipelines to synthesize wave e ects. The Wigner Distribution Function is exploited to create transmissive, re ective, and emissive BSDFs for various di raction phenomena in a physically accurate way. In contrast to previous methods for computing interference, there is no need to explicitly keep track of the phase of wave by using a BSDF that includes positive as well as negative coe cients. These negative values, derived from the WDF allow creating destructive interference; however the rendered result will always end up with non{negative light intensities. The theory is described and compared in relation to well understood concepts in rendering and demonstrate a straightforward implementation. In conjunction with standard ray tracers, such as PBRT, wave e ects are demonstrated for a range of scenarios such as multi{bounce di raction materials, holograms, audio midair di raction and re ection of high frequency surfaces. We demonstrate its e ciency using modern graphics hardware, which allow for real{time rendering and is interesting for rapid prototyping of complex optical constructions. A discussion is provided about its validity in the near{ eld, far{ eld, and under the paraxial approximation. Finally, although the WDF representation contains negative values, an intuition is provided that any projection always yields a non-negative intensity value.