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Diffraction shading models in computer graphics

Emmanuel Onuora Agu, University of Massachusetts Amherst


Diffraction and interference are optical phenomena that split light into its component wavelengths, hence producing a full spectrum of iridescent colors. This thesis develops computer graphics models for iridescent colors produced by diffractive media. One of the requirements for diffraction is a surface that has periodically spaced grooves or obstructions; hence diffractive media tend to be manufactured parts such as diffraction gratings. A variety of apertures are known including rectangular and circular ones of both reflective and transmissive types. Certain animal skins and the crystal structure of some precious stones are also known to produce diffraction. Diffraction is distinguished from a related phenomenon of interference that produces colorful effects due to the phase difference caused by a wave traversing thin media of different indices of refraction. Examples of interference are the soap bubble and oil slicks. Interference, unlike diffraction is more easily modeled using the ray theory of light. In the optics literature, diffraction theory is treated under geometrical optics. Several techniques can be employed to derive solutions to this problem including: (1) Solutions derived by applying boundary value methods and consideration of the electromagnetic boundary conditions; (2) Solutions based on Huygens-Fresnel principle; (3) Kirchoff-Fresnel based solutions; (4) Solutions using fourier optics. Thorman [53] first attempted to develop a simple computer graphics model for diffraction in 2D by using the grating equation derived by applying electromagnetic boundary value methods. Stam [49] has published work using Fourier optics solutions. Fourier optics solutions are believed to give the most accurate but also most complex solutions. No models using Huygens-Fresnel principle have been published. This thesis derives a set of solutions based on the Huygens-Fresnel principle. The diffraction models developed extend well-known illumination models (such as Phong and Cook-Torrance shading models) and are incorporated into a ray tracer. A thorough discussion of ray tracing, our chosen rendering technique, as well as issues which arise in rendering our models, is also included. Extensive literature surveys and our results are presented.

Subject Area

Electrical engineering

Recommended Citation

Agu, Emmanuel Onuora, "Diffraction shading models in computer graphics" (2001). Doctoral Dissertations Available from Proquest. AAI3027173.