An Efficient Level Set Method for Constructing Wavefronts in Three Space Dimensions

Wavefront construction in geometrical optics has long faced the twin difficulties of dealing with multivalued forms and resolution of wavefront surfaces. A recent change in viewpoint, however, has demonstrated that working in phase space on bicharacteristic strips using eulerian methods can bypass both difficulties. The success of the level set method in science and engineering makes it a suitable choice for such an eulerian method. Unfortunately, in three-dimensional space, the setting of interest for most practical applications, the advantages of this method are largely offset by a new problem: the high dimension of phase space. In this work, we present new types of level set algorithms that remove this obstacle and demonstrate their abilities to accurately construct wavefronts under high resolution. These results propel the level set method forward significantly as a competitive approach in geometrical optics under realistic