Fast-marching level-set methods for three-dimensional photolithography development

The fast marching method, introduced by Sethian, is a numerical technique for solving the Eikonal equation, and results from combining upwind schemes for viscosity solutions of Hamilton-Jacobi equations, narrow band level set methods, and a fast min-heap algorithm. On a rectangular grid of N total points, the fast marching level set method computes the solution to the Eikonal equation from given initial data in O(N log N) steps. In a series of papers, we have applied this technique to a wide collection of problems, including construction of geodesics on surfaces, computer vision, and shape-from-shading. In this paper, we analyze the application of the fast marching method to photolithography development.