  We consider the inverse problem of determining an optical mask that produces
a desired circuit pattern in photolithography. We set the problem as a shape
design problem in which the unknown is a two-dimensional domain. The
relationship between the target shape and the unknown is modeled through
diffractive optics. We develop a variational formulation that is well-posed and
propose an approximation that can be shown to have convergence properties. The
approximate problem can serve as a foundation to numerical methods.
