Phase reconstruction by the weighted least action principle

The problem of phase reconstruction from intensity is considered in the paraxial geometrical optics regime. The data consist of intensity measurements on two planes orthogonal to the direction of propagation. A new variational principle is used to find the ray mapping between the planes. The mapping is found by minimizing an appropriate function. The minimization process involves a nonlinear partial differential equation. A numerical algorithm for solving this equation is described. The phase is then integrated from the ray mapping. Finally, the method and code are examined by applying them to simulated data.