Solving the inverse problem of focusing laser radiation in a plane region using geometrical optics

We proposed a method for calculating the eikonal function of a light field from the condition of generating a desired intensity distribution in a predetermined region of the focal plane. To improve the efficiency of solving the problem of focusing we developed a modification of a method of rectangle matching, which enables designing diffractive optical elements (DOE) intended to focus into a plane region. The novelty of our approach consists in a method of reconstructing the eikonal function from the known ray map of points on the DOE onto points in the focal plane. We presented the results of the DOE-aided focusing into a circle, a rectangle, a rhombus, and a superellipse. The simulation results showed the high quality of focusing, thus corroborating the efficiency of the proposed method. We expect to use the diffractive optical elements (DOE) for lighting the area of interest from low-flying drones used for night-time Earth remote sensing.