Variational interpretation of the eikonal calculation problem from the condition of generating a prescribed irradiance distribution

Abstract

The problem of calculation of the light field eikonal defined on a certain surface from the condition of generating a prescribed irradiance distribution on another surface is formulated as a Monge-Kantorovich mass transportation problem. We show that the cost function in this mass transportation problem corresponds to the distance between a point on the initial surface (on which the eikonal function is defined) and a point on the target surface, where the prescribed irradiance distribution is to be generated. An analytical expression for the gradient of a “cost functional” describing the mass transportation problem is derived. It enables using gradient descent methods for the calculation of the eikonal function.

Keywords

• geometrical optics
• nonimaging optics
• inverse problem
• eikonal function
• Monge-Kantorovich mass transportation problem