On the use of the supporting quadric method in the problem of the light field eikonal calculation

A new iterative technique for calculating the eikonal function of a light field providing the focusing into a set of points is introduced. This technique is a modification of the supporting quadric method widely used for design of reflecting and refracting optical surfaces for generating prescribed illuminance distributions at given discrete set of points. As an example, we design a refractive optical element which focuses an incident beam into a set of points with energy pattern forming an image of a keyboard of a calculator. It is shown that the proposed technique is well-suited for the design of diffractive optical elements producing continuous intensity distributions within the scalar theory of diffraction. It is also shown that the calculated eikonal function is a good initial guess when designing diffractive optical elements using the iterative Gerchberg-Saxton algorithm.