Method for calculating the eikonal function and its application to design of diffractive optical elements for optical beam shaping

We develop a method for calculating the eikonal function (or the phase function) of the light field, ensuring the formation of a prescribed irradiance distribution in the geometrical optics approximation. In the proposed method, the problem being solved is formulated in a semi-discrete form as a problem of the maximization of a concave function. For finding the solution to the latter problem, a gradient method is used, with analytical expressions obtained for the gradient. Using the developed method, we calculate an eikonal function that provides the formation of a "discontinuous" hexagram-shaped irradiance distribution. We demonstrate that the use of the solution obtained in the framework of the geometrical optics as an initial approximation in iterative Fourier transform algorithms allows one to calculate diffractive optical elements having a quasi-regular microrelief.