Numerical solution of the problem of image formation in two planes using the integral fresnel formula

The paper considers numerical solution of the problem of constructing a plane phase optical element which forms prespecified images in two focal planes when illuminated by a plane wave front. The propagation of radiation from the optical element to the focal planes obeys the integral Fresnel formula. The phase function defining the optical element, is from the space of feasible phase functions satisfying both computational and technological constraints. The computer algorithm is based on efficient numerical solution of the inverse directional diagram problem. The phase function is constructed using the projector on the space of feasible phase functions. The efficiency of the phase optical element produced by the proposed procedure is demonstrated by solving a prototype problem involving simulation of the direct operator. The corresponding optical element was manufactured by electron-beam lithography. Physical experiments with a laser source illuminating the element confirmed the findings of the numerical experiment. Translated from Prikladnaya Matematika i Informatika, No. 1, pp. 86–89, 1999.