Diffraction investigation of focusators

I review the problems of diffractive optics, possible devices and of information technologies needed to create diffractive optical elements (DOEs). I analyze the possibility of computational experiment in investigation of DOEs for focusing laser radiation. I argued the need for the use of computer simulation when choosing a method for ill-posed inverse problems of diffraction theory. I argue the need for diffraction studies to create new types of focusing DOEs as well as to analyze the performance of optical elements for given physical parameters of the optical system.