The Institute of Image Processing Systems of the Russian Academy of Sciences (IPSI RAS, now a branch of the Federal Scientific Research Center of the Russian Academy of Sciences “Crystallography and Photonics”) was founded in 1988 on the basis of a research group at Samara State University. The team is led by Victor Alexandrovich Soifer, a member of the Russian Academy of Sciences. One of the research directions of the research group is the development of numerical methods and experimental studies of multi-channel laser beams. These studies began in 1982, when the first multi-channel diffracted optical element (DOE) was realized in collaboration with the team of Nobel Laureate in physics, Academician Alexander Mikhailovich Prokhorov. In the years that followed, IPSI RAS scientists proposed, simulated and studied many types of DOE elements on computers, and then fabricated them in the form of various superimposed phase holograms with consistent transverse laser patterns. Examples include optical vortices, Lacroerre-Gauss mode, Hermi-Gauss mode, Bessel mode, Zernick function (for aberration analysis), etc. This DOE, made using electron lithography, is applied to beam analysis based on optical mode decomposition. The measurement results are obtained in the form of correlation peaks at certain points (diffraction orders) in the Fourier plane of the optical system. Subsequently, the principle was used to generate complex beams, as well as demultiplexing beams in optical fibers, free space, and turbulent media using DOE and spatial Optical modulators.