Applied Physics and Mathematics Annotation << Back STUDY OF THE PROPERTIES OF ORTHOGONAL ABERRATIONS AND OPTICAL SYSTEMS. OPTIMIZATION PROGRAMS WITH REDUCED LOCAL CONSTRAINT S.N. BEZDIDKO Using the representation of wave aberration in the form of an expansion in orthogonal polynomials in a four-dimensional region determined by the field of view and aperture of the optical system made it possible to form a new system of orthogonal aberrations. And it was precisely the unique properties of orthogonal aberrations that made it possible to carry out research to identify previously unknown properties of optical systems, analyze their maximum correction capabilities, identify the reasons for the local limitations of optimization programs and significantly reduce the oscillations of merit functions. These results give possibility to create new effective programs that we called “pseudo-global” optimization programs. This article presents a study of the properties of orthogonal aberrations and the identified new properties of optical systems. Keywords: design of optical systems, theory of aberrations, higher order aberrations, orthogonal aberrations, synthesis, optimization. DOI: 10.25791/pfi m.01.2024.1285 Pp. 03-19.