Engineering Physics Annotation << Back ORTHOGONAL ABERRATIONS AND THEIR MAIN PROPERTIES S.N. BEZDIDKO The elegance and effi ciency of using Zernike polynomials is mainly due to their orthogonality, and their disadvantages are due to the two-dimensionality of the polynomials, which did not allow them to be used in the general case of representing aberration functions. In this article, four-dimensional orthogonal polynomials are formed that provide the decomposition of wave aberration in the four-dimensional field of view – aperture region. This made it possible to formulate the theory of orthogonal aberrations and obtain a powerful tool for increasing the efficiency of design of optical systems. Keywords: design of optical systems, theory of aberrations, higher order aberrations, orthogonal aberrations, synthesis, optimization. DOI: 10.25791/infizik.10.2023.1358 Pp. 03-24.