Sergey N. BEZDIDKO

JSC “Krasnogorsky Zavod”, Krasnogorsk, Moscow Region 143400, Russia

(Received March 31, 2014; Accepted June 23, 2014)

The author introduces a complete set of polynomials that are orthogonal in the three-dimensional region (generalized Zernike polynomials). These polynomials make it possible to obtain orthogonal expansion of the wave aberration in the three-dimensional region of field–pupil 0 ≤ r ≤ 1, 0 ≤ ρ ≤ 1, 0 ≤ φ ≤ 2π. This permits us to determine the orthogonal system of individual aberrations and introduce a classification of individual aberrations depending on the degree of field r and pupil ρ, φ variables. The author shows that orthogonal aberrations have a number of unique properties. The developed approach, describing the aberration properties of optical systems by means of orthogonal aberrations, and its use in the construction of new methods and techniques for the design of optical systems form a new section of lens design, namely, “Theory of orthogonal aberrations and its applications in the design of optical systems”.

Key words: theory of aberrations, lens design, wave aberration, Zernike polynomials, orthogonal polynomials, expansion of the wave aberration, image quality, higher-order aberrations