Abstract
We generalize the Zernike polynomials to a three-dimensional region in order to provide an orthogonal representation of the wave aberration over a field or pupil, describing the wave aberration as a sum of individual orthogonal aberrations of various orders. We show that the individual orthogonal aberrations have several unique properties. The use of orthogonal aberrations led to the discovery of several previously unknown aberration properties of optical systems and has made it possible to substantially improve the formal description of the optical system design process and increase the efficiency of optical calculations.
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