The optimization of an optical system is generally carried out by minimizing the wave-front aberrations, the <i>x</i> and <i>y</i> transverse aberrations, or a combination of both. In the last-named, most general case, the optimization implies the treatment of a large number of functions of quite a different nature. We propose to use, together with the Zernike polynomials that orthogonalize the wave-front aberrations, a new set of wave-front polynomials that orthogonalize the transverse aberrations. These polynomials turn out to be a simple linear combination of Zernike polynomials. The combination of these two sets of wave-front polynomials with proper weighting yields the possibility of optimizing the frequency response of both slightly and severely aberrated systems in a formally identical way. The advantage of the method is that one does not have to leave the domain of the wave-front aberration to characterize an optical system, even when severe aberrations are present. The polynomials that minimize the transverse aberrations yield optimum response at very low frequencies; other linear combinations of Zernike polynomials are shown to maximize the frequency response at relatively high spatial frequencies.
© 1987 Optical Society of America
Joseph Braat, "Polynomial expansion of severely aberrated wave fronts," J. Opt. Soc. Am. A 4, 643-650 (1987)