The optimization of an optical system is generally carried out by minimizing the wave-front aberrations, the x and y 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 AmericaFull Article | PDF Article
Appl. Opt. 7(4) 667-672 (1968)
John S. Loomis
Appl. Opt. 31(13) 2211-2222 (1992)
J. L. Rayces
Appl. Opt. 31(13) 2223-2228 (1992)