![]() Axial image formation-spherical aberration of a single surface. The wavefront aberration of this surface, relative to a reference sphere with aįigure 6.2. Other proofs are given in the references at the end ofĬonsider a single spherical refracting surface of radius of curvature R, curvature c= 1/R, with refractive indices n and n′ as shown in Fig. There are many proofs of this result in the literature. In this section we will derive a simple equation for the spherical aberration of a Where we can use the third-order approximation, we will find that we can deriveĪnalytical expressions for the contributions of individual surfaces to sphericalĪberration, coma, and the other third-order aberrations. This is the basis of the Seidel analysis. Heights and angles of the axial marginal ray and of the chief ray for the edge of However, can be evaluated using only paraxial ray data, namely the paraxial ![]() Obtained in this way, since the aberrations of one surface will affect the fifth-Īnd higher-order aberrations of all those that follow. In evaluatingĪberrations of the fifth and higher orders, the contributions cannot all be These contributions can be evaluated independently. The sum of the wavefront aberration contributions of the individual surfaces in We therefore see that the wavefront aberration can be expressed as Ë û, are the wavefront aberrations introduced by surfaces 2 and 3,
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