Induced aberrations in optical systems.

Abstract

The total wave aberration of an optical system can be broken down into surface contributions. These surface contributions can be further differentiated into induced and intrinsic components. The intrinsic aberration is the aberration introduced by a given surface, based on a perfect incoming wavefront. The induced component is the additional aberration introduced by the surface as a consequence of monochromatic aberrations of the incoming wavefront. This distinction is made without decomposing the aberration or its components into orders. Because no methods have previously been developed to properly analyze this induced component, there is very little known about its significance. As a result, the behavior of lenses is not well understood beyond third order, and designers must depend upon optimization to find solutions with the necessary overall higher-order correction. The first part of this investigation is concerned with developing appropriate methods for separating the surface contributions to the total wave aberration of an optical system into induced and intrinsic components. These systems are limited to rotationally symmetric optical systems with spherical or aspheric surfaces. Three different methods are developed to describe the induced aberrations. These methods emphasize the aberrations of wavefronts rather than rays; rays are simply used for calculation purposes. The first is a numerical approach that determines the true shapes of the wavefront components, without separating the aberrations into orders. A second numerical method, based on a procedure developed by G. W. Hopkins, determines aberration coefficients to seventh order describing the induced, intrinsic, and complete aberrations. Because of the choice of reference surfaces, the third-order aberrations are entirely intrinsic. Thus, the induced component is described only by fifth- and higher-order coefficients. A third method uses an algebraic approach to calculate the fifth-order induced aberration coefficients in terms of third order coefficients. The second part is an exploration of the nature and significance of the induced component. The various analysis methods are used to explore the behavior of induced aberrations in many basic optical systems.