Irreducible aberrations of a lens used for a range of magnifications

Abstract

Maxwell has proved that a lens cannot be free from aberrations at more than one magnification. Yet many lenses, with SLR macrolenses and photographic enlarger lenses as obvious examples, are used over a wide range of magnifications. What are the theoretical limitations on the performance of these lenses? We use eikonal function theory to examine this question and obtain practical results by using numerical techniques rather than conventional series developments. The lens is represented by an eikonal not fully determined by the external constraints and, therefore, depending on a number of parameters freely at our disposal. The aberrations for various magnifications are determined by an iterative ray tracing process,1 and, using a suitable merit function, the eikonal is optimized by variation of the free parameters. The resulting ray trace curves show the best image quality possible in the conditions imposed, no matter how complicated we make the lens. We show detailed results for a 50-mm f/2.8 SLR macrolens.