A One-Ray System for Designing Spherical Condensers

Abstract

A spherical condenser is a simple lens of relatively large aperture. The outer portions of such a lens focus the rays much nearer to the lens than do the center portions. As a result the lens as a whole fails to produce a sharp image. This defect of the lens is known as spherical aberration. — While in the case of spherical aberration no sharp image is produced, an imagelike region of best focus does exist. This is known as the disk of least confusion. Its diameter may be minimized by shaping the lens so as to minimize spherical aberration. It is with this disk of least confusion and its required location that the designer of a spherical condenser must deal. — Without a knowledge of the properties of the disk of least confusion a designer might compute rays through a large number of trial lenses until, by an extensive and costly trial-and-error process, a condenser, having the correct shape for minimal spherical aberration and the disk of least confusion at the required location, is obtained. — The present paper examines some simple properties of the disk of least confusion. In consequence it shows how, by computing the course of a single ray through the proposed lens, a spherical condenser will result having the correct shape for minimizing spherical aberration, and the correct center thickness for its assumed diameter and edge thickness; and for which, finally, the location of the disk of least confusion is known. The method is applicable to condensers comprising more than one lens, and leads to the required design with a minimum of relatively simple trials.