The theory and design of zoom lenses

Abstract

This thesis contains a new approach to the paraxial and third order design and theory of zoom lenses, especially those consisting of thin elements. Equations describing the paraxial and third order behaviour of zoom lenses are derived and are used to design a series of three element zoom lenses. In the paraxial theory the derivatives, with respect to the axial separations, of the paraxial coefficients are required. Optimization processes for the automatic design of lenses require the availability of the derivatives, with respect to axial separations and curvatures, of the third and fifth order aberration coefficients. These derivatives can be calculated from formulae given herein and these form the basis of a FORTRAN programme for calculating such derivatives. The derivatives, with respect to axial separations, of the paraxial coefficients, occur in the formulae describing the paraxial properties as functions of the zoom parameter. These formulae may be solved to obtain the powers and initial (z = 0) separations of the elements of the zoom lens. For two and three element zoom lenses the equations are solved analytically. Formulae are obtained for the third order aberration coefficients as functions of the zoom parameter. Using the thin lens approximation the shapes of the individual elements are introduced and from the resulting expressions sets of simultaneous equations are obtained in the particular case of the three (thin) element zoom lens. The solutions of these sets of equations give zoom systems for which selected third order aberrations are substantially corrected over the whole zoom range. Whereas optimization processes give one solution to a particular problem, the present method gives all possible solutions by a simple analytic or semi-analytic approach.