Foci in ray pencils of general divergency

W F Harris,R D Van Gool

doi:10.4102/aveh.v68i3.161

Abstract

In generalized optical systems, that is, in systems which may contain thin refracting elements of asymmetric dioptric power, pencils of rays may exhibit phenomena that cannot occur in conventional optical systems. In conventional optical systems astigmatic pencils have two principal meridians that are necessarily orthogonal; in generalized systems the principal meridians can be at any angle. In fact in generalized systems a pencil may have only one principal meridian or even none at all. In contrast to the line foci in the conventional interval of Sturm line foci in generalized systems may be at any angle and there may be only one line focus or no line foci. A conventional cylindrical pencil has a single line focus at a finite distance but it can be regarded as having a second line focus at infinity. Only in generalized systems is a single line focus possible without a second at infinity or anywhere else. The purpose of this paper is to illustrate the types of pencils possible in generalized systems. Particular attention is paid to the effect of including an antisymmetric component in the divergency of the pencil.

Highlights

A recent paper[1] describes thin lenses with asymmetric dioptric power
The lenses are built up of small prisms and the power is of a type that has no equivalent in the traditional spherocylindrical representation employed in optometry
We shall refer to optical systems which may contain such lenses as generalized optical systems

Summary

Introduction

A recent paper[1] describes thin lenses with asymmetric dioptric power. Conventional optical systems do not contain such lenses; they constitute a subset of generalized optical systems. The state of a pencil is represented by a 2 × 2 matrix, called the divergency, which may be symmetric or asymmetric. In conventional systems it is the negative of the vergence matrix[3,4,5,6]. Equations are derived[2] which allow step-along divergency calculations through generalized optical systems similar to step-along vergence calculations[7] in conventional systems

Objectives

Conclusion