Introduction

In chapter 9 we derived the laws of paraxial optics by developing the angle eikonal of a lens into a Taylor series and keeping the quadratic terms only. We now investigate the result of taking along the fourth degree terms as well. We base our treatment on T. Smith's celebrated 1921/2 paper ‘The changes in aberrations when the object and stop are moved’ [43]. Other approaches may be found in, for example, Herzberger [7], [8], Buchdahl [11], [12], and Luneburg [27].

A word about the notation. So far it has been shown explicitly how the refractive indices of the object space and the image space enter into the formulas. In this chapter we take a different approach. We assume that all distances in the object space, transverse as well as axial, are multiplied by the object space refractive index, and similarly that all distances in the image space are multiplied by the image space refractive index. In other words: lengths are expressed in units that are a constant multiple of the local wavelength. This is almost always a useful notation; the only exception (and the reason that we have not adhered to it throughout this book) is the paraxial calculations discussed in chapter 10. It is useful to introduce a reduced magnification G as well.