ABSTRACT
This chapter examines the relationship between the two main definitions of aberration and it introduces a classification of aberrations with formulae and nomenclature suitable for the purposes of optical design. These relationships between the definitions are best obtained by introducing the characteristic function of Hamilton, a remarkable concept which can be used to obtain the several useful theoretical results although in its original form it does not have much direct application in optical design. The chapter examines the Seidel aberrations and spherical aberration. It considers the effects of each of the Seidel aberrations separately in order to see how they appear in the image; in practice, they occur in combination with each other and with higher order aberrations. The analysis into aberration terms appears naturally when the values of the primary aberration coefficients are computed numerically for a given system.
