Introduction

Aberrations were introduced in Chapter 5 but only discussed qualitatively. Now they will be discussed quantitatively and in greater detail. Equations will be presented for calculating aberration levels as a function of system construction parameters, aperture stop size, conjugate plane positions and position of the object point in the field-of-view for any rotationally symmetric system. However, since the derivations of these equations are complex, space consuming and adequately covered in other texts, most of the equations will be presented here without any derivation. The equations will be mostly drawn from two texts: Hopkins (1950) and Welford (1986). Derivations of equations will only be included if the derivations are not adequately or suitably covered elsewhere.

The calculation of exact aberrations requires time consuming and tedious tracing of real rays. On the other hand, an estimate of the aberration levels can be found relatively simply from the results of two suitable paraxial ray traces. For many purposes, these estimates of aberration levels are adequate. The two paraxial rays are the marginal and pupil rays. The ray angles {u} and ray heights {h} along with other system constructional parameters are fed into equations for the calculations of these aberrations. One such set of equations is the Seidel aberration equations and the resulting estimates of aberrations are called Seidel aberrations. These equations will be introduced and discussed in the next section. While these equations are approximate, they have three very useful attributes: (a) they allow the identification and quantification of different aberration types such as spherical aberration and coma, (b) they give the aberration contribution by each surface and (c) they become more accurate the smaller the aperture and field size.