Basic properties

Thin lenses are made up of elements that are so thin, separated by air gaps that are so small, that all the axial distances may, for all practical purposes, be set equal to zero. Doublets and triplets used as telescope objectives are common examples. For lenses of this nature the effect on the aberrations of introducing the thicknesses is small, so that only small changes in the surface curvatures are needed when, in the end, the finite thicknesses must be accounted for. We will only consider thin lenses used in air.

The rays through the axial point of the lens are undeviated as they emerge into the image space. This point is therefore imaged free from spherical aberration, and, because Abbe's sine rule is clearly satisfied, free from coma as well. If the pupil coincides with the lens, the rays through the center of the lens are the chief rays. As they move on undeviated, there can be no distortion. There is, however, a great deal of astigmatism.

To evaluate the astigmatism, we consider, in the spirit of chapter 23, rays close to one of the chief rays. In the calculation of the four-by-four matrix for these rays the thicknesses are set to zero, so the translation matrices reduce to unit matrices and can be left out of the product. First consider a single thin element. The field angle, i.e. the angle between the axis and the chief ray outside of the lens, is ψ.