An Introduction to Hamiltonian Optics

PREFACE
Although the propagation of light is described in all its details
by Maxwell's equations, many optical problems can be solved to
a sufficient degree of approximation on the basis of the laws of
geometrical optics. On this level a thorough understanding of the
over-all features of the imagery produced by the types of systems
commonly encountered in practice is most easily gained through
Hamilton's method. This presentation of it is partly intended to
stimulate the teaching of the subject; in at least equal measure it is
directed towards those whose task it is actually to design image-
forming instruments. For this reason, if no other, the mathematical
knowledge required of the reader has been kept to a minimum.
For example, although the whole theory arises directly from a
variational principle, Euler's equations or formal variational
derivatives are never considered explicitly. They are replaced
throughout by elementary geometrical constructions. If some of the latter
pages look a little bewildering at first glance, this is solely because
they concern themselves with the kind of detail which is often
quietly swept under the carpet; without which, however, one has
merely a general framework, far removed as yet from what one
needs to know in everyday practice.