This book employs homogeneous coordinate notation to compute the first- and second-order
derivative matrices of various optical quantities. It will be one of the important mathematical
tools for automatic optical design. The traditional geometrical optics is based on raytracing
only. It is very difficult if possible to compute the first- and second-order derivatives of
a ray and optical path length with respect to system variables since they are recursive
functions. Consequently current commercial software packages use a finite difference
approximation methodology to estimate these derivatives for use in optical design and analysis.
Furthermore previous publications of geometrical optics use vector notation which is
comparatively awkward for computations for non-axially symmetrical systems.
