  The various non-linear transformations incurred by the rays in an optical
system can be modelled by matrix products up to any desired order of
approximation. Mathematica software has been used to find the appropriate
matrix coefficients for the straight path transformation and for the
transformations induced by conical surfaces, both direction change and position
offset. The same software package was programmed to model optical systems in
seventh-order. A Petzval lens was used to exemplify the modelling power of the
program.

Optics