Computer Algebra Derivation of
Florian Bociort
Research Institute for the Applications of Computer
Algebra,
Kruislaan 419, 1098 VA Amsterdam, The Netherlands
Abstract:
The use of computer algebra software enables a
considerable simplification of the derivation of analytic expressions for the
aberration coefficients of optical systems. In this paper, an algorithm for the
symbolic computation of the intrinsic and extrinsic contributions of spherical
surfaces to the higher-order aberration coefficients is described. This
algorithm can be easily implemented in any major computer algebra language. As
an example, two Mathematica programs producing the analytic expressions are
given. With these programs, all aberration coefficients of third, fifth and
seventh order have been obtained.
