Variations of spherical aberration and central coma of conceptual thin lenses

Based on our earlier matrix algorithms [J. Mod. Opt.55, 105 (2008)JMOPEW0950-034010.1080/09500340701308740] for evaluating the variations of Seidel aberrations, new concise equations are derived to directly evaluate the variations of spherical aberration and central coma of conceptual thin lenses when the incident marginal and chief rays are arbitrarily changed. In the earlier algorithms, four cases with distinct translation factors and matrix equations are required according to the relationships of the object and pupil positions; otherwise, division-by-zero errors or insufficient numerical accuracy will be encountered. Conversely, the new versatile equations are always accurate for all kinds of object and pupil positions; one example verifying this property is illustrated. Another example is given to explain why a symmetrical thin lens can provide only one, rather than two, degrees of freedom for correcting Seidel aberrations.