ABSTRACT
A method is presented that allows the design of third order achromats consisting of a sequence of cells, in which subsequent cells agree with this base cell up to symmetry reflections. By correcting certain suitably chosen aberrations of the cell, the sequence of cells can be made free of all aberrations. Using methods of computational theorem proving, a complete classification of all n-cell systems requiring the least number of corrections in the base cell is obtained for 2≤n≤8. It turns out that four cell systems utilizing mirror symmetry are particularly suitable for the design of achromats, and that there is a class of 32 different designs all requiring the same number of corrections.
