Control of parasitic aberrations in multipole optics

A method is described to find the optimal fourth order setup of a quadrupole-octupole third-order aberration corrector. Given accurate measurements of aberrations to fifth order, stimulus/response experiments can be used to synthesize pure controls for each measured aberration up to fourth order, including those which are caused by parasitic effects - symmetry violations, misalignments, construction mistakes, post-construction drift or other problems.