Lens first-order transfer matrices incorporating third-order aberrations

Abstract

Abstract Transfer matrices of electrostatic or other lenses are useful for ray-tracing through combinations of two or more lenses [see e.g. J.H. Moore et al., Building Scientific Apparatus (Addison-Wesley, 1983)]. In this letter we present a simple modification than can be made to the first-order transfer matrix of a lens to incorporate the effects of all meridional third-order aberrations. The modified transfer matrix is intended for use within computer programs in which the third-order spherical aberration coefficients C S for point axial objects are either stored or can be calculated using a suitable numerical approximation [such as that given by E. Harting and F.H. Read, Electrostatic Lenses (Elsevier, 1976)].