Quadrupoles in Electron Lens Design

Appendix II: The shadow projection method of measuring aberration coefficients

This is at present the standard method of measuring aperture aberrations. This brief account of the essentials follows Deltrap (1964a), who first applied the method to the measurement of quadrupole aberrations, and Hardy (1967) closely.

We consider a system that produces separated line images of a (stigmatic or astigmatic) object on the optic axis at z = z_i and z = z_j, and we consider the points of intersection of rays that pass through these line images with two planes: the grid plane, z = z_G and the plane of the fluorescent screen, z = z_S (Fig. A1). Let us consider a ray making angles α, γ (in image space) with the optic axis in the principal sections. It will ...