Defocus in cathode lens instruments

Accurately measuring defocus in cathode lens instruments (Low Energy Electron Microscopy - LEEM, and Photo Electron Emission Microscopy - PEEM) is a pre-requisite for quantitative image analysis using Fourier Optics (FO) or Contrast Transfer Function (CTF) image simulations. In particular, one must establish a quantitative relation between lens excitation and image defocus. One way to accomplish this is the Real-Space Microspot LEED method, making use of the accurately known angles of diffracted electron beams, and the defocus-dependent shifts of their corresponding real-space images. However, this only works if a sufficiently large number of diffracted beams is available for the sample under investigation. An alternative is to shift the sample along the optical axis by a known distance, and measure the change in objective lens excitation required to re-focus the image. We analytically derive the relation between sample shift and defocus, and apply our results to the measurement and analysis of achromats in an aberration-corrected LEEM instrument.