A Contrast Transfer Function approach for image calculations in standard and aberration-corrected LEEM and PEEM

We introduce an extended Contrast Transfer Function (CTF) approach for the calculation of image formation in low energy electron microscopy (LEEM) and photo electron emission microscopy (PEEM). This approach considers aberrations up to fifth order, appropriate for image formation in state-of-the-art aberration-corrected LEEM and PEEM. We derive Scherzer defocus values for both weak and strong phase objects, as well as for pure amplitude objects, in non-aberration-corrected and aberration-corrected LEEM. Using the extended CTF formalism, we calculate contrast and resolution of one-dimensional and two-dimensional pure phase, pure amplitude, and mixed phase and amplitude objects. PEEM imaging is treated by adapting this approach to the case of incoherent imaging. Based on these calculations, we show that the ultimate resolution in aberration-corrected LEEM is about 0.5 nm, and in aberration-corrected PEEM about 3.5 nm. The aperture sizes required to achieve these ultimate resolutions are precisely determined with the CTF method. The formalism discussed here is also relevant to imaging with high resolution transmission electron microscopy.