Fourier optics of image formation in aberration-corrected LEEM

Highlights: • We developed an extended and generalize Fourier optics formalism for modeling image formation of one or two-dimensional objects in aberration-corrected low energy electron microscopy. • Comparison of this mathematically rigorous approach to the contrast transfer approach developed earlier identifies the class of objects that must be treated with Fourier optics. • Implementation of a multi-core, multi-threading programming architecture for performing Fourier optics simulations partially mitigates the drawback of its slow computational speed. -- Abstract: We present the extended Fourier Optics (FO) approach for modeling image formation in aberration-corrected low energy electron microscopy (ac-LEEM). The FO formalism is also generalized for image simulations of one or two-dimensional objects in ac and uncorrected (nac) LEEM. A comparison is made of the extended FO approach presented here and the extended contrast transfer function (CTF) approach for ac-LEEM that was developed earlier. The mathematically rigorous extended FO approach gains an advantage under conditions, particularly defocus, that partial coherence of the illumination may compromise the validity of the approximate CTF intensity calculation. The drawback of the FO approach compared to the CTF approach, which is its slow computational speed, is mitigated partly here by the implementation of a multi-core, multi-threading programming architecture. This work broadens our capabilities to understand the origins of LEEM image contrast and to perform quantitative evaluation of contrast observed in an image focal series.