{'fraction_non_alphanumeric': 0.020594965675057208, 'fraction_numerical': 0.0, 'mean_word_length': 5.628787878787879, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Electrostatic ray-tracing calculations in VLEED

The present ray-tracing scheme employs the electrostatic potential calculation by finite-difference solution of the Laplace equation in three dimensions. The run time reduction, achieved by using successively refined grids and optimizing the iteration cycle, allows one to perform calculations on a personal computer. The code is applied to a standard four-grid LEED optics, operated in the retarding field mode, to calculate electron trajectories in the case of off-symmetry incidence. In particular, dependences of incidence on the sample rotation and primary energy are calculated. A simple empirical formula is derived, which allows accurate experimental determination of without extensive calculations. Ray-tracing calculations are further applied to analyse the influence of residual asymmetries of the electron optics.