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 K-parallel to on the sample rotation cr and primary energy E(p) are calculated. A simple empirical formula is derived, which allows accurate experimental determination of K without extensive calculations. Ray-tracing calculations are further applied to analyse the influence of residual asymmetries of the electron optics.