This book (Practical Electron Microscopy and Database) is a reference for TEM and SEM students, operators, engineers, technicians, managers, and researchers.
 

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Band structure (BS) methods used in EELS modeling are applied in reciprocal space based on density functional theory (DFT) [1 - 2]. BS methods were originally developed to derive the electron density. The advantage of BS methods is that based on ELNES and low loss spectra, many physical properties can be derived from the same calculation. Those properties can be band structure diagrams, density of states, elastic constants, optical properties, electron densities, etc. The drawback of BS methods is that they yield only ground states properties, and thus the calculation of excited states properties is not guaranteed to work. However, the calculation of ELNES and of low loss spectra with DFT works very well [3].

In a BS method ELNES is calculated within the first Born approximation under the assumption that the incoming and outgoing fast electrons are plane waves with wave vectors k_i and k_f (see page3375).

[1] Hohenberg, P., Kohn, W., 1964. Inhomogeneous electron gas. Phys. Rev. 136 (3B), B864–B871.
[2] Kohn, W., Sham, L.J., 1965. Self-consistent equations including exchange and correlation effects. Phys. Rev. 140 (4A), A1133–A1138.
[3] Rez, P., Bruley, J., Brohan, P., Payne, M., Garvie, L.A.J., 1995. Review of methods for calculating near edge structure. Ultramicroscopy 59, 159–167.