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Electron spectroscopic diffraction (ESD) in an energyfiltering electron transmission microscope (EFTEM) is used to record
electron diffraction patterns with selected energy windows.
Based on the theory described by Reimer etc. [1], the angular intensity distribution of inelastically scattered electrons from element i can be given by a
twodimensional convolution,
 [3505a]
where,
dI_{el,i}/dΩ  angular intensity distribution of elastically scattered electrons of element i (see page4774),
dΩ = 2πθdθ (between θ and θ + dθ independent of azimuth),
dσ_{in,i}/dΩ  angular distribution of inelastically
scattered electrons of element i which can be approximated by,
(for θ < θ_{c})  [3505b]
= 0 (for θ > θ_{c})  [3505c]
where,
θ_{E} (≈ΔE/2E)  the characteristic angle, which increases with increasing energy loss ΔE.
θ_{c}  () Compton angle, which is the cutoff angle of inelastic scattering and increases in diameter with increasing ΔE [2,3] .
For a complex material, the total elastic crosssection of the components in the material can be evaluated by summing all the crosssections of the elements (see page4424).
Figure 3505a shows the radial intensity of the diffraction pattern of a 27 nm amorphous Ge film: (a) unfiltered, (b) zerolossfiltered and (c) plasmonlossfiltered (ΔE = 17 eV).
Figure 3505a. Radial intensity of the diffraction pattern of a 27 nm amorphous Ge film: (a) unfiltered, (b) zerolossfiltered and (c) plasmonlossfiltered (ΔE = 17 eV). [1] 
Figure 3505b shows twodimensional (2D) convolution of a radial zeroloss intensity distribution by the inelastic differential cross section for energy losses of ΔE = 1 and 17 eV.
Figure 3505b. 2D convolution of a radial zeroloss intensity distribution, of a 27 nm amorphous Ge film, by the inelastic differential cross section for energy losses of ΔE = 1 and 17 eV. [1] 
[1] L. Reimer, I. Fromm, I. Naundorf, Electron spectroscopic diffraction, Ultramicroscopy, 32 (1990) 8091. [2] L. Reimer, 1. Fromm and R. Rennekamp, Ultramicroscopy 24 (1988) 339.
[3] L. Reimer and R. Rennekamp, Uhramicroscopy 28 (1989)
258.
