The background of electron diffraction originates from different mechanisms:
i) amorphous TEM specimen:
Linear contrast transfer theory can be applied to weakly scattering objects, for instance thin amorphous TEM specimen, which leads only to a small phase shift on the diffracted electron wave. The diffractogram intensity is the power spectrum of the recorded image and can be given in the simple coherent form,
D(g) ≈ |O(g)|2 sin2[χ(g)] -------------------------------- 
g -- Object frequency vector
χ -- Wave aberration function
sin2[χ(g)] -- Oscillating patterns of circular, elliptic, or hyperbolic shape (Thon rings )
|O(g)|2 -- Scattering power of thin amorphous objects
|O(g)|2 decreases slowly towards higher spatial frequencies and is azimuthally isotropic.
In practice, the diffractogram intensity does not really follow Equation 4176. One of the reasons is due to the existence of substantial background, which can be larger in magnitude than the oscillation amplitude of the ideal pattern. The background can consist of sine and cosine contrast-transfer components produced by thicker objects (e.g. nanocrystals) in the TEM specimen.
ii) Perfect crystal:
In the electron diffraction pattern of a perfect crystal, the background
(between Bragg spots) arises mainly from inelastic scattering, which can be described by EELS measurement.