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Simply speaking, Fourier transform is a limiting case of Fourier series. The structure factor F(u) is proportional to the Fourier components I_{im}(u) of the HREM image. For a weakphaseobject, the Fourier transform of the HREM image I_{im}(u) can be given by [1],
 [4974a]
 [4974b]
 [4974c]
where,
Δf  The defocus value
C_{s}  The spherical aberration
coefficient
k’  A constant
F(u)  Structure factor of electron diffraction (ED), which is the Fourier transform of the potential distribution φ(r) of the object
λ  The electron wavelength
u  The reciprocallattice vector within the resolution limit
D  The standard deviation of the Gaussian distribution of defocus due to the chromatic aberration [2]
The values of Δf (defocus value), C_{s} (spherical aberration coefficient), and D (standard deviation of the Gaussian distribution of defocus due to the chromatic aberration) can be obtained by TEM image deconvolution.
[1] X. D. Zou. Crystal Structure determination by crystallographic image processing. in
“Electron Crystallography”, eds. D. L. Dorset, S. Hovmöller, X. D. Zou, Nato ASI Series C,
Kluwer Academic Publishers, Dordrecht, 1997, pp163181.
[2] Fijes PL. 1977. Approximations for the calculation of highresolution
electronmicroscopy images of thin films. Acta Cryst A33:109–113.
