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Figure 3732 gives a very simplified illustration of how the incident electrons travel through the TEM column. r is the real space coordinates in the sample or image, u is the reciprocal space coordinates and θ is the scattering angle.
Figure 3732. Simplified illustration of how an image is formed in a TEM column.
Ideally, an electron microscope can be simplified as a contrast transfer function (CTF). For a perfect coherent illumination in reciprocal space the CTF can be represented by T(k, g) as [1]
 [3732a]
where,
A(k)  The aperture function describing the effect of the objective aperture,
k  The reciprocal space vector,
g  The spatial frequency,
χ  The phase shift from defocus and spherical aberration.
The effect of the post specimen imaging process is given by applying the CTF to the frequency components of the wave function,
 [3732b]
where,
F  The Fourier transform,
F^{1} The inverse Fourier transform.
Considering the nonconstant wavelength of an incident electron beam and the astigmatism, the phase shift function can be described by,
 [3732c]
where,
Δf  The defocus,
λ  The electron
wavelength,
C_{s}  The coefficient of third order spherical aberration,
C_{5}  The coefficient of fifth order spherical aberration.
The last and the second terms describe the effects of the nonconstant wavelength and astigmatism, respectively.
Adjusting defocus and defocus spread, in CTEMs with LaB_{6} or W electron guns and FEEMs, affects the intensity of diffractogram and real images.
[1] Cowley, J. M., Diffraction Physics, HorthHolland, Amsterdam, 1990.
