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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 non-constant 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,
Cs -- The coefficient of third order spherical aberration,
C5 -- The coefficient of fifth order spherical aberration.
The last and the second terms describe the effects of the non-constant wavelength and astigmatism, respectively.
Adjusting defocus and defocus spread, in CTEMs with LaB6 or W electron guns and FE-EMs, affects the intensity of diffractogram and real images.
[1] Cowley, J. M., Diffraction Physics, Horth-Holland, Amsterdam, 1990.
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