TEM Image Formation/Imaging Process
- Practical Electron Microscopy and Database -
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This book (Practical Electron Microscopy and Database) is a reference for TEM and SEM students, operators, engineers, technicians, managers, and researchers.
 

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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.

TEM Image Formation Process

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]

         perfect coherent illumination in reciprocal space the CTF ---------------------------- [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,

         perfect coherent illumination in reciprocal space the CTF ---------------------------- [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,

         (P)CTF. --- [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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