Electron-beam-tilt-induced Image Displacement in TEM
- Practical Electron Microscopy and Database -
- An Online Book -


This book (Practical Electron Microscopy and Database) is a reference for TEM and SEM students, operators, engineers, technicians, managers, and researchers.


The electron-beam-tilt-induced image displacement in TEM can be given by, [1]

           electron-beam-tilt-induced image displacement in TEM ---------------- [1914a]
        w = α exp(iϕ) ------------------ [1914b],
        Cs -- The spherical aberration coefficient,
        z -- The defocus (the difference of TEM specimen height from the standard focus height),
        a2 = A2 exp(i2ϕ2),
        b = B exp(iϕB),
        a3 = A3 exp(i3ϕ3),
        α -- The scattering angle,
        A2 -- The two-fold astigmatism coefficients,
        A3 -- The three-fold astigmatism coefficients,
        B -- The coefficients corresponding to coma displacement,
        ϕ2, ϕB, and ϕ3 -- The initial phases of corresponding aberrations.

The overbar in Equation 1914a denotes a complex conjugate. Equation 1914a represents the image displacement terms related to spherical aberration, defocus, two- and three-fold astigmatisms, and coma.

One of the most commonly used autofocus methods in TEM is based on a beam-tilt induced image displacement [2]. This method is especially applied for life-sciences.







[1] Koji Kimoto, Kazuo Ishizuka, Nobuo Tanaka, Yoshio Matsui, Practical procedure for coma-free alignment using caustic figure, Ultramicroscopy 96 (2003) 219–227.
[2] A.J. Koster, A. van den Bos, K. van der Mast, An autofocus method for a TEM, Ultramicroscopy 21 (3) (1987) 209–222.



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