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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The electronbeamtiltinduced image displacement in TEM can be given by, [1]
 [1914a]
where,
w = α exp(iϕ)  [1914b],
C_{s}  The spherical aberration coefficient,
z  The defocus (the difference of TEM specimen height from the standard focus height),
a_{2} = A_{2} exp(i2ϕ_{2}),
b = B exp(iϕ_{B}),
a_{3} = A_{3} exp(i3ϕ_{3}),
α  The scattering angle,
A_{2}  The twofold astigmatism coefficients,
A_{3}  The threefold astigmatism coefficients,
B  The coefficients corresponding to coma displacement,
ϕ_{2}, ϕ_{B}, and ϕ_{3 } 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 threefold astigmatisms, and coma.
One of the most commonly used autofocus methods in TEM is based on a beamtilt induced image displacement [2]. This method is especially applied for lifesciences.
[1] Koji Kimoto, Kazuo Ishizuka, Nobuo Tanaka, Yoshio Matsui, Practical procedure for comafree 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.
