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The plane wave of electron beam propagating in zdirection (optical axis) can be given by,
 [4202a]
where,
a  Amplitude
k  Wavenumber (=1/λ)
λ  Wavelength
ω  Frequency
The vector r = (x, y) defines a position in a wavefront perpendicular to the electron propagation direction z. In offaxis electron holography as shown in Figure 4202, the plane wave of the electron beam is split to two partial waves which are deflected by a very small angle towards each other,
(for x < 0 in Figure 4202)  [4202b]
(for x > 0 in Figure 4202)  [4202c]
where
k_{⊥} ≈ kβ/2
k_{z} ≈ k
Figure 4202. Schematic diagram of offaxis electron holography in TEMs.
The two tilted waves are laterally shifted to the right (for the left part) and to the left (for the right part) by a width of W, respectively, and thus are superimposed in the hologram (W). In the point r of the detector the points and of the two partial waves with the unit vector e_{x} in x direction, forming the intensity (I) in a format of cosinoidal interference pattern,
 [4202d]
where,
q_{c}  Spatial frequency
(=kβ)
β  The angle of the
superposition
The cosinoidal term produces the fringes in the measurements of offaxis electron holography.
