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The electrons in the beam in EMs undergo different phase shifts when propagating through the objective lens because every electron source has a finite energy width. The maximum phase shift due to the energy width of the electron source is given by,
 [4158a]
where,
C_{c}  Chromatic aberration coefficient
ΔE  Energy width of the electron source
E_{0}  Accelerating voltage of the electron beam
λ  Wavelength of the electron beam
k  Spatial frequency
Conventionally, the phase shift (phase distortion function) due to the objective lens can be combined into a single phase factor χ, given by,
 [4158b.a]
 [4158b.b]
where,
C_{s}  The spherical aberration coefficient, defining the quality of objective lens,
Δf  The defocus value,
g  Also the spatial frequency, the same as k above,
α  The convergence semiangle.
Considering the nonconstant wavelength of an incident electron beam and the astigmatism, the phase shift function can be described by,
 [4158c]
The last and the second terms describe the effects of the nonconstant wavelength and astigmatism, respectively.
Note that for an ideal lens, the phase shift induced by objective lens, χ(α), is equal to 0.
