Incoherent Aberrations in Electron Microscopes
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Optical aberration can be described by the so-called wave aberration functions. There are two types of aberrations:
         i) Coherent aberrations falsify amplitude and phase information of the wave [1],
         ii) Incoherent aberrations act like a soft aperture due to the lack of spatial and temporal coherence [2].

Incoherent aberrations limit the spatial resolution of EMs because they always appear due to the restricted coherence of electron illumination. For instance, chromatic aberration, one type of incoherent aberrations is often the most important and is a well-known factor limiting the spatial resolution. Similar to geometric aberrations, incoherent aberrations also distort the wavefront but do not distort all the waves in the same way. Due to the illumination aperturec) of the EMs (lateral coherence) and the energy spread (ΔE) of the beam (longitudinal coherence) the envelope functions dampen the Fourier spectrum of the wavefront, especially the signal of the beam scattered at high angles and imposes a maximum to the transmitted spatial frequency. For instance, axial chromatic aberration moves the focal point of the wave depending on the energy of the wave. Incoherent aberrations act as an aperture in Fourier space filtering the contributions of the higher spatial frequencies and thus, the information in the image is blurred by the addition of these different contributions. We could also consider mechanical and electrical instabilities as a kind of incoherent aberration.




[1] Hanßen, K.-J. (1971). The optical transfer theory of the electron microscope: Fundamental principles and applications. Adv Optics
Electron Microsc 4, 1–84.
[2] Frank, J. (1973). The envelope of electron microscopic transfer functions for partially coherent illumination. Optik 38, 519–536.



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