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


Optical aberration can be described by the so-called wave aberration function.  For the ideal cases without aberrations, when an object is imaged using a perfect lens the wave at the back focal plane of a lens is spherical and is converged in the image plane (Ig). In actual lenses as shown in Figure 3701, the wave aberration function is defined as the phase difference (χx,y) or the distance difference (Wx,y) in the optical path from the perfect (reference) spherical wave to the actual wavefront for the given lens. Since the area on the sample that is viewed at most of the time in EMs (especially in TEMs) is very small the wave aberration function’s dependence on the location of the point source in the object plane can be usually ignored, which is known as the isoplanatic approximation.

Schematic illustration of wave aberration and ray aberration

Figure 3701. Schematic illustration of wave aberration function (Wx,y or χx,y) and ray aberration (δr).




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