Electron microscope lens defects

We are know about the next lens defects: spherical aberration, chromatic aberration, astigmatism.

Spherical aberration is an inability of a lens to focus all incident beams from a point source to a point. The outer zones of the lens have a greater strength, and light rays or electrons originating from a point are not imaged at a point. The one point the envelope of the imaged rays has a minimum diameter known as the circle or disc of least confusion. This limiting disc has a diameter d_s given by: d_s =1/2*C_s*α³ =>C_s- spherical aberration coefficient, α - semi–angular aperture of the lens.

Chromatic aberration, the other major distortion, is caused by the faster (shorter wavelength) electrons focusing at a different position from the slower ones, a problem that only a perfect electron beam could solve completely. The chromatic aberration coefficient C_s is the parameter which expresses this quality , and the resolution d_c as limited by chromatic effects is given by

Where α is the objective semi-angular aperture.

Astigmatism is a defect of magnetic field asymmetry resulting in differing lens strengths in two directions at right angles. The amount of the astigmatism of the lens is defined as the distance between the focal lines. The astigmatism of an objective lens in a good microscope will be typically 1 μm or less.