Asymmetrical dark field detectors in the STEM

Although the annular dark field detector in the STEM collects a large fraction of the elastically scattered electrons, it does not use all the information carried by these electrons because it ignores the distribution of electrons over its surface. This information can be obtained by dividing the detector into sections. This paper calculates the number of electrons scattered by a single atom onto each side of an annular dark field detector split in half by a line passing through its center. This scattering problem is unusual becuase the incident wave is not a plane wave in the STEM. The sum and difference signals are calculated for a single atom from its scattering amplitude for a STEM limited by primary or secondary spherical aberration operating at 10 kV, 70kV, or 100 kV. All the cases calculated show that a single thorium atom should give an observable difference signal which is very sensitive to the focal conditions of the STEM.