Lawrence Berkeley National Laboratory
Alpha-null defocus: An optimum defocus condition with relevance for
- Author(s): O'Keefe, Michael A.
- et al.
Two optimum defocus conditions are used in high-resolution transmission electronmicroscopy. Scherzer defocus produces an image of the specimen "projected potential" to the resolution of the microscope, and Lichte defocus minimizes dispersion. A third optimum defocus is best for focal-series reconstruction; alpha-null defocus maximizes transfer of high-frequency diffracted beam amplitudes into the microscope image. Beam transfer is confined by incident-beam convergence to a Gaussian "packet" of defocus values centered on the alpha-null defocus. For a diffracted beam hkl, with a spatial frequency of u, the envelope for incident beam convergence has null damping effect when defocus is set to -Cs. (wavelength.u)**2. On either side of this alpha-null defocus value, the damping effect of incident-beam convergence reduces diffracted-beam transfer. The position of alpha-null defocus for any spatial frequency depends only on the value of Cs, but defocus-packet width around the alpha-null defocus depends only on the convergence semi-angle. Under NCEM OAM (one-Angstrom microscope) conditions, a  diamond image with the correct 0.89A spacing appears when the Si (004) alpha-null defocus is selected. The alpha-null defocus should be included as the (furthest underfocus) limit for all high-resolution focal series reconstruction.