The effect of mechanical vibration and drift on the reconstruction of exit waves from a through focus series of HREM images

Experimental HREM images can show a limited resolution as a result of mechanical vibration and drift. In this paper the effect of such mechanical vibrations on the accuracy of the through focus exit wave reconstruction method is investigated for different thicknesses of a test structure of La₃Ni₂B₂N₃. A through-focus series of HREM images for this structure is simulated for different kinds of mechanical vibration corresponding to an information limit g of about 7 nm⁻¹: (1) no mechanical vibration, (2) isotropic mechanical vibration, and (3) several anisotropic mechanical vibrations. From these through-focus series the reconstructed exit wave is calculated (Ultramicroscopy 64 (1996) 109). The above isotropic and anisotropic mechanical vibrations have a large effect on the reconstructed exit waves when compared with the reconstructed exit wave without mechanical vibration, i.e. the range of amplitudes and phases in a reconstructed exit wave decreases and the background intensity increases. The initial thickness and orientation can be obtained using a least-squares refinement procedure (Acta Crystallogr. A 54 (1998) 91) when there is no mechanical vibration present. In the case of isotropic or anisotropic vibration, the refined thickness and orientation are likely to give wrong results depending on the size of the vibrations and on the number of significant reflections (which is related to the size of the unit cell, the thickness and the misorientation).