A method for crystal potential retrieval in HRTEM

Quantitative structure retrieval using scanning transmission electron microscopy

“…The most direct forms of structure retrieval rely on very thin samples and assume either a single scattering approximation, in which there is a direct correspondence between the complex exit wave and the projected potential of the specimen, or a phase-object approximation, in which there is a direct correspondence between the phase of the exit wave and the projected potential of the specimen. Early attempts to move beyond these approximations by iterative methods include the work of Gribelyuk (1991) and Beeching & Spargo (1993). However, the stability of these algorithms remained limited to small thicknesses.…”

Inversion of nonperiodic wavefields to determine localized defect structure

“…Several methods for the retrieval of ψ H ( r ) have been proposed and evaluated including holography (Lichte, 1991), genetic and simulated annealing algorithms (Thust et al ., 1994; Bierwolf & Hohenstein, 1994) and variants of the focus‐variation method (FVM) in which several images recorded in a through‐focus series (TFS) are combined by image‐processing techniques (Kirkland, 1984; Van Dyck & Op de Beeck, 1992; Beeching & Spargo, 1992). An alternative scheme, based on a series of images obtained using systematically tilted illumination and then recombined using a suitable restoration filter, has been proposed (Kirkland et al ., 1995) but, while it has promised resolution gains, the reliability and robustness remain to be demonstrated.…”

“…Less confidence, however, has emerged on the second stage of the task, namely the inversion to obtain the crystal structure, although the initial result using the direct structure determination method based on electron channelling theory (Op de Beeck & Van Dyck, 1996) has shown impressive promise. Application of a method based on simulated annealing techniques (Lentzen & Urban, 1996) has shown a breakdown at thicknesses similar to those at which failure was encountered in the multislice inversion technique of Beeching & Spargo (1993). These breakdowns would appear to be associated with the thickness approaching half an extinction distance for the main beam (Spargo et al ., 1994).…”

Computation in electron microscopy

“…The ambitious project of inverting the whole threedimensional scattering (an inverse multislice or Bloch wave calculation) is somewhat difficult and has been considered by Gribelyuk (1991), Beeching & Spargo (1993, Spargo et al (1994), Allen et al (1998Allen et al ( , 1999Allen et al ( , 2000, Spence (1998) Calculated intensity in two directions in gold at 40 kV using a standard multislice calculation (stnd) and a special multislice calculation permitting arbitrarily small slices with increased accuracy to test accuracy.…”