Test of a method for phase retrieval in HREM

Abstract

1. IntroductionSeveral methods of phase retrieval from HRTEM image intensity distributions have been proposed but no standard method has emerged. We report on the results achieved using a technique based on a development of the “focus variation method”. The dependence of the retrieved wavefunction on various experimental parameters is investigated and the method tested using computer simulated images. The method is shown to be useful in finding the complex wavefield at the exit surface of the specimen, but the relationship of this to the specimen structure is left as a seperate problem.

Inversion of nonperiodic wavefields to determine localized defect structure

“…The exit‐surface wavefields similar to those in Fig. 3 were used as input for the inversion routine described by Beeching & Spargo (1993), and the wavefield propagated back to the slice just following the defect‐core slice as shown in Fig. 4.…”

“…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).…”

“…Given that the (complex) wavefield exiting from a crystal can now be measured (by the focus variation method, for example), presumably for both perfect and imperfect crystals, it remains to be seen if the associated structure of a defect in the crystal can be determined by inversion of the dynamical scattering. This possibility is examined here using a method based on reversal of the multislice routine as detailed for perfect crystal wavefields by Beeching & Spargo (1993). It is the methodology and validity of the inversion process that is highlighted in this paper rather than the feasibility of recording and retrieving the complex wavefield itself.…”