Extension of HRTEM resolution by semi-blind deconvolution method and Gerchberg–Saxton algorithm: application to grain boundary and interface

A generalized maximum entropy method coupled with Gerchberg–Saxton algorithm has been developed to extend the resolution from high-resolution TEM image (s) for weak objects. The Gerchberg–Saxton algorithm restores spatial resolution by operating real space and reciprocal space projections cyclically. In our methodology, a generalized maximum entropy method (Kullback–Leibler cross entropy) dealing with weak objects is used as a real space (P1) projection. After P1 projection, not only are the phases within the input spatial frequencies improved, but also the phases in the next higher frequencies are extrapolated. An example of semi-blind deconvolution (P1 project only) to improve the resolution in SiC twin boundary is shown. The nature of the bonding in this twin boundary is Si-C but it was rotated 180° along the boundary normal. The optimum solution from P1 projection can be further improved by a P2 projection. The square roots of diffraction intensities from a diffraction pattern are then substituted to complete a cycle operation of the Gerchberg–Saxton algorithm. Application examples of Gerchberg–Saxton algorithm to solve the atomic structure of defects (2 × 1 interfacial reconstruction and dislocation) in NiSi2/Si interfaces will be shown also.