Abstract

Reconstruction in HREM of the complex wave function at the exit face of a crystal foil out of a focal series of HREM images, and with correction for the microscope's aberrations, can be performed with a variety of algorithms depending on the approximations involved for the HREM image formation. The maximum-a-posteriori (MAP) recursive reconstruction algorithm of Kirkland is the most general one with the full benefit of the effects of non-linear imaging and partial coherence, which are correctly treated in terms of a transmission-cross-coefficient (TCC). However, the routine application of the Kirkland algorithm has thusfar been hampered by its enormous computational demands, especially when large image frame sizes (5122) and a large number of HREM images (≥20) are aimed at. In this paper, we present a modified version of the Kirkland method within a maximum-likelihood (MAL) framework, and with a new numerical implementation yielding a workable algorithm with a much higher computational efficiency.

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