Resolution extension and exit wave reconstruction in complex HREM

Direct methods in real and reciprocal space are developed for structural reversion. The direct method in real space involves the use of a novel method to retrieve the phase in the image plane using transport of intensity equation/maximum entropy method (TIE/MEM) and exit wave reconstruction by self-consistent propagation. Since the exit wave is restored from the complex signal in the image planes, no image model between the exit wave and image is assumed. The structural information in the reconstructed exit wave is then further extended by a "complex" maximum entropy method as a direct method in reciprocal space to extrapolate the phase to higher frequencies.