The wrap-around problem and optimal padding in the exit wave reconstruction using HRTEM images

A free fast Fourier transform software FFTW (www.fftw.org) is used in the exit wave reconstruction and shown to be able to handle images of any size effectively. The wrap-around problem commonly encountered in the exit wave reconstruction is investigated, and a new padding scheme is proposed and its performance is investigated. It is shown that while the usual wrap-around problem may be solved via padding the input high-resolution transmission electron microscopy (HRTEM) images with zero or averaged image intensities, the reconstructed exit wave at its boundary is inevitably distorted by the discontinuity of image intensities at the boundary. The proposed new padding scheme is shown to be able to provide a good estimate of the image intensities immediately outside the boundaries of the HRTEM images, reducing the estimated image intensity discontinuity across the boundaries and therefore providing a larger undistorted view of the exit wave.