An improved image alignment procedure for high-resolution transmission electron microscopy.

Image alignment is essential for image processing methods such as through-focus exit-wavefunction reconstruction and image averaging in high-resolution transmission electron microscopy. Relative image displacements exist in any experimentally recorded image series due to the specimen drifts and image shifts, hence image alignment for correcting the image displacements has to be done prior to any further image processing. The image displacement between two successive images is determined by the correlation function of the two relatively shifted images. Here it is shown that more accurate image alignment can be achieved by using an appropriate aperture to filter the high-frequency components of the images being aligned, especially for a crystalline specimen with little non-periodic information. For the image series of crystalline specimens with little amorphous, the radius of the filter aperture should be as small as possible, so long as it covers the innermost lattice reflections. Testing with an experimental through-focus series of Si[110] images, the accuracies of image alignment with different correlation functions are compared with respect to the error functions in through-focus exit-wavefunction reconstruction based on the maximum-likelihood method. Testing with image averaging over noisy experimental images from graphene and carbon-nanotube samples, clear and sharp crystal lattice fringes are recovered after applying optimal image alignment.