Experimental evaluation of spatial resolution in phase maps retrieved by transport of intensity equation

The transport of intensity equation (TIE) is a convenient method of obtaining a potential distribution, as it requires only three transmission electron microscopy images with different amounts of defocus. However, the spatial resolution of the TIE phase map has not yet been evaluated experimentally. In this study, we investigated the phase distribution of spherical gold nanoparticles and its dependence on the defocus difference and found that the spatial resolution was finer than 2 nm, even for a defocus difference of 4 µm. Theoretical calculations reproduced the experimental results well.