An Efficient Electron Ptychography Method for Retrieving the Object Spectrum from Only a Few Iterations.

We present an efficient approach for electron ptychography based on a mathematical relationship that differs from that underlying the established algorithms of the ptychography iterative engine or the noniterative algorithms like the Wigner-distribution-deconvolution or the single-side-band method. Three variables are handled in this method-the transfer function of the objective lens, the object spectrum, and the diffraction wave whose phase is unknown. In the case of an aberration-corrected electron microscope, one is able to obtain a well-estimated transfer function of the lens. After reducing the number of three variables down to two, we construct an iterative loop between the object spectrum and the diffraction wave, which retrieves the object spectrum within a small number of iterations. We tested this object spectrum retrieval method on both a calculated and an experimental 4D-STEM datasets. By applying this method, we explore the influence of sampling, dose, and the size of illumination aperture on the reconstructed phase images.