Phase-contrast imaging of multiply-scattering extended objects at atomic resolution by reconstruction of the scattering matrix
Philipp Pelz, Hamish G. Brown, Scott Stonemeyer, Scott D. Findlay, Alex Zettl, Peter Ercius, Yaqian Zhang, Jim Ciston, Mary Scott, Colin Ophus
Abstract
Three-dimensional phase-contrast imaging of multiply-scattering samples in x-ray and electron microscopy is challenging due to small numerical apertures, the unavailability of wave front shaping optics, and the highly nonlinear inversion required from intensity-only measurements. In this work, we present an algorithm using the scattering matrix formalism to solve the scattering from a noncrystalline medium from scanning diffraction measurements and simultaneously recover the illumination aberrations. We demonstrate our method experimentally in a scanning transmission electron microscope, recovering the scattering matrix of a heterogeneous sample with two layers of multiwall carbon nanotubes filled with TaTe 2 core-shell structures, spaced 10 nm apart in the axial direction. Our work enables phase contrast imaging and materials characterization in multiply-scattering samples at high resolution for a wide range of materials.