Phase-contrast imaging of multiply-scattering extended objects at atomic resolution by reconstruction of the scattering matrix

Philipp M. Pelz, Hamish G. Brown, Scott Stonemeyer, Scott D. Findlay, Alex Zettl, Peter Ercius, Yaqian Zhang, Jim Ciston, M. C. Scott, Colin Ophus

Research output: Contribution to journalArticleResearchpeer-review

12 Citations (Scopus)


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 TaTe2 core-shell structures, spaced 10nm 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.

Original languageEnglish
Article number023159
Number of pages14
JournalPhysical Review Research
Issue number2
Publication statusPublished - Jun 2021

Cite this