  Transmission electron microscopes use electrons with wavelengths of a few
picometers, potentially capable of imaging individual atoms in solids at a
resolution ultimately set by the intrinsic size of an atom. Unfortunately, due
to imperfections in the imaging lenses and multiple scattering of electrons in
the sample, the image resolution reached is 3 to 10 times worse. Here, by
inversely solving the multiple scattering problem and overcoming the
aberrations of the electron probe using electron ptychography to recover a
linear phase response in thick samples, we demonstrate an instrumental blurring
of under 20 picometers. The widths of atomic columns in the measured
electrostatic potential are now no longer limited by the imaging system, but
instead by the thermal fluctuations of the atoms. We also demonstrate that
electron ptychography can potentially reach a sub-nanometer depth resolution
and locate embedded atomic dopants in all three dimensions with only a single
projection measurement.
