  We have introduced an improved X-ray phase-retrieval method with
unprecedented speed of convergence and precision, and used it to determine with
sub-{\AA}ngstrom resolution the complete atomic structure of an ultrathin
superconducting bilayer film, composed of La$_{1.55}$Sr$_{0.45}$CuO$_{4}$ and
La$_{2}$CuO$_{4}$ neither of which is superconducting by itself. The results
show that phase-retrieval diffraction techniques enable accurate measurement of
structural modifications in near-surface layers, which may be critically
important for elucidation of surface-sensitive experiments. Specifically we
find that close to the sample surface the unit cell size remains constant while
the copper-apical oxygen distance shows a dramatic increase, by as much as 0.45
{\AA}. The apical oxygen displacement is known to have a profound effect on the
superconducting transition temperature.
