  Exploiting the emerging nanoscale periodicities in epitaxial, single-crystal
thin films is an exciting direction in quantum materials science: confinement
and periodic distortions induce novel properties. The structural motifs of
interest are ferroelastic, ferroelectric, multiferroic, and, more recently,
topologically protected magnetization and polarization textures. A critical
step towards heterostructure engineering is understanding their nanoscale
structure, best achieved through real-space imaging. X-ray Bragg coherent
diffractive imaging visualizes sub-picometer crystalline displacements with
tens of nanometers spatial resolution. Yet, it is limited to objects spatially
confined in all three dimensions and requires highly coherent, laser-like
x-rays. Here we lift the confinement restriction by developing real-space
imaging of periodic lattice distortions: we combine an iterative phase
retrieval algorithm with unsupervised machine learning to invert the diffuse
scattering in conventional x-ray reciprocal-space mapping into real-space
images of polar and elastic textures in thin epitaxial films. We first
demonstrate our imaging in PbTiO3/SrTiO3 superlattices to be consistent with
published phase-field model calculations. We then visualize strain-induced
ferroelastic domains emerging during the metal-insulator transition in Ca2RuO4
thin films. Instead of homogeneously transforming into a low-temperature
structure (like in bulk), the strained Mott insulator splits into nanodomains
with alternating lattice constants, as confirmed by cryogenic scanning
transmission electron microscopy. Our study reveals the type, size,
orientation, and crystal displacement field of the nano-textures. The
non-destructive imaging of textures promises to improve models for their
dynamics and enable advances in quantum materials and microelectronics.
