  Acousto-optic imaging (AOI) enables optical-contrast imaging deep inside
scattering samples via localized ultrasound-modulation of scattered light.
While AOI allows optical investigations at depths, its imaging resolution is
inherently limited by the ultrasound wavelength, prohibiting microscopic
investigations. Here, we propose a novel computational imaging approach that
allows to achieve optical diffraction-limited imaging using a conventional AOI
system. We achieve this by extracting diffraction-limited imaging information
from 'memory-effect' speckle-correlations in the conventionally detected
ultrasound-modulated scattered-light fields. Specifically, we identify that
since speckle correlations allow to estimate the Fourier-magnitude of the field
inside the ultrasound focus, scanning the ultrasound focus enables robust
diffraction-limited reconstruction of extended objects using ptychography, i.e.
we exploit the ultrasound focus as the scanned spatial-gate 'probe' required
for ptychographic phase-retrieval. Moreover, we exploit the short speckle
decorrelation-time in dynamic media, which is usually considered a hurdle for
wavefront-shaping based approaches, for improved ptychographic reconstruction.
We experimentally demonstrate non-invasive imaging of targets that extend well
beyond the memory-effect range, with a 40-times resolution improvement over
conventional AOI, surpassing the performance of state-of-the-art approaches.
