  Synthetic aperture radar (SAR) utilizes an aircraft-carried antenna to emit
electromagnetic pulses and detect the returning echoes. As the aircraft travels
across a designated area, it synthesizes a large virtual aperture to improve
image resolution. Inspired by SAR, we introduce synthetic aperture
ptycho-endoscopy (SAPE) for micro-endoscopic imaging beyond the diffraction
limit. SAPE operates by hand-holding a lensless fiber bundle tip to record
coherent diffraction patterns from specimens. The fiber cores at the distal tip
modulate the diffracted wavefield within a confined area, emulating the role of
the 'airborne antenna' in SAR. The handheld operation introduces positional
shifts to the tip, analogous to the aircraft's movement. These shifts
facilitate the acquisition of a ptychogram and synthesize a large virtual
aperture extending beyond the bundle's physical limit. We mitigate the
influences of hand motion and fiber bending through a low-rank spatiotemporal
decomposition of the bundle's modulation profile. Our tests demonstrate the
ability to resolve a 548-nm linewidth on a resolution target. The achieved
space-bandwidth product is ~1.1 million effective pixels, representing a
36-fold increase compared to that of the original fiber bundle. Furthermore,
SAPE's refocusing capability enables imaging over an extended depth of field
exceeding 2 cm. The aperture synthesizing process in SAPE surpasses the
diffraction limit set by the probe's maximum collection angle, opening new
opportunities for both fiber-based and distal-chip endoscopy in applications
such as medical diagnostics and industrial inspection.
