  Conventional fiber-bundle-based endoscopes allow minimally invasive imaging
through flexible multi-core fiber (MCF) bundles by placing a miniature lens at
the distal tip and using each core as an imaging pixel. In recent years,
lensless imaging through MCFs was made possible by correcting the core-to-core
phase distortions pre-measured in a calibration procedure. However, temporally
varying wavefront distortions, for instance, due to dynamic fiber bending, pose
a challenge for such approaches. Here, we demonstrate a coherent lensless
imaging technique based on intensity-only measurements insensitive to
core-to-core phase distortions. We leverage a ptychographic reconstruction
algorithm to retrieve the phase and amplitude profiles of reflective objects
placed at a distance from the fiber tip, using as input a set of diffracted
intensity patterns reflected from the object when the illumination is scanned
over the MCF cores. Our approach thus utilizes an acquisition process
equivalent to confocal microendoscopy, only replacing the single detector with
a camera.
