Fig. 1: Principle of SAPE.
From: Ptycho-endoscopy on a lensless ultrathin fiber bundle tip
a In SAR, an airborne antenna emits a series of electromagnetic pulses to illuminate a target scene, and the returning echoes are processed to synthesize a large virtual aperture that exceeds the physical size of the antenna. b SAPE uses a handheld fiber bundle tip as a ‘moving antenna’ to illuminate the object and record the resulting diffraction patterns. The natural hand motion induces shifts at the fiber bundle tip, mirroring the aircraft’s movement in SAR. These shifts enable ptychographic data collection and the creation of an expanded synthetic imaging aperture extending beyond the bundle’s physical limit. c Imaging model of SAPE. Panel 1: The object is illuminated with an extended beam in either a transmission or reflection setting. Panel 2: The object’s diffracted wavefield reaches the plane of the distal fiber bundle tip. Alternatively, when implementing SAPE for distal-chip endoscopy, a thin coded layer can replace the small lens of the miniaturized camera at the distal end, serving the same purpose of modulating the diffracted wavefield. Panel 3: The fiber bundle tip or coded surface modulates the diffracted wavefield over a confined region, acting as an equivalent spatially-confined probe beam in ptychography. Panel 4: The modulated wavefield, upon exiting the proximal end of the bundle, travels a distance h before its intensity is recorded by an image sensor. For distal-chip endoscopy, this distance corresponds to the space between the coded surface and the pixel array of the image sensor. d SAPE compensates for hand motions and fiber bending by decomposing the modulation profile into low-rank spatiotemporal modes \({P}_{{st}}(x,y)\)
