Fig. 5: Surpassing the diffraction limit with SAPE.

a The black curve plots the diffraction-limited NA of conventional imaging systems, constrained by the maximum collection angle of the imaging probe. SAPE overcomes this limitation through the handheld motion of the fiber bundle tip, analogous to the aircraft movement in SAR. The translation motion not only facilitates the acquisition of a ptychogram but also synthesizes an imaging aperture exceeding the bundle’s physical size. b The recovered diffracted wavefield \(W(x,y)\) at the plane of the distal fiber bundle tip, located ~5.5 mm from the specimen. The dashed white circle represents the fiber bundle’s physical aperture, while the wavefield synthesis at this plane facilitates aperture synthesis that exceeds the diffraction limit. c The Fourier spectrum of the wavefield \(W(x,y)\) from (b), contrasting the SAPE’s expanded bandwidth against the inherent diffraction-limited bandwidth. d SAPE reconstruction by propagating the recovered wavefield \(W(x,y)\) for 5.5 mm, successfully resolving the 1.95-µm linewidth. The width of the entire group 8, element 1 is 10 μm. e A SAPE reconstruction with a minimum 1.5-μm scanning step size, approximating the diffraction-limited performance for comparison