Long‐Range Horizontal‐Path Fourier Ptychography: A 1.4‐km Experimental Demonstration

ABSTRACT Fourier ptychography (FP), a synthetic‐aperture methodology independent of phase coherence, has emerged as a compelling approach for extending imaging capabilities beyond the conventional diffraction limit. However, existing FP demonstrations remain confined to laboratory settings, with working distances typically restricted to only a few meters. Moreover, resolution enhancement does not scale indefinitely with the enlargement of the synthetic aperture, and the quantitative relationship between actual resolution gain and aperture size remains insufficiently understood. Here, we demonstrate a horizontal‐path macroscopic FP achieving an imaging distance exceeding 1.4 km. By scanning a 100 mm single‐aperture system along a meter‐scale translation stage, a resolution enhancement of over 2.3× compared to the diffraction limit of an equivalent single‐aperture system is achieved. A rigorous analysis of undersampling effects in kilometer‐scale FP is presented, yielding the criterion for the single‐aperture f‐number required to avoid undersampling in reconstructed images, together with a comprehensive undersampling‐ratio formulation whose validity is experimentally confirmed and benchmarked against prior studies. The derivation of operational conditions for horizontal‐path FP provides constructive guidance in synthetic‐aperture optics, clarifying the relationship between synthetic aperture size and the actual resolution gain in kilometer‐scale super‐resolution imaging.