Non-iterative Far-field Synthetic Aperture Imaging via Space-domain Kramers-Kronig Relations

Non-interferometric synthetic aperture imaging (SAI) shows significant potential in Earth observation, astronomy, and remote sensing. However, these methods often involve time-consuming processes for wave field acquisition and iterative image reconstruction. In this Letter, we present a non-iterative far-field synthetic aperture imaging method, macroscopic space-domain Kramers-Kronig relations synthetic aperture imaging (MSKR-SAI). Unlike traditional macroscopic Fourier ptychography (FP), MSKR-SAI bypasses redundant iterations and requirements for highly overlapping images, reducing reconstruction time from 4.97 s to 0.17 s-a 26-fold speedup. By utilizing only six sub-aperture intensity images, MSKR-SAI reconstructs complex amplitude information and synthesizes the aperture in a fully determinist manner. Simulations and experimental results show a twofold resolution improvement with accurate detail recovery and minimal artifacts. Furthermore, MSKR-SAI maintains robustness even when the Kramers-Kronig relations are not strictly met. The combination of non-iterative reconstruction, noise resilience, and computational efficiency positions MSKR-SAI as a promising method for high-resolution, artifact-free far-field imaging.