PI-FPM: pupil initialization for Fourier ptychographic microscopy directly from measurement data

Fourier ptychographic microscopy (FPM) is a powerful computational imaging technique that enables the reconstruction of high-resolution, wide field-of-view complex images by fusing multiple low-resolution intensity measurements obtained under varying illumination angles. In practice, FPM remains sensitive to calibration and, in particular, to the initialization of the pupil function in the non-convex joint recovery of object and pupil. We introduce pupil-initialized FPM (PI-FPM), a physically informed pupil-phase initialization computed directly from standard FPM measurements prior to reconstruction. PI-FPM exploits the relationship between lateral shifts in brightfield images and local pupil-phase gradients, and estimates low-order aberrations via a Zernike least-squares fit. The method is hardware-agnostic, algorithm-independent, and requires no additional calibration or specialized acquisition, enabling retroactive use on existing datasets. Across synthetic and real experiments, PI-FPM improves convergence stability and reconstruction fidelity, with gains up to 8 dB PSNR and robust performance under strong aberrations (up to 2π radians root mean square (RMS) wavefront error), particularly in outer field regions. As a result, PI-FPM reduces the reliance on expert calibration and significantly enhances the practical applicability of FPM for routine use in real-world imaging scenarios, including large-field whole-slide imaging where outer-field robustness is critical.