Wavelet‐Forward Family Enabling Stitching‐Free Full‐Field Fourier Ptychographic Microscopy

Abstract Fourier ptychographic microscopy (FPM) breaks through the resolution limitations of conventional optical systems, which offer a full‐field view and high resolution without additional mechanical scanning. However, conventional image‐domain optimizations require trade‐offs between correction efficacy, data redundancy, and reconstruction accuracy. Furthermore, the existing linear time‐invariant model for actual nonlinear, time‐varying optical systems leads to forward model mismatch, complicating the corrections of the vignetting effect. To overcome these challenges and achieve stitching‐free FPM, a family of forward wavelet‐transform models (WL‐FPM) is proposed. WL‐FPM employs the reversibility of the wavelet transform for high‐fidelity reconstruction in the multiscale feature domain. The wavelet loss function is updated in each iteration, and non‐convex optimization is solved by complex back diffraction. WL‐FPM offers stitching‐free, high‐resolution, and robust reconstruction under various challenging conditions, including vignetting effects, LED position mismatch, intensity fluctuations, and high‐level noise environments, which outperform conventional FPM methods. Under a 4X objective with NA 0.1, WL‐FPM achieves a 435‐nm resolution and stitching‐free full‐field reconstruction of a 3.328 × 3.328 mm 2 pathological section with distinct subcellular organelles. In live cell imaging, it provides a full‐field observation with distinct lipids in a single cell. A large number of simulation and experimental results demonstrate its potential for biomedical applications.