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

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 x 3.328 mm2 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.WL-FPM provides a universal framework of reconstruction for Fourier ptychographic microscopy based on the wavelet transform. This model works in the multi-scale feature domain and learns the gradient information through multi-scale translation, which suppresses the effect of practical issues such as LED position mismatch, LED intensity fluctuation, various noises, and vignetting effects. The high flexibility of WL-FPM significantly enhances reconstruction robustness and high-resolution imaging of various biomedical samples. image