Uncertainty-aware Fourier ptychography.

Fourier ptychography (FP) offers both wide field-of-view and high-resolution holographic imaging, making it valuable for applications ranging from microscopy and X-ray imaging to remote sensing. However, its practical implementation remains challenging due to the requirement for precise numerical forward models that accurately represent real-world imaging systems. This sensitivity to model-reality mismatches makes FP vulnerable to physical uncertainties, including misalignment, optical element aberrations, and data quality limitations. Conventional approaches address these challenges through separate methods: manual calibration or digital correction for misalignment; pupil or probe reconstruction to mitigate aberrations; or data quality enhancement through exposure adjustments or high dynamic range (HDR) techniques. Critically, these methods cannot simultaneously address the interconnected uncertainties that collectively degrade imaging performance. We introduce Uncertainty-Aware FP (UA-FP), a comprehensive framework that simultaneously addresses multiple system uncertainties without requiring complex calibration and data collection procedures. Our approach develops a fully differentiable forward imaging model that incorporates deterministic uncertainties (misalignment and optical aberrations) as optimizable parameters, while leveraging differentiable optimization with domain-specific priors to address stochastic uncertainties (noise and data quality limitations). Experimental results demonstrate that UA-FP achieves superior reconstruction quality under challenging conditions. The method maintains robust performance with reduced sub-spectrum overlap requirements and retains high-quality reconstructions even with low bit sensor data. Beyond improving image reconstruction, our approach enhances system reconfigurability and extends FP's capabilities as a measurement tool suitable for operation in environments where precise alignment and calibration are impractical.