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 application is challenging due to the need for a precise numerical forward model that accurately matches real-world imaging systems. This mismatch sensitivity makes FP vulnerable to physical uncertainties, such as misalignment, optical element aberrations, low quality data, and etc. Conventional methods typically involve extensive manual calibration or digital correction of misalignment; reconstructing the pupil or probe to mitigate aberrations through alternative optimization strategies; or improving data quality by adjusting exposure time or using high dynamic range (HDR) techniques. However, none of these methods can simultaneously address all these issues. All of the uncertain factors interacts within the imaging systems, and neglecting any of them can degrade imaging performance or limit the system’s capabilities and applicability. In this work, we introduce an Uncertainty-Aware FP (UA-FP ) that addresses the issues of optical element aberrations, misalignment, and low-quality data simultaneously without relying on complex calibration. We achieve this by developing a differentiable forward imaging model of FP, and utilizing automatic differentiation to solve the inverse problem. Key system parameters, such as optical element aberrations and system misalignment, are treated as variables of differentiable functions. Additionally, we design the objective function with domain-specific priors to handle noisy data. This approach enables high imaging performance with low quality data under loose system alignment, while also allowing some system characteristics to be recovered. This not only facilitates system reconfigurability but also extends the system’s capability to function as a measurement tool and to operate under extreme conditions.