TurbFPNet: neural far-field turbulent Fourier ptychography with a camera array

Although phase retrieval techniques empower macroscopic Fourier ptychography (FP) to boost spatial resolution, such iterative methods need indispensable data redundancy and tend to be time-consuming for image acquisition and reconstruction and are prone to ill-posedness because of the entanglement of pixel displacement, blur, and noise when increasing the imaging distance. This work proposes a turbulent Fourier ptychographic network (TurbFPNet), a physics-based neural framework designed to address these challenges. In contrast to recently proposed methods, we investigate implicit neural representations with optics processing steps, termed Fourier ptychographic phase-to-space (FP-P2S) transform for data synthesis based on a real coherent imaging system, where real sub-aperture images are captured by an assembled camera array, mitigating the scarcity of training and testing coherent data with turbulence. In addition, we present a pyramid residual transformer to extract both coarse-grained and fine-grained features by taking advantage of convolutional neural networks and transformers. We further introduce the FP reconstruction loss to obtain a desired underlying mapping by making the best of our FP-P2S to produce extra sub-aperture images. Experimental results indicate that our TurbFPNet surpasses the recent baselines in performance. This study tackles the challenges, including turbulence, negative overlap ratio, and speckle, together for single-shot far-field FP imaging, making macroscopic FP more applicable for far-field scenarios.