Precise and independent position correction strategy for Fourier ptychographic microscopy

Based on a commercial microscope, Fourier ptychographic microscopy (FPM) can achieve high-resolution imaging with wide field-of-view (FOV) by simply replacing traditional light source with a LED array. Since the spatial position of each LED directly determines the location of corresponding collected low-resolution image in the Fourier frequency domain, the positional error of LEDs, which is however inevitable in practical systems, would hurt reconstruction quality. To mitigate this, based on in-depth analysis of the relationship between LED's positional error and reconstruction degradation across spatial and frequency domains, we propose a novel strategy for correcting random positional errors of LED directly in frequency domain by tackling two key challenges faced by existing position correction methods: (1) to reduce inaccuracy caused by global position error model, we utilize a per-LED frequency-domain position error model with a correlation loss function to lift correction precision; (2) to accelerate correction process, we introduce a high-magnification image, in place of the conventional intensity image that need to be iteratively updated, as a complete new reference for positional correction, enabling correction to be free from time-consuming iterative reference update process. Extensive quantitative and qualitative evaluation on both simulation and real data well demonstrate that our algorithm can greatly improve reconstruction quality with high efficiency.