Self-calibrating Fourier ptychographic microscopy using automatic differentiation

Fourier ptychographic microscopy (FPM) can provide high-throughput imaging by computationally combining low-resolution images at different spatial frequencies within the Fourier domain. The core algorithm for FPM reconstruction draws upon phase retrieval techniques, including methods such as the ptychographic iterative engine (PIE), regularized PIE (rPIE), and embedded pupil function FPM (EPRY-FPM). The calibration of the physical setup plays a crucial role in the quality of the reconstructed high space-bandwidth product (SPB) image. Despite advances, many methods, incorporating either machine learning or calibration algorithm, face challenges. These include the need for extensive parameter tuning and extra optical system information, hindering their practical use. To address these limitations, we introduce a novel, to the best of our knowledge, self-calibrating FPM reconstruction approach that utilizes automatic differentiation. This method diverges from traditional iterative phase and amplitude updates, opting instead to simultaneously recover a complex 2D image and refine the optical system's physical parameters. Our approach matches the effectiveness of existing recovery techniques while significantly reducing the calibration burden. In this report, we will demonstrate our method is capable of self-calibrating without needing extra system information. We validate our algorithm's performance through numerical simulations and then show its practicality by reconstructing a full field of view of cervical cell slides using ultraviolet Fourier ptychographic microscopy (UV-FPM).