Sharpness-statistic based autofocus algorithm for Fourier ptychographic microscopy

Fourier ptychographic microscopy is a computational imaging technique that achieves high-resolution imaging by combining phase retrieval algorithms with synthetic aperture methods. However, defocus errors due to the misalignment of the sample can significantly degrade the reconstruction quality, leading to increased background noise and blurred details. In this manuscript, we propose a novel sharpness-statistic based autofocus algorithm to address defocus errors in Fourier ptychographic microscopy. Unlike conventional methods that infer defocus errors indirectly, our method directly applies a sharpness detection strategy to the reconstruction results, enabling more accurate correction of defocus-induced blurring. We validate the effectiveness and robustness of the sharpness-statistic based autofocus algorithm through both simulations and optical experiments, demonstrating its superiority over existing methods such as the embedded optical pupil function recovery aberration correction algorithm and lateral shift correction method. Multiple sets of quantitative experiments show that the defocus distances estimated by the proposed method under different defocusing scenarios are at least 40% more accurate than the ones estimated by the commonly used method. Consequently, the contrast of the reconstructed images is more than twice that of the commonly used method. The image quality of biological specimen is also improved with sharper details. The results indicate that the sharpness-statistic autofocus algorithm can effectively correct defocus error and enhance the image quality.