AUTHOR=Wu Yumin , Lu Linpeng , Zhang Jialin , Li Zhuoshi , Zuo Chao TITLE=Autofocusing Algorithm for Pixel-Super-Resolved Lensfree On-Chip Microscopy JOURNAL=Frontiers in Physics VOLUME=Volume 9 - 2021 YEAR=2021 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2021.651316 DOI=10.3389/fphy.2021.651316 ISSN=2296-424X ABSTRACT=In recent years, lensfree on-chip imaging has developed a new wide-field optical imaging technique that is widely used for quantitative microscopic imaging, especially in medical and engineering applications. However, lens-free on-chip imaging generally suffers from low imaging resolution which is far from enough to meet the recent demand due to the limited sensor pixel size. Fortunately, image super-resolution algorithms can solve this problem by processing a series of low-resolution holograms. The prerequisite is to obtain accurately the reconstructed distance of each hologram. However, there are two major challenges to accurately determine the focus distance: on the one hand, twin-image can produce image blurring, which reduces image resolution; on the other hand, the displacement between the sample and the sensor is usually done mechanically, which may cause mechanical errors. In this study, we proposed a high-precision pixel-super-resolved autofocusing method based on the multi-height lensfree on-chip imaging, which consists of two steps: individual preliminary estimation and global precise estimation. First, an improved critical function that combines differential critical function and frequency domain critical function has been proposed to obtain the preliminary focus distances of different height planes. Second, we transform a problem of focusing on different planes into the problem of solving the optimal solution of the overall imaging. Through the proposed method, we can determine the focus distances of different planes more accurately. Simulations and experiments have verified the validity and reliability of the proposed algorithm. The proposed algorithm has the potential to further improve the imaging resolution of lensfree on-chip imaging.