Enhancing phase reconstruction fidelity via reflective Fourier ptychographic microscopy

Fourier ptychography microscopy (FPM) is a computational imaging technique that combines a wide field of view with high resolution. Although its primary use has been in transmission mode, the reflective mode of FPM has emerged as a powerful tool for surface inspection in various industrial applications. Despite its potential, the practical implementation of reflective FPM is constrained by challenges related to achieving accurate phase retrieval, which is critical for precise surface characterization. Existing approaches have attempted to mitigate this by employing various strategies including modification of reconstruction algorithms or hardware configurations, but they often involve iterative procedures that can suffer from convergence issues. To address this challenge, we employed an existing analytic reconstruction method, named Angular Ptychographic Imaging with Closed-form method (APIC), which eliminates the need for iterative procedures, thereby avoiding convergence-related problems. The APIC algorithm begins by reconstructing the complex field for the low spatial frequency using the Kramers-Kronig relations, applied to intensity measurements obtained through NA-matching illumination. From this reconstructed field, we then extract the aberrations of the imaging system. High spatial frequency components are subsequently recovered using darkfield measurements, allowing us to achieve high-resolution topographic imaging. We validated this approach through both simulations and experimental demonstrations on various patterned reflective samples, conducting a comparative analysis against results obtained using conventional FPM reconstruction methods. While our method shows potential, the results highlight certain limitations that require further refinement for practical applications.