Phys-trans FPM: a real-time nanometer solution for industrial circuit inspection using reflective Fourier ptychographic microscopy

• First successful fusion of physical-based and transformer-based deep learning for ultraviolet reflective Fourier ptychographic microscopy. • Significantly reduced time required for reconstructing a high- resolution image either a specific segment or a full field-of-view. • No need for the pre-calibration process of bright-field and dark-field for the system. • Performance verified through simulation and experiments using USAF 1951 target and IC circuit. In this study, we present a novel integration of physics-based models with transformer-based deep learning (Phys-trans FPM) to enhance reflective Fourier ptychographic microscopy (rFPM). This approach addresses key limitations of traditional rFPM methods by integrating physical priors with the advanced feature extraction capabilities and global optimization potential of transformer architectures. As a result, our proposed method significantly reduced reconstruction time for a high-resolution image of either a single segment or an entire full field-of-view (FOV) while preserving accuracy. This improvement is particularly beneficial for practical applications requiring fast and reliable high-resolution imaging, including semiconductor inspections and analyses of reflected samples. A notable advantage of the proposed method is the elimination of pre-calibration requirements for bright-field and dark-field settings, streamlining the imaging workflow by removing cumbersome misalignment correction steps. The effectiveness and robustness of the Phys-trans FPM method were validated through extensive simulations, USAF 1951 target measurements, and integrated circuit inspections. The results consistently demonstrated superior image quality, resolving fine structures with minimal background noise. These findings confirm that the fusion of physical modeling and transformer-based deep learning not only enhances the performance of rFPM but also offers promising potential for broader applications in optical metrology and imaging systems.