Efficient misalignment correction method for dark-field aperture in reflective Fourier ptychographic microscopy

Reflective Fourier ptychographic microscopy (FPM) enables high-resolution, wide-field imaging of opaque surfaces, but its calibration remains challenging due to the unique illumination geometry. Unlike transmissive FPM, which typically employs a regular planar LED array, reflective systems use spatially separated bright-field and dark-field illuminations, with dark-field LEDs arranged around the outer periphery of the objective lens. This non-coplanar, discontinuous configuration invalidates conventional LED calibration methods that generally rely on array continuity or bright-field sub-aperture priors. Here, we propose a non-iterative dark-field misalignment correction method tailored for reflective FPM, referred to as dmc-rFPM. This method formulates a residual cost function based on the structural similarity index between the predicted and measured dark-field intensity images. Each dark-field sub-aperture is independently aligned via heuristic search, and global geometric consistency is enforced using a RANSAC-based circular fitting strategy. This approach eliminates the need for object reconstruction or bright-field-based initialization, supports efficient parallel implementation, and significantly reduces correction time. Simulations and experiments on resolution targets and semiconductor chips demonstrate that dmc-rFPM effectively and precisely corrects 72 dark-field images (each with 400 000 pixels) within 0.5 s using GPU acceleration, achieving a lateral resolution of 583 nm with a 4× objective. dmc-rFPM enables diffraction-limited imaging performance and provides a practical solution for high-throughput calibration in reflective FPM systems for industrial inspection and precision metrology applications.