Transformed pupil-function misalignment calibration strategy for Fourier ptychographic microscopy

Fourier ptychographic microscopy (FPM) is an enabling quantitative phase imaging technique with both high-resolution (HR) and wide field-of-view (FOV), which can surpass the diffraction limit of the objective lens by employing an LED array to provide angular-varying illumination. The precise illumination angles are critical to ensure exact reconstruction, while it s difficult to separate actual positional parameters in conventional algorithmic self-calibration approaches due to the mixing of multiple systematic error sources. In this paper, we report a pupil-function-based strategy for independently calibrating the position of LED array. We first deduce the relationship between positional deviation and pupil function in the Fourier domain through a common iterative route. Then, we propose a judgment criterion to determine the misalignment situations, which is based on the arrangement of LED array in the spatial domain. By combining the mapping of complex domains, we can accurately solve the spatial positional parameters concerning the LED array through a boundary-finding scheme. Relevant simulations and experiments demonstrate the proposed method is accessible to precisely correct the positional misalignment of LED array. The approach based on the pupil function is expected to provide valuable insights for precise position correction in the field of microscopy.