Stable and robust frequency domain position compensation strategy for Fourier ptychographic microscopy

Fourier ptychographic microscopy is a computational microscopy technique to achieve wide-field and super-resolution complex imaging which has been developed in recent years. The method is based on illuminating the sample by a light source array, and then computationally integrating different images correspondent to each of the sources, in the Fourier domain. Knowledge of the exact relative position of the light sources and the sample is critical for the quality of the final recovered image. In this paper, we present an iterative approach towards correcting the position in the Fourier domain based on Newton's method. Also, an analysis is presented which shows the relation between the position error and the deterioration of the final recovery quality. The effectiveness of the presented method in improving the quality of the final recovered image is demonstrated using simulation and experimental results. Moreover, the method is shown to be more stable and robust to noises in comparison with the state-of-the-art algorithm.