Long-range fourier ptychographic imaging of the object in multidimensional motion

Fourier Ptychographic (FP) is a cutting-edge technique for achieving high resolution in long-range imaging, holding significant research value. However, most of the research on FP has been limited to high-resolution imaging of stationary objects, considerably narrowing the scope of its applications. In real-world scenarios, the object may move in three dimensions and rotate during the image acquisition process. To address such scenarios, this paper proposes a method for achieving FP of the object in multidimensional motion using a single camera. Starting from the principles of Fourier optics and diffraction, the paper calculates the effects of an object's movement in different dimensions on the light field. The Fourier-Mellin algorithm is to be applied to deduce changes in the light field from captured intensity images and align all collected data under a chosen reference light field. During image reconstruction, we propose an additional phase retrieval algorithm that integrates total variation regularization to address aperture offset issues. The paper validates the proposed method's effectiveness through simulations and experiments. FP is successfully applied to objects in multidimensional motion. The method also doubles the imaging system's resolution.