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Fourier ptychography (FP) has emerged as a powerful tool to improve spatial resolution. In order to apply FP technique to long-distance imaging for example remote sensing, many factors have to be overcome, such as diffraction, noise, turbulence and so on. In this paper, we mainly aims at studying the influence of atmospheric turbulence on FP technique, and using iterative algorithms to restore high-legible image and eliminating the residual errors, so it will meet or reach the diffraction limit of imaging system. The optical imaging systems which work in atmospheric circumstance will face the problem of imaging through atmospheric turbulence, which causing the blurring of image and badly impact the imaging capability of optical systems. We combine the FP with the theory of adaptive optics to achieve the effective recovery of the long-range target, which is subject to the effect of atmospheric turbulence. In this work, we firstly introduce a Fourier Series (FS) atmospheric phase screen generator to simulate the atmospheric-induced wave front phase distortions and represent the wave front phase as a two dimensional periodic function. Both the spatial and temporal correlations between wave-front phase screens separated by time and/or angle are properly modeled. And using the adaptive optics， we complete the correction of the atmospheric turbulence in large distance imaging through the developed algorithm. Then we propose using laser arrays coupled with coherent illumination as an effective method of improving spatial resolution in long distance images. We emulate a laser arrays realized by optical fiber conduction and also show that appropriate phase retrieval based reconstruction algorithm which can be used to effectively recover the lost high resolution details from the multiple low resolution acquired images. Finally we analyze the effects of the atmospheric turbulence on the reconstructed image quality. The results prove that under the influence of atmospheric turbulence at outer scale of 1-m, inner scale of 0.1-m, Fourier ptychographic reconstruction can obtain good image quality for object 200 meters far away. The spatial resolution is increased six-fold.
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