In adaptive optics (AO), multiple different incident wavefronts correspond to a same far-field intensity distribution, which leads to a many-to-one mapping. To solve this problem, a single far-field deep learning adaptive optics system based on four-quadrant discrete phase modulation (FQDPM) is proposed. Our method performs FQDPM on an incident wavefront to overcome this many-to-one mapping, then convolutional neural network (CNN) is used to directly predict the wavefront. Numerical simulations indicate that the proposed method can achieve precise high-speed wavefront correction with a single far-field intensity distribution: it takes nearly 0.6ms to complete wavefront correction while the mean root mean square (RMS) of residual wavefronts is 6.3% of that of incident wavefronts, and the Strehl ratio of the far-field intensity distribution increases by 5.7 times after correction. In addition, the experiment results show that mean RMS of residual wavefronts is 6.5% of that of incident wavefronts and it takes nearly 0.5 ms to finish wavefront reconstruction, which verifies the correctness of our proposed method.