The optical field at the exit end of multi-mode fiber is treated as a quasi-homogeneous source, while that of single-mode fiber is treated as homogeneous partial coherence source. The second-order statistical correlation function and angular correlation function are used to analyze the correlation properties of the exit end and the near and far field of optical fibers. The transverse and angular coherent lengths and the optical intensity distribution parameters have been obtained. The theoretical results are compared to those of experiments.