For advanced X-ray sources such as synchrotron radiation facilities and X-ray free electron lasers, a smooth, structure-free beam on the far-field plane is usually strongly desired. The formation of the fine structures in far-field images downstream from imperfect optics must be understood. Although numerous studies have discussed the impacts on focused beams, there are still few quantitative theories for the impacts on beams in the far field. This article is an advance on our previous work, which discussed the uniformity of the intensity distribution in the far field. Here, a new theoretical approach is presented. It not only eases the assumptions needed to relate the fine structures to the wavefront curvature, but it also provides a quantitative estimation of the impacts of optical errors. The theoretical result is also verified by X-ray experiments.