The coherence of light includes temporal coherence and spatial coherence. However, whether it is the size of the coherence area to measure the spatial coherence or the coherence time to measure the temporal coherence, it is not a clear boundary, that is, 100% will not interfere as long as it is within their boundary, and once it exceeds the boundary, it will not interfere; Instead, the interference fringes gradually disappear, the contrast changes from large to small, and gradually drops to zero. In short, light with interference contrast between 0 and 1 can be called partially coherent light.

Based on the generalized Huygens-Fresnel diffraction integral equation (Collins formula), it is proved that the intensity distribution of Gaussian partially coherent beams is focused by a lens, and the intensity distribution near the geometric focus strongly depends on the spatial coherence of partially coherent beams. Based on this, the spatial coherence of partially coherent beams can be directly controlled to obtain the required light intensity distribution.

By choosing an appropriate coherent form, a partially coherent flat-topped beam or a partially coherent hollow beam can be obtained.

The research on beam shaping of partially coherent beams provides a new beam shaping method for potential applications such as material processing, optical therapy and atomic optics.

Partially coherent light and coherent light have the same expression of orbital angular momentum, and the orbital angular momentum spectrum of partially coherent light is more and more dispersed with the deterioration of coherence. The orbital angular momentum spectrum of partially coherent light with orbital angular momentum is more easily affected by coherence than that of partially coherent light without orbital angular momentum.