This paper focuses on an overview of the phase reconstruction method under partially coherent laser illumination and its application in the measurement of partially coherent light correlation structure. The above detailed phase reconstruction methods applicable for partially coherent illumination can be classified into four types: 1) Mode decomposition method which is applicable to iterative method. It converts the problem to a completely coherent lighting, and only the information of the light source is known. Phase reconstruction can be achieved by substituting it into the iterative loop; 2) Perturbation method,which is a non-iterative method ,reducing the four-dimensional analysis in the partial coherence theory to two dimensions by selecting an appropriate reference point; 3) The generalized intensity transmission equation using the axial differentiation of the light intensity to calculate the phase of the partially coherent light field; 4) The focal variation method. The complex information of the object surface can be deduced by the inverse Fourier transform and the summation of the light intensity corresponding to the continuous focal variation. The idea of mode decomposition combined with the current iterative algorithm is able to obtain reconstruction information with higher accuracy, but the information of the light source must be known, and its reconstruction accuracy depends on the number of modes representing partially coherent light. With the decrease of the spatial coherence of the illumination, the accuracy requirements of mode decomposition and data processing time will increase, and when the spatial coherence width is less than half of the sample size, good results cannot be obtained. The perturbation method of the non-iterative method does not need to be used with the iterative algorithm. Besides, data acquisition and processing are faster. This type of method is suitable for illumination sources with more complex or even unknown related structures, and the complete reconstruction information of the sample can be obtained when the spatial coherence width is smaller than the sample size. However, sacrifices have been made to the complexity and the spatial resolution of the device due to the introduction of perturbation and its phase assignment. The improvement of the spatial resolution requires the perturbation size to infinitely approximate thefunction set by the theory, but a size which is too small will also bring the sacrifice of the signal-to-noise ratio of the reconstructed image. Generalized intensity transmission equation has shown more advantages in data acquisition, processing time, and requirements for the light source, but this method also has the problem of balancing the defocusing distance and noise suppression. The higher the accuracy of the finite difference approximation, the smaller the defocusing distance is required, and thus not only improving the experimental accuracy, but also bringing noise to the experiment. In order to meet the low noise and high accuracy at the same time, the time on experiment needs to be sacrificed, and it may need to collect as much light intensity of transmission distance as possible. The focus variation method and the perturbation method can achieve the reconstruction of large field in the case of a small space size, but it has similar problems with the intensity transmission equation method. The accuracy of defocusing distance needs to be as high as possible, and the data of defocusing light intensity needs to be as much as possible. In short, in order to reduce the dimension, most non-iterative methods introduce thefunction, which also introduces errors.

For the future research, it is necessary to consider how to invent a new phase reconstruction method or improve existing phase reconstruction methods to solve the phase reconstruction problem in the case of low spatial coherence of the light source. Researchers also need to consider how to improve the resolution of the phase reconstruction of this kind of method. Furthermore, the reduced spatial coherence and complicated spatial coherence structure of the light source may not only bring negative effects, better and higher resolution phase reconstruction results may be achieved by clever use of partially coherent light and partially coherent light with special correlation structure.