Maintenance of the coherence of a light wave on weak scattering

In the light of the perspective of statistical similarity, we examine the maintenance of the second-order coherence of a light wave on weak scattering from a random medium. Some new and nontrivial results relating to properties of the scattered field which remains the second-order coherence of the incident field are presented. By assuming that the scattered field remains the second-order coherence, we can show that all of higher order correlation functions of Fourier component of the scattering potential can reduce to the like-factorization forms with a series of constant coefficients. These coefficients furnish an efficient and direct way to describe the higher order coherence property of the scattered field. We also show that the combination of the maintenance of second- and fourth-order coherence implies the scattered field coherence to all orders. Finally, the structure feature of the random medium is also discussed when the coherence of the incident field is retained up to 2nth order, in particular, in the case of the second-order coherence. Our theory is an important contribution for understanding of spatially fully coherent scattered fields, and also gives a general and new method to discuss the variation of the coherence of the scattered field.