Reflective ghost diffraction (GD) for objects with rough surfaces is investigated theoretically and numerically. Using a speckle model to describe the reflectivity of the object with variable rough surfaces, the incident and reflective angle-dependent diffraction condition is obtained, and the analytical expression of the reflective GD is derived. Numerical simulations are given to show how the height variance and correlation length of the object and the reflective angle in the experimental scheme can affect the quality of the reflective GD. Specifically, we find that the changes of diffraction patterns of both the simple objects and the complicated objects are sensitive to parameters such as the reflective angle and the surface fluctuation. Additionally, comparative studies on both reflective GD and ghost imaging (GI) have also been performed. We find that reflective GI is more robust against system parameters than reflective GD. These results may be useful for future experimental works.
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