The SMART-1 spacecraft pioneered European lunar exploration with its orbiting mission in 2004-2006. Among its instruments was the optical/near-infrared camera AMIE which mapped the lunar surface with a resolution between 40 to 200 metres per pixel. We have taken a sample of over eight hundred AMIE frames, representing most of the mare regions of the near side. We extracted multi-angular photometry from the images by sampling the brightness of the surface and estimating the local observational geometry (the directions to the camera and the Sun compared to the surface normal). We assume that the photometric properties of mare surfaces are similar in all the regions studied and consider the entire data set as representing "average" mare properties. Mare surfaces were chosen because they are smooth, making the estimation of the observational geometry simple, and also because they are dark, justifying the use of the Lommel-Seeliger scattering law. Using a numerical ray-tracing code with a simulated regolith medium we compute the effect of mutual shadowing of surface particles. This simulation considers the full observational geometry and includes azimuthal shadowings effects. The contribution of shadowing can then be removed from the data, resulting in a phase function for the lunar mare surfaces. In all cases, the reduced phase function shows a significant opposition effect, indicating that the lunar opposition effect is not explainable through shadowing effects only. Physical properties of the surface such as porosity and surface roughness affect the shadowing function. By varying these properties in the ray-tracing simulation, some information of the corresponding properties of the lunar surface may be gained. Research supported, in part, by the Academy of Finland (contract 127461) and by the NASA Lunar Advanced Science and Exploration Research Program (contract NNX11AB25G).