This determination comprises: - for each of a plurality of illumination positions (110n), non-collimated illumination of the surface (102), and acquisition, at one and the same acquisition point (114) for all of the illumination positions (110n), of an image called a raw image; - for each illumination position (110n) and for each pixel (Pm) of the raw images, determination of a possible orientation (θn,m, φn,m) of crystalline facets, considering a propagation of light from the illumination position (110n) under consideration to the acquisition position (114), with
specular reflection from the crystalline facets; - based on the raw images and the possible orientations (θn,m, φn,m) associated with their pixels (Pm), construction of a reflectance profile (PR); - determination of a real orientation (θr, φr) of the facets based on the reflectance profile (PR).