A technique integrating the bidirectional reflectance distribution function (BRDF) is proposed to generate realistic high-quality colour computer-generated holograms (CGHs). We build on prior work, namely a fast computer-generated holography method for point clouds that handles occlusions. We extend the method by integrating the Phong illumination model so that the properties of the objects{\textquoteright} surfaces are taken into account to achieve natural light phenomena such as reflections and shadows. Our experiments show that rendering holograms with the proposed algorithm provides realistic looking objects without any noteworthy increase to the computational cost.