Intensity distribution of the parhelic circle and embedded parhelia at   low solar elevations: theory and experiments
  We describe the intensity distribution of the parhelic circle for plate-oriented hexagonal ice crystals at very low solar elevations using geometrical optics. An experimental as well as theoretical study of in-plane ray-paths provides details on the mechanism for several halos, including the parhelia, the $120^{\circ}$ parhelia, the blue spot and the Liljequist parhelia. Azimuthal coordinates for associated characteristic features in the intensity distribution are compared to data obtained using a rotating hexagonal glass prism. 
Sarah Borchardt and Markus Selmke
physics.ao-ph