There have, however, been considerable advances in
our understanding of cirrus and halos. Modern works on halos can be credited in part to Walter Tape. Tape recently co-authored a paper with Gunther P. Konnen
entitled "A general setting for halo theory." This paper
puts forth a framework for the systematic treatment of halos due to refraction in preferentially oriented ice wedges, and an atlas is constructed of such halos. Initially, Tape is not constrained either by the interfacial angles, or the orientations of real ice crystals. Instead, he
considers "all possible" refraction halos. As a result, no
assumptions arc made regarding the wedge angle, and only a weak assumption is made regarding the allowable wedge orientations. The atlas is thus a very general collection of refraction halos that includes known halos as a small fraction.