Halo (optical phenomenon)

The so-called "Sun Dog Painting" (Vädersolstavlan) depicting Stockholm in 1535 and the celestial phenomenon at the time interpreted as an ominous presage

While mostly known and often quoted for being the oldest color depiction of the city of Stockholm, Vädersolstavlan (Swedish; "The Sundog Painting", literally "The Weather Sun Painting") is arguably also one of the oldest known depictions of a halo display, including a pair of sun dogs. For two hours in the morning of 20 April 1535, the skies over the city were filled with white circles and arcs crossing the sky, while additional suns (i.e., sun dogs) appeared around the sun.

Analogous refraction demonstration experiment for the Circumzenithal Arc.[9] Here, it is mistakenly labelled as an artificial rainbow in Gilberts book[10]

This approach employs the fact that in some cases the average geometry of refraction through an ice crystal may be imitated / mimicked via the refraction through another geometrical object. In this way, the Circumzenithal arc, the Circumhorizontal arc and the suncave Parry arcs may be recreated by refraction through rotationally symmetric (i.e. non-prismatic) static bodies.[9] A particularly simple table-top experiment reproduces artificially the colorful circumzenithal and circumhorizontal arcs using a water glass only. The refraction through the cylinder of water turns out to be (almost) identical to the rotationally averaged refraction through an upright hexagonal ice crystal / plate-oriented crystals, thereby creating vividly colored circumzenithal and the circumhorizontal arcs. In fact, the water glass experiment is often confused as representing a rainbow and has been around at least since 1920.[10]

Following Huygens' idea of the (false) mechanism of the 22° parhelia, one may also illuminate (from the side) a water-filled cylindrical glass with an inner central obstruction of half the glasses' diameter to achieve upon projection on a screen an appearance which closely resembles parhelia (cf. footnote [39] in Ref.,[9] or see here[11]), i.e. an inner red edge transitioning into a white band at larger angles on both sides of the direct transmission direction. However, while the visual match is close, this particular experiment does not involve a fake caustic mechanism and is thus no real analogue.

The earliest chemical recipes to generate artificial halos has been put forward by Brewster and studied further by A. Cornu in 1889. [12] The idea was to generate crystals by precipitation of a salt solution. The innumerable small crystals hereby generated will then, upon illumination with light, cause halos corresponding to the particular crystal geometry and the orientation / alignment. Several recipes exist and continue to be discovered.[13] Rings are a common outcome of such experiments.[14] But also Parry arcs have been artificially produced in this way.[15]

The earliest experimental studies on halo phenomena have been attributed[16] to Auguste Bravais in 1847.[17] Bravais used an equilateral glass prism which he spun around its vertical axis. When illuminated by parallel white light, this produced an artificial Parhelic circle and many of the embedded parhelia. Similarly, A. Wegener used hexagonal rotating crystals to produce artificial subparhelia.[18] In a more recent version of this experiment, many more embedded parhelia have been found using commercially available[19] hexagonal BK7 glass crystals.[20] Simple experiments like these can be used for educational purposes and demonstration experiments.[13][21] Unfortunately, using glass crystals one cannot reproduce the circumzenithal arc or the circumhorizontal arc due to total internal reflections preventing the required ray-paths when ${\displaystyle n<{\sqrt {2}}}$.

Even earlier than Bravais, the Italian scientist F. Venturi experimented with pointed water-filled prisms to demonstrate the circumzenithal arc.[22][23] However, this explanation was replaced later by the CZA's correct explanation by Bravais.[17]

Artificial Halo projected on a spherical screen.[24][25] Visible are: Tangential arcs, Parry arcs, (sub)parhelia, parhelic circle, heliac arcs

Artificial ice crystals have been employed to create halos which are otherwise unattainable in the mechanical approach via the use of glass crystals, e.g. circumzenithal and circumhorizontal arcs.[26] The use of ice crystals ensures that the generated halos have the same angular coordinates as the natural phenomena. Other crystals such as NaF also have a refractive index close to ice and have been used in the past.[27]

In order to produce artificial halos such as the tangent arcs or the circumscribed halo one should rotate a single columnar hexagonal crystal about 2 axes. Similarly, the Lowitz arcs can be created by rotating a single plate crystal about two axes. This can be done by engineered halo machines. The first such machine was constructed in 2003;[28] several more followed.[25][29] Putting such machines inside spherical projection screens, and by the principle of the so-called sky transform,[30] the analogy is nearly perfect. A realization using micro-versions of the aforementioned machines produces authentic distortion-free projections of such complex artificial halos.[9][24][25] Finally, superposition of several images and projections produced by such halo machines may be combined to create a single image. The resulting superposition image is then a representation of complex natural halo displays containing many different orientation sets of ice prisms.[24][25]

The experimental reproduction of circular halos is the most difficult using a single crystal only, while it is the simplest and typically achieved one using chemical recipes. Using a single crystal, one needs to realize all possible 3D orientations of the crystal. This has recently been achieved by two approaches. The first one using pneumatics and a sophisticated rigging,[29] and a second one using an Arduino-based random walk machine which stochastically reorients a crystal embedded in a transparent thin-walled sphere.[21]