Halo (optical phenomenon)

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A 22deg halo around the Sun, as seen in the sky over Annapurna Base Camp, Annapurna, Nepal Halo in the Himalayas.jpg
A 22° halo around the Sun, as seen in the sky over Annapurna Base Camp, Annapurna, Nepal
From top to bottom:
A circumzenithal arc, supralateral arc, Parry arc, upper tangent arc, and 22deg halo Solar halos, Salem, MA, Oct 27, 2012.JPG
From top to bottom:
A circumzenithal arc, supralateral arc, Parry arc, upper tangent arc, and 22° halo

Halo (from Greek ἅλως, halōs [1] ) is the name for a family of optical phenomena produced by sunlight interacting with ice crystals suspended in the atmosphere. Halos can have many forms, ranging from colored or white rings to arcs and spots in the sky. Many of these appear near the Sun or Moon, but others occur elsewhere or even in the opposite part of the sky. Among the best known halo types are the circular halo (properly called the 22° halo), light pillars, and sun dogs, but many others occur; some are fairly common while others are (extremely) rare.

Greek language language spoken in Greece, Cyprus and Southern Albania

Greek is an independent branch of the Indo-European family of languages, native to Greece, Cyprus and other parts of the Eastern Mediterranean and the Black Sea. It has the longest documented history of any living Indo-European language, spanning more than 3000 years of written records. Its writing system has been the Greek alphabet for the major part of its history; other systems, such as Linear B and the Cypriot syllabary, were used previously. The alphabet arose from the Phoenician script and was in turn the basis of the Latin, Cyrillic, Armenian, Coptic, Gothic, and many other writing systems.

Sunlight portion of the electromagnetic radiation given off by the Sun

Sunlight is a portion of the electromagnetic radiation given off by the Sun, in particular infrared, visible, and ultraviolet light. On Earth, sunlight is filtered through Earth's atmosphere, and is obvious as daylight when the Sun is above the horizon. When the direct solar radiation is not blocked by clouds, it is experienced as sunshine, a combination of bright light and radiant heat. When it is blocked by clouds or reflects off other objects, it is experienced as diffused light. The World Meteorological Organization uses the term "sunshine duration" to mean the cumulative time during which an area receives direct irradiance from the Sun of at least 120 watts per square meter. Other sources indicate an "Average over the entire earth" of "164 Watts per square meter over a 24 hour day".

Ice crystals

Ice crystals are solid ice exhibiting atomic ordering on various length scales and include hexagonal columns, hexagonal plates, dendritic crystals, and diamond dust.

Contents

The ice crystals responsible for halos are typically suspended in cirrus or cirrostratus clouds in the upper troposphere (5–10 km (3.1–6.2 mi)), but in cold weather they can also float near the ground, in which case they are referred to as diamond dust. The particular shape and orientation of the crystals are responsible for the type of halo observed. Light is reflected and refracted by the ice crystals and may split into colors because of dispersion. The crystals behave like prisms and mirrors, refracting and reflecting light between their faces, sending shafts of light in particular directions.

Cirrus cloud genus of atmospheric cloud

Cirrus is a genus of atmospheric cloud generally characterized by thin, wispy strands, giving the type its name from the Latin word cirrus, meaning a ringlet or curling lock of hair. This cloud can form at any altitude between 16,500 ft and 45,000 ft above sea level. The strands of cloud sometimes appear in tufts of a distinctive form referred to by the common name of "mares' tails".

Cirrostratus cloud genus of clouds

Cirrostratus is a high-level, very thin, generally uniform stratiform genus-type of cloud, composed of ice-crystals. It is difficult to detect and is capable of forming halos when the cloud takes the form of thin cirrostratus nebulosus. The cloud has a fibrous texture with no halos if it is thicker cirrostratus fibratus. On the approach of a frontal system, the cirrostratus often begins as nebulosus and turns to fibratus. If the cirrostratus begins as fragmented fibratus it often means the front is weak. Cirrostratus is usually located above 5.5 km (18,000 ft). Its presence indicates a large amount of moisture in the upper atmosphere.

Troposphere The lowest layer of the atmosphere

The troposphere is the lowest layer of Earth's atmosphere, and is also where nearly all weather conditions take place. It contains approximately 75% of the atmosphere's mass and 99% of the total mass of water vapor and aerosols. The average height of the troposphere is 18 km in the tropics, 17 km in the middle latitudes, and 6 km in the polar regions in winter. The total average height of the troposphere is 13 km.

Atmospheric optical phenomena like halos were used as part of weather lore, which was an empirical means of weather forecasting before meteorology was developed. They often do indicate that rain will fall within the next 24 hours, since the cirrostratus clouds that cause them can signify an approaching frontal system.

Atmospheric optics

Atmospheric optics is "the study of the optical characteristics of the atmosphere or products of atmospheric processes .... [including] temporal and spatial resolutions beyond those discernible with the naked eye". Meteorological optics is "that part of atmospheric optics concerned with the study of patterns observable with the naked eye". Nevertheless, the two terms are sometimes used interchangeably.

Weather forecasting application of science and technology to predict the conditions of the atmosphere for a given location and time

Weather forecasting is the application of science and technology to predict the conditions of the atmosphere for a given location and time. People have attempted to predict the weather informally for millennia and formally since the 19th century. Weather forecasts are made by collecting quantitative data about the current state of the atmosphere at a given place and using meteorology to project how the atmosphere will change.

Meteorology Interdisciplinary scientific study of the atmosphere focusing on weather forecasting

Meteorology is a branch of the atmospheric sciences which includes atmospheric chemistry and atmospheric physics, with a major focus on weather forecasting. The study of meteorology dates back millennia, though significant progress in meteorology did not occur until the 18th century. The 19th century saw modest progress in the field after weather observation networks were formed across broad regions. Prior attempts at prediction of weather depended on historical data. It was not until after the elucidation of the laws of physics and more particularly, the development of the computer, allowing for the automated solution of a great many equations that model the weather, in the latter half of the 20th century that significant breakthroughs in weather forecasting were achieved.

Other common types of optical phenomena involving water droplets rather than ice crystals include the glory and rainbow.

Glory (optical phenomenon) optical phenomenon that resembles an iconic saints halo about the shadow of the observers head

A glory is an optical phenomenon, resembling an iconic saint's halo around the shadow of the observer's head, caused by sunlight or moonlight interacting with the tiny water droplets that compose mist or clouds. The glory consists of one or more concentric, successively dimmer rings, each of which is red on the outside and bluish towards the centre. Due to its appearance, the phenomenon is sometimes mistaken for a circular rainbow, but the latter has a much larger diameter and is caused by different physical processes.

Rainbow meteorological phenomenon

A rainbow is a meteorological phenomenon that is caused by reflection, refraction and dispersion of light in water droplets resulting in a spectrum of light appearing in the sky. It takes the form of a multicoloured circular arc. Rainbows caused by sunlight always appear in the section of sky directly opposite the sun.

History

While Aristotle had mentioned halos and parhelia, in antiquity, the first European descriptions of complex displays were those of Christoph Scheiner in Rome (circa 1630), Hevelius in Danzig (1661), and Tobias Lowitz in St Petersburg (c. 1794). Chinese observers had recorded these for centuries, the first reference being a section of the "Official History of the Chin Dynasty" (Chin Shu) in 637, on the "Ten Haloes", giving technical terms for 26 solar halo phenomena. [2]

Aristotle philosopher in ancient Greece

Aristotle was an ancient Greek philosopher and scientist born in the city of Stagira, Chalkidiki, Greece. Along with Plato, he is considered the "Father of Western Philosophy". Aristotle provided a complex and harmonious synthesis of the various existing philosophies prior to him, including those of Socrates and Plato, and it was above all from his teachings that the West inherited its fundamental intellectual lexicon, as well as problems and methods of inquiry. As a result, his philosophy has exerted a unique influence on almost every form of knowledge in the West and it continues to be central to the contemporary philosophical discussion.

Christoph Scheiner Jesuit father, physicist and astronomer

Christoph Scheiner SJ was a Jesuit priest, physicist and astronomer in Ingolstadt.

The Sevenfold Sun Miracle was an atmospheric phenomenon witnessed in Danzig in 1661. It was a complex halo phenomenon, and was described by Georg Fehlau, the pastor of the St Marien church, in a sermon two weeks later, which was then published under the title Siebenfältiges Sonnenwunder oder sieben Nebensonnen, so in diesem 1661 Jahr den 20. Februar neuen Stils am Sonntage Sexagesima um 11 Uhr bis nach 12 am Himmel bei uns sind gesehen worden The same event was also described by the astronomer Johan Hevelius the following year in his book Mercurius in Sole visus Gedani.

Vädersolstavlan

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

Stockholm Capital city in Södermanland and Uppland, Sweden

Stockholm is the capital of Sweden and the most populous urban area in the Nordic countries; 960,031 people live in the municipality, approximately 1.5 million in the urban area, and 2.3 million in the metropolitan area. The city stretches across fourteen islands where Lake Mälaren flows into the Baltic Sea. Just outside the city and along the coast is the island chain of the Stockholm archipelago. The area has been settled since the Stone Age, in the 6th millennium BC, and was founded as a city in 1252 by Swedish statesman Birger Jarl. It is also the capital of Stockholm County.

<i>Vädersolstavlan</i> painting by Jacob Heinrich Elbfas

Vädersolstavlan  is an oil-on-panel painting depicting a halo display, an atmospheric optical phenomenon, observed over Stockholm on 20 April 1535. It is named after the sun dogs appearing on the upper right part of the painting. While chiefly noted for being the oldest depiction of Stockholm in colour, it is arguably also the oldest Swedish landscape painting and the oldest depiction of sun dogs.

Swedish language North Germanic language spoken in Sweden

Swedish is a North Germanic language spoken natively by 10 million people, predominantly in Sweden, and in parts of Finland, where it has equal legal standing with Finnish. It is largely mutually intelligible with Norwegian and to some extent with Danish, although the degree of mutual intelligibility is largely dependent on the dialect and accent of the speaker. Both Norwegian and Danish are generally easier for Swedish speakers to read than to listen to because of difference in accent and tone when speaking. Swedish is a descendant of Old Norse, the common language of the Germanic peoples living in Scandinavia during the Viking Era. It has the most speakers of the North Germanic languages.

Light pillar

A light pillar, or sun pillar, appears as a vertical pillar or column of light rising from the sun near sunset or sunrise, though it can appear below the sun, particularly if the observer is at a high elevation or altitude. Hexagonal plate- and column-shaped ice crystals cause the phenomenon. Plate crystals generally cause pillars only when the sun is within 6 degrees of the horizon; column crystals can cause a pillar when the sun is as high as 20 degrees above the horizon. The crystals tend to orient themselves near-horizontally as they fall or float through the air, and the width and visibility of a sun pillar depend on crystal alignment.

Light pillars can also form around the moon, and around street lights or other bright lights. Pillars forming from ground-based light sources may appear much taller than those associated with the sun or moon. Since the observer is closer to the light source, crystal orientation matters less in the formation of these pillars.

Circular halo

Among the best-known halos is the 22° halo, often just called "halo", which appears as a large ring around the Sun or Moon with a radius of about 22° (roughly the width of an outstretched hand at arm's length). The ice crystals that cause the 22° halo are oriented semi-randomly in the atmosphere, in contrast to the horizontal orientation required for some other halos such as sun dogs and light pillars. As a result of the optical properties of the ice crystals involved, no light is reflected towards the inside of the ring, leaving the sky noticeably darker than the sky around it, and giving it the impression of a "hole in the sky". [3] The 22° halo is not to be confused with the corona, which is a different optical phenomenon caused by water droplets rather than ice crystals, and which has the appearance of a multicolored disk rather than a ring.

Other haloes can form at 46° to the sun, or at the horizon, or around the zenith, and can appear as full haloes or incomplete arcs.

Bottlinger's ring

A Bottlinger's ring is a rare type of halo that is elliptical instead of circular. It has a small diameter, which makes it very difficult to see in the Sun's glare and more likely to be spotted around the dimmer Subsun, often seen from mountain tops or airplanes. Bottlinger's rings are not well understood yet. It is suggested that they are formed by very flat pyramidal ice crystals with faces at uncommonly low angles, suspended horizontally in the atmosphere. These precise and physically problematic requirements would explain why the halo is very rare. [4]

Other names

In the Anglo-Cornish dialect of English, a halo round the sun or the moon is called a cock's eye and is a token of bad weather. The term is related to the Breton word kog-heol (sun cock) which has the same meaning. [5] In Nepal, the halo round the sun is called Indrasabha with a connotation of the assembly court of Lord Indra – the Hindu god of lightning, thunder and rain. [6]

Artificial halos

The natural phenomena may be reproduced artificially by several means. Firstly, by computer simulations, [7] [8] or secondly by experimental means. Regarding the latter, one may either take a single crystal and rotate it around the appropriate axis/axes, or take a chemical approach. A still further and more indirect experimental approach is to find analogous refraction geometries.

Analogous refraction approach

Analogous refraction demonstration experiment for the Circumzenithal Arc. Here, it is mistakenly labelled as an artificial rainbow in Gilberts book Artificial CZA.png
Analogous refraction demonstration experiment for the Circumzenithal Arc. Here, it is mistakenly labelled as an artificial rainbow in Gilberts book

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.

Chemical approaches

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]

Mechanical approaches

Single axis

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 .

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

Two axes

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]

Three axes

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]

See also

Related Research Articles

Sun dog atmospheric phenomenon

A sun dog or mock sun, formally called a parhelion in meteorology, is an atmospheric optical phenomenon that consists of a bright spot to one or both sides of the Sun. Two sun dogs often flank the Sun within a 22° halo.

Anthelion a rare optical phenomenon appearing on the parhelic circle opposite to the sun as a faint white halo

An anthelion is a rare optical phenomenon of the halo family. It appears on the parhelic circle opposite to the sun as a faint white spot, not unlike a sundog, and may be crossed by an X-shaped pair of diffuse arcs.

Fog bow

A fog bow, sometimes called a white rainbow, is a similar phenomenon to a rainbow; however, as its name suggests, it appears as a bow in fog rather than rain. Because of the very small size of water droplets that cause fog—smaller than 0.05 millimeters (0.0020 in)—the fog bow has only very weak colors, with a red outer edge and bluish inner edge.

Circumhorizontal arc optical phenomenon that belongs to the family of ice halos

A circumhorizontal arc is an optical phenomenon that belongs to the family of ice halos formed by the refraction of sun- or moonlight in plate-shaped ice crystals suspended in the atmosphere, typically in cirrus or cirrostratus clouds. In its full form, the arc has the appearance of a large, brightly spectrum-coloured band running parallel to the horizon, located far below the Sun or Moon. The distance between the arc and the Sun or Moon is twice as far as the common 22-degree halo. Often, when the halo-forming cloud is small or patchy, only fragments of the arc are seen. As with all halos, it can be caused by the Sun as well as the Moon.

Circumzenithal arc optical effect

The circumzenithal arc, also called the circumzenith arc (CZA), upside-down rainbow, and the Bravais arc, is an optical phenomenon similar in appearance to a rainbow, but belonging to the family of halos arising from refraction of sunlight through ice crystals, generally in cirrus or cirrostratus clouds, rather than from raindrops. The arc is located at a considerable distance above the sun and at most forms a quarter of a circle centered on the zenith. It has been called "a smile in the sky", its first impression being that of an upside-down rainbow. The CZA is one of the brightest and most colorful members of the halo family. Its colors, ranging from violet on top to red at the bottom, are purer than those of a rainbow because there is much less overlap in their formation.

Parhelic circle

A parhelic circle is a halo, an optical phenomenon appearing as a horizontal white line on the same altitude as the sun, or occasionally the Moon. If complete, it stretches all around the sky, but more commonly it only appears in sections.

22° halo

A 22° halo is an optical phenomenon that belongs to the family of ice crystal halos, in the form of a ring with a radius of approximately 22° around the Sun or Moon. When visible around the moon, it is called a moon ring or winter halo. It forms as the sun- or moonlight is refracted in millions of hexagonal ice crystals suspended in the atmosphere. The halo is large; the radius is roughly the size of an outstretched hand at arm's length. A 22° halo may be visible on as many as 100 days per year—much more frequently than rainbows.

120° parhelion

A 120° parhelion is a relatively rare halo, an optical phenomenon occasionally appearing along with very bright sun dogs when ice crystal-saturated cirrus clouds fill the atmosphere. The 120° parhelia are named for appearing in pair on the parhelic circle ±120° from the sun.

Upper and lower tangent arcs

Tangent arcs are a type of halos, an atmospheric optical phenomenon, which appear above and below the Sun or Moon, tangent to the 22° halo. To produce these arcs, rod-shaped hexagonal ice crystals need to have their long axis aligned horizontally.

Supralateral arc

A supralateral arc is a comparatively rare member of the halo family which in its complete form appears as a large, faintly rainbow-colored band in a wide arc above the sun and appearing to encircle it, at about twice the distance as the familiar 22° halo. In reality, however, the supralateral arc does not form a circle and never reaches below the sun. When present, the supralateral arc touches the circumzenithal arc from below. As in all colored halos, the arc has its red side directed towards the sun, its blue part away from it.

An infralateral arc is a rare halo, an optical phenomenon appearing similar to a rainbow under a white parhelic circle. Together with the supralateral arc they are always located outside the seldom observable 46° halo, but in contrast to supralateral arcs, infralateral arcs are always located below the parhelic circle.

46° halo

A 46° halo is a rare member of the family of ice crystal halos, appearing as a large ring centred on the Sun at roughly twice the distance as the much more common 22° halo. At solar elevations between 15–27°, the 46° halo is often confused with the less rare and more colourful supralateral and infralateral arcs, which cross the parhelic circle at about 46° to the left and right of the sun.

A Liljequist parhelion is a rare halo, an optical phenomenon in the form of a brightened spot on the parhelic circle approximately 150–160° from the sun; i.e., between the position of the 120° parhelion and the anthelion.

Parry arc

A Parry arc is a rare halo, an optical phenomenon which occasionally appears over a 22° halo together with an upper tangent arc.

The Kern arc is an extremely rare atmospheric optical phenomenon belonging to the family of ice crystal halos. It is a complete and faint circle around the zenith, in contrast to the related and much more common circumzenithal arc, which is only ever a partial circle.

A Lowitz arc is an optical phenomenon that occurs in the atmosphere; specifically, it is a rare type of ice crystal halo that forms a luminous arc which extends inwards from a sun dog (parhelion) and may continue above or below the sun.

Atmospheric optics ray tracing codes - this article list codes for light scattering using ray-tracing technique to study atmospheric optics phenomena such as rainbows and halos. Such particles can be large raindrops or hexagonal ice crystals. Such codes are one of many approaches to calculations of light scattering by particles.

Optical phenomena observable events that result from the interaction of light and matter

Optical phenomena are any observable events that result from the interaction of light and matter. See also list of optical topics and optics. A mirage is an example of an optical phenomenon.

References

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  2. Ho Ping-Yu, Joseph Needham Ancient Chinese Observations of Solar Haloes and Parhelia Weather April 1959 (vol14, issue 4) p124-134
  3. ""Disk with a hole" in the sky". Atmospheric Optics. Retrieved 3 August 2016.
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  5. Nance, Robert Morton; Pool, P. A. S. (1963). A Glossary of Cornish Sea-Words. Cornwall: Federation of Old Cornwall Societies. p. 61.
  6. "Nepal skies graced with extraordinary 'circular rainbow' halo around sun". The Himalayan Times. 9 July 2015. Retrieved 3 August 2016.
  7. HaloSim3 by Les Cowley and Michael Schroeder link
  8. HaloPoint 2.0 link Archived 2016-10-07 at the Wayback Machine
  9. 1 2 3 4 "Artificial circumzenithal and circumhorizontal arcs", M. Selmke and S. Selmke, American Journal of Physics (Am. J. Phys.) Vol 85(8), p.575-581 link
  10. 1 2 Gilbert light experiments for boys – (1920), p. 98, Experiment No. 94 link
  11. Webpage detailing several DIY experiments link
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  19. Homogenizing Light rods / Light pipes link
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  21. 1 2 "Artificial Halos", American Journal of Physics (Am. J. Phys.), Vol. 83(9), 751–760, M. Selmke, 2015. link
  22. F. Venturi, "Commentarii sopra ottica", p. 219, Tav VIII, Fig 17, arc: PGQ, Fig 27, p. 213.
  23. Johann Samuel Traugott Gehler (1829). Physikalisches Wörterbuch: neu bearbeitet von Brandes, Gmelin, Horner, Muncke, Pfaff. E. B. Schwickert. p. 494.
  24. 1 2 3 Article with images on BoredPanda: Spherical projection screen for artificial halos
  25. 1 2 3 4 "Complex artificial halos for the classroom", American Journal of Physics (Am. J. Phys.), Vol. 84(7), 561–564, M. Selmke and S. Selmke, 2016. link
  26. Homepage: Arbeitskreis Meteore e.V. link
  27. "An Analog Light Scattering Experiment of Hexagonal Icelike Particles. Part II: Experimental and Theoretical Results", JOURNAL OF THE ATMOSPHERIC SCIENCES, Vol. 56, B. Barkey, K.N. Liou, Y. Takano, W. Gellerman, P. Sokolkly, 1999.
  28. “Halo and mirage demonstrations in atmospheric optics,” Appl. Opt. 42(3), 394–398, M. Vollmer and R. Greenler, 2003. link
  29. 1 2 “Artificially generated halos: rotating sample crystals around various axes”, Applied Optics Vol. 54, Issue 4, pp. B97-B106, Michael Großmann, Klaus-Peter Möllmann, and Michael Vollmer, 2015. link
  30. "Sky Transform" on atoptics.co.uk: link