Using ray theory, the Möbius shift of the (p-1)-order rainbow angle for a particle having an elliptical cross section is obtained to first order in the ellipticity as a function of the tilt of the ellipse with respect to the propagation direction of the incoming rays. The result is then adapted to the geometry of scattering of light rays from the sun by a falling water drop as a function of sun height angle. The variation in the angular spacing between the supernumeraries is determined as a function of location along the rainbow arc, the conditions under which the rainbow angle is insensitive to drop flattening were determined, and the dependence of the Möbius shift on the drop refractive index is shown for rainbows up to fourth order (p = 5).
Rainbows, halos, coronas, and glories are aesthetic features admired over millennia by man. They are also carriers of useful information about the physical properties of drops and solid particles floating in the atmospheres of Earth and other planets. Although atmospheric optics is a centuries-old discipline, significant progress in the understanding of these phenomena has been achieved during the past 40 years, as well as of their relation to the physical properties of the individual scatterers. At the same time, with the development of planetary exploration, the number of observations of rainbows, halos, and glories in the atmospheres of planets other than Earth is steadily growing. In this article we describe these phenomena and their information content and illustrate them with pictures mostly showing their typical appearance rather than presenting the “best pictures ever.”
We present a stacked and
contrast-enhanced image comprised of 12 digital photographs that shows a series
of color hues in the correct order and location to be part of the seventh-order
rainbow. The observation was made on September 22, 2013, near
Sirius was spotted with the naked eye at
broad daylight by looking along the finder of a
The degree of polarization of rainbows of order k with k≥3 is bounded in the interval [75%, 78%], where 75% is the limit for k→¥. A polarization filter can improve the signal-to-background ratio of the third and fourth rainbows by a factor of 2, which may lift their visibilities in natural circumstances above the threshold of human visual perception. Under optimal circumstances, the latter may be true for the recently photographed green fingerprint of the fifth rainbow, even without the aid of a polarization filter. The prospects for observing the sixth rainbow are unclear. There exists a possibility that the signal of the natural seventh rainbow (appearing at 64° from the Sun) may be separated from its background if photographed under perfect conditions through a polarization filter
A ‘broken rainbow’ teaches us that seawater is salt – in the same way that the Venus rainbow once taught us that the cloud drops on Venus are sour.NB: the topic is also discussed in my article ‘Rainbows, halos, coronas and glories: beautiful sources of information’, BAMS 2017.
We took a picture of a submoon. The meteorological conditions during the observation are outlined. The mechanism of formation is discussed. A search in the literature yields only nine earlier submoon reports. An explanation is given for the extreme rarity of submoon reports compared to subsun reports.
From an aircraft, a short distinct vertical structure is sometimes seen above the setting sun. Such a feature can be understood as a halo which is the counterpart of the well-known subsun. Whereas the latter arises from reflections off basal faces of plate-oriented ice crystals when illuminated from above, what we call the supersun emerges when these crystals are illuminated from below. The supersun occurs when the sun is below the true horizon and is only visible from elevated positions. The curvature of the Earth causes the ensemble of reflecting crystal faces to act as a hollow mirror and the supersun appears as a vertical band of uniform width, extending from the sun upwards to its supersolar point. We discuss the geometrical properties of the phenomenon and simulate its shape and radiance distribution with an extended version of an atmospheric ray-tracing program.
The find of Eva Seidenfaden of Scheiner’s original diagram of the 1630
NB: the Nature article has been republished on 30 Sep
The salt/fresh water rainbow combination photographed by J. Dijkema in 1981 in the Pacific is republished in the section After Image of OPN.
The anomalous red twilights observed in mid-February 2008 over Western Europe can be attributed to the presence of a large field of Stratospheric Polar Clouds (PSCs). The vertical sounding of De Bilt indicates that a tropospheric high pressure system triggered an excess stratospheric cooling. Pictures of the twilight taken from several spots are shown.
Usually a glory is perfectly round, but sometimes it can be deformed to such a degree that it is hardly recognizable as such. In this article we discuss some examples of deformed glories.
The limiting magnitude during totality is +3.5. Diffraction coronas and even halos around the totally eclipsed sun may nevertheless occur. Rainbows during totality seem impossible.
The two Rome halo displays of 1629 and 1630 are prominent in the early halo literature, and the 1629 display is still cited today for having contained a 28° circular halo. We have examined seventeenth century correspondence and publications in order to learn as much as possible about the existing documentation of the two displays. We find the documentation to be too weak to support a definitive interpretation of either display, and we see little evidence for a 28° halo or for other rare halos. The two displays remain important for their role in initiating modern halo science.
An isolated colourless spot of 1° diameter located at the antisolar point was observed from a plane on the clouds beneath it. The spot can be explained by light scattering on randomly oriented ice crystals, via light paths similar to those responsible for the subparhelic circle. Its peculiar polarization properties potentially enable its detecting in cases where the spot is embedded in a glory.
A response is given to a Letter by G. Watts questioning the identification of subsuns in general and of the bright steak on Mars in terms of halo scattering.
A bright subsun is spotted on a satellite picture of Mars. To our knowledge this is the first time that a halo is identified on a picture of a planet other than the Earth.
The prospects of the Huygens probe to detect during its descent halos from methane or ethane crystals on Titan are discussed. Diagrams of potential halo displays on Titan are shown.
There is an ancient myth that the light in Holland is different from anywhere else. It's the legendary light we see in old Dutch paintings. The reality of this elusive effect is discussed by several people. My explanation is that the light is just a contrast effect, cause by the flat and featureless Dutch landscape which attracts the eyes to the near-horizon sky, where remote cumulus clouds can a spectacular sight. (versions in English, Dutch, German, French, and Spanish)
NB: This documentary won in 2003 a ‘Gouden Kalf' award
Polarization and radiance profiles of parhelia were measured as a function of scattering angle. The wavelength dependence of the width of the parhelion polarization peak agrees with Fraunhofer diffraction theory, indicating that the broadening of the halos is caused primarily by diffraction. Hence our hypothesis that a spread of interfacial angles is the dominating cause of halo broadening, has proved untenable. The conflicting results between the width of the halo polarization peaks and the observed size distribution of the replicated crystals originates from a strong size-dependent collection efficiency in the sampling. This implies that shapes of sampled crystals need not necessarily be representative for the shapes of the halo-making crystals in a swarm.
Ray-tracing analyses show that the NZ effect distorted the relative positions of Jupiter and the Moon in such a way that the looked-for fingerprint of the 1597 conjunction occurred almost 2 h after the true conjunction. The quoted direction for the apparent Moon-Jupiter conjunction is then found to be accurate to within 1°. This delay of the apparent conjunction largely explains the error of 29° in their longitude determination. The truthfulness of the observations brackening the first recording of the NZ effect, debated for four centuries, now appears to be beyond doubt.
It is found that halo displays are always left-right (L-R) symmetric if the crystals are formed from the surrounding vapor. This leaves room for two types of halo display only: a full symmetric one (mmm -symmetric), and a partial symmetric one (mm2 -symmetric) in which halo constituents lack their counterparts on the other side of the parhelic circle. Partial symmetric displays can occur only for point halos and only if the halo-making crystals lack a center of inversion, any rotatory-inversion axis that is parallel to the crystal spin axis P, a mirror plane perpendicular to the P axis, and a twofold rotation axis perpendicular to the P axis. A simple conceptual method is presented to reconstruct possible shapes of the halo-generating crystals from the halos in the display. Halos that may occur on the Saturnian satellite Titan are briefly discussed.
Systematics of the Novaya Zemlya (NZ) effect are discussed in the context of sunsets. We distinguish full mirages, exhibiting oscillatory light paths and their onsets, the subcritical mirages. Ray-tracing examples and sequences of solar images are shown. We discuss two historical observations by Fridtjof Nansen and by Vivian Fuchs, and we report a recent South Pole observation of the NZ effect for the Moon.
In the caption to a Weather-picture of a parhelion reflected on a water surface it was suggested that the polarization difference between sky and parhelion enhanced the contrast. I show that this effect does not lead any perceptible enhancement of the contrast.
We describe a general framework for systematically treating halos that are due to refraction in preferentially oriented ice wedges, and we construct an atlas of such halos. The atlas is thus a very general collection of refraction halos that includes known halos as a small fraction. Each halo in the atlas is characterized by three parameters: the wedge angle, the zenith angle of the spin vector, and the spin vector expressed in the wedge frame. The theory reveals order in what seems initially to be a staggering variety of halo shapes, and in particular it explains why halos look the way they do.
Preannouncement of our unifying halo theory, published later in Appl. Opt. 38, 1552-1625 (1999).
Parhelic circles due to plate-oriented crystals (hence, with main axes vertical) and 120° parhelia change in position when viewed through a rotating polarizer. The parhelic circle moves vertically; its largest shift is found at an azimuthal distance between 90° and 120° from the Sun. The 120° parhelia move both vertically and horizontally. The magnitudes of the shifts are between 0.1° and 0.3°, depending on solar elevation. The mechanism is polarization-sensitive internal reflection by prism faces of the ice crystals. We outline the theory and present three visual and one instrumental observation of the displacements of these halos in polarized light.
The direction of the inner-edge polarization of a halo can serve as an observational diagnostic for determining the actual nature of a halo arc if two competing explanations exist. The observation can be decisive for the identification of a spot that might be either a 44° parhelion or a 46° parhelion, of an arc that might be either a 22° sunvex Parry arc or a 20° Parroid arc arising from plate-oriented pyramidal crystals, and of an arc that might be either a 22° suncave Parry arc or a 23° Parroid arc from plate-oriented pyramidal crystals. Practical hints are given for observing visually the inner-edge polarization of halos.
Polarization and radiance profiles of refraction halos were measured as a function of scattering angle. The width of the halo polarization peaks conflicts the observed size distribution of the replicated crystals. This discrepancy can be explained if the interfacial angles are not always exact integer multiples of 60°, but have an average deviation from this value of 0.49° ± 0.05°.
Scanning the polarization of Venus at scattering angles 18-32° and at wavelengths 402-850 nm, we found a dip in polarization in the scattering angle range 23-25° for wavelengths 622 nm and longer. The width of the dip was 1-3°, its magnitude 0.4% in degree of polarization. The dip is consistent with the occurrence of a halo in the Venus atmosphere due to H2SO4-contaminated ice crystals in the upper haze layer of Venus. It remains unclear however why the halo is manifesting itself only at long wavelengths.
See the abstract of Endeavor New Series 10, 121-124 (1986)
Preliminary results on the Antarctic halo project performed at US Amundsen-Scott South Pole Station (season 1989/90) and the Russian station Vostok (season 1990/91) are described.
The linear polarization and intensity of a 22° halo has been measured simultaneously at seven wavelengths as a function of scattering angle. The polarization pattern is found to be dominated by a narrow peak centered at the halo angle. Its width indicate a effective diameter of the hexagonal face of the halo-generating crystals is found to be 41 and 54 μm for two separate scans. Halo angles could be determined with precisions better than 0.05°. An independent single-wavelength parhelion observation indicates a stronger polarization peak concentrated in an even smaller angular scattering range and a crystal diameter of 220 μm.
An account is given about our attempts at La Palma Observatory to detect ice crystals in the Venus's atmosphere, including the drawback of a temporary instrumental malfunction and our subsequent fortune that we got the opportunity to scan a terrestrial halo in a Venus-spoiling cirrus deck.
The secondary rainbow scattering angle for spheroidal drops of water is virtually independent of aspect ratio for most visible wavelengths. For most solar heights the residual aspect-ratio dependence shifts the bow toward a smaller deviation angle if the drop size increases. These two facts explain why the supernumeraries of the secondary rainbow are never seen in rain showers. At high solar elevations the flattening of drops results in a shift of the secondary rainbow toward a larger deviation angle. This shift is still large enough to cause the formation of the first supernumerary in red light. This red supernumerary of the secondary rainbow may be observable by eye in natural showers if a red filter is used to remove the obscuring contribution of shorter wavelengths to the light of the rainbow.
The polarization distribution in the sky during a total solar eclipse is calculated with a simple secondary light scattering model. The model can explain various observations during totality, including the measurements by Shaw of the polarization distribution of the sky in the solar vertical during the 1973 total eclipse.
In the open, we are surrounded no only by a mass of colour, but also by much polarization. The latter remains normally invisible to us, but with the aid of a simple polarizing sheet, one suddenly becomes aware how much polarization there is. In this article, a number of observations are described and regularities in the natural polarization pattern are discussed.
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An outline is given of polarization of natural phenomena, like the blue sky, rainbows, halos, beetles and reflections. The effects are illustrated with 89 pictures.
NB: The size of the download is 24 Mb
The intensity distributions of halos as a function of scattering angle are found to depend on the number of degrees of freedom of the generating set of crystals. The polarization of refraction halos as a function of scattering angle is calculated, in which birefringence is taken into account. The polarization of parhelia and tangent arcs shows a strong maximum near the inner edge of the halo over an angular range of 0.1°, followed by a similar maximum of reversed polarization at 0.5° from the first one. The 22° halo polarization shows a less strong maximum near its edge over an angular range of 0.5°. Halos at 46° from the sun also show a strong polarization near their inner edges, but the direction of the polarization is perpendicular to the polarization of the 22° halo edges.
The Airy theory of the rainbow is extended to polarized light. The degree of polarization of the rainbow is less than expected from geometrical optics; it increases with droplet size. For a droplet diameter >1 mm the locations of the supernumerary rainbows are equal for both polarization directions, but for a diameter <1 mm the supernumerary rainbows of the weaker polarization component are located between those in the strong component.
Because of birefringence, 22° halos consist of two polarised components, mutually shifted by 0.11°, which is about one quarter of the angle subtended by the moon. By rotating a polarizer before the naked eye we could be easily observed that the halo's inner boundary is about 0.1° closer to the sun for polarized light for which the E vector is radial with respect to the sun. To our knowledge, observations of this kind have never been published.
The shadow of the annual eclipse of 29 April 1976 stands clearly out against the Sahara on the picture taken on 09:37 UT by the NOOA-4 weather satellite.
A bright subsun was spotted on the image taken by the ESSA-8 weather satellite. The subsun appeared on a frontal system east of
A double tangent arc was observed above the setting sun and photographed with a 17-mm lens. The mutual distance between the arcs was 1.7°. The distance to the sun of the lower component of 21.5° indicate that it is an ordinary tangent arc to the 22° halo. The upper component might have been either a tangent arc to the 24½° halo or a Parry arc II. The shape and distance to the sun rules the first possibility out.
We observed and photographed from a plane a parhelion, a subparhelion and a vertical arc connecting these two.