Category Archives: rainbow and fogbow

Third and fourth order rainbow

In the late afternoon of July the 7th 2017 there were strong thunderstorms in the area around Berlin, Germany. AKM member Andreas Möller was driving trough heavy rainfall, when suddenly the sun came out. His report:

On my way home, I could observe a beautiful bright primary and secondary rainbow. It was still raining heavily and my intension was to observe the area towards the sun. Therefore I turned into a side street and stopped in front of an old industrial area.

Location details:

  • Ferdinand-Schultze-Straße 18, 13055 Berlin, Germany
  • Weather: Strong rain
  • Sun altitude: ~19°
  • Date: 2017-07-07
  • Time: 19:00 – 19:08 CEST


I took a lot of pictures in hope to get the third and fourth order rainbow. My equipment was a Nikon D750 with a Tamron SP 15-30mm f/2.8 at 15mm. The rain was strong and I had problems cleaning my lens from waterdrops. Later at home, I started to process the pictures directly. Amazingly, I could discover the third and fourth order in almost all of the pictures I took.

The image processing did clearly point out a colorful third and fourth order rainbow.

Processing details:

  1. stack of 8 frames
  2. unsharp masking (USM)
  3. contrast and light adaption with Photoshop
  4. unsharp masking with Photoshop


Here is another image processed out of a single RAW file. (USM)


Binary double rainbows


In past years I have done spot light rainbows when the rain was a fine mist. After seeing the results of a nice fog bow my LED flashlight made and since I had two I thought why don’t I try doing two at once. So I turned both lights on the hi-power mode which yielded a very bright beam of light and both lights were placed on fence posts 2 meters apart. I angled the lights so the beams crossed and at the point where they crossed is where I placed the camera. I took a shot was blown away by the results! There it was two full circle double rainbows crossing one another. I took quite a few shots before I was getting chill and wet. Just think if you landed on an Earth like exo-planet orbiting a binary star system and upon exiting your space craft you look up and see twin suns shining above then you hear a rumble of thunder. You retreat into your ship for shelter and later the storm moves on but its still raining but you look on the opposite side of the sky and see two double rainbows displaced a few degrees apart and the bows would cross one another. These flashlight binary double rainbows show how rainbows would look to civilizations living on Earth like Exo-planets orbiting double, triple, or even quadruple star systems. Next time I will use 3 and 4 LED flashlights. On the nights I was doing these bows the wind was blowing and I could see the primary bow in particular would move from side to side and one pic even shows that it could be twinned!!!

Author: Michael Ellestad, USA

Three possible photographic detections of the natural fifth order rainbow from Germany

In 2014, Harald Edens reported ten cases of photographically detected natural quinary rainbows, recorded during 2009-2013 in New Mexico, USA, at altitudes of 1.8-3.2 km. These and some newer observations can also be found on his website.

So far, no reports from other locations have been published. In the German observers’ network, we analyzed many candidate photographs showing bright primary and secondary rainbows, but from most of them no reliable traces of quinary rainbows could be extracted. Such analyses are not easy, as the quinary signal is weak compared to the neighboring secondary rainbow, and processing methods such as unsharp masking can cause a leakage of colors into Alexander’s dark band. Furthermore, the processing operator will experience disturbing afterimage issues from the intense renditions of the primary and secondary on the screen after a couple of minutes.

Despite these difficulties, we now believe that we have identified three cases of genuine quinary rainbows. In cases 1 and 3, the quinary could be extracted from several photographs. Nonetheless, in order to keep this blogpost brief, we restricted ourselves to show only one image (or the results from one polarization series in case 1) per observation. We chose a straightforward processing method (= only increasing contrast and saturation, no local filtering such as unsharp masks) similar to the one applied by Harald Edens to allow for an easier comparison with his results. Alternative processing routes will be presented at a later stage.

1) April 22nd, 2012, near Göttingen, Germany (51° 31’ N, 9° 58’ E, altitude 250 m), 19:16 CEST, sun elevation 10.2°, photographed by Frank Killich after a moderate shower

The original intention of Frank Killich was to use the primary and secondary rainbows as test objects for a home-built photopolarimetric setup made from a Canon 20D camera and a linear polarizer precisely rotatable by a stepper motor. By recording four successive images at polarizer positions of 0°, 45°, 90° and 135° with respect to the vertical, it is possible to reconstruct the first three components of the Stokes vector for each viewing direction (pixel coordinates) and color channel (red, green, blue) individually. These images can be numerically combined to reconstruct the unpolarized intensity (= the ordinary photographic result without a polarizer) and, moreover, the linearly polarized portion of the recorded light distribution (= the total intensity with the unpolarized background removed for each pixel). In the case of rainbows, this corresponds effectively to a subtraction of the radial (weak) component from the azimuthal (strong) polarization component equally all along the visible part of the circumference. As known from theory, also the quinary will be easier to detect in such a polarization contrast image.

Unpolarized intensity as calculated from the original images, f = 22 mm:


Unpolarized intensity, increased saturation and contrast:


Linearly polarized portion as calculated from the original images:


Linearly polarized portion, increased saturation and contrast:


The expected broad bands of green and blue are clearly visible in the processed linearly polarized portion picture, and might be slightly visible also in the unpolarized intensity.

The other two photographic observations were carried out without any polarizers, i.e. only the unpolarized intensity information is available in these cases.

2) March 20th, 2013, near Pforzheim, Germany (48° 56’ N, 8° 36’ E, altitude 312 m), 16:21 CET, sun elevation 21.1°, photographed by Michael Großmann after an intense shower

Original (Canon EOS 450D, f = 22 mm):


Increased saturation and contrast:


A slight green/blue hue is visible inside the secondary at and slightly above the horizon.

3) May 15th, 2016, Mt. Zschirnstein, Germany (50° 51’ N, 14° 11’ E, altitude 560 m), 19:57 CEST, sun elevation 6.2°, photographed by Alexander Haußmann after a moderate shower

A description of this observation (without discussing the quinary rainbow) can be found here. The images shown here are cropped from a fisheye photograph.

Original (Pentax K-5, f= 17 mm, cropped):


Increased saturation and contrast:


Again, a slight green/blue hue appears close to the horizon.

At this point it is of course not possible to draw any statistical conclusions about the frequency of detectable quinary rainbows. However, it seems worthwile that every rainbow observer re-examines his photographical treasure trove for previously overlooked rarities, even if no polarizer enhancement was involved during photographing.

Fogbows in Tenerife

11th of May, 2016  Roberto Porto observed in the Teide National Park (Tenerife, Spain) wunderful fogbows in top of a deeper cloud layer. The moderate climate of Tenerife is controlled to a great extent by the tradewinds, whose humidity is condensed principally over the north and northeast of the island, creating cloud banks that range between 600 and 1,800 metres in height. If moves out of the cloud layer as far as  you can see the sun, one has with the sun behind the best observing conditions for a fog bow.

As the name might suggest, a fogbow is the name given to a phenomenon created by the same process of refraction and reflection that creates rainbows, but formed instead by the water droplets in fog, mist or cloud, rather than raindrops.

The timelapse video show 3 different fogbows in the sea of clouds of Volcano Teide. The sun low in the horizon produced the beautiful fogbows.

Photo data: Nikon D5300 and Nikon D90 with Nikkor fish eye 10,5 f:2,8  and tamrom  18-200mm

Unpaired reflection rainbow


Webcam Cully at Lake Geneva on May 25th, 2016. By courtesy of

The ever growing number of webcams is worth to be checked for both common and rare atmospheric optics phenomena, e.g., like in the case of these twinned rainbow, rainbow at high and low sun (1234), red rainbows (1234) or moonbows (1234).

The Swiss webcam located in Cully at the North shore of Lake Geneva (Lac Leman) has shown a most unusual pair of images within 10 minutes on May 25th, 2016. Starting from the last image (see top right) taken at 20.40 Central European Daylight Saving Time we see fragments of a normal primary rainbow before sunset, which happened at 21.08 CE-DST. From its beginnings on the lake’s surface it is immediately slanted toward the antisolar azimuth in the East.

However, the image taken 10 minutes earlier (see top left), at 20.30 CE-DST, shows not just a weaker bow, but also, that it starts at the lake’s surface slanted toward the West, i.e. away from the antisolar azimuth!

This strange sight is an isolated reflection rainbow, which is also centered on the antisolar point, but, at the solar elevation of 4.9°, somewhat larger than a semicircle, thus explaining the odd slant at its foot. The missing of a normal rainbow (except of, may be, a slight trace) in this image can be explained by a very patchy type of rainfall or shadowing of the corresponding regions. Additionally, the images show hints of a reflected rainbow and a reflected reflection rainbow, respectively, projected on to the lake’s surface.

Authors: Elmar Schmidt and Claudia Hinz

Twinned rainbow from Russia


Twinned rainbow in Siberia, Russia in Original and with unsharp mask. Photo: Ivanna Dark

In June 21, 2016 Ivanna Dark observed Yurga, Kemerovo region in Western Siberia, Russia an clear twinned rainbow: “At 19:45 local time (UTC + 7) began to fall to the ground a few large drops of very weak rain. I decided to look at the rainbow, because I know that it will appear in the presence of the sun. Imagine my surprise when I saw that the rainbow has a certain strangeness. It was not a Supernumerary Rainbows, but seen clearly, that the top part split into equal pieces. Later I found out the name of this phenomenon – Twinned Rainbow. Although the rainbow was very faint and lasted about two minutes, it did not stop to notice the duality of top.”

Three quarters of a double rainbow, plus an accidental snapshot of a tertiary, Mt. Zschirnstein, Germany, May 15th, 2016

Over the past two decades it has become a tradition among my friends to carry out a bicycle tour to the Elbe Sandstone Mountains (“Saxon Switzerland“) at the Pentecost weekend. We then often pay a visit to a table hill named “Großer Zschirnstein“ (561 m), which features a remarkable cliff of 70 m in height at its south-eastern edge.

Almost 15 years ago, on the evening of June 3rd, 2001, we had the opportunity to observe from there a rainbow extending well below the horizon almost down towards its bottom. Unfortunately, we only had a compact camera without a fisheye lens at hand back then, so the old photos show only some sections of the whole phenomenon.

This year, on May 15th, we were finally granted the proverbial second chance. I already anticipated some rainbow potential in the “Icelandic” weather that day. In the early afternoon, there had already been a rain shower while the sun was shining, but as we had not yet ascended the mountain and the sun was still high in the sky, there was no chance for a rainbow observation.

Some minutes after reaching the plateau in the evening, we had to retreat to the shelter when a rather strong shower of hail and rain set in. To the west a stripe of clear sky widened, and sunshine seemed at hand soon. It took longer than expected, as the clouds were moving rather slow. On the left side, a small rainbow fragment suddenly appeared at the horizon, resulting from sunlit drops a few kilometers off. It was a rather unusual observation to see this rainbow streak vanish and reappear again, as its sight was repeatedly obstructed by scudding (and non-illuminated) mist around the Zschirnstein massif:


(19:42 CEST, f = 88 mm, Pentax K-5)

Finally the great moment came: Sunshine was reaching the Zschirnstein while the shower, now mostly composed of rain instead of hail, still continued. Within a few minutes we could enjoy this marvelous view:


(19:56 CEST, f = 10 mm / fisheye)

Unfortunately there was no safe way to access a viewpoint which would have allowed to study the missing quarter, as this would have required some careful climbing around the sandstone rocks for which I already felt too excited at that moment. The fisheye picture can hardly express how huge both rainbows looked like, and how beautiful the raindrop clusters glittered as they drifted around the cliff some 10 m further down. These are certainly the moments that make you understand that famous “double rainbow enthusiasm”, thought not everyone is as outgoing as other people on the internet. Maybe we also stayed a bit calmer because the strong and cold wind added a rather painful component to the taking of photographs and videos.

Later the right part of the primary close to the horizon became especially bright:


(19:59 CEST, f = 80 mm)

This photo has been processed in a way that no color channel reaches saturation, which is a necessary prerequisite for analyzing possible kinks in the rainbow. In this case, the red rim looks as if would bend inside a bit below the horizon, but this might only be an illusion due to the intensity gradient.

The primary’s right foot above the horizon remained still visible for a rather long time, as the shower withdrew in this direction:


(20:19 MESZ, f = 50 mm)

But the story does not end here. When going through the pictures later at home, I suddenly realized that I had missed to look for higher order rainbows, or to deliberately take some pictures in the appropriate directions. I was a bit disappointed about my inattentiveness, since this had been my best rainbow display in years and, moreover, I had not been hindered by the limited field of view from a window in a city building. I am often forced to decide between the sunward or antisolar hemisphere when observing rainbows from there.

Luckily I had taken two pictures (an exposure bracket) towards the sun just at the moment when the three-quarter rainbows started to evolve. The reason for this was only the lighting atmosphere – it was the moment when the sun rays had first reached the Zschirnstein plateau. As I deduced later from the movement direction of the shower, there had been rather good conditions for the formation of tertiary and quaternary rainbows when the picture pair was taken. So I decided to apply the strong filtering procedures which are needed to extract higher-order rainbows from photographs. The shorter exposure just gave noise in the interesting region. However, in the longer exposed version something interesting popped up.

Original image:


(19:54 MESZ, f = 17 mm / fisheye)

Processed image:


Slightly to the right above the stone pillar, a red-green stripe in the color ordering of the tertiary rainbow can be discerned. For an unambiguous identification it would, however, be necessary to calibrate the picture in order to assign scattering coordinates to the photo’s pixel matrix. Though I had previously calibrated the projection of the lens for the used focal length (the upper end of the zoom range), I would need two reference marks with known elevation and azimuth which are included in this specific photograph to complete the analysis. On the horizon, no distinct remote references could be found. This means that I would have to reconstruct my precise position on the plateau to minimize parallax errors, and then to record a starfield image from there at night, enabling me finally to use the stone pillar or nearby trees as references. Unfortunately, it would take an inconvenient amount of time to access the spot again and the effort for such a trip would be a bit over-the-top for the sole purpose of calibrating a photograph.

But there was still a piece of hope: From the shorter exposed version (-2 EV),  I could estimate the position of the sun quite accurately, as there is only a small overexposed area around it. This allowed me at least to draw lines of constant angular distance from the sun into the photograph in order to decide if the colored stripe appeared at the correct position or not. Using the previously measured spectral sensor response of my camera, and estimating the temperature of the water drops to be around 5°C, I derived the following values for the Descartes angles of the tertiary and quaternary rainbows: 41.7° / 43.7° (red, 620 nm), 40.6° / 45.1° (green, 530 nm), and 39.3° / 46.8° (blue, 460 nm). In the following animation, these angular distances from the estimated position of the sun have been marked by their respective colors:


The colored stripe seems to fit reasonably well to the Descartes angles of the tertiary rainbow, especially when taking into account that the positions of maximal intensity are shifted a bit inward from the Descartes angles for the tertiary (and outward for the quaternary) due to wave-optical effects. This shift was also noted in the analysis of the very first photograph of a tertiary rainbow. Further contributions form distorted drop shapes are of minor importance here, as the sun elevation is small and we are looking at the rainbow’s sides. Therefore the effective cross section of the drops should remain nearly circular, even if they are squeezed in the vertical. I leave it to the readers to decide if also traces of the quaternary might be visible among the color noise slightly to the left above the stone pillar.

Addendum: A short video clip from the observation can be found here.

Moonbow with Alexander’s dark band


On July 31, 2015 was a “blue moon” (second full moon in a month). The weather forecast for that night in Spain was storms and heavy rains. I was travelling from Madrid airport to the north of Spain. The first atmospheric phenomenon was a 22 degree halo that I photographed in the rural areas of Castilla. Then the storms began and the blue moon disappeared. At 5am I was already at my home in Villaverde, Leon. It was raining all night but then only for a few minutes the moon appeared again on the wester horizon and produced this double moonbow with Alexander’s dark band.

I created also a short timelapse video of a second  moonbow , late that night, just before dawn. Pictures taken with Nikon D5300, Nikkor fisheye 10,5 mm, f:2,8, ISO 400, 20 sec exposure.

Author: Roberto Porto, Spain

Oblique supernumeraries to the primary rainbow

August 1, 2015: Rainbow with oblique supernumeries. Photo: Claudia Hinz

August 1, 2015: Rainbow with oblique supernumeries. Photo: Claudia Hinz

Last fall, two AKM members observed a rainbow with supernumeraries, which were clearly oblique to the primary rainbow.

On August 1, 2015, they were observed by Claudia Hinz on a red rainbow just before sunset in the Fichtelgebirge / Erzgebirge mountains. A rain front had just passed and the last precipitation from the departing clouds evaporated in the air, so that the raindrops did not reach the ground anymore. Virga were clearly visible and at the same time an intensive Zero order glow could be seen at the Sun side.

On October 5, 2015, Sirko Molau observed in Günzburg/Bavaria a similar phenomenon. Also here the rain shower had already passed and a strip of blue skies was visible near the horizon. Over one hour after the rain Sirko was surprised to see a bright rudiment of the rainbow. On the first glimpse it looked like a split rainbow. However, a closer look revealed that two interference bows disemminated obliquely from the root of the rainbow.


October 5, 2015: Rainbow foot with oblique supernumeries. Photo: Sirko Molau

The oblique interference arcs can be explained best with different raindrop sizes. In both cases, the rainbow appeared after the rain had disapperead and just when the Sun showed up. We can assume that dry air had already moved in, causing the last drops to evaporate on their way to the ground. So the raindrops quickly reduced in size after they left the cloud. The simulation of Les Cowley shows that with reduced drop size not only the number, but also the distance of the interference bows decreases.

Authors: Claudia Hinz, Sirko Molau, Germany

Reflected Sunlight Dewbow


Reflected Sunlight Dewbow. Photos: Jérémie Gaillard

On August 19, 2010, Jérémie Gaillard made an interesting discovery when looking at the surface of the lake Etang de l´Alleu which is located in the French community of Saint-Arnoult-en-Yvelines. The water was covered with pollen, on which droplets of dew had formed. In these droplets two colourful rainbows were visible. Dewbows can be understood as the lower part of a rainbow projected onto a horizontal plane. When a dewbow is fully developed, a semi-circle which opens towards the sides should be visible, the apex of which is situated at the lower end of the observer´s shadow. Equivalent to normal rainbows, primary and secondary dewbow should run parallely, but in Jérémie Gaillard´s observation they did not.

Instead, the second colourful bow fragment is a reflected sunlight dewbow. The surface of the water acts as a large mirror reflecting the sun. The reflected image of the sun now acts as a second source of light, which is situated as far below the horizon as the sun is above it. (angle of incidence = emergent angle). So the antisolar point for the reflection of the sun is above the horizon. This reflected antisolar point, which is located the double of the real sun´s elevation above the antisolar point, is the centre of the two rainbow circles for the reflected sunlight. So the additional rainbows are displaced upwards by the double sun elevation compared to the primary and secondary rainbow, making a rather unfamiliar appearance in the open nature.

Author: Claudia Hinz