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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:

2012_04_22_3541_S0

Unpolarized intensity, increased saturation and contrast:

2012_04_22_3541_S0_b

Linearly polarized portion as calculated from the original images:

2012_04_22_3541_LPA

Linearly polarized portion, increased saturation and contrast:

2012_04_22_3541_LPA_b

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):

2013_03_20_05

Increased saturation and contrast:

2013_03_20_05_b

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):

2016_05_15_IMGP6762_A

Increased saturation and contrast:

2016_05_15_IMGP6762_A_b2

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.

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3rd and 4th order rainbows – technical details

The lens has a distortion, but nevertheless I tried to compare the width of the first, second and third order rainbows. I selected three fragments, each of them at an approximately identical distance from the center of the photo to get an identical distortion.
The first order rainbow has supernumeraries.
The second order rainbow seems to be wider than that of the first order.
The width of the third order rainbow appears the same as or greater than that of the second order rainbow. The digital colour noise didn´t allow an exact comparison.
I tried to calculate the width of the rainbow, it seems to be between 1 and 5 degrees, but I think it is probably 2 or 3 degrees (graphic 1 and 2).
 
I estimate the radius of the third order rainbow at about 39 to 43 degrees, with the blue colour at 39 and the red colour at 43 degrees. It seems to me that the brightest part of the rainbow had a radius of 41 degrees, but it also was very faint. I don´t know which colour corresponds to this radius, I think it is green or perhaps yellow. It is difficult to see because of the colour noise.
Author: Sergei Antipov, Russia

Third and Fourth Order rainbow in Russia

Sergei Antipov observed on June 22, 2013 in the Vladimir region, Russia (100km from Nizhny Novgorod city) beside a primary and secondary rainbow, the rainbow third and fourth order too.

Time: 14:00 (UTC + 4h)

Weather condition:
+20.1ºС, relative humidity 98%
atmospheric pressure 747mmHg (normal at 82m is 752-753mmHg)
Min/Max: +14.0º / +20.8º
Rain during the day: 3 times, thunder-storm and heavy rain.
wind: in the morning northern, in the afternoon and in the evening eastern
Light breeze, 1 – 3 meter per second, gusts were not stronger than 10 meters per second

Photo time with 1st and 2nd order rainbows: 19:37 (+4)
Photo time with 3rd and 4th order rainbows: 19:47 (+4) (1st, 2nd were visible too)
sunset: 21:52 (+4), azimuth 315º
sun azimuth @ 19:47 291º, height 15º

In late afternoon there were black clouds that came from the east (usually cumulonimbus comes from the west). Cumulonimbus covered almost all the sky and although it was not raining, there was a bright primary and a good secondary rainbow. The sun was covered by clouds. You can see that on a roof of the house there is no shadow. But two rainbows were visible and were bright!
10 minutes later there was bright sunshine (you can see a shadow on a roof of the house).
The sun appeared at 19:47. Till this time the sun was hidden).
The rain began at about 19:45. 3rd and 4th rainbows are photographed from under an umbrella.
But the rain was very weak. From the sky rare droplets of water fell.
Even the roof of the house remained dry (but with traces of drops).
At this moment the rare rainbow also was observed.
The heavy rain began much later (>20:00)
The sun became covered by a cloud, and the first rainbow gradually disappeared.

Chronology:

  • Good weather (the last hour)
  • clouds (from the East) and sun (in the west) ~ 19:00
  • dark clouds (sky half) and sun ~ 19:20
  • gray clouds (3/4 of sky) and NO sun, No rain (Or very slight rain that I didn’t feel it) = 19:37
  • Beginning of observation of the first rainbow (without rain and without sunshine) within a few minutes there was a sunshine
  • very dark clouds (more, than 3/4 of sky) and bright sunshine (the sun shone from beneath a cloud border)
  • Slight rain (isolated droplets)
  • photo of observation of 3rd rainbow at 19:47

The panorama is made of two photos with an interval 10 minutes; photos are made from different places (about 10 meters). The lens has a bad distortion towards the edge…

Weather that evening was unusual. Cumulonimbus clouds came from the East (usually they come from the West). Therefore I well remember that evening.

The Quality of the original photo is not really good therefore all colors of a rainbow are visible only on “psuedo-HDR” processing (combination of 15 files from one raw with different parameters of brightness, contrast, an exposition and a saturation (12).

From one file it is difficult to receive such picture: red color smoothly passes in green color without orange, without the yellow (edited photo).

Each method of processing has the merits and demerits. For example, processing in the LAB mode very well showed 4th order, but a bad color rendition of 3rd order rainbow.
Processing with imaginary hdr shows 4th worse, but much better color at 3rd order rainbow.

This sketch show the most interesting moment.

My 3rd and 4th order rainbows are very similar to rainbows of Michael Theusner: strictly at level (at height) the sun, rainbows seem vertical. From below and from above, rainbows sharply are rounded. This effect (I think) is explained by that rainbows have the best brightness at sun height. Very much reminds ice halo: at it too (very often) the brightest piece at the left and to the right of the sun.

Nicolas Lefaudeux invented a search method 3rd order rainbow. His method is outlined here and given in more detail.

I used an other (own) method. It is a Processing scheme to find a rainbow in the photo from one 16bit tiff file from RAW (in LAB mode in Photoshop):
RAW file -> Lightroom3 -> zeroed preset -> 16bit tiff file -> Photoshop -> LABmode

I don’t think that my Processing scheme can be suitable for all photos of other photographers.
But, this method very well shows rainbows in my photo (Frankly speaking, I couldn’t repeat Nikolos’s method – I am the novice user of photoshop 🙂 ).
For faint Rainbows it is necessary to work with layers of A and B (in LAB mode).
You can see a layer “L” on this picture and here the result of work with use of my method.

Author: Sergei Antipov, Russia

Related Post: Natural tertiary rainbow 3rd order

“Spektrodrom” – A Laboratory of Rainbow

The simulation of rainbows of many orders with hanging or standing water drops and laser light is straightforward, but often unrealistic due to deformation of the drops. Therefore, a modern version of Billet’s experiments was designed, which uses a laminar cylindrical flow of water, and white light by just a few pixels of a video projector. It is surrounded by a circular projection screen. Using slightly skewed rays, which are therefore “climbing” up the cylindrical beam of water and exiting from it in proportion to the number of partial reflections, is able to produce a simultaneous display of the first six rainbow orders in white light.

The 2nd and 3rd order.

The 1st, 4th and 5th order.

The first 4 orders.

Both 1st and 2nd orders.

Both 3rd and 4th orders.

The first six orders.

Animation about the different refraction angle beetween salty water and fresh water.

Author: Michael Großmann, Kämpfelbach, Germany

3rd and 4th order rainbows

Last evening (11 June 2011) thunderstorms approached my home town Schiffdorf near Bremerhaven in Northern Germany. I went to a field road by car to take some photos of the storm clouds. Just after I had arrived (about 18:00 UTC), heavy rain started which lasted for nearly 20 minutes. To my disappointment, the rain covered the gust front and most of the interesting features of the storm. So I waited and hoped that the sun would come out soon and produce some nice rainbows. When it did I realized that the dark clouds covered the sky to the right of the Sun – just the situation Michael Großmann had had when he took the the first image of a 3rd order rainbow only four weeks ago. I decided to try this out as well. Instead of one image I took sequences of five to stack them and, thus, increase the signal-to-noise ratio. I hoped this would increase my chances to detect the 3rd order bow. I took the images from my car through the open window to protect my camera (Canon 40D) from the rain. Visually, I did not see a 3rd order rainbow. However, in my back, the 1st and 2nd order bow developed nicely.

Back home I converted the raw images to 16-bit-Tiff and stacked them in Photoshop. Adjusting saturation already showed the 3rd order bow in the image sequences taken between 18:17 and 18:22 UTC (first image).  Applying unsharp masking revealed something unexpected in one of the stacked images (from 18:19 UTC): There seemed to be another rainbow close to the 3rd order bow, but, with reversed colors (second image). I checked Les Cowley’s website and realized that my image likely showed the 4th order rainbow!

After some more sophisticated processing including denoising (Neat Image), unsharp masking and increasing saturation, the 3rd and 4th order rainbows both were clearly visible. Finally, I created a composite using masks to retain the natural look of the foreground while still showing the 3rd and 4th order rainbows (third image).

Author:  Michael Theusner, Bremerhaven, Germany

Natural tertiary rainbow 3rd order

On May 15, 2011, a rain area moved from north to south. When it started to rain at my position, I immediately rushed to my observing site which is reachable within 2 minutes for me.

Once there, I saw beautiful specimen of the primary and secondary rainbow. During my observation,  the rain intensified, and now I knew hat I had to look for!

On the left side of the sun there was a relatively dark cloud bank providing ideal conditions for a possible sighting of the 3rd order rainbow.

In fact, I had the idea of seeing a very faint arc at the expected position of about 40° away from the sun. It is really exaggerated to say that I saw it, but there seemed to be something.

I went into the shadow of a tree in order not to be blinded by the sun.

Now I did not take any care to protect the camera from the rain, I just had a little box with me to put the camera into. The arc could not be seen for more than 30 seconds, but I´m sure there was something at that position.

As under those lighting conditions a correct exposure is hard to get, I took my photographs in RAW mode. All the “little helpers” of the camera had to be set off.

To my disappointment, I did not find anything at the expected position when examining my pictures on the PC screen. But when putting an unsharp mask over the pictures, I saw it immediately. A bow! You can see that the outer part of the bow is slightly red and the inner part is light green.

Here is an animation showing the original image and three different settings: Unsharp mask, intensified colours and inverted.

If you need more information about the measurements of this tertiary rainbow, take a look at this pdf-file written by Dr.Alexander Haußmann. Thank you very much for your calculation!

Author: Michael Großmann, Kämpfelbach, Germany

High order bows

A rainbow is a product of millions of falling raindrops interacting with sunlight. A single reflection form the primary bow, a double reflection forms the secondary bow. However, under ideal conditions there can be many more orders of reflection. As shown above, five, six and even ten internal reflections can be observed. Moreover, it’s theoretically possible to detect twenty internal reflections, but the problem is to produce a perfectly spherical water droplet. The drops I used for this experiment were formed artificially. The light source is a 5 mW green laser pointer. Note that the bright spot at left center is the laser illuminated water drop.

The third and fourth order reflections aren’t shown here because they, along with the seventh and eighth order reflections, are positioned on the other side of the picture in the direction of the light source. The primary and secondary bows will be viewed in the direction you’re facing opposite the sun The fifth, sixth, ninth, and tenth order reflections are also in this direction. However, the third and fourth (as well as the seventh and eighth) order reflections can’t be seen because they’re behind you.

Under exceptional atmospheric conditions it may be feasible to see the third and fourth order bows if you’re facing the sun, but they’re quite faint. A third order bow, for instance, is one quarter as bright as a primary bow. A fifth order rainbow is only about one tenth as intense as the primary bow.

If you need more information about the experiments with high order bows, you can read this pdf.

Nikon D40X, focal length 18mm, 100 ISO, 2,5 sec. at f/6,3

Author: Michael Großmann, Kämpfelbach, Germany

Tertiary Glass-Sphere Bow

I have discovered a spectral reflection phenomenon inside a transparent plexiglass-sphere. The phenomenon, of which I am almost sure it is NOT the equivalent of the Primary or Secondary Rainbow, is in fact the equivalent of the Tertiary Rainbow, visible as a bright illuminating spectral colored ring all along the limb of the sphere. To see this ring, one should look “from behind” the sphere, toward the sun, with the sun “in front” of it (appearing exactly “in the centre” of the sphere).

The photo show the sphere with appearance of the red component of the spectrum. The distance of the observing eye (or camera’s lens) to the sphere is VERY important, because the focal point of the ring is not a point, it’s a spectral colored line (red at the far end, blue at the near end).

As far as I know, no one has ever observed or photographed the ring-like appearance of, what I call, the Tertiary Glass-sphere Bow (which has a focal point or “line”, behind the globe!).

Author: Danny Caes, Ghent-Belgium