Michael Theusner / Applied Optics

A third-order and fourth-order rainbow can be seen at the center of this photograph, taken from the countryside in northern Germany. The tertiary and quaternary rainbows appear on the sunward side of the sky, rather than the opposite side of the sky, as is the case for primary and secondary rainbows. This is the first picture of a quaternary rainbow in nature, and the second picture ever of a tertiary rainbow.

Look out, Double Rainbow Guy: You just might have a double-double freakout over this first-ever picture documenting a quadruple rainbow, which is the subject of a scientific paper in the journal Applied Optics.

Seeing two rainbows in the sky is a visual treat, leading a YouTube user named Paul Vasquez to rhapsodize to the point of tears. But three or four rainbows at the same time? That's the stuff of legend. Triple-rainbow reports have been bubbling up since the days of Aristotle, but only five reports from scientifically knowledgeable observers have been recorded during the past 250 years.

Not until this year has a triple rainbow or a quadruple rainbow been photographed and published in the scientific literature.

Such rainbows are more technically referred to as tertiary or quaternary rainbows. Like the better-known primary or secondary rainbows that Vasquez gushed over, these rare rainbows appear when sunlight bounces around the inside of a raindrop, is refracted and spread through a range of visible-light wavelengths and shines out to the observer as a multicolored arc in the sky.

The light beams that creates single or double rainbows take one or two bounces inside the raindrop, as shown in this diagram, and they're always visible in the part of the sky opposite the sun. In contrast, third-order and fourth-order rainbows require a triple or quadruple bounce, and appear on the sunward side of the sky, at angles of 40 and 45 degrees with respect to the sun.

That makes it well nigh impossible to capture all four rainbows in the same picture — and because some light is lost with each bounce, the third and fourth rainbows are incredibly faint. Even if there are raindrops in the right place, the effect is easily overwhelmed by the sun's glare.

Last year, U.S. Naval Academy meteorologist Raymond Lee and a colleague, Philip Laven, laid out a prediction for the conditions that would produce third-order rainbows, and they challenged rainbow-chasers to go out and find one. Among the requirements: dark thunderclouds, and either a heavy downpour or a rainstorm with nearly uniform rain droplets. If the sun broke through the clouds under these conditions, it could project a dim tertiary rainbow against the dark clouds nearby, they said.

Michael Grossmann / Applied Optics

Michael Grossmann's photograph of the skies over Kampfelbach during an evening rain shower is at left, with two points marked A and B as a reference for image orientation. A processed version of the image is at right, revealing a faint tertiary rainbow between the white arrows.

Some experts thought it'd be impossible to make out the rainbow, but amateur rainbow-chasers rose to the challenge. On the evening of May 15, the required conditions came together for Michael Grossman, an observer in Kampfelbach in southwestern Germany. He turned toward the sun and started snapping pictures where the tertiary rainbow should have shown up.

"It is really exaggerated to say that I saw it, but there seemed to be something," he said in an Optical Society news release.

When the pictures were put through contrast expansion and unsharp masking, the faint arc of the tertiary rainbow came through.

Grossmann's feat made an impression on another German rainbow-chaser, Michael Theusner, and he had his camera at the ready on the evening of June 11 when a rainstorm came toward his home in Schiffdorf in northern Germany. Here's how he described the event to me in an email:

"Actually, the chasing started as a normal storm-chasing effort. I was on my way home when the storm front approached from the southwest. A nice shelf cloud had formed at the base of the storm, and I hurried home to fetch my camera (Canon 40D + Canon EF-S 17-55 mm lens) to take some photos. Then I went to a nearby field road, where you have an unobstructed view of the sky. However, when I finally reached that location, the shelf cloud had largely disappeared. So I was disappointed at first, but hoped for the rear of the storm to show some interesting cloud features. So I waited while heavy rain was falling.

"When the sun started to come out, I realized that the situation was just like the one Michael Grossmann had had when he took the first photo of the third-order rainbow. I had read about his observation on June 3 in a German Internet discussion forum for atmospheric phenomena — only about a week earlier. Thus, I tried to catch that rare rainbow, too.

"I had asked Michael Grossmann in the forum whether or not he had taken several images so as to stack them to increase the signal-to-noise ratio — a technique well known to amateur astronomers like me. Using that technique, it is possible to increase the visibility of faint signals in images. Unfortunately, he had not. I decided to use that technique to increase the chances to record the third-order rainbow. I took several image series until the rain stopped at my location. I did not see that rainbow visually.

"Back home I started processing, and already the first image series that I took when the sun brightly lit the raindrops showed the third-order rainbow! I was excited and started converting and stacking the order image series. One of them looked strange, however. Another rainbow was visible just to the third-order bow's right. Fainter, but still visible. I checked the Internet for higher order bows and quickly realized that that image series likely showed the fourth-order rainbow. I roughly calculated the radius of that bow and it matched the predicted location of the quaternary bow.

"I was stunned, as I discovered that this was very likely the very first image in the world to show this rainbow."

Theoretically, it's possible to have a quintuple or a sextuple rainbow, but the optical geometry of the bounces within the raindrop is such that the fifth- and sixth-order rainbows would be overwhelmed by the light from the first- and the second-order rainbows. "So it may never be possible to image those," Theusner said.

The research papers describing the observations, and providing guidance for future rainbow-chasers, appear in a special issue of Applied Optics. The bottom line is that the phenomenon is too dim to see with the naked eye, "with the possible exception of very rarely combined circumstances of favorable illumination, background and the strength of rain," Grossmann said. You'd have to point your camera in the right direction without actually seeing the bow, and then do some heavy-duty image processing. But Grossmann and Theusner have proven that it can be done. And for Lee, the meteorologist who issued the original challenge, that's like a ray of sunshine.

"It was as exciting as finding a new species," he said.

More about atmospheric phenomena:

• Strange optical illusions and light shows
• 'Tis the season for sky oddities
• Somewhere under the moonbow
• Two 'suns' spotted in China defy explanation

Here are the three papers published this week in the Applied Optics, the journal of the Optical Society:

• "Visibility of Natural Tertiary Rainbows" by Raymond L. Lee Jr. and Philip Laven
• "Photographic Evidence for the Third-Order Rainbow" by Michael Grossmann, Elmar Schmidt and Alexander Haussmann
• "Photographic Observation of a Natural Fourth-Order Rainbow" by Michael Theusner

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