Examining an optical phenomenon that makes an observer look like an angel.
The aureole effect surrounding the photographer’s shadow. [Willowpix/Getty Images]
In summer 2019, I took a lake cruise with my wife. Having done our “Jack and Rose” moment from Titanic at the prow, we were near the bow as the ship pulled in to a stop, and I looked down at the water. There, surrounding the shadow of my head, was a series of wavering, ever-changing “rays” that originated somewhere within my head’s shadow. These moved along with my shadow, always centered on it, and gave me an air of undeserved sanctity.
I had seen this same effect many times before on looking into turbid water. It was clearly one of those optical effects, like heiligenschein, sylvanshine or a glory, in which the medium very nearly retroreflects light in such a way that it is centered on the observer (see “Mistbow Versus Glory,” OPN, January 2022).
This one was different, however. The other effects are circularly symmetric and unchanging, whereas this one took the form of discrete radial “beams” whose precise appearance and location changed with time. The effect wasn’t seen in clear or very shallow water, so it required water with some scattering material—yet not enough to make the water opaque. And it needed a bright light source sending parallel rays of light behind me.
In the aureole effect, parallel light rays striking the convex-upward surface of water that contains suspended matter are focused downward and scattered back—giving the appearance, due to perspective, of lines radiating outward from the antisolar point.
I later learned that what I saw is called the aureole effect. I don’t know who first called it that or offered an explanation, but the Dutch astronomer Marcel Gilles Jozef Minnaert did both in his classic 1954 book The Nature of Light and Colour in the Open Air, a wonderful treasury of atmospheric optical phenomena. An explanation also appears in Color and Light in Nature (1995, 2001) by David K. Lynch and William Charles Livingston and in Marine Optics (1976) by N. G. Jerlov, who cites Minnaert.
In essence, the explanation is that the water surface acts like a very irregular collection of lenses. Where the surface is effectively flat, or even concave relative to the air, no effect is seen. But in some locations where the surface is convex toward the air, light will be focused by these “lenses” into the water. It doesn’t matter if the radii of curvature at any point are different along different directions (which makes that local point effectively a toric lens). The net effect is that light focuses down along the direction the solar rays are traveling.
If there is suspended matter in the water—as required for the effect—this will scatter some of the light. Looking from the side, you would see a trail of scattered light proceeding from the water surface downward along a direction that is parallel to the direction of the sun’s rays striking the surface. It will be brighter and more concentrated in the vicinity of the foci, and then will decrease as you get farther from the surface as the light becomes less intense because it scatters and spreads out after being focused down.
The result will be a light “streamer” from the surface along the direction of the sunlight, eventually trailing out. Several such light streamers will each originate at a convex lenslet formed by the wave surface, all of them parallel to each other because they parallel the direction the sunbeams are traveling. The field of such streamers is constantly changing as the wave surface of the water changes, but the streamers will always look about the same, and lie along the same direction.
“The interesting and mysterious effect has a relatively simple explanation, even if an exact solution is unlikely.”
What does this look like from the observer’s point of view? The streamers of light will all appear to be lines radiating outwards from the anti-solar point, within the shadow of the observer’s head. This is a perspective effect, because the streamers, like the solar rays, are all parallel. Like the lines formed by the corners of a long hallway, they appear to be tending toward the same common point at infinity. The “end” of the apparent rays closest to the observer’s head thus corresponds with the deepest part of the “streamer” and the “end” farthest from the head is at the point where the ray enters the water.
Clearly, the effect will not be seen if the water surface is smooth, or if the scattering material is either too sparse or too dense. What’s more, it won’t be visible if the surface is too greatly disturbed.
In a 1984 paper in Izvestiya, Atmospheric and Oceanic Physics, V.P. Veber of the Institute of Atmospheric Physics, USSR Academy of Sciences, made a determined effort to place this effect on a firm mathematical foundation. The paper includes a series of equations expressing the intensity of the resulting streamers that, while rigorously correct, rely on several unknown variables, including the shape of the water surface and the density variation of scattering material. Those variables can, however, be calculated using appropriate models.
And so, the interesting and mysterious effect has a relatively simple explanation, even if an exact solution is unlikely.
Stephen R. Wilk (email@example.com) is with Xenon Corp., Wilmington, MA, USA.