# Ivars Peterson's MathTrek

September 20, 2004

## Sunlight Speckle

As a physics teacher in the 1970s, I had access to a classroom laser. One of the many wonders that I and my students could observe was the distinctive pattern of rapidly shifting speckles—tiny bright red and black spots—when the laser's red light illuminated a small patch of white paper or a painted wall. You can see the same effect today with a simple laser pointer.

A laser produces light of a single wavelength, originating from a single point in space. When this light reflects from a surface that isn't completely smooth, the waves no longer line up perfectly. These scattered waves interfere constructively (where crest meets crest) to create red spots and destructively (where crest meets trough) to create dark spots.

Interestingly, what you see depends on your eyesight. People with excellent vision often see no motion at all and sometimes have trouble seeing the speckles. When a nearsighted person moves his or her head, the speckles tend to move opposite to the head motion. The reverse is true for farsighted people.

The idea of optical speckle isn't new. In 1871, Lord Rayleigh (1842–1919) described how coherent light would show random intensity fluctuations when scattered from a rough surface. At the same time, he concluded that, because available light sources, including sunlight, lack coherence, it wouldn't be possible to observe speckle.

It wasn't until the invention of the laser in 1960 that it became easy to see the speckle pattern that Lord Rayleigh had predicted would occur.

Contrary to what Lord Rayleigh expected, however, it's possible to see speckle in sunlight, says Stewart McKechnie of ITT Industries.

Under suitable viewing conditions, you can see a speckle pattern created by sunlight scattered from a rough surface.
Credit: Stewart McKechnie

McKechnie first became interested in the topic in the 1970s when he did a PhD thesis on how to get rid of laser speckle. He then worked out and published a theory describing the conditions under which speckle would be observed when light has an arbitrary state of coherence. His theory showed that, under the right conditions, it would be possible to observe sunlight speckle.

Although sunlight is composed of light of many different wavelengths, you can minimize the impact of this factor by looking at a surface with a fine roughness structure, McKechnie says. And, even though the light doesn't come from a point source, the sun's width extends only a half-degree across the sky, as seen from Earth.

To view high-contrast sunlight speckle, four conditions must be met, McKechnie says.

1. The surface should be rough, but not too rough.
2. The surface should be placed as close to the eye as possible, consistent with being able to maintain good focus. (Reading glasses help.)
3. The viewer should have reasonably good eyesight, free of significant astigmatism.
4. The surface should be viewed from the direction in which the sunlight would reflect if the surface were smooth and mirror-like.

Arrangement for viewing sunlight speckle.
Credit: Stewart McKechnie

On a bright, sunny day, you can see sunlight speckle simply by looking at your fingernails from close range. "Fingernails have ideal surface roughness, rough enough to eliminate most of the specular reflection but not too rough," McKechnie says.

The effect would be even stronger if you were on the surface of Pluto, where the sun would be just a tiny (but dim) point of light in the sky. The optical geometry suggests that a standing, 6-foot person would be able to see a distinct speckle pattern on the ground, McKechnie says.

Back in the physics classroom, McKechnie's findings provide a nice excuse for going outdoors on a bright, sunny day.