THE FIRST GAS LASERS (some 20 years ago) not only made laser light but also called attention to a curious phenomenon: when the light fell on a surface, the surface often had a granular or speckled appearance. The speckled pattern, now simply called speckle, was surprising even though similar patterns had long been observed on surfaces illuminated by sunlight. Speckle appears whenever laser light scatters from a surface whose irregularities are about equal to the wavelength of the light. Speckle from sunlight normally passes unnoticed because of its faintness and lack of contrast and motion. Recently, however, Robert N. Sollod, a professor of psychology at Cleveland State University, described to me an optical effect that I believe is a kinetic example of sunlight speckle. When he puts a spoon with a shallow puddle of coffee with cream in it in direct sunlight, he observes a dynamic, colorful array of flashing points moving randomly through the fluid. The ; array seems to me to be speckle created by the scattering of sunlight from the colloidal particles in Brownian motion in the liquid. Previous studies have suggested that such an effect would be unlikely or even impossible. If my interpretation is correct, Sollod's demonstration may be the only one in which Brownian motion can be detected by the unaided eye.

A sheet of ground but otherwise transparent glass will help to explain speckle. A laser beam travels through the glass and illuminates a screen or a piece of photographic paper some distance away. Think of the initial beam as consisting of many parallel rays, with a wave propagating along each one. A unique characteristic of a laser is that the process whereby the atoms in the laser medium are made to emit light guarantees that the waves are all in phase, that is, they are all in step as they cross an imaginary line perpendicular to the beam. Such light is said to be coherent. Light from other common sources, such as an incandescent bulb, is incoherent. The waves crossing the imaginary line lack a fixed relation in phase and constantly shift in the difference between their phases.

Laser light passing through the glass scatters from the rough surface of the ground side of the glass. The scattered rays are no longer in phase and are unlikely to be traveling in the same direction. The change in phase is caused by the slight variation in the thickness of the glass because of the irregularity of the ground surface. The speed of light is effectively slower in glass than it is in air because of the time required for the light to interact with the atoms in the glass. The thicker the glass is, the more time is lost to the interactions and the longer the light takes to pass through the glass. Since the surface of the ground glass is rough, the rays emerging from the surface of it have passed through the glass with a variety of transit times. Hence they emerge with a variety of phases.

An example of what might happen is shown in Figure 2. Two waves traverse a sheet of glass that has a "step" on one side to represent roughness. The waves enter the glass and travel through it exactly in phase. Within the glass they are reduced equally in wavelength (because of the effective slowing of the light), and once they emerge they again have their former wavelength. For the sake of simplicity they are shown emerging with no change in their direction of travel. Because of the roughness of the glass one ray emerges exactly out of phase with the other. (This is one of many phase differences the waves could have.) Such a difference in phase determines how the waves interfere with each other at the screen.

Consider light reaching a particular point on the screen after emerging from points A and B on the ground glass, as is shown in Figure 3. If the waves arrive exactly in phase, they interfere constructively, giving rise to the maximum possible brightness. Because of the rough surface of the glass and also because of the different distances from A and B to the point on the screen the rays are unlikely to arrive at the point exactly in phase. Their interference probably results in a brightness that is less than the maximum. If they arrive exactly out of phase, they interfere destructively, giving rise to darkness at the point.

All the points on the ground glass contribute light waves to the point on the screen. The waves interfere with one another to determine the brightness perceived at the point. Other points on the screen also receive rays of light, which also interfere. The result is that the screen is dappled with a complex array of bright, dim and dark regions. This is the speckle pattern. It lacks any regular design partly because the surface of the ground glass lacks any.

The brightness at a given point on the screen remains constant only if the rays maintain a constant phase relation. If a wave crest emerges from A whenever a wave trough emerges from B, the rays from the two points always interfere in exactly the same way at the screen. If the phase relation shifts, the interference varies. A rapidly shifting relation causes a rapidly varying degree of brightness at the point. Since the eye and the brain average the brightness over many fluctuations, the pattern disappears, and the screen appears to be uniformly illuminated.

When an ordinary light bulb is substituted for the laser, the speckle pattern vanishes. Although at any given instant the

light rays emerging from the ground glass have some particular phase relation with one another, the relation changes randomly in the next instant. The speckle pattern therefore varies randomly. The perceptual apparatus averages the patterns over time, and so no trace of an interference pattern remains (which is fortunate, because otherwise every common light source would coat its surroundings with speckle patterns).

Speckle patterns can be seen in light from a source other than a laser if the source occupies a sufficiently small angle in the field of view. For example, speckle can be seen in sunlight because the sun is a light source only .5 degree in diameter. A distant pinhole can serve the same purpose. (Although the pinhole might be illuminated by a light bulb, speckle can still appear if the pinhole subtends only a small angle as it is seen from the screen.)

The speckle pattern from sunlight or a pinhole illuminated by white light is complicated by the fact that the light consists of the full visible spectrum. It is simpler to consider light filtered to a single wavelength. The creation of speckle by a nonlaser source depends on the spatial coherence of the light rather than on the temporal coherence. Suppose you could sample the light passing a particular point on its way to the ground glass. Temporally coherent light would show at the sampling point a continuous variation between crest and trough, meaning that the frequency of the wave is constant. Such light must originate in a laser because there are no such naturally occurring sources on the earth.

Suppose you also sample light simultaneously at another point equally distant from the source. If you find that the waves passing the two sampling points maintain some particular phase relation, the light is said to be spatially coherent. (Sometimes it is said to be transversely coherent.) For example, if a wave crest passes through one point whenever a wave trough passes through the other, the two waves are spatially coherent. The measure of the extent of spatial coherence is the distance by which the two sampling points can be separated without destroying the fixed phase relation. The contrast of speckle depends on the extent of the spatial coherence of the light. Since laser light has great spatial coherence, it yields high-contrast speckle.

Light from a pinhole illuminated by a bulb has some spatial coherence if the pinhole is relatively distant from the sampling points. The smaller the angle the light occupies in the field of view from the sampling points, the greater the spatial coherence of the light. When light traveling from a distant pinhole passes through ground glass on its way to a screen, it creates a speckle pattern of interference.

At any given instant the rays from the glass all have some phase relation. An instant later the light has no particular phase relation to the earlier light, but still all the rays emerging from the glass have the same phase relation to one another. The interference pattern is maintained and perceived.

As the pinhole is brought closer to the ground glass the light illuminating the glass becomes less spatially coherent and the contrast of the speckle wanes. Eventually the spatial coherence is essentially lost. Then the rays emerging from the glass have no fixed phase relation and the speckle pattern disappears.

Speckle was first studied in the reflection of laser light from a rough surface. When spatially coherent light reflects from the surface, the rays of light reaching an observer have traveled over paths of differing length. Although they may have approached the surface while they were exactly in phase, they are no longer all in phase when they reach the observer. Hence they interfere with one another at the observer's retina.

White light from a pinhole or the sun provides a multicolored speckle pattern because the light has a broad spectrum of colors. The ultimate phase difference of the interfering rays depends partly on their wavelength. Therefore a slightly different speckle pattern appears for each color in the spectrum. The result is colorful but lacks contrast.

Eugene Hecht of Adelphi University employs a black viewing surface to see speckle patterns in sunlight. Spray flat-black paint on smooth paper. Examine the illuminated paper at an angle of about 45 degrees. With a little practice you can see a multicolored, fine-grained pattern on the black surface. Hecht suggests that once you have seen the pattern you will also see it on many common objects illuminated by direct sunlight. His examples include "a tarnished coin, the weathered hood of an old car and even a fingernail."

Vincent P. Mallette of the Georgia Institute of Technology has described a speckle pattern in the light from a carbon arc. Speckle appears if the scattering surface is relatively distant from the arc. As the surface is brought closer to the arc the light falling on the surface becomes progressively less coherent spatially and the pattern disappears.

The apparent size of the elements in a speckle pattern derived from a reflection depends in part on the aperture of the eye. When the pupil is wide, rays of light within a large range of angles can enter the eye. They interfere with one another at the retina to create a pattern with relatively small elements. With a narrower pupil the range of angles of the rays decreases. Fewer rays enter the eye, and they generate at the retina a less complicated interference pattern with larger elements.

You can demonstrate how the speckle size depends on the size of the aperture through which the pattern is observed. Examine the size of a speckle pattern arising from reflection as you sight through an aperture that can be varied in size. As you decrease the aperture the speckle elements should appear to grow larger.

When either the observer or the reflecting surface that exhibits speckle moves quickly perpendicular to the observer's line of sight, the speckle pattern disappears. Within the averaging time of human perception the moving speckle pattern smears into what seems to be a uniform reflection from the scattering surface. If the motion is slow, however, the speckle pattern usually seems to migrate across the surface. The movement can be to the left or to the right.

The early reports of speckle attributed the direction of movement to the condition of the observer's vision. If the observer moves his head to the right (or the reflecting surface moves to his left), a nearsighted observer sees the speckle migrate to the left. For a farsighted person it moves to the right.

In the early explanation the apparent motion was attributed to parallax, which displays its effect when you can see two objects, one near and one far. Move your head to one side. The objects do not retain their alignment. You might interpret the realignment as an apparent motion of one or both of the objects. If you do assign motion to them, the nearby object will be given a motion opposite to the movement of your head. The more distant object will be assigned a motion that is in/the same direction as your head. In truth neither object moved. Given enough clues you know this, but without clues you might believe the objects really did move.

In the demonstration of speckle motion the apparent motion derives from the accommodation (focusing) of the eye. A person with far sight or normal sight can accommodate to focus a distant object on the retina. When the perception lacks clues to the distance of the object, the brain allows the eye to focus as if the rays were coming from a considerable distance. This is what happens when a farsighted person or one with normal vision studies a speckle pattern. The speckle is truly a pattern created directly on the retina, but the insufficient accommodation of the eye gives the illusion that the pattern is distant.

In this situation the screen is closer to the observer than the apparent position of the pattern. When the observer moves his head to one side, the more distant object (the speckle pattern) appears to move in the same direction. If the reflecting surface is moved perpendicular to the line of sight of a stationary observer, the speckle appears to move across the screen in the opposite direction.

A nearsighted person cannot focus on an object at a large distance. Suppose the screen is beyond the maximum focusing distance for such an observer. The speckle pattern will be interpreted as lying at the maximum distance of focusing. When the observer moves his head, the closer object (the speckle pattern) seems to move in the opposite direction.

In 1965 Douglas C. Sinclair of the University of Rochester pointed out that this explanation is incomplete for a person with normal sight. Under proper conditions the apparent motion of the speckle pattern for such a person depends on the color of the light. In the early days of gas lasers all the laser emissions were in the red. Reports on the apparent motion of speckle assumed that the same results would be obtained with other colors. Discrepancies appeared, however, when lasers emitted in the blue and green.

Suppose a person with normal vision examines the apparent motion of two speckle patterns, first one from a blue laser beam and then one from a red laser beam. The person is to focus on the scattering surface, which is also illuminated by ambient white light from the room. The red speckle pattern appears to lie behind the scattering surface and the blue pattern in front of it.

The difference arises from the chromatic aberration of the eye. Light of a long wavelength (such as red light) is refracted less by the eye and requires a longer focal distance inside the eye than light of a shorter wavelength (such as blue). This difference means the apparent position of a red speckle pattern is beyond that of a blue speckle pattern.

When the observer moves his head across the line of sight, the apparently distant red pattern moves in the same direction as his head and the apparently closer blue pattern moves in the opposite direction. If the color of the laser light is closer to the center of the range of colors to which the eye responds, the speckle pattern appears to be closer to the scattering surface. The apparent motion of the pattern when the observer's head moves becomes progressively harder to discern. When the pattern seems to lie at approximately the same distance as the scattering surface, the pattern does not migrate as a whole across the surface when the observer's head moves. It does display a random motion that is often called boiling, since it resembles bubbles reaching the surface of boiling water.

A more detailed examination of the migration of speckle involves the motion of the points scattering the rays responsible for a bright patch in the pattern. Figure 5 shows a rough surface scattering two rays to an observer. Suppose they result in a bright patch in the speckle pattern. Accommodation by the observer's eye makes the rays seem to emerge from a single point on an imaginary plane behind the actual scattering surface.

Suppose the surface moves to the left across the observer's line of sight, but not so much that the bright patch loses its

identity in the changing pattern. The apparent location of the single origin of the two rays also moves, but in a direction opposite to the true motion of the scattering surface. When the observer's eye is underaccommodated for the scattering surface (that is, it is focused for something behind the surface), the apparent motion of the speckle is opposite to the true motion of the scattering surface and in the same direction as the true motion of his head. The reverse is true when the eye is overaccommodated. The apparent speed of the speckle patch depends on its apparent distance from the scattering surface.

In neither instance does a patch of the pattern actually travel completely across the scattering surface. Soon after a patch seems to have traveled a short distance it disappears because the motion of either the scattering surface or the observer's head changes the geometry of the rays entering the eye. Fresh patches pop up, however, and move as the former patch did. The observer therefore has the illusion that all the patches survive for a full trip across the scattering surface.

When the eye is accommodated for the scattering surface (the surface is in --focus on the retina), motion of the surface or the head results in no organized migration of the pattern. Instead the individual patches in the pattern move across the line of sight until the angles of the scattered rays change so much that the patches lose their identity. With continued motion of the surface or the head new patches appear, move in some random direction and then disappear. The surface appears to boil.

Some investigators have suggested that the observation of speckle patterns might replace the conventional tests of eyesight, particularly for people who cannot read the letters employed in the normal test. A surface is moved across the field of view of an observer. Laser light of low intensity is scattered from the surface to provide a speckle pattern. The observer notes the direction of migration of the pattern. Lenses of increasing strength are then inserted into the visual field until the direction is reversed. Reducing the lens strength, the examiner finds the strength at which the speckle appears to boil on the scattering surface. This is the strength of lens needed to correct the observer's vision.

Some observers encounter another peculiarity in the perceived motion of the speckle patterns. If the eye of the observer is astigmatic, the pattern might move at an angle to the horizontal axis along which his head moves. This two-dimensional motion of the speckle arises because of different focal lengths for rays crossing the eye through different cross-sectional planes.

The astigmatic eye is normally described as having two major planes through it. They are depicted schematically in the illustration on the left. Initially parallel rays crossing the eye along one of these imaginary planes are focused at a certain distance inside the eye. Initially parallel rays crossing the eye in the other plane require more distance for focusing. Although the two planes are perpendicular to each other, they are probably not horizontal and vertical.

Rays contributing the speckle pattern to an observer enter the eye at a large range of angles. To simplify the situation I consider the rays as crossing the eye in one or the other of the imaginary planes through the eye. When the observer moves his head horizontally, the speckle patches appear to move partly parallel to the short-focus plane and partly parallel to the long-focus - one. The speed of the patch appears to be greater along the long-focus plane. The brain interprets the composite motion as being along a line lying between the two planes. Since that line is likely also to be tilted to the horizontal, the patches seem to move along a tilted line when the astigmatic eye moves horizontally.

I was fascinated by Sollod's description of kinetic colors in a spoon of coffee with cream in it. Previously published accounts of speckle had dismissed the possibility of seeing speckle in solutions. For example, one study concluded that speckle cannot be seen when spatially coherent light is reflected and scattered from the surface of milk unless the milk is frozen. In principle speckle should be visible because each of the colloidal particles in milk scatters light to an observer. Since the path lengths of the various scattered rays differ, the observer should see an interference pattern.

Speckle is missing, however, because the colloidal particles are constantly moving in random directions. The motion, called Brownian motion, is due to the constant jostling of the particles by the surrounding molecules, which have thermal motion. At any given instant the array of particles does send a speckle pattern to an observer, but the continuously shifting position of the particles smears out the pattern over the averaging time of the perception process. The result is that the surface of milk seems to reflect light uniformly. The speckle patterns would emerge if the colloidal particles were slowed in their random motion. Freezing the milk essentially halts the motion. The speckle pattern is then stationary, as it is in all my preceding examples.

I believe Sollod's demonstration is one in which speckle can be seen in a fluid still free to flow. The trick is to arrange for a very thin or diluted layer of the fluid to be illuminated with spatially coherent light. Light scatters from a few particles on its way to the reflecting surface of the spoon, scatters from a few more on its return path to the observer and then creates the speckle pattern on the observer's retina. A thicker or more concentrated layer has too many particles in the way. The light reflecting from the spoon is feeble and the pattern is smeared.

A very thin layer of milk may have another function. The colloidal particles in it have slower Brownian motion not because the molecules are any cooler but because the viscosity of the fluid is greater when the fluid is in a thin layer. The slower motion shifts the fluctuating speckle patterns into the time range in which individual patterns can be perceived.

The specks of light from Sollod's arrangement are colorful because the speckle patterns depend on the wavelength of the light. At one instant the observer might be at the correct orientation to receive blue light from a particular particle. In the next instant the particle has moved and green light might be sent to the observer from a particle somewhere near the former position of the first particle.

When I hold a spoon partly filled with milk in the sunlight, I sometimes have trouble spotting the kinetic speckle pattern. Over the dry areas of the spoon lies a faint, stationary speckle pattern as on most objects illuminated by direct sunlight. Only at the edge of the pool of milk is the milk thin enough to create the kinetic speckle pattern. To study it better I gently swirl the milk in the spoon so that most of the surface is coated with milk. As the milk drains back into the pool, the coating on the rest of the spoon thins. Gradually these thin layers break up into kinetic speckle arrays. After a while the layers dry completely and the speckle pattern becomes stationary and less colorful.

I spot kinetic speckle patterns in thin layers of milk when the layers lie on reflecting surfaces such as a mirror or the spoon in Sollod's demonstration. Any surface painted flat black does not work. I believe the reason lies in how light is scattered from the colloidal particles. The scattering appears to be more intense in the forward direction than it is back toward the observer. Hence the light scattered by the particles should be reflected by a surface in order to reach the observer if the speckle pattern is to be bright enough to be perceived. If the surface fails to reflect the light, the kinetic speckle is probably too dim.

To verify this hypothesis I caused sunlight to pass through a thin layer of milk in a transparent plastic dish. When I looked at the transmitted sunlight from below the dish, I found the familiar kinetic speckle pattern. From above the dish no speckle was apparent. The demonstration showed that the particles in the milk were scattering the light primarily in the forward direction.

Suspended particles much larger than small molecules are essential for kinetic speckle patterns. Thin layers of water give no kinetic displays, but a thin layer of water doped with a little milk does. The kinetic speckle apparently requires particles in the size range of roughly a micrometer.

Scattering from molecules of water, which are considerably smaller, does not result in speckle. One reason is the almost continuous distribution of these molecules. Another is that they move faster than the larger particles. Both the distribution and the speed result in a uniform reflection. Particles larger than about 100 micrometers do not generate kinetic speckle patterns because they are too large to be set moving by Brownian motion. They do, however, yield stationary speckle patterns.

Last August I described interference patterns that one can see in a misty or dusty mirror. The patterns require light that has at least partial spatial coherence. Laser light, sunlight or light from a pinhole will serve. As a final note I mentioned that the central sections of the pattern called the Fraunhofer rings (or corona) should be uniformly textured but instead had noticeable streaks. The streaks are part of a speckle pattern created by the scattering of the light from the dust motes or water droplets. Coherent waves can scatter from adjacent motes or droplets and then travel to the observer to interfere at the retina. The result is that the observer sees either bright or dim light or darkness at the position of the motes or droplets. The intensity depends partly on the distance separating the two motes or droplets. Since the separations between other pairs of scattering particles are sure to be different, the interference varies between bright, dim and dark over the entire scattering surface.

Bibliography

THE GRANULARITY OF SCATTERED OPTICAL MASER LIGHT. J. D. Rigden and E. I. Gordon in Proceedings of the IRE (Institute of Radio Engineers), Vol. 50, No. 11, pages 2367-2368; November, 1962.

LASER SPECKLE AND SURFACE ROUGHNESS. W. T. Welford in Contemporary Physics, Vol. 21, No. 4, pages 401-412; July/August, 1980.

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