IF YOU WERE ASKED TO envision the uses that might be made of a ball bearing, you probably would not think of it as a tool for the study of light or as a kind of photographic lens. It can be both of those things, and thereby hangs a tale about the nature of light.

Is light a wave? In the early years of the 19th century the idea met with much opposition. Physicists still hewed strongly to Newton's model of light as particles. In 1818 a wave model for light was proposed by Augustin Jean Fresnel in a competition held by the French Academy. The judging committee included the mathematicians Pierre Simon de Laplace and Simeon Denis Poisson and the physicists Dominique Francois Arago, Jean Baptiste Biot and Joseph Louis Gay-Lussac.

Fresnel's work was opposed, notably by Poisson, who put forward a thought experiment intended to discredit it. If a bright beam illuminates an opaque object of circular cross section, he said, then according to Fresnel's work a bright spot should appear at the center of the shadow of the object. Since such a result was clearly absurd, the model must be erroneous.

Arago soon arranged the experiment and found the bright spot, thereby vindicating both Fresnel and the wave model of light. The spot had actually been seen in 1773 by other workers but had been forgotten. Today the phenomenon is often and ironically called the Poisson spot. A spot of this kind is surrounded by bright and dark circles, all within the shadow of the sphere or disk creating the pattern.

In an experiment illustrating this principle, devised by Dale Blaszczak of Cleveland State University, I photo- graphed the pattern cast by a ball bearing. We were also able to employ the bearing as a lens so that it formed an image in its shadow. The Poisson pattern and the image from an opaque ball both derive from diffraction, a property due to the wave nature of light.

The propagation of a light wave sometimes considered in terms of tiny wave generators positioned along a wave front at any given instant. These generators, which are merely mathematical inventions, emit small waves strongly forward (in the direction of travel of the light), less strongly sideways and not at all backward. As these small waves interfere with each other (overlap) they re-create the wave front ahead of its previous position. Thus the wave front is described as moving by means of the continuous generation and interference of the small waves from the generators.

Although the generators and their waves do not exist, they help physicists in picturing many aspects of light. One important example is the diffraction of light by a narrow slit (about the width of a razor blade) in an otherwise opaque screen. When the wave front travels into the slit, most of it is eliminated by the screen, together with most of the generators. The remaining generators still emit waves in the forward direction, but they no longer interfere enough to re-create the previous wave front. Instead of traveling along a straight line through the slit, the light spreads from it.

If the light intercepts a surface such as a sheet of paper, the spreading can be seen. Many places are brightly lighted because the light waves arriving there are in phase and interfere constructively: the wave crests arrive simultaneously, thereby creating a large light wave. Other places are dark because the waves arrive out of phase and interfere destructively: a crest of one wave arrives with the trough of another, so that the waves cancel.

The spread in the pattern of bright and dark places depends on the size of the slit. Suppose the slit is rectangular and the long side is vertical. The configuration creates a pattern well spread horizontally and condensed vertically Such a pattern is called the diffraction pattern of the aperture.

Sometimes the shape of an aperture and its diffraction pattern are related in a simple way. For example, an aperture resembling the letter H has essentially three slits. The short horizontal slit creates a vertical diffraction pattern, and the two vertical slits yield overlapping horizontal patterns.

You might try to guess the shapes of the apertures that created the patterns in the illustration above [Figure 5]. Each aperture was a letter that I typed on smooth paper as a capital in the Letter Gothic style. I had each one photographed with Kodak direct positive film, which was then processed with the kit designed for that film. The resulting slides were opaque except for the letters, which were transparent.

To photograph the diffraction patterns I mounted a slide in the beam from a helium-neon laser so that the letter was fully illuminated. About 20 meters on the other side of the slide I positioned a 35-millimeter camera in the diffraction pattern. I removed the lens so that the pattern would directly illuminate the film when the shutter was released.

With the room lights off I photographed the pattern with a range of shutter speeds. Can you guess the letters from the diffraction patterns? The letters are approximately in the correct places to spell a name that has long been associated with this magazine, but I have eliminated any repeated letter and cannot guarantee that the patterns are oriented properly.

A second way of explaining diffraction is useful when the aperture is circular. Surrounding its center are Fresnel zones, which direct light to the paper that makes it possible to view the rings of the diffraction pattern.

Look at the center of the pattern. Light arriving there from the central zone is exactly out of phase with light arriving from the second zone because of a difference in the travel distances. Light from the third zone reaches the center of the diffraction pattern exactly out of phase with the contribution from the second zone for the same reason. The zones of higher order are defined in a similar way. Each zone directs light (to the center of the diffraction pattern) that is out of phase with the light from an adjacent zone.

The size of the zones depends on the distances between the aperture, the light source and the paper. Thus these distances determine how many zones lie in the aperture. Suppose the paper is far enough away for the central zone to fill the aperture. Then the center of the diffraction pattern is bright. If the paper is brought closer, a second zone appears in the aperture. Then the center of the diffraction pattern is dark because the light arriving from the central zone and the light arriving from the second zone interfere destructively.

When the paper is brought even closer, the third zone appears in the aperture. Although light waves from the central zone and the next zone still cancel, the center of the diffraction pattern is bright because of light from the third zone. As the paper is moved toward the aperture the center of the diffraction pattern alternates between being bright (when the number of zones filling the aperture is odd) and dark (when the number of zones is even).

During the dark stages the light is never fully canceled because of what is called the obliquity factor. Light from a zone proceeds strongly in the direct forward direction but less strongly to the sides. The light from a zone of large radius is therefore slightly weaker at the center of the diffraction pattern than light from an adjacent zone with a smaller radius. The two contributions interfere destructively at the paper sheet but are not completely destructive.

Diffraction patterns can also be created by opaque objects. Blaszczak investigated the phenomenon by examining the Poisson pattern cast by a circular metal disk three-eighths of an inch in diameter. He glued the disk to a thin metal wire (30 gauge) and then suspended the wire between two holders attached to a ring stand. The disk was approximately 10 meters from the laser. A lens expanded the beam. The shadow fell on white paper 30 meters behind the disk. Blaszczak examined the small shadow with a magnifying lens after adjusting the orientation of the disk. When the disk was perpendicular to the beam (thereby presenting a circular cross section to it), the Poisson pattern appeared.

Sometimes Blaszczak placed a lens in front of the laser to spread the light. Sometimes he then recollimated the light into a wider beam without divergence. (To recollimate make the first lens focus the light onto a pinhole. Light passing through the pinhole then travels through a second lens that has its focal point on the pinhole.) The Poisson pattern appeared in each case.

We tried to form an image with the disk by placing a photographic slide of a human face in the recollimated light about midway between the laser and the disk. The shadow region displayed a complex interference pattern, but it bore no resemblance to the face.

We replaced the disk with a one-centimeter ball bearing that was exceptionally round and smooth. It cast a brilliant

Poisson pattern. We made the pattern larger by spreading the laser beam and then moving the bearing close to the laser. This arrangement provided more distance between the bearing and the paper that displayed the pattern.

We examined the pattern through a magnifying lens. Then we employed a camera as the magnifier. When the lens was removed and the camera intercepted the shadow of the bearing, we looked through the viewfinder and saw a magnified Poisson pattern.

I must warn you that such an arrangement is dangerous. If you look through the viewfinder of a camera that is in the path of a laser beam, your eye focuses the light onto your retina. A pattern that is quite bright can ruin the retina resulting in blindness. Your only sensation may be that the light seems uncomfortably bright, and you may not be aware of the full damage being done.

It is much safer to examine the patterns on paper by means of a magnifying lens because the intensity of the light is reduced by scattering from the paper. (We looked through the viewfinder because on paper the pattern is so small that it is hard to see.) Even the paper arrangement can be dangerous with a high-powered laser. Our laser is rated at 10 milliwatts, which means it has a maximum output of 10 milliwatts. All the patterns we saw could be generated just as easily with a laser of lower power.

You might try to photograph the Poisson pattern on a paper sheet. Place the camera off to one side in order not to block the light going toward the paper. Since from such an angle the pattern will no longer be circular, rotate the paper so that a line perpendicular from it lies midway between the incident light and the line of view from the camera.

The camera must have a lens to focus the pattern onto the film. My attempts with this arrangement were disappointing because light scattered from the paper often ended up washing out the delicate Poisson pattern.

I tried another approach. With the room lights out and the lens off I placed the camera directly in the shadow of the ball bearing and exposed the film at several camera speeds. Using color film of 400 ASA speed, I made my best photographs with the shortest exposure times, usually 1/1,000 or 1/500 second. If you have a dim laser, use film rated at 1,000 ASA. For classroom work I prefer color slides (400 ASA) so that the results can be projected.

The Poisson pattern derives from the diffraction of light around the sides of the bearing. Suppose the bearing is illuminated by light with a straight wave front. When the wave front reaches the bearing, some of its mathematical generators are blocked and eliminated by the bearing. The remaining ones still produce small forward waves, but the interference between waves can no longer re-create the original wave front. Instead some of the light spreads into the shadow region of the bearing.

All the generators on the wave front passing the bearing are in phase. When the light waves reach the paper, their phase and their interference are determined by how far they have traveled. The light reaching-the center of the shadow from one side of the bearing travels just as far as the light from the opposite side. This light remains in phase and interferes constructively, producing the Poisson spot.

Surrounding the spot is a dark circle, created by destructive interference. Consider any point on the circle. The point is dark because the light arriving from one side of the bearing must travel farther than the light from- the side directly opposite. The extra distance of travel puts the two waves of light exactly out of phase.

Slightly farther off center is a circle produced by constructive interference. Again light coming from one side of the bearing must travel farther than light coming from the side directly opposite, but this time the extra distance puts the waves back in phase. (One wave lags behind the other by a full wavelength.) Usually quite a few bright and dark circles can be seen surrounding the Poisson spot.

The pattern can also be explained in terms of Fresnel zones. The bearing blocks the light from the central zones. (In our experimental arrangement the first several hundred zones are blocked.) Just outside the bearing lies the first exposed zone. The center of the shadow receives light from this zone and all the other exposed zones lying at greater distances from-the bearing. Since adjacent zones are out of phase with each other, they interfere destructively. The obliquity factor, however, diminishes the contributions from the outer zones in such a way that the intensity at the center of the shadow is roughly a fourth what it would be if only the first exposed zone illuminated it.

Consider the zones illuminating a point in the first dark circle in the Poisson pattern. From the view of that point the bearing is not centered on the zones. Thus some of the zones near the bearing are only partially exposed. The net result is that the zones cancel each other and the resulting point in the Poisson pattern is dark.

Next consider a point on the first bright circle in the Poisson pattern. For this point the bearing is even more off center from the zones. Again some of the zones near the bearing are only partially exposed. This time the net result is brightness.

If the bearing presents a noncircular cross section to the laser beam, the Poisson pattern is distorted or missing. One concludes that the wave generators on one side of the bearing are not matched by generators placed symmetrically on the opposite side. In terms of the Fresnel zones one argues that the innermost zones are not fully exposed because the bearing lacks circular symmetry. The resulting pattern on the paper can be complicated. If the asymmetry is great enough, the exposed portions of the zones can cancel the light at all points on the paper, leaving the shadow dark.

Since the ball bearing diffracts light into its shadow, it can produce an image somewhat as a convex lens does, except that the image arises from diffraction rather than reaction. Blaszczak and I figured that imaging would be easier with the ball bearing since the disk requires careful orientation to present a circular cross section to the laser beam

We first obtained a bright Poisson pattern. Then in the beam we placed a slide that was opaque except for a small transparent 2. The figure, which was fully illuminated, created a diffraction pattern across the ball bearing. We gradually shifted the position of the bearing while checking its shadow for an image of the 2.

We searched for days without success. We moved the experiment into two rooms joined by a door so that we could extend the baseline to about 80 meters. The laser was at one end, the paper sheet was at the other end and the bearing was about midway between them. We replaced the crude mounting for the bearing with micrometer mounts so that we could vary the position of the bearing smoothly. One micrometer mount moved the bearing vertically, the other one moved it horizontally.

Part of our problem was the diffraction pattern cast by the wire to which the bearing was glued. Sometimes part of that pattern extended into the region we searched for a 2. We also tried slides of letters and other numbers.

Finally, we experimented with a slide containing a rectangular grid of black lines, each line separated from the next by about two millimeters. Blaszczak figured that the repeated pattern might reduce the severe requirements of positioning the bearing. He was right. When

we examined the shadow of the bearing, we found an image of the grid at the center. Outside the shadow was the portion of the grid's original diffraction pattern that bypassed the bearing. The central pattern was formed only because the bearing diffracted some of the light, sending it into the shadow region.

We returned to the slide of the 2 with greater patience. We adjusted the placement of the bearing in the diffraction pattern cast by the 2. We varied the distance between the slide and the bearing and between the bearing and the paper (or the camera). Nearly always the center of the shadow consisted of a complex interference pattern that never resembled a 2. At last we got it with the bearing at approximately the center of the diffraction pattern from the 2.

Was the figure truly an image of the slide or merely a fortunate orientation of dark and bright interference bands? One way to check is to examine the orientation of the image. If the bearing serves-as a convex lens, the image will be inverted and reversed left and right from the orientation of the object. The image of the 2 we found was indeed so reoriented.

As seen from the laser the slide had a 2 that was inverted and reversed. What we saw on the paper was a 2 of the proper orientation. We were also successful with imaging an 1, but we always failed with more complex shapes such as a face. (Some older textbooks on optics mention that investigators imaged faces with coins or metal spheres but give little detail on how.)

To understand how an inverted image can form in the shadow of the bearing imagine a slide with two pinholes positioned in a laser beam. Each pinhole acts as a point source of light for the bearing, creating a Poisson pattern centered on a line running from the pinhole through the center of the bearing. Th

center spots of these patterns are the images of the pinholes. Their separation matches the separation between the pin holes if the bearing is midway between the slide and the paper. If the bearing is closer to the sheet, the images are closer. If the bearing is closer to the slide, the images are farther apart. Thus the bearing can magnify the separation of the pinholes.

The imaging of the pinholes is far murkier from a bearing than it is from a lens because of the severe distortions in the overlap of the Poisson patterns surrounding each pinhole image. Depending on the alignment of the slide and the bearing, the overlap can result in many different designs, some of which make recognition of the images difficult.

Our easy success in imaging the grid was probably due to the repetition of the pattern. Usually the bright and dark lines near the center of the shadow confuse the imaging of an object. With the grid as the object the lines were forced into a grid formation, thereby aiding the identification of the image.

Similar imaging and distortion should result when other slides are put in the laser beam. For example, an aperture in the shape of an I can be considered as a series of pinholes forming the letter. Each pinhole creates a Poisson spot in the shadow of the bearing. If the imaging is successful, the composite of the spots forms an I.

When we tried the experiment, we sometimes found in a string of Poisson spots that each spot was surrounded by a dark ring. Sometimes the overlap of patterns yielded two dark, roughly parallel lines that more closely outlined an I. Similar distortion appeared when we put an M in the beam. If we adjusted the position of the bearing properly, the images of the vertical sections of the M resembled the image of an I. The internal lines appeared as small spots.

Often the diffraction pattern cast by the suspension wire seemed to distort the center of the bearing's shadow. To avoid this problem we glued the bearing to a microscope slide, which we attached by tape to the micrometer mounts. Although small scratches in the glass still caused some distortion of the bearing's shadow patterns, the patterns were clearer than before.

We wondered what would happen if part of the light diffracting around the bearing was blocked. We held a card near the bearing. The edge of the card created a strong diffraction pattern of its own in the shadow region.

We then resorted to a different arrangement, putting a slide with a single pinhole in the laser beam and moving the bearing close to it. The pinhole diffracted the light into a pattern of bright and dark circles around a bright center. In our previous work the bearing was far enough away to be bathed with light from the center of the pattern.

We moved the bearing close enough to make the first dark circle in the pinhole's pattern fall on the perimeter of the bearing. Hence all along the perimeter of the bearing's cross section the light from the pinhole interfered destructively, leaving the perimeter in darkness. The Poisson pattern in the shadow of the bearing disappeared.

Next we moved the bearing close enough to make the first bright circle of the pinhole's diffraction pattern graze the perimeter of the bearing. The Poisson pattern reappeared. We moved the bearing slightly to one side so that it was off-center in the pinhole's diffraction pattern. On one side the center of the pattern brightly illuminated the perimeter of the bearing. On the opposite side part of a dark circle grazed the bearing's surface. This time the shadow of the bearing showed a bright flare through the center. The Poisson pattern was washed out.

Apparently the creation of the Poisson pattern depends on the diffraction of light around opposite sides of the bearing. When the side of the bearing lies in a dark part of the pinhole's diffraction pattern, the light rays passing that side are out of phase. Although they are diffracted into the shadow region, they remain out of phase and so interfere destructively.

When the pinhole's dark ring grazed the full perimeter of the bearing, none of the light reaching the shadow region survived destructive interference. The region was dark. If part of the perimeter was grazed with a dark ring, light passing that side could not interfere constructively with light passing the opposite side. This time the shadow region received light from one side of the bearing but lacked the pattern of concentric circles.

Although imaging by a sphere or a disk has been investigated since 1818, I can find no record of detailed studies. The amateur experimenter therefore has plenty of scope. How far should a ball bearing be from the slide and the point of observation in order to enhance the image? Where should the bearing be in the diffraction pattern cast by the slide? Should the bearing be large or small? Can a sphere much larger than a ball bearing form images in its shadow region? Is there any way to reduce the distortion of the image due to the overlap of Poisson patterns?

Bibliography

LARGE-SCALE DIFFRACTION PATTERNS FROM CIRCULAR OBJECTS. Phillip M.

Rinard in American Journal of Physics, Vol. 44, No. 1, pages 70-76; January, 1976.

FRAUNHOFER ALPHABET. Alan Winter in Physics Education, Vol. 15, No. 5, pages 290-291; September, 1980.

THE SPOT OF ARAGO: NEW RELEVANCE FOR AN OLD PHENOMENON. James E. Harvey and James L. Forgham in American Journal of Physics, Vol. 52, No. 3, pages 243-247; March, 1984.

The Society for Amateur Scientists (SAS) is a nonprofit research and educational organization dedicated to helping people enrich their lives by following their passion to take part in scientific adventures of all kinds.