LASER ART WAS INVENTED ALMOST simultaneously with the laser. Because a laser emits coherent light it can be employed to give dazzling displays of interference effects, visual spectacles that could not be achieved with ordinary lamps. This month I shall describe some of the laser-art techniques I use in my slide shows at Cleveland State University.

In each show 10 slide projectors cast five simultaneous slide images on wall-to-wall screens. All the images are synchronized to music. During certain parts of a show the projectors hold blanks and therefore do not project an image. Instead two 15-milliwatt helium-neon lasers are turned on and directed through an optical array to create displays of interference patterns and Lissajous figures on the screens. Immediately before introducing the lasers I set off four explosions in front of the screens. When the laser beams pass through the smoke, the paths of light above the audience sparkle brilliantly, giving the impression that the narrow lines of bright red are less than real.

The laser techniques I shall describe are of two kinds, one kind based on the interference of light waves and the other on

mechanical oscillation to redirect the laser beam. The interference techniques were worked out by David Yoel, a student at Cleveland State, to whom I am indebted for his labors. The best displays were created with diffraction gratings sold by the Lumens Corporation, a California-based company that supplies optical materials for laser-light shows. The gratings I have give a dispersion of medium quality, but the company also sells gratings that give high quality dispersion.

All the gratings are made of transparent plastic on which a pattern has been laid. The procedure for making the gratings is undisclosed. One grating generates a diffraction pattern of the kind seen in an introductory physics class; when the grating is held in a laser beam, a row of bright dots is cast on a screen. A second grating creates a cluster of bright dots surrounded by dimmer ones. A third grating creates a similar cluster except that the bright dots are arranged rectangularly.

A fourth kind of filter has been constructed from pie-shaped segments of the first type of grating. All the apexes of the segments are grouped at the center of the filter. When the filter is placed in an expanded beam from the laser, a row of dots is produced by each segment. Since there are 48 segments, 48 rows of bright dots extend radially outward from the center of the pattern.

The display is impressive, but it is outshined by the pattern cast by the fifth filter, which Lumens calls a Chromasphere grating. That filter creates the illusion of a Christmas-tree ball brilliantly decorated in red. The center of the pattern has an extremely bright dot of light. Around it is a circle of bright dots. On both sides of the circle are dots of red in an array that gives the illusion of the surface of a ball. (For a limited time I can supply readers with a small sample of this Christmas-ball diffraction grating that is suitable for use with a student-oriented laser. Send $1 and a mailing label to me: Physics Department, Cleveland State University, Cleveland, Ohio 44115.)

All the gratings work by means of the wave interference of light and particularly by the diffraction of light. The simplest example of diffraction involves light passing through a small slit in an otherwise opaque filter. The slit is very long and narrow, being, say, a few micrometers wide. Indeed, the width is close to the wavelength of the light being passed through the slit. With such a narrow aperture the light is diffracted, that is, it is spread outward along a line parallel to the width of the slit. Hence the light passing through the slit does not entirely continue traveling in its initial direction; instead it spreads to the sides.

Something else happens to the light. It is not spread uniformly to the sides but is relatively intense at certain angles and less intense or even absent at other ones. If the light falls on a screen, a pattern of bright and dark lines (usually called fringes) can be seen. This diffraction pattern (both the spreading of the light and the resulting bright and dark lines) arises from the interference of the light waves passing through the aperture.

In the mathematical construction of the interference one imagines that the wave front in the slit at any instant consists of a series of small wave generators, each generator sending out a semicircular wave. With a large number of generators side by side the semicircular waves would interfere with one another as they expanded, thereby creating another straight wave front displaced to the side from the initial one. The new wave front would also have an infinite number of such wave generators, each of which would send out a semicircular wave. Again the semicircular waves would interfere with one another and create still another straight wave front displaced from the preceding one. With this model one can describe mathematically how a wave front moves.

Although such wave generators are imaginary (at least there is no compel" ling evidence that nature truly works this way), describing the model of a light wave as the composite interference of small semicircular wave generators enables one to predict the outcome of a host of experiments in optics and in particular to predict the pattern cast by a narrow slit illuminated with laser light. As a wave passes through the slit there is no longer an infinite number of wave generators on each side of the generators in the slit. The number was infinite before the wave front entered the slit, but the opaque screen eliminated the rest of the generators.

Still, each generator that did enter the slit sends out its usual semicircular wave. The important difference is that the number of semicircular waves is now too small to interfere to reconstruct the straight wave front that entered the slit. Some of the semicircular waves will spread to the sides instead of going straight in the direction perpendicular to the filter. Moreover, at some angles with respect to the forward direction the wave produced by some of the generators will be exactly out of step with the wave produced by the other generators. As a result no net light wave will be sent out at that angle. If a screen is inserted into the diffracted light, this cancellation of a light wave results in a dark line on the screen. At other places the waves reinforce one another and produce a bright line on the screen.

A diffraction grating, which consists of many slits, works in essentially the same way except that the light diffracted through each slit interferes with the light from each of the other slits. A grating may have tens of thousands of slits. The effect on the diffraction pattern on the screen is that the bright places are narrower and sharper than they are in the pattern cast by a single slit.

Many of the inexpensive gratings now on the market are plastic replicas of a master grating etched on glass or metal. I do not know how Lumens makes gratings, but one can detect the grating structure by examining a grating under a microscope. The "lines" are about two micrometers wide. This estimate is consistent with one I can make when I compare the Lumens grating with the replica grating sold by the Edmund Scientific Company. The bright fringes on the side from the Lumens grating are approximately one-third as far from the center as the ones from the Edmund grating, which means that the Edmund grating has lines spaced three times closer, providing greater dispersion. Dispersion is not the objective, however, when one uses the diffraction gratings in a laser show. One wants the side fringes to be distinctly bright. Therefore the Lumens grating is better suited for the purpose.

A grating with equally spaced lines of transmission and opaqueness is termed a Ronchi filter. Such a filter creates a diffraction pattern that consists of one bright central spot and two other bright spots, one on each side of the central spot. Dimmer spots lie farther out to each side. The entire pattern lies along a line.- The first side spots are almost as bright as the central spot, but the others are noticeably dimmer. At least one type of filter from Lumens appears to be a normal Ronchi filter.

If two Ronchi filters are placed in a laser beam so that their "lines" are at right angles to one another, each filter produces its own diffraction pattern. The result is a composite of the two patterns, with one bright central spot and eight slightly dimmer spots lying in a rectangular array around it. Noticeably dimmer spots lie farther from the center. One of the Lumens filters appears to be of this type.

Crossing more Ronchi filters, each at a different angle with respect to the previous ones, creates an increasingly complex diffraction pattern. In each case a bright central spot is surrounded by an array of slightly dimmer secondary spots. The display is also filled with noticeably dimmer spots from higher orders of interference.

The Christmas-ball filter from Lumens appears to be essentially three or four crossed Ronchi filters, some of which have different spacing between the lines. The filter is not merely the result of gluing together three or four normal Ronchi gratings, each with its lines oriented at an angle to the preceding set of lines. The people at Lumens have hit on a method of putting the crossed Ronchi filters on a single surface by appropriately shaping the raised areas of the surface. When I examined the filter under a microscope, I saw a linear arrangement of hexagonal bumps. The arrangement of parallel rows of bumps acts as one Ronchi filter. A line perpendicular to the rows can be designated as axis No. 1. Another filter (axis No. 2) is due to the distance from one of the hexagonal surfaces across the gap to another hexagonal surface. This axis is at an angle to the first one. Another filter (with axis No. 3) lies tilted at the same angle but in the opposite sense. A fourth Ronchi filter may be the result of the periodic structure along each row of bumps.

The Lumens workers are experimenting with filters that produce concentric squares or circles. They have also begun marking their products with a new method of indicating copyright. Within each filter is a hologram that identifies the company and the copyright. Even if the filter is cut into small sections, the copyright information is still contained in each section because the holographic image can be reconstructed from each section. The hologram in the filter does not interfere with the filter's main purpose of acting as a diffraction grating.

More beautiful decorations can be created by placing two filters in a laser beam. For example, I directed my laser beam through both the Christmas-ball filter and a normal Ronchi filter. (The order of the filters does not matter.) The result is a Christmas-ball interference pattern for each of the three brightest spots cast by the normal Ronchi filter. When I substitute the orthogonal crossed Ronchi filters for the single Ronchi filter, the display is even more complex but is less appealing because of the confusion of dots. The optical illusion of a curved three-dimensional surface is lost in the confusion. Another interesting pattern appears when the beam is expanded with a lens and then f. directed through both the pie-shaped grating and the Christmas-ball one. By rotating the first grating one generates an illusion that swarms of red fireflies are moving on the screen.

During a laser-light show you could move the filters around in the beam of light in order to change the display on the screen. The motion can be accomplished automatically by mounting the filters on a shaft turned by a low-speed motor. The beauty is enhanced further if the speed of the motor (and the direction in which it turns) is controlled by adjusting the voltage with a Variac. With such a control you can vary the rate at which the display changes to coincide with the tempo of the music.

You can make simple and complex Ronchi filters and many other types of filter by photographing large geometric designs. For example, you could draw a series of black stripes on a large sheet of white paper. Put the sheet on the floor and illuminate it with two floodlights whose beams intersect the sheet from opposite sides at an angle of 45 degrees. Photograph the sheet with a 3 5-millimeter camera aimed downward and triggered with a cable release. If you use slide film, the resulting slide can act as the filter.

Many types of optical-transform filter are described in Laser Art & Optical Transforms, by T. Kallard. He points out that drawing the geometric pattern with ink results in stripes that have "soft borders" because of the slight running of the ink. A gradual change in the transmission of light near the borders causes a loss of the greater orders in the interference pattern. If you want the higher order spots in the display, the borders should have abrupt transitions in transmission. Kallard recommends that you use black tape of the kind sold in art supply stores. Lay the tape to form whatever pattern you want.

A different kind of interference pattern can be obtained by inserting patterned glass or plastic in the laser beam. I have tried various types of the plastic that is used to cover the recess in which fluorescent lamps are mounted in an office ceiling. All these plastic covers have patterns, but not all the patterns are pleasing in the laser beam. The cover that works best has a surface that looks as though it was sculptured with a putty knife. Other surfaces have hexagonal or semispherical bumps. The surfaces are less interesting when they are merely inserted in the beam, but they yield highly interesting designs when they are slid to and fro across the beam so that the interference pattern constantly changes. Combining the pieces of plastic with one of the diffraction filters can give rise to stunning interference patterns. If either object is mounted on a rotating shaft, the varying pattern can be kaleidoscopic.

A ruffled piece of plastic generates an interference pattern because the light rays are refracted as they pass through the plastic. The different rays in the laser beam pass through different surfaces, each of which is tilted in a slightly different way. The rays therefore travel different lengths inside the plastic and emerge through surfaces of different tilt. The result is that although the rays were initially parallel to one another (or nearly so, depending on the divergence of the laser), they are no longer parallel after they pass through the plastic. The overlapping rays interfere with one another at the screen to create bright and dark lines.

The same effects can be achieved by applying airplane glue or Duco cement to a plate of clear plastic or glass. I distort the glue as it dries, ensuring not only that the surface is rough but also that the glue dries with several small bubbles. The rough surface gives rise to a complicated interference pattern on the screen. The bubbles generate simpler but more pleasing interference patterns consisting of closely spaced dark and bright fringes in a geometric pattern. During a

laser show I move a bubble in and out of the beam in order to give motion to the interference pattern on the screen. To achieve any of these interference effects I first have to adjust the distance between the optical components and the screen until images of a suitable size appear on the screen.

A completely different set of laser images can be created by using loudspeakers into which an audio signal is fed and from which the laser beam is reflected. Ray Laning, a former student of mine, built such a system with two small speakers (the type commonly found in an automobile radio) driven by two audio oscillators. The idea is to have one speaker deflect the laser beam horizontally as the other one deflects it vertically. The combined deflection can create on the screen the complicated patterns called Lissajous figures.

The reflection of the laser beam was achieved by means of a small mirror that Laning mounted on the inside of each speaker. The center of the cone of a speaker is a slightly curved region that oscillates when an audio signal is fed to the speaker. There Laning glued a small piece of Styrofoam that he had shaped to match the slight curvature in the region. The outer surface of the Styrofoam was flat so that he could glue one end of a small, lightweight mirror to it. The other end of the mirror was glued to a portion of the cone about midway between the central region and the rim. Laning used a glue that was somewhat elastic and therefore would not crack or break during the oscillation.

The mount and the mirror had to be light in weight because the additional weight Laning was adding would damp or eliminate the normal oscillations of the cone. When an audio signal was fed into the speaker, the oscillations of the cone forced the mirror to pivot (more or less) around the point where it was glued to the Styrofoam. To increase the amplitude of the oscillations Laning cut symmetrical slits into the cone so that they radiated from the central region out to the edge. The slits allowed more play in the oscillations of the speaker so that when the system was in use in the laser show, it gave larger deflections of the laser beam on the screen.

After Laning had mounted mirrors in both speakers he fastened them to a wood mount in such a way that the plane of each speaker opening formed an angle of about 45 degrees with the horizontal. When the speakers were excited by an audio signal, the bottom mirror oscillated horizontally (that is, around a vertical axis) and the top mirror vertically (around a horizontal axis). A laser beam directed at the bottom mirror was reflected up to the top mirror, which then reflected it to the screen. The alignment of the beam, the mirrors and the final image on the screen took a fair amount of patience.

After alignment the image on the screen was a single spot of light. Laning then connected an audio oscillator to each speaker. Each oscillator produced a sinusoidal electrical signal that caused its speaker to oscillate, thereby moving the mirror in the laser beam. When the bottom mirror was oscillated, the beam was deflected horizontally and therefore moved back and forth across the top mirror and horizontally across the screen. The oscillations of the top mirror in turn caused a vertical oscillation of the beam. The beam was deflected vertically and horizontally simultaneously and moved across the screen accordingly.

Two mirrors and two audio oscillators were put in the system so that the frequency and amplitude of the two deflections could be controlled independently. For example, suppose the mirrors were oscillated at the same frequency. Several patterns could appear on the screen according to the phase relation of the oscillations. Consider an x-y coordinate system superposed on the screen. The center of the coordinate system is the position of the undeflected beam. If the bottom mirror begins to deflect the beam to the right as the top mirror begins to deflect it upward, the beam moves across the screen to the upper right. If the amplitudes of the two deflections are equal, the beam traces on the screen a straight line that forms an angle of 45 degrees with the horizontal. After the deflection is complete the beam retraces the line back through the origin of the coordinate system and continues it to the lower left. As the oscillations continue, the beam traces the same slanted line repeatedly. The pattern of a straight line is not particularly interesting, but it is an example of a simple Lissajous figure. It develops when the oscillations are at the same frequency, have the same amplitude and are in phase (meaning that both signals increase at the same time).

Suppose instead the horizontal deflection of the beam is at a maximum to the right when the vertical deflection is just beginning to send the beam upward. The oscillations are said to be 90 degrees out of phase. As the beam is brought back horizontally it is also being sent upward. When the maximum vertical deflection is reached, the horizontal deflection is zero. What you see on the screen is part of another kind of Lissajous figure; the spot of light traces out a part of a circle, moving from the far right to the uppermost part of the circle. As the oscillations continue, the circle is eventually completed and the tracing begins to repeat the circle. If the oscillations of the mirrors are of low frequency, you can see the spot of light actually trace out the circle. At the frequencies we employed in the light shows the circle was generated so quickly that our persistence of vision gave us the illusion that a completed circle was always on the screen.

Laning could control the amplitude of oscillation of each mirror by adjusting the amplitude controls on the audio oscillators. When he made the amplitude of the horizontal oscillation greater than that of the vertical oscillation, the pattern we saw on the screen was an ellipse with a horizontal long axis. Similarly, he could create an ellipse having its long axis vertical.

Laning could also control the frequencies of the oscillations by adjusting the frequency controls on the audio oscillators. Suppose he gave equal amplitudes to the oscillation of each mirror but made one mirror oscillate twice as often as the other. Suppose further the higher frequency is on the horizontal oscillation and the two sets of oscillations are in phase. Consider the beam as being initially at the origin of the coordinate system. It begins to move both to the right and upward, but because of the difference in frequencies it has reached only half of its maximum vertical deflection by the time it has reached its full horizontal deflection. It continues to move upward but now has begun to move back to the left. By the time its horizontal deflection has again been reduced to zero it is at its maximum vertical deflection. The path it has traced out is part of a figure eight in its proper vertical orientation. The rest of the figure eight is traced out as the oscillations continue. If the mirrors are oscillating fast enough, persistence of vision gives the illusion of a bright red figure eight on the screen. Similarly, a horizontal figure eight can be created by giving the vertical deflection of the beam twice the frequency of the horizontal deflection.

Laning had no way to control the relative phases of the two oscillations. Indeed, the relative phases varied in an unknown way every time he reset the frequencies on the audio oscillators. During the show he therefore varied the frequencies and amplitudes on the audio oscillators until a pleasing pattern appeared on the screen. He could create not only straight lines, circles and figure eights but also more elaborate Lissajous figures. At some adjustments he could create a pattern that slowly changed from a straight line to an ellipse and back again. The changing pattern gave the illusion of a three-dimensional circle revolving slowly on the screen. Sometimes we saw the full circle as if it were slightly tilted out of the plane of the screen. At other times we saw the circle edge on, seemingly perpendicular to the screen.

Laning fiddled with the controls during a show so that he could switch from one illusion to another. When he hit on a circle, he sometimes quickly changed the amplitude on both audio oscillators. We then saw a pattern that rapidly and smoothly switched from a large circle to a small one and back again. I had the impression I was peering into the open end of a large pipe. At slower oscillations, when the persistence of vision was not as dominant, the spot of laser light seemed to map out a spiral that constantly came and went on the screen. Laning could pace the illusion to match the beat of the music.

A direct response of the laser display to the music can be achieved by using a speaker driven by an audio signal from the source of the music for the show. Yoel ran an audio line from my cassette player, which provided the music, to one of his old stereophonic speakers that he had modified. Over the opening of the woofer cone he stretched a sheet of plastic food wrap and glued it to the rim. (This procedure is easier if the cone is pointed upward.) He worked with common white glue because it was sufficiently strong and stretched the plastic tighter as it dried. During the drying he left a few heavy books on the rim. When the glue was dry, he glued a lightweight mirror directly in the center of the plastic.

When the audio signals from Yoel's cassette player excited the speaker, the pressure variations in the air trapped between the cone and the plastic caused the plastic and the mirror to oscillate Yoel then caused a laser beam to reflect from the mirror onto the screen. The constantly changing patterns were therefore in response to the music entering the speaker and were not pure Lissajous figures, but the display was pleasing because it was in time with the music the audience was hearing. The main response was to the low frequencies in the music because of the relatively large volume of air that had to be moved in the cone.

Both of these speaker systems require lightweight mirrors, which can be obtained from scientific supply houses. Most mirrors, however, do not reflect very well. If your laser is high-powered, losing some of the light to absorption by the mirror will not matter much. There might still be enough light on the screen for the audience to see. Another problem is that many common mirrors do not give a clean reflection and so add divergence to the laser beam. We bought a mirror of high quality from the Newport Research Corporation (18235 Mount Baldy Circle, Fountain Valley, Calif. 92708) and then had a glass cutter slice it into pieces small enough to be mounted on the speakers.

For the deflection system of Laning's design one could replace both the speakers and the mirrors with galvanometer mounts salvaged from surplus galvanometers. These mounts have a much faster and cleaner response than the speakers and therefore give cleaner patterns on the screen. Commercial laser shows that include drawing or writing with laser beams on a screen use galvanometers. With any design one must be careful not to feed too much signal to the system. In setting up our systems we on several occasions blew off mirrors.

I have mentioned only a few of the laser-art techniques that can be applied in a light show. In another column I shall describe how to make the laser beam visible as it passes over the audience. I shall also describe a variety of other techniques by which to cast interference patterns on the screen. As a final note let me remind you that laser light is dangerous. If you direct a beam toward a screen, you must be careful that no one in the audience can possibly stand up to intercept the beam. You must also take care that the light scattered from the screen is not dangerously bright. Strict Federal regulations apply to the use of lasers in public shows.

Bibliography

OPTICAL SPECTRUM ANALYSIS. Arnold Roy Schulman in Optical Data Processing. John Wiley & Sons, Inc., 1970.

FUNDAMENTALS OF OPTICS. Francis A. Jenkins and Harvey E. White. McGraw-Hill Book Company, 1976.

LASER ART & OPTICAL TRANSFORMS. T. Kallard. Optosonic Press, 1979.

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