WHEN HOLOGRAMS FIRST BECAME available, they presented the user with a difficulty: he needed monochromatic light, such as the light from a laser, to illuminate a hologram so that he could see it. In white light the images were blurry because each wavelength of the visible spectrum formed its own image, slightly displaced from the others. Rainbow holograms, developed in 1969 by Stephen A. Benton of the Polaroid Corporation, are designed to minimize blurring while still producing colorful images in white light. They are employed in works of art and novelty items and as a security measure on certain credit cards.

I have looked into this phenomenon with the help of Douglas S. Hobbs, who studied rainbow holography under the direction of Richard W. Henry of Bucknell University. I have also relied on two excellent books. Seeing the Light: Optics in Nature, Photography, Color, Vision, and Holography, by David Falk, Dieter Brill and David Stork, examines the optics of holograms and related devices. Holography Handbook: Making Holograms the Easy Way, by Fred Unterseher, Jeannene Hansen

and Bob Schlesinger, is rich in detail about how to produce all kinds of hologram on a limited budget. Because a rainbow hologram is usually made from a standard hologram, one needs to know the essential features of that remarkable artifact. It is not a conventional photograph made when a lens focuses an image of an object onto photographic film. Instead it is a photographic record of the interference pattern formed by two beams of light, one of which has been reflected from the object.

In one arrangement the beam from a laser is split with a partially silvered mirror. The part that passes through the mirror goes next through a spatial filter, which consists of a lens focused on a pinhole. The pinhole is at the focal point of a concave mirror. When the light is reflected from the mirror, the resulting beam (the reference beam) consists of plane waves: the wavefronts are straight and the rays are perpendicular to the wavefronts and parallel to one another.

The part of the light that is reflected from the partially silvered mirror is directed by other mirrors and spread by a lens until it is reflected from the object. This beam (the object beam) consists of waves that have curved wavefronts and diverging rays. To make matters simpler I assume the object is a point; the rays diverge from the point and the wavefronts are partial circles centered on it.

The reference beam and the object beam pass through a photographic film. There they interfere with each other. As a result the film records thin lines where the beams interfere constructively (wave crests coincide with crests and valleys coincide with valleys) to yield bright light that exposes the silver grains. Between the lines are other thin lines arising where the beams interfere destructively (crests coincide with valleys), yielding darkness and leaving the grains unexposed. When the film is developed, the unexposed regions are transparent and the exposed regions are opaque. The film is then a hologram: a permanent record of the interference pattern of the two beams.

The possibility of recording an interference pattern depends on the fact that at each point in the film the waves in the object beam always have a fixed relation of phase with the waves in the reference beam. If they did not each point in the film would receive destructive interference at one instant and constructive interference at another instant. The entire film would be exposed and no single pattern would be recorded.

Creating a fixed phase relation between the two beams requires coherent light, such as the light from a laser. One can think of the output from a laser as a succession of long trains of waves. Each train is made up of a continuous wave with a length (the coherence length) roughly the length of the laser tube. When the object beam and the reference beam arrive at the film, they have a fixed phase relation if they are parts of the same train. One achieves this condition by making the distances the two beams travel to reach the film approximately equal. Then each point in the film receives a single type of interference; as a result a single interference pattern is recorded by the film.

The pattern is too fine to be seen. If you examine the hologram in room light, you do not see an image of the object. Nevertheless, the details of the object are recorded there. To display the object the hologram is positioned in a beam of laser light (called the reconstruction beam) identical with the original reference beam. This beam is diffracted as it passes through the pattern of lines within the hologram. Much of the light passes directly through with no change in direction, but some of the light is diffracted to form two new beams, one on each side of the direct beam.

If you look at the hologram when your eyes are intercepting one of these side beams, you see an image of the object. In one of the beams the waves emerge from the hologram traveling in the same directions as the waves in the original object beam did. Intercepted waves are focused onto the retina of each eye. Since your eyes are separated and intercept different parts of the diverging waves, the locations of the images on the retina differ, an effect called parallax. Your visual system interprets the difference in location as evidence that the source of the light lies on the other side of the hologram at the spot originally occupied by the object. In effect your visual system extrapolates the rays of light backward until they cross at the location of the perceived image. For this reason you perceive depth in the scene. The image is said to be a virtual one because if you place a blank card at its apparent location, no image forms on the card. The image is only a product of your visual system.

The other beam of diffracted light consists of waves that first converge and then diverge. If you place a blank card at the point of convergence, a real image of the object appears on it. You can also see the image by intercepting with your eyes the light diverging from the image. Again you perceive the image to be at a certain location because of parallax. In this case you see the image in front of the plane of the hologram. The image, however, is usually too distorted to be recognizable; with some arrangements of equipment it may not appear at all.

An undistorted real image can be produced by sending a beam of light through the hologram in a direction opposite to the direction of the original reference beam. This reconstruction beam is said to be conjugate to the reference beam. As before, part of the light diffracts into two side beams, one beam capable of producing a real image and the other a virtual image. This time it is the virtual image that is distorted or missing.

A hologram is actually a diffraction grating. A standard diffraction grating consists of fine, equally spaced parallel lines. The lines in a hologram are not equally spaced because the object beam diverges. At any location in the film the spacing of the lines depends on the angle between the rays in the object and reference beams reaching that point. If the angle is small, the lines are widely spaced. If the angle is large, the lines are narrowly spaced. The variation in the spacing of the lines is the factor that gives rise to the convergence or divergence of the beams diffracted to the sides when the hologram is illuminated by a reconstruction beam.

Suppose the object is extended instead of being a point. Each point on its surface reflects diverging light to the film, interfering there with the reference beam. The interference pattern recorded on the film is quite complex. Still, when the reconstruction beam is sent through the developed film along the reference-beam path or the conjugate to it, side beams form. Two of them provide undistorted images. If your eyes intercept either beam, the image is three-dimensional because of parallax. If you change your viewpoint within a beam to intercept different parts of the waves, you see a different perspective of the image. This feature enables you to see the front of the object or, by changing your viewpoint, to see along the sides, just as you would if you looked at the original object. (You cannot see an image of the back of the object with this arrangement of equipment because rays from the back never reach the film.)

The undistorted real image that is produced by a conjugate reconstruction beam can be displayed on a card. It is blurry, however, because only parts of it are in focus at any given location of the card. When you see it by intercepting the rays, it has inverted depth. For example, the front of the object seems to be farther away than the sides, giving the impression that the image is inside out. The image is said to be pseudoscopic.

This image from a hologram can be valuable in a technique in which a second hologram is made from the first. Such an arrangement is called focused-image or image-plane holography since the copy is positioned with in the real image cast by the master. The real image is produced by sending through the master hologram a reconstruction beam conjugate to the master's reference beam.

In order to avoid rearranging the positions of the laser and various optical h devices, one would like to employ the same beam that previously served as the reference beam. This can be accomplished by rotating the master 180 degrees about a vertical axis so that what was the reference beam now becomes the conjugate reconstruction beam. Because of the rotation, the light passes through the master in the direction opposite to the path of the original reference beam.

The beam that forms the real image then functions as the object beam for the copy. A reference beam also illuminates the copy. The film records the resulting interference pattern of the two beams. After the copy is developed it is rotated about a vertical axis so that what was a reference beam is now the conjugate reconstruction beam. When your eyes intercept the light diffracted from the beam by the copy, you perceive a three-dimensional image that appears to straddle the plane of the hologram. The part in front of the plane is a real image. The part that seems to be behind the plane is a virtual image.

The image forms as follows. The light traveling from the master to the copy converges to form a real three dimensional image through which the copy film makes a two-dimensional slice. The rays that form an image of the front of the object converge in front of the film. When they pass through the film, they are diverging The rays that form an image of the other sides of the object converge behind the film. As those rays pass through the film they are still converging. The interference between these two sets of rays and the reference beam records the convergence and divergence of the rays.

When the copy is developed and a conjugate beam is sent through it, the diffraction of the light reverses what the rays did during the exposure of the copy. Where rays had been converging they now diverge and where they diverged they now converge. When your eyes intercept the rays, you see a real image of the front of the object lying in front of the copy and a virtual image of the other sides of the object lying behind the copy. Although the master's real image is pseudoscopic, the final image shows normal depth.

If white light is sent through the copy instead of monochromatic light from a laser, each wavelength in the visible spectrum is diffracted by a slightly different amount, creating its own image. The resulting overlap of many colored images yields a blurry composite image. Benton discovered a way for an observer to be able to see clear images when a copy is illuminated by white light. The result is called a rainbow hologram because of the vivid colors of its images.

In making a rainbow hologram only a narrow strip of the master is illuminated by its reconstruction beam. A1though information about depth perpendicular to the strip is lost, information about depth parallel to the strip is preserved. Hence a rainbow hologram is a compromise: the possibility of parallax is eliminated in one direction so that the image can be seen in white light without blurring.

In one method the master is masked except for an aperture running across its width. In the top illustration at the left, which shows the setup from overhead, the aperture is vertical. Parallax information about the object is kept in the vertical direction but is lost in the horizontal direction. The aperture's width is also recorded in the copy.

The developed copy is viewed in a conjugate laser beam. (Again, in order for the laser beam that served as a reference beam for the copy to now serve as the conjugate reconstruction beam, the copy is rotated about the vertical axis.) The rays of light emerging from the copy pass through a real image of the aperture that lies in front of it. In the illustration at the left the aperture image extends into the page. You can see the image of the object if you position your eyes anywhere in the aperture image. By moving your eyes to a new location within the aperture image you see a different perspective of the object. Information about depth is retained along the direction of the aperture image (vertically in this case). If you move your eyes out of that image, however, the image of the object disappears. Information about depth is lost along the direction at right angles to the aperture image.

When white light is sent through the developed copy, each wavelength is diffracted by different amounts and creates an

aperture image at a different location in front of the hologram. If you position your eyes in the aperture image created by red light, you see a red image of the object. As you move your eyes through the other aperture images, the image smoothly changes color. No blurring results from this procedure if your eyes are at an aperture image. If you move too close to or too far from the hologram, the rays passing through the various aperture images overlap and a blur results.

Hobbs experimented with ways of making and conveniently viewing a rainbow hologram. Assuming it would be held vertically in descending light that strikes the far side, he decided to turn the object onto its side when he made the master. After the copy was developed he rotated it so that the descending light was conjugate to the reference beam the copy had when it was exposed. By this procedure he made the top of the object appear at the top of the hologram.

Hobbs also arranged for viewing along a line approximately perpendicular to the plane of the copy. Since green light is in the middle of the visible spectrum, the rays forming the green aperture image should represent that perpendicular line. By moving your eyes upward and closer to the hologram you bring up the red aperture image; moving downward and farther from the hologram makes the image blue.

Hobbs calculated that if the rays of green light are to leave the copy approximately perpendicular to its plane after reaching the copy at about 45 degrees, the spacing between diffraction lines within the hologram should be about .78 micrometer. (This number and the other numbers that follow are only representative. The complex pattern of lines actually has a range of spacings.) At that spacing light at the red end of the spectrum (wavelength .7 micrometer) is diffracted about 11 degrees to one side of the green rays and light at the blue end (wavelength .4 micrometer) is diffracted about 11 degrees to the other side. Intermediate colors are diffracted at intermediate angles. The full spectrum of aperture images lies in a fan covering an angle of about 22 degrees.

Hobbs also gave thought to the distance between the copy and the observer's eyes. If the green aperture image is 35 centimeters from the copy, the extreme red one is about 28 centimeters away and the extreme blue one is about 48 centimeters away. These distances make viewing quite convenient.

The line separation within the copy I depends on the wavelength of the light that made it and on the angle between the reference beam and the object beam (from the aperture on the master) that illuminate it. If the light from a helium-neon laser (wavelength .63 micrometer) is to produce a line separation of about .78 micrometer, the angle between the two beams should be about 54 degrees.

Finally Hobbs considered the light source that would serve as the reconstruction beam. If the source is the sun, the beam consists of approximately plane waves. Since the beam is supposed to be conjugate to the reference beam employed in making the copy, the reference beam must also consist of plane waves. If the light source is a light bulb, the reconstruction beam consists of diverging rays. The conjugate of such a beam is a beam of converging rays, and so the reference beam would have to be made up of converging rays too.

Many suggestions about the making of rainbow holograms can be found in Holography Handbook. They include ways to concentrate the light passing through the aperture on the master by means of a cylindrical lens made from a test tube filled with glycerin. With such a lens you may even be able to do without making the master. The lens can focus a narrow, real image of the object directly onto the copy.

Bibliography

HOLOGRAPHY HANDBOOK: MAKING HOLOGRAMS THE EASY WAY. Fred Unterseher, Jeannene Hansen and Bob Schlesinger. Ross Books, 1982.

SEEING THE LIGHT: OPTICS IN NATURE, PHOTOGRAPHY, COLOR, VISION, AND HOLOGRAPHY. David Falk, Dieter Brill and David Stork. Harper & Row, Publishers, 1986.

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.