30.10

*Holography

One of the most familiar applications of lasers is in holography, which is a process for producing three-dimensional images. The information used to produce a holographic image is captured on photographic film, which is referred to as a hologram. Figure 30-32 illustrates how a hologram is made. Laser light strikes a half-silvered mirror, or beamsplitter, which reflects part and transmits part of the light. In the drawing, the reflected part is called the object beam because it illuminates the object (a chess piece). The transmitted part is called the reference beam. The object beam reflects from the chess piece at points such as A and B and, together with the reference beam, falls on the film. One of the main characteristics of laser light is that it is coherent. Thus, the light from the two beams has a stable phase relationship, like the light from the two slits in Young’s double-slit experiment (see Section 27.2). Because of the stable phase relationship and because the two beams travel different distances, an interference pattern is formed on the film. This pattern is the hologram and, although much more complex, is analogous to the pattern of bright and dark fringes formed in the double-slit experiment.

Figure 30-32 An arrangement used to produce a hologram.

The physics of holography.

Figure 30-33 shows in greater detail how a holographic interference pattern arises. This drawing considers only the reference beam and the light () coming from point A on the chess piece. As we know from Section 27.1, constructive interference between the two light waves leads to a bright fringe; it occurs when the waves, in reaching the film, travel distances that differ by an integer number m of wavelengths. In the drawing, is the distance between point A and the place on the film where the mth-order bright fringe occurs. is the perpendicular distance that the reference beam would travel from point A to the m = 0 bright fringe. In addition, rm is the distance along the film that locates the bright fringe. In terms of these distances, we know that

The first of these equations indicates that , which can be substituted into the second equation. The result can be rearranged to show that

Since is typically much larger than (for instance, m and m), it follows that . In other words, rm is roughly proportional to . Therefore, the fringes are farther apart near the top of the film than they are near the bottom. For example, for the m = 1 and m = 2 fringes, we have , whereas for the m = 2 and m = 3 fringes, we have .

Figure 30-33 This drawing helps to explain how the interference pattern arises on the film when light from point A (see Figure 30-32) and light from the reference beam combine there.

In addition to the fringe pattern just discussed, the total interference pattern on the hologram includes interference effects that are related to light coming from point B and other locations on the object in Figure 30-32. The total pattern is very complicated. Nevertheless, the fringe pattern for point A alone is sufficient to illustrate the fact that a hologram can be used to produce both a virtual image and a real image of the object, as we will now see.
To produce the holographic images, the laser light is directed through the interference pattern on the film, as in Figure 30-34. The pattern can be thought of as a kind of diffraction grating, with the bright fringes analogous to the spaces between the slits of the grating. Section 27.7 discusses how light passing through a grating is split into higher-order bright fringes that are symmetrically located on either side of a central bright fringe. Figure 30-34 shows the three rays that correspond to the central and first-order bright fringes, as they originate from a spot near the top and a spot near the bottom of the film. The angle , which locates the first-order fringes relative to the central fringe, is given by Equation 27.7 as , where d is the separation between the slits of the grating. When the slit separation is greater, as it is near the top of the film, the angle is smaller. When the slit separation is smaller, as it is near the bottom, the angle is larger. Thus, Figure 30-34 has been drawn with smaller than . Of the three rays emerging from the film at the top and the three at the bottom, we use the uppermost one in each case to locate the real image of point A on the chess piece. The real image is located where these two rays intersect, when extended to the right. To locate the virtual image, we use the lower ray in each of the three-ray bundles at the top and bottom of the film. When projected to the left, they appear to be originating from the spot where the projections intersect—that is, from the virtual image.

Figure 30-34 When the laser light used to produce a hologram is shone through it, both a real and a virtual image of the object are produced.

A holographic image differs greatly from a photographic image. The most obvious difference is that a hologram provides a three-dimensional image, whereas photographs are two-dimensional. The reason that holographic images are three-dimensional is inherent in the interference pattern formed on the film. In Figure 30-32 part of this pattern arises because the light emitted by point A travels different distances in reaching different spots on the film than does the light in the reference beam. The same can be said about the light emitted from point B and other places as well. As a result, the total interference pattern contains information about how much farther from the film the various points on the object are, and because of this information holographic images are three-dimensional. Furthermore, as Figure 30-35 illustrates, it is possible to “walk around” a holographic image and view it from different angles, as you would the original object.

Figure 30-35 A hologram of a galleon spaceship approaching earth. Two views of the same hologram are shown: (a) looking at the hologram perpendicularly and (b) looking at an angle to the right of the perpendicular. (©Holographics North, Inc., and Sprint. Reproduced with permission of Sprint Corporation)

A vast difference between the methods used to produce holograms and photographs exists. As Section 26.7 discusses, a camera uses a converging lens to produce a photograph. The lens focuses the light rays originating from a point on the object to a corresponding point on the film. To produce a hologram, lenses are not used in this way, and a point on the object does not correspond to a single point on the film. In Figure 30-32, light from point A diverges on its way to the film, and there is no lens to make it converge to a single corresponding point. The light falls over the entire exposed region of the film and contributes everywhere to the interference pattern that is formed. Thus, a hologram may be cut into smaller pieces, and each piece will contain some information about the light originating from point A. For this reason, each smaller piece can be used to produce a three-dimensional image of the object. In contrast, it is not possible to reconstruct the entire image in a photograph from only a small piece of the original film.
The holograms discussed here are typically viewed with the aid of the laser light used to produce them. There are also other kinds of holograms. Credit cards, for example, use holograms for identification purposes. This kind of hologram is called a rainbow hologram and is designed to be viewed in white light that is reflected from it. Other applications of holography include head-up displays for instrument panels in high-performance fighter planes, laser scanners at checkout counters, computerized data storage and retrieval systems, and methods for high-precision biomedical measurements.

Copyright © 2007 John Wiley & Sons, Inc. All rights reserved.