Holography The Whole Picture
At the Spring 1964 meeting OF THE OPTICAL SOCIETY OF America, in Washington, D.C., Emmett Leith and Juris Upatnieks, from the University of Michigan, gave a presentation about their work in holography. When Upatnieks concluded his address, he announced that one of these images, a hologram of a toy train, was on display in a suite in the conference hotel. A line soon formed out the door of the suite, down the hall, and around the corner, with everyone eager to get a glimpse of this three-dimensional photograph. But the scientists had trouble believing what they saw. “They were all asking, ‘Where is the train?’” Leith says. “We had to tell them, ‘Back in Ann Arbor.’”
If you have never seen a “display hologram,” reconstructed with monochromatic light, you might not believe your eyes either. At the MIT Museum, in Cambridge, Massachusetts, holographic portraits hover in the air in front of their frames, begging to be touched. Images projected a foot in front of the frame are common, and projections up to four feet are obtainable with some large holograms.
If a magnifying glass is included in the image, the magnifying glass in the projected image is fully functional. If you stand off a little to the side, you can see the object in profile, just as if it were there. Moving directly in front of the image, you get a head-on view. Walking to the other side, you notice a vase of flowers that you didn’t see before. In some cases, you can see over the top of the object or bend down to look at it from be- low, since the three-dimensional effects are active in the vertical direction too.
What you can’t do is walk around the back to look at the image from behind, for a threedimensional transmission hologram can be seen only within a limited viewing angle. Move too far to the side and the image disappears; walk behind the frame and you will see the hardware that makes the hologram work, a diffuse laser or white halogen light illuminating the back of a piece of holographic film, projecting the image through the frame. By taking multiple holograms of an object on a revolving stand, however, and then bending the resulting film into a cylinder and lighting it from the inside, a 360-degree image can be created.
Though holograms can be recorded on various media, including foils, plastics, and solid gels, most often a silver halide film similar to the kind found in a 35-millimeter camera is used. The main difference is that in holographic film, the silver halide crystals must be smaller and more densely packed, to give approximately 50 times better resolution.
But here the similarity to photography ends. If you look at a photographic negative, you can see the image that is recorded there. Not so with holographic film. If you look at an exposed piece of holographic film in normal light, it appears to be featureless and gray, like an overexposed negative. Examination with a magnifying glass shows that it contains patterns of whorls and bull’s-eyes but no hint of an image.
The information on holographic film is contained in tiny interference fringes that were created when two beams of laser light struck the film during exposure. One of these beams (the “object beam”) bounced off the subject, while the other (the “reference beam”) traveled straight from the laser to the film (or was bounced off a mirror). Instead of creating an image on the film, the two beams left an interference pattern of finely spaced fringes. Thousands of these fringes can be packed into a millimeter of high-resolution film.
The interference patterns contain all the information needed to reconstruct the three-dimensional image, and a duplicate of the reference beam is all that’s needed to do the job. When you shine this beam through the holographic film, the interference patterns bend the reference beam in such a way as to re-create the missing object beam, the one that reflected from the subject during exposure. Your eyes receive the exact same optical information they would get if the actual subject were in front of you.
The uses of holographic technology are not limited to dramatic visual displays. Sometimes, in fact, they have nothing to do with three-dimensional images at all. Holographic films can be made to interact with light in other ways, performing the same function as lenses, filters, mirrors, or other types of standard optical devices. Such holographic films are referred to as holographic optical elements. The spacing and intensity of the interference fringes determine the function of the element. Like standard optical elements, they can focus, bend, reflect, and filter light; their modest weight, flexibility, and low cost can make them cheaper and easier to use than regular lenses and mirrors.
Holographic optical elements are in constant use at the supermarket. The bar-code scanner contains a rotating disk with a set of holographic films that act like distorted lenses, bending light from a laser into odd patterns on the package containing the code. As the disk rotates, each holographic lens creates a unique laser pattern, with rays that reach out at different angles and distances to “search” for the bar code on a package. These changing patterns make sure that the bar code will be read regardless of its orientation, so the checkout clerk doesn’t have to line up the package at any specific angle.
The “head-up display” used in airplanes is another holographic optical element. A transparent holographic mirror in front of the windshield reflects a bright green image of flight data (projected from a cathode-ray tube) back to the pilot. The mirror is transparent, allowing the pilot to see into the distance, and the use of holography yields a much sharper image than a conventional flat-screen projection would.
Perhaps the most important practical application of holography to date is for security purposes. Credit cards, driver’s licenses, and some countries’ currencies contain embossed holograms to prevent alteration or counterfeiting. But there is much more. Aerospace engineers use holography in supersonic wind tunnels to analyze the shock waves that the space shuttle experiences during flight; geologists use seismic-wave holography to model the earth’s interior; and acoustical engineers use holography to study the vibration of violin bodies to determine what makes a Stradivarius a Stradivarius.
Dennis Gabor, the Hungarian physicist who conceived the idea of holography on Easter Sunday in 1947 while waiting for a tennis court in Rugby, England, had none of these applications in mind. He had been pondering ways to improve the electron microscope and overcome the physical limitations that were preventing the instrument from reaching its ultimate potential, the ability to see atoms. “A solution suddenly dawned on me,” Gabor said in his Nobel Prize lecture in 1971. “Why not take a bad electron picture, but one which contains the whole information, and correct it by optical means?”
Sudden bursts of insight were not new for Gabor. When he was growing up, his father, Bertalan Gabor, director of the Hungarian General Coal Mining Company, regaled his son with stories of the great inventors, especially Thomas Edison. In 1910, while walking in the town park, young Dennis saw a merry-go-round with its seats in miniature airplanes instead of on horses. When a real airplane flew low over the park, he put the two events together and ran home to draw up plans for an amusement park ride with real, functioning airplanes tethered to a pole by a wire. His father helped him put the plans in order and submitted them to the Hungarian Patent Office. On November 14, 1911, at the age of 11, Dennis Gabor was awarded Patent No. 54,703 for his airplane merry-go-round.
Physics fascinated the young Gabor, but at college he chose to study electrical engineering, since, as he later wrote, “Physics was not yet a profession in Hungary, with a total of half-adozen university chairs—and who could have been presumptuous enough to aspire to one of these?” He earned a doctorate at the Technische Hochschule, in Berlin, in 1927 and went to work for Siemens & Halske, where he developed the mercury-vapor lamp now commonly used in streetlights.
In 1933, with the rise of the Nazis, Gabor left Germany. He settled in England the next year and got a job with the British Thomson-Houston Company, where he continued his work in illumination before branching out into other areas. He was still at BTH when he had his tennis-court epiphany, but in 1949 he joined the faculty of London’s Imperial College of Science and Technology, where he stayed until his retirement in 1967.
The idea that popped into Gabor’s mind in 1947 was this: If he could record all the information contained in an electron microscope’s beam of electrons, the need to improve electron optics would disappear. Microscopists were recording only the intensity of their electron waves; any information about the phases was lost. The same is true, of course, of ordinary photographs, which record only the intensity of the incident light waves (which are, in any case, a jumble of frequencies and phases). Gabor realized that by recording what he came to call the “hologram” of the waves—from the Greek words holos for whole and gramma for message—he could achieve much higher resolution with existing electron lenses.
To picture these concepts more clearly, think of the waves that form when you drop a stone into a pond. They contain high points, or peaks, and low points, or troughs. The height of a peak or depth of a trough is a measure of the intensity of the wave. If you drop two pebbles into the pond some distance apart, their concentric rings of waves will eventually meet. When the peaks of one coincide with the peaks of another, or the troughs match up with the troughs, they are said to be “in phase.” This is called “constructive interference.” The peaks add together to give one higher peak, and the troughs add to give a lower trough. If, on the other hand, the troughs of one match up with the peaks of a second, they cancel out. This is called “destructive interference.” In the case of optics, the surprising result is, as Gabor put it, “that light added to light can produce darkness.” Of course, any state of partial interference between these two extremes is also possible.
A hologram is a recording of the interference patterns created when two beams of coherent light—or any other coherent waves, such as sound waves or microwaves—meet. Only coherent waves can form useful interference patterns. By coherent, we mean that the waves in the light beam must be monochromatic (be temporally coherent) and have a constant phase difference (be spatially coherent). Laser light has this quality, but before lasers were available, holographers had to generate monochromatic light some other way and make sure that it emanated from a point source to guarantee coherence. This meant that holography was limited to monochromatic images. Today it’s possible to create color holograms by taking multiple images and combining them. Soon after his Easter Sunday tennis match in 1947, Gabor was back in his laboratory at BTH to test his ideas. Instead of using electron waves, he decided to work with light waves from an intense mercury-arc lamp to demonstrate the principle. For his first hologram, he used standard photographic reduction techniques to produce a tiny transparency 1.4 millimeters in diameter with the names of three giants in the history of optics—Huygens, Young, and Fresnel—written in black inside a circle. The transparency had to be very small because the light beam that would be illuminating it would necessarily have a small diameter.
In Gabor’s Original Setup , light from the mercury-arc lamp passed first through a filter to make it monochromatic and then through a pinhole to ensure that it was spatially coherent. The light then passed through the transparency and was recorded on a glass plate coated with the most sensitive photographic emulsion available. So far it sounds like an ordinary photograph, but Gabor’s specially prepared light made the difference.
Light waves that passed through the clear part of the transparency proceeded directly to the emulsion, but those that passed through the dark letters were diffracted. Since the diffracted and undiffracted waves traveled different distances and at different angles, their phase differences had changed by the time they reached the photographic plate, so they interfered with each other irregularly. The irregularly spaced interference patterns were recorded on the emulsion. The result was a dark, hazy pattern consisting of numerous wavy, concentric circles, with illegible black smudges where the letters should have been.
This was exactly what Gabor had expected. And when he took his holographic image and shined a beam from the mercury lamp through it, the reconstructed image of the circle with the three names again appeared. Gabor published a photograph of this first hologram in the May 15, 1948, issue of Nature under the title “A New Microscopic Principle.”
Almost in passing, he mentioned, “It is a striking property of these diagrams that they constitute records of threedimensional as well as of plane objects.” Gabor’s first subject, though, had been essentially two-dimensional, since mercuryarc lamps and pinhole light sources were not intense enough to allow him to work in three dimensions. Gabor was confined to using transparencies, and by the mid-1950s holography was largely forgotten. It would take the invention of the laser in 1960 to resurrect it.
Emmett Leith was a Michigan boy born and raised, so it was no surprise that after his graduate studies in physics at Wayne State University, in Detroit, he took a job at the University of Michigan, in Ann Arbor. In 1954 he was a young physicist working at the university’s Willow Run Laboratory on a classified military radar program called Project Michigan. The military wanted radar images with resolution as good as that of aerial photography. But since radio waves are about 10,000 times as long as optical light waves, this would require the reconnaissance plane to carry an antenna about 10,000 times the size of a typical optical lens. Because this hardly seemed practical, the researchers decided to use what amounted to a synthetic antenna, by storing the phases and intensities of reflected radio waves that a small antenna collected along its flight path.
Looking for a way to store this large amount of data, they decided—”as a wild scheme,” Leith later said—to use optical methods. If they recorded the information from the reflected radar waves on photographic film, they could read it back by scan- ning the film with a light beam. As one of the few physicists in a group of electrical engineers, Leith volunteered to work on the optical processor. Considerable compression would be involved: “Data collected along 1 km of flight path gets recorded on a few cm of photographic film,” Leith wrote.
While analyzing the mathematics of the process, Leith discovered “a most astonishing thing going on. When you shine light on the optical data transparency, you get a miniature recreation of the scanned object.” Essentially, he realized, his team would be recording the interference patterns of radar waves reflected from the ground. Leith had rediscovered holography.
Because he was merely working it out on paper, he had no actual reconstructed images to show his colleagues. All he had were equations showing what they would see. Still, “we developed the complete theory of holography in the microwave region from the fall of 1955 to April of 1956,” Leith recalls. “The following October I came across a paper about holography and read about Gabor’s work.” He was both disappointed and delighted: disappointed that what he’d done was not new, but delighted that it was significant enough to have been considered before by a scientist of Gabor’s magnitude.
In the Soviet Union in 1958, Yuri Denisyuk became the third person to discover holography independently. As a boy he had dreamed of working with quantum mechanics and relativity, and after graduating from the Leningrad Institute of Fine Mechanics and Optics in 1954, he went to work at the Vavilov State Optical Institute. He was frustrated to find himself stuck working with everyday glass lenses and prisms, and he longed for more interesting research.
An insight came while he was reading a sciencefiction story called “Star Ships,” by the Soviet writer Yuri Efremov. In it, archeologists excavating a site on earth that aliens had once visited find a strange-looking plate. “From a deep, absolutely transparent layer, a strange face was looking at them,” wrote Efremov. “The face was enlarged by some unknown optical method to its natural size and was three dimensional in its shape.” Denisyuk was inspired. “A bold idea occurred to me,” he wrote. “Why not try to create such photos by means of modern optics?”
In 1958, oblivious of Gabor’s and Leith’s work, he set about rediscovering the basic principles of wave-front reconstruction. Denisyuk took a slightly different approach. Like Gabor, he recorded the interference between a deflected beam and a reference beam, but he put the object on one side of the film and the reference beam on the other. These two beams struck the film (which was transparent) from front and back, and the interference pattern was formed across the entire depth of the emulsion instead of just on its surface.
A hologram recorded with this arrangement had “the most wonderful reflecting properties,” Denisyuk wrote. “It is capable of reproducing the precise values of the phase, amplitude (intensity) and spectral composition of the object wave.” He called his invention a “wave photograph,” but it has come to be called a “volume reflection hologram” or a “Denisyuk hologram.”
One major benefit of Denisyuk holograms is that the image can be viewed in ordinary reflected white light. Although the hologram was made with monochromatic light from a mercury-arc lamp, the viewer does not need a similar source to unlock the image. When white light, which contains all visible wavelengths, strikes the fringes and reflects toward the viewer, the emulsion transmits only the wavelength that was used to record the hologram. The resulting three-dimensional image is faint but visible.
While writing up his findings, Denisyuk came across a reference to Gabor’s 1948 paper. He felt the same disappointment and delight that Leith had when he found out that he had not been first. But his frustration mounted when he realized that some skeptical Soviet scientists were trying to block publication of his work. Denisyuk finally managed to publish three important papers between 1962 and 1965, but because of the delay, his discoveries were not widely known in the West until the late 1960s. In 1970, when his contributions were fully recognized, Denisyuk received the Lenin Prize, the U.S.S.R.’s highest scientific award.
Meanwhile in 1960 Leith teamed up with Juris Upatnieks, an electrical engineer fresh from the University of Akron, to work on another problem: getting rid of the annoying double image that was part of the reconstruction process. By now they were making actual holograms. During reconstruction the interference pattern on the holographic film causes some of the light to be bent in a converging manner and some in a diverging manner, resulting in two images of the object. The “virtual” image forms behind the holographic film and has the same orientation as the original object; the “real” image appears to float in front of the film and is reversed.
This problem was inherent in Gabor’s method. And because he had placed his transparency directly between the light source and the film, the reconstructed images were in the same line of sight. The observer had to look through the reversed image that floated in front of the film to see the correctly oriented image behind the film. Gabor had found ways to nullify the unwanted image, but they made a complicated procedure even more so.
Using experience from his previous work, Leith adopted the principle of “side looking radar,” which had helped reduce the noise in radar signals. For his first holography experiments, he moved the reference beam off to the side of the object (a piece of wire) and used a diffraction grating to split the beam. Half the light (the object beam) was scattered by the wire, while the other half (the reference beam) passed straight through to the film. These two beams met on the surface of the film, forming a holographic pattern of the wire’s silhouette.
This technique of “off-axis holography” had an enormous impact. Because the reference beam had struck the film at a different angle from the object beam, upon reconstruction the real and virtual images were separated in space—by an angle twice as large, it turned out. Now an observer could look straight through the film to see the virtual image in its original orientation without the annoyance of the intervening reversed image. This solution was crucial to the advance of holography as a useful technology. Among other things, it made it possible to pack scores, even hundreds, of images on a single plate, each one taken and stored at a slightly different angle.
Despite all this progress, one major problem remained. With only mercury-arc lamps available as a light source, the range of objects that could be imaged by the holographer was limited mainly to transparencies. By the time the source light made it through a monochromatic filter and a pinhole, its short coherence length and low intensity precluded high resolution. Then in 1960 Theodore Maiman, of the Hughes Aircraft Company, produced the first pulsed ruby laser, which gave holography a whole new life. It became commercially available in 1962. Finally, here was a source of bright, coherent, monochromatic light.
“Everybody in optics wanted to see what the laser would do for them, and we were no exception,” Leith said. But his first experiments were disappointing. Substituting a laser for the lamp he and Upatnieks had used in their radar optical processor produced mostly noise. “Is this what we were waiting for?” Leith recalls asking himself. Perhaps the breakthrough was no breakthrough at all.
A careful investigation revealed the problem: Laser light was too demanding for their experimental setup. Its high coherency made dust particles on lenses into sources of noise, and bubbles or scratches in the glass could scatter the light in any direction. These same sources of distortion had always been there, but the lesser coherence of pinhole-selected mercury-arc light made them unimportant. Now they were a serious problem. By tightening their standards of polishing and cleanliness and eliminating extraneous reflections, Leith and Upatnieks brought the noise into line and began producing high-quality laser holograms. Instead of a diffraction grating, they now used a partially silvered mirror to split the beam. A lens spread the beam to cover the entire object.
More important , by combining laser light with the off-axis technique, they opened up the world of holography to realworld three-dimensional objects. When the object was placed between the light source and the film, holographers were confined to working with transparencies or simple objects like a wire. But now the light reflected from any three-dimensional object could be captured holographically. “As soon as we showed we could make pictures of three-dimensional real-world objects,” Leith remembers, “that caused some excitement.”
Edwin Land, the founder, president, and director of research of the Polaroid Corporation, was aware of Gabor’s early work on holography, and he had targeted it as a key technology for three-dimensional motion pictures that would not require special glasses. When news broke of Leith and Upatnieks’s stunning success at the Optical Society meeting in 1964, he was quick to get involved. He invited George Stroke, an engineer in the Michigan group, to give a presentation at Polaroid on March 25, 1965. Stephen Benton, a young Ph.D. student at Harvard University who was doing his thesis research at Polaroid, was in the audience. When Stroke showed a laser reconstruction of a coffee cup, Benton recalls, “it was transfixing.” He could not wait to try holography himself: “That night, my wife and I and two friends from Polaroid scrounged up a laser and made a very simple hologram of a diffuser, just trying to duplicate what we had seen. It was one of those pivotal days. ”
The next year, Benton went to summer school at the University of Michigan, where Leith and Upatnieks filled him in on the details. When he returned to Polaroid, he was given the back ten feet of the coffee room to set up a laboratory, and he began experimenting with holographic techniques. “The way life was with Land,” he explains, “if you had something new in your pocket every time you bumped into him in the halls, you were okay. So we kept pushing to make new kinds of holograms.”
A breakthrough came in late 1968, while Benton was working on holographic video. The problem with making it practical was—and still is—the enormous amount of information needed to encode a three-dimensional moving image. While 2-D video requires approximately one-quarter of a megabyte per frame, a holographic image requires 36 megabytes per frame. To reduce this number, Benton decided to eliminate the parallax effect—the ability to see around the holographic object—from the vertical direction. This was not much of a sacrifice for the viewer, but the reduction in required data was significant.
He eliminated the vertical parallax by first making a hologram the conventional way and then making a second hologram of that image, shining the object laser beam through a narrow horizontal slit on the imaging mirror. When this image was reconstructed, it had horizontal parallax—you could still move your head sideways to see around an object—but the scene remained unchanged when you moved your head vertically.
Benton soon realized that he had done more than make three-dimensional video a bit more feasible. When he shined white light through his holographic film, the film essentially acted as a prism and broke up the light into its component colors. Just as with a prism, different wavelengths of light were bent at different angles. In this case the image from the horizontal slit was reproduced in different colors at different viewing angles, yielding a rainbow effect. The result is the “rainbow” or “Benton” hologram that is used on credit cards to prevent alteration or counterfeiting. Tilt the card up and down, and you can see the color change; tilt it side to side and the parallax effect is evident.
The first rainbow hologram , taken in i968, was of a plastic dinosaur. When Benton showed it to Land, the company founder remarked, “Well, it looks like holography has a future after all.” The rainbow hologram contributed greatly to that future. It was the first bright hologram that could be viewed in normal white light, and it could be embossed on foil or plastic—stamped out like a vinyl record album—enabling cheap mass production. It is most responsible for making holography into the substantial industry that it is today.
Another major advance in holography for industrial purposes came in 1965, when Karl Stetson and Robert Powell of the University of Michigan discovered the phenomenon called holographic interferometry. Because of the extremely fine detail that had to be recorded in a hologram, great care had always been taken to prevent any movement during exposure. Objects and optical components were placed on very heavy tables supported by shock absorbers. Movements of as little as a millionth of a millimeter would produce dark areas, similar to a blur in normal photography.
Stetson and Powell decided to study these blurry holograms instead of throwing them out. They soon realized that the dark areas contained information about the nature of the movement that had taken place. Some objects move in the course of their operation, like the vibrating surface of a loudspeaker. Having a way to see and record their movements would help researchers understand how they worked.
If an object, such as a guitar’s body, vibrates at a known frequency while a holographic exposure is taken, its vibrational characteristics can be revealed upon reconstruction of the hologram with a process called time averaged interferometry. Contours on the surface of the object, looking like the elevation contours on a map, indicate the regions of vibration; the darker the region, the greater the movement.
Along these same lines, double-exposure holographic interferometry is a nondestructive testing technique that can reveal defects that are not visually detectable. Consider an automobile tire. A first holographic exposure of it is taken with the tire inflated at low pressure; a second exposure is made on the same piece of film after the tire has been expanded slightly with a puff of hot air. If the tire is structurally sound, it will expand uniformly, and the reconstructed hologram will have very broad contour lines, indicating that each point on the surface has moved approximately the same distance.
If, however, there is a flaw in the tire that causes one part to expand more than the rest, the reconstructed hologram contains interference patterns that look like bull’s-eyes around the defective region. Before holography, the only way to find such a defect would have been to test the tire destructively—cut it apart and look for the trouble. Nondestructive testing is the most important industrial application for holographic technology.
Portraits of human subjects became possible around 1967, thanks to the work of Lawrence D. Siebert of the Conductron Corporation, of Ann Arbor. Human subjects had presented two fundamental difficulties: People tended to move during the exposure time, and they could be blinded if they looked directly into the laser. Even if the subject remained completely still, the movement of his or her skin caused by the pulsing of blood through the veins would be enough to ruin the hologram. Siebert solved this problem by using a pulsed laser whose brief flash of light, lasting only a few milliseconds or nanoseconds, froze the subject in place. He also used a diffusing device to spread the laser light over a larger area, eliminating the danger of blindness. Shortly before Gabor received his Nobel Prize in 1971, he sat for a holographic portrait.
Museums began to use holography as a means of displaying rare or delicate artifacts. There are hundreds of copies of a hologram circulating among the world’s archeologists and art collectors of the remains of the Lindow Man, a 2,300year-old preserved body found in a peat bog called Lindow Moss in Cheshire, England, in 1984. Researchers and the general public can view the famous corpse without exposing the artifact to the potentially damaging conditions of the open air. The original is kept in a climate-controlled case at the British Museum, in London.
In medicine, full three-dimensional images of an eye have been obtained in a flash using an ophthalmic holocamera. The resulting data can be used to monitor cataract formation or retinal detachment. Three-dimensional images of a brain can be built up from the two-dimensional slices of data produced by CAT scans or MRI systems.
Other applications currently under development include holoprinters that will allow you to print a hologram directly from your home computer; data-storage devices that will record data throughout the whole volume of a CD, instead of just on its surface, increasing its capacity enormously; three-dimensional television, movies, and video games; and haptic holography, which uses springs and feedback mechanisms to create a system in which holographic models can be modified by hand in real time.
And what of Gabor’s original intention to improve the electron microscope’s resolution? In the early days, as Gabor realized, it was not possible to produce the coherent beam of electrons that would have been needed to perform electron holography. But while most of the holographic world moved on to other applications, small groups of electron microscopists continued to improve their instruments over the years.
In 1955 Gottfried Möllenstedt and Heiner Düker of the University of Tübingen in Germany developed the electron biprism. This is a conductive fiber in the microscope’s imaging lens that splits the electron beam and, if a positive voltage is applied to the fiber, causes the two waves to overlap and create an interference pattern. In subsequent decades improvements in electron sources for transmission electron microscopes made it possible to produce a coherent stream of electrons. In recent years researchers have made minutely detailed mappings of electrical and magnetic fields and made video recordings of swirling vortexes in a superconductor using the holographic electron microscope. This technique can also be used on biological or geological samples, though for most purposes the scanning tunneling microscope gives better resolution.
Dennis Gabor, who died in 1979, said during his Nobel Prize lecture in 1971, “I am one of the few lucky physicists who could see an idea of theirs grow into a sizable chapter of physics.” He would be pleased to know that his original problem has been solved and his idea is still growing.
