# Diffraction

## CONCEPT

Diffraction is the bending of waves around obstacles, or the spreading of waves by passing them through an aperture, or opening. Any type of energy that travels in a wave is capable of diffraction, and the diffraction of sound and light waves produces a number of effects. (Because sound waves are much larger than light waves, however, diffraction of sound is a part of daily life that most people take for granted.) Diffraction of light waves, on the other hand, is much more complicated, and has a number of applications in science and technology, including the use of diffraction gratings in the production of holograms.

## HOW IT WORKS

### Comparing Sound and Light Diffraction

Imagine going to a concert hall to hear a band, and to your chagrin, you discover that your seat is directly behind a wide post. You cannot see the band, of course, because the light waves from the stage are blocked. But you have little trouble hearing the music, since sound waves simply diffract around the pillar. Light waves diffract slightly in such a situation, but not enough to make a difference with regard to your enjoyment of the concert: if you looked closely while sitting behind the post, you would be able to observe the diffraction of the light waves glowing slightly, as they widened around the post.
Suppose, now, that you had failed to obtain a ticket, but a friend who worked at the concert venue arranged to let you stand outside an open door and hear the band. The sound quality would be far from perfect, of course, but you would still be able to hear the music well enough. And if you stood right in front of the doorway, you would be able to see light from inside the concert hall. But, if you moved away from the door and stood with your back to the building, you would see little light, whereas the sound would still be easily audible.

### Wavelength and Diffraction

The reason for the difference—that is, why sound diffraction is more pronounced than light diffraction—is that sound waves are much, much larger than light waves. Sound travels by longitudinal waves, or waves in which the movement of vibration is in the same direction as the wave itself. Longitudinal waves radiate outward in concentric circles, rather like the rings of a bull’s-eye.
The waves by which sound is transmitted are larger, or comparable in size to, the column or the door—which is an example of an aperture— and, hence, they pass easily through apertures and around obstacles. Light waves, on the other hand, have a wavelength, typically measured in nanometers (nm), which are equal to one-millionth of a millimeter. Wavelengths for visible light range from 400 (violet) to 700 nm (red): hence, it would be possible to fit about 5,000 of even the longest visible-light wavelengths on the head of a pin!
Whereas differing wavelengths in light are manifested as differing colors, a change in sound wavelength indicates a change in pitch. The higher the pitch, the greater the frequency, and, hence, the shorter the wavelength. As with light waves—though, of course, to a much lesser

Holograms are made possible through the principle of diffraction. Shown here is a hologram of a space shuttle orbiting Earth.
extent—short-wavelength sound waves are less capable of diffracting around large objects than are long-wavelength sound waves. Chances are, then, that the most easily audible sounds from inside the concert hall are the bass and drums; higher-pitched notes from a guitar or other instruments, such as a Hammond organ, are not as likely to reach a listener outside.

## Observing Diffraction in Light

Due to the much wider range of areas in which light diffraction has been applied by scientists, diffraction of light and not sound will be the principal topic for the remainder of this essay. We have already seen that wavelength plays a role in diffraction; so, too, does the size of the aperture relative to the wavelength. Hence, most studies of diffraction in light involve very small openings, as, for instance, in the diffraction grating discussed below.
But light does not only diffract when passing through an aperture, such as the concert-hall door in the earlier illustration; it also diffracts around obstacles, as, for instance, the post or pillar mentioned earlier. This can be observed by looking closely at the shadow of a flagpole on a bright morning. At first, it appears that the shadow is “solid,” but if one looks closely enough, it becomes clear that, at the edges, there is a blur-

The checkout scanners in grocery stores use holographic technology that can read a universal product code (UPC) from any angle.
ring from darkness to light. This “gray area” is an example of light diffraction.
Where the aperture or obstruction is large compared to the wave passing through or around it, there is only a little “fuzziness” at the edge, as in the case of the flagpole. When light passes through an aperture, most of the beam goes straight through without disturbance, with only the edges experiencing diffraction. If, however, the size of the aperture is close to that of the wavelength, the diffraction pattern will widen. Sound waves diffract at large angles through an open door, which, as noted, is comparable in size to a sound wave; similarly, when light is passed through extremely narrow openings, its diffraction is more noticeable.

## Early Studies in Diffraction

Though his greatest contributions lay in his epochal studies of gravitation and motion, Sir Isaac Newton (1642-1727) also studied the production and propagation of light. Using a prism, he separated the colors of the visible light spectrum—something that had already been done by other scientists—but it was Newton who discerned that the colors of the spectrum could be recombined to form white light again.
Newton also became embroiled in a debate as the nature of light itself—a debate in which diffraction studies played an important role. Newton’s view, known at the time as the corpuscular theory of light, was that light travels as a stream of particles. Yet, his contemporary, Dutch physicist and astronomer Christiaan Huygens (1629-1695), advanced the wave theory, or the idea that light travels by means of waves. Huygens maintained that a number of factors, including the phenomena of reflection and refraction, indicate that light is a wave. Newton, on the other hand, challenged wave theorists by stating that if light were actually a wave, it should be able to bend around corners—in other words, to diffract.

### GRIMALDI IDENTIFIES DIFFRACTION

Though it did not become widely known until some time later, in 1648— more than a decade before the particle-wave controversy erupted—Johannes Marcus von Kronland (1595-1667), a scientist in Bohemia (now part of the Czech Republic), discovered the diffraction of light waves. However, his findings were not recognized until some time later; nor did he give a name to the phenomenon he had observed. Then, in 1660, Italian physicist Francesco Grimaldi (1618-1663) conducted an experiment with diffraction that gained widespread attention.
Grimaldi allowed a beam of light to pass through two narrow apertures, one behind the other, and then onto a blank surface. When he did so, he observed that the band of light hitting the surface was slightly wider than it should be, based on the width of the ray that entered the first aperture. He concluded that the beam had been bent slightly outward, and gave this phenomenon the name by which it is known today: diffraction.

### FRESNEL AND FRAUNHOFER DIFFRACTION

Particle theory continued to have its adherents in England, Newton’s homeland, but by the time of French physicist Augustin Jean Fresnel (1788-1827), an increasing number of scientists on the European continent had come to accept the wave theory. Fresnel’s work, which he published in 1818, served to advance that theory, and, in particular, the idea of light as a transverse wave.
In Memoire surla diffraction de la lumiere, Fresnel showed that the transverse-wave model accounted for a number of phenomena, including diffraction, reflection, refraction, interference, and polarization, or a change in the oscillation patterns of a light wave. Four years after publishing this important work, Fresnel put his ideas into action, using the transverse model to create a pencil-beam of light that was ideal for lighthouses. This prism system, whereby all the light emitted from a source is refracted into a horizontal beam, replaced the older method of mirrors used since ancient times. Thus Fresnel’s work revolutionized the effectiveness of lighthouses, and helped save lives of countless sailors at sea.
The term “Fresnel diffraction” refers to a situation in which the light source or the screen are close to the aperture; but there are situations in which source, aperture, and screen (or at least two of the three) are widely separated. This is known as Fraunhofer diffraction, after German physicist Joseph von Fraunhofer (1787-1826), who in 1814 discovered the lines of the solar spectrum (source) while using a prism (aperture). His work had an enormous impact in the area of spectroscopy, or studies of the interaction between electromagnetic radiation and matter.

## REAL-LIFE APPLICATIONS

### Diffraction Studies Come of Age

Eventually the work of Scottish physicist James Clerk Maxwell (1831-1879), German physicist Heinrich Rudolf Hertz (1857-1894), and others confirmed that light did indeed travel in waves. Later, however, Albert Einstein (1879-1955) showed that light behaves both as a wave and, in certain circumstances, as a particle.
In 1912, a few years after Einstein published his findings, German physicist Max Theodor Felix von Laue (1879-1960) created a diffraction grating, discussed below. Using crystals in his grating, he proved that x rays are part of the electromagnetic spectrum. Laue’s work, which earned him the Nobel Prize in physics in 1914, also made it possible to measure the length of x rays, and, ultimately, provided a means for studying the atomic structure of crystals and polymers.

### Scientific Breakthroughs Made Possible by Diffraction Studies

Studies in diffraction advanced during the early twentieth century. In 1926, English physicist J. D. Bernal (1901-1971) developed the Bernal chart, enabling scientists to deduce the crystal structure of a solid by analyzing photographs of x-ray diffraction patterns. A decade later, Dutch-American physical chemist Peter Joseph William Debye (1884-1966) won the Nobel Prize in Chemistry for his studies in the diffraction of x rays and electrons in gases, which advanced understanding of molecular structure. In 1937, a year after Debye’s Nobel, two other scientists—American physicist Clinton Joseph Davisson (1881-1958) and English physicist George Paget Thomson (1892-1975)—won the Prize in Physics for their discovery that crystals can bring about the diffraction of electrons.
Also, in 1937, English physicist William Thomas Astbury (1898-1961) used x-ray diffraction to discover the first information concerning nucleic acid, which led to advances in the study of DNA (deoxyribonucleic acid), the building-blocks of human genetics. In 1952, English bio-physicist Maurice Hugh Frederick Wilkins (1916-) and molecular biologist Rosalind Elsie Franklin (1920-1958) used x-ray diffraction to photograph DNA. Their work directly influenced a breakthrough event that followed a year later: the discovery of the double-helix or double-spiral model of DNA by American molecular biologists James D. Watson (1928-) and Francis Crick (1916-). Today, studies in DNA are at the frontiers of research in biology and related fields.

## Diffraction Grating

Much of the work described in the preceding paragraphs made use of a diffraction grating, first developed in the 1870s by American physicist Henry Augustus Rowland (1848-1901). A diffraction grating is an optical device that consists ofnot one but many thousands of apertures: Rowland’s machine used a fine diamond point to rule glass gratings, with about 15,000 lines per in (2.2 cm). Diffraction gratings today can have as many as 100,000 apertures per inch. The apertures in a diffraction grating are not mere holes, but extremely narrow parallel slits that transform a beam of light into a spectrum.
Each of these openings diffracts the light beam, but because they are evenly spaced and the same in width, the diffracted waves experience constructive interference. (The latter phenomenon, which describes a situation in which two or more waves combine to produce a wave of greater magnitude than either, is discussed in the essay on Interference.) This constructive interference pattern makes it possible to view components of the spectrum separately, thus enabling a scientist to observe characteristics ranging from the structure of atoms and molecules to the chemical composition of stars.

### X-ray Diffraction

Because they are much higher in frequency and energy levels, x rays are even shorter in wavelength than visible light waves. Hence, for x-ray diffraction, it is necessary to have gratings in which lines are separated by infinitesimal distances. These distances are typically measured in units called an angstrom, of which there are 10 million to a millimeter. Angstroms are used in measuring atoms, and, indeed, the spaces between lines in an x-ray diffraction grating are comparable to the size of atoms.
When x rays irradiate a crystal—in other words, when the crystal absorbs radiation in the form of x rays—atoms in the crystal diffract the rays. One of the characteristics of a crystal is that its atoms are equally spaced, and, because of this, it is possible to discover the location and distance between atoms by studying x-ray diffraction patterns. Bragg’s law—named after the father-and-son team of English physicists William Henry Bragg (1862-1942) and William Lawrence Bragg (1890-1971)—describes x-ray diffraction patterns in crystals.
Though much about x-ray diffraction and crystallography seems rather abstract, its application in areas such as DNA research indicates that it has numerous applications for improving human life. The elder Bragg expressed this fact in 1915, the year he and his son received the Nobel Prize in physics, saying that “We are now able to look ten thousand times deeper into the structure of the matter that makes up our universe than when we had to depend on the microscope alone.” Today, physicists applying x-ray diffraction use an instrument called a diffractometer, which helps them compare diffraction patterns with those of known crystals, as a means of determining the structure of new materials.

## Holograms

A hologram—a word derived from the Greek holos, “whole,” and gram, “message”—is a three-dimensional (3-D) impression of an object, and the method of producing these images is known as holography. Holograms make use of laser beams that mix at an angle, producing an interference pattern of alternating bright and dark lines. The surface of the hologram itself is a sort of diffraction grating, with alternating strips of clear and opaque material. By mixing a laser beam and the unfocused diffraction pattern of an object, an image can be recorded. An illuminating laser beam is diffracted at specific angles, in accordance with Bragg’s law, on the surfaces of the hologram, making it possible for an observer to see a three-dimensional image.
Holograms are not to be confused with ordinary three-dimensional images that use only visible light. The latter are produced by a method known as stereoscopy, which creates a single image from two, superimposing the images to create the impression of a picture with depth. Though stereoscopic images make it seem as though one can “step into” the picture, a hologram actually enables the viewer to glimpse the image from any angle. Thus, stereoscopic images can be compared to looking through the plate-glass window of a store display, whereas holograms convey the sensation that one has actually stepped into the store window itself.

## KEY TERMS

Aperture: An opening.
Diffraction: The bending of waves around obstacles, or the spreading of waves by passing them through an aperture.
Electromagnetic spectrum:
The complete range of electromagnetic waves on a continuous distribution from a very low range of frequencies and energy levels, with a correspondingly long wavelength, to a very high range of frequencies and energy levels, with a correspondingly short wavelength. Included on the electromagnetic spectrum are long-wave and short-wave radio; microwaves; infrared, visible, and ultraviolet light; x rays, and gamma rays.
Frequency: The number of waves passing through a given point during the interval of one second. The higher the frequency, the shorter the wavelength.
Longitudinal wave: A wave in which the movement of vibration is in the same direction as the wave itself. A sound wave is an example of a longitudinal wave.
Prism: A three-dimensional glass shape used for the diffusion of light rays.
Propagation: The act or state of traveling from one place to another.
Radiation: In a general sense, radiation can refer to anything that travels in a stream, whether that stream be composed of subatomic particles or electromagnetic waves.
Reflection: A phenomenon whereby a light ray is returned toward its source rather than being absorbed at the interface.
Refraction: The bending of a light ray that occurs when it passes through a dense medium, such as water or glass.
Spectrum: The continuous distribution of properties in an ordered arrangement across an unbroken range. Examples of spectra (the plural of “spectrum”) include the colors of visible light, or the electromagnetic spectrum of which visible light is a part.
Transverse wave: A wave in which the vibration or motion is perpendicular to the direction in which the wave is moving.
Wavelength: The distance between a crest and the adjacent crest, or the trough and an adjacent trough, of a wave. The shorter the wavelength, the higher the frequency.

### Developments in Holography

While attempting to improve the resolution of electron microscopes in 1947, Hungarian-English physicist and engineer Dennis Gabor (1900-1979) developed the concept of holography and coined the term “hologram.” His work in this area could not progress by a great measure, however, until the creation of the laser in 1960. By the early 1960s, scientists were using lasers to create 3-D images, and in 1971, Gabor received the Nobel Prize in physics for the discovery he had made a generation before.
Today, holograms are used on credit cards or other identification cards as a security measure, providing an image that can be read by an optical scanner. Supermarket checkout scanners use holographic optical elements (HOEs), which can read a universal product code (UPC) from any angle. Use of holograms in daily life and scientific research is likely to increase as scientists find new applications: for instance, holographic images will aid the design of everything from bridges to automobiles.

### Holographic Memory

One of the most fascinating areas of research in the field of holography is holographic memory. Computers use a binary code, a pattern of ones and zeroes that is translated into an electronic pulse, but holographic memory would greatly extend the capabilities of computer memory systems. Unlike most images, a hologram is not simply the sum of its constituent parts: the data in a holographic image is contained in every part of the image, meaning that part of the image can be destroyed without a loss of data.
To bring the story full-circle, holographic memory calls to mind an idea advanced by a scientist who, along with Huygens, was one of Newton’s great professional rivals, German mathematician and philosopher Gottfried Wilhelm Leibniz (1646-1716). Though Newton is usually credited as the father of calculus, Leibniz developed his own version of calculus at around the same time.
As a philosopher, Leibniz had apparently had a number of strange ideas, which made him the butt of jokes among some sectors of European intellectual society: hence, the French writer and thinker Voltaire (Francois-Marie Arouet; 1694-1778) satirized him with the character Dr. Pangloss in Candide (1759). Few of Leibniz’s ideas were more bizarre than that of the monad: an elementary particle of existence that reflected the whole of the universe.
In advancing the concept of a monad, Leibniz was not making a statement after the manner of a scientist: there was no proof that monads existed, nor was it possible to prove this in any
scientific way. Yet, a hologram appears to be very much like a manifestation of Leibniz’s imagined monads, and both the hologram and the monad relate to a more fundamental aspect of life: human memory. Neurological research in the late twentieth century suggested that the structure of memory in the human mind is holographic. Thus, for instance, a patient suffering an injury affecting 90% of the brain experiences only a 10% memory loss.

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