## Interferometry

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# Interferometry

The Michelson-Morley experiment

Interferometers

Applications

Resources

Interferometry is the use of the principles of interference to determine properties of waves, their sources, or wave propagation media. Acoustic interferometry

has been applied to study the velocity of sound in a fluid. Radio astronomers use interferometry to get accurate measurements of the position and properties of stellar radio sources. Optical interferometry is used in the creation and readback or display of holographs (records of interference patterns that may be used to record digital information or three-dimensional images). In interferometry, light beams pass along different paths and they combine at an observation point or region, where interference effects occur. Interpreting the interference effects reveals information about optical surfaces, the precise distance between the source and the observer, spectral properties of light, or the visualization of processes such as crystal growth, combustion, diffusion, and shock wave motion.

## The Michelson-Morley experiment

The observation and explanation of interference fringes dates back to Robert Hooke (16351703) and Isaac Newton (16421727), but the invention of interferometry is generally attributed to the American physicist Albert Michelson (18521931). The Michelson interferometer consists of two perpendicular arms with a half-silvered mirror (a beam splitter) at the intersection (see Figure 1).

Each arm has a mirror at one end. Light from the source enters the interferometer along one arm, and is equally split at the beam splitter. Half the light travels to mirror #1 and reflects back toward the beam splitter. It passes through the beam splitter and continues to the detector, which can be like a motion picture screen. The other half of the light first travels straight through the beam splitter, reflects off mirror #2, and then returns to the beam splitter, where it is reflected and sent to the detector. When the two beams combine at the detector, they interfere and produce a pattern of fringes that depends upon the path they traveled and the time it took them to travel this path.

In 1887, Michelson, along with the physicist Edward W. Morley (1838-1923), set out to determine if the speed of light was dependent on the speed of the observer. According to the accepted theory of the time, light had to propagate in a medium called the ether. The motion of Earth traveling through the ether would affect the fringe pattern on Michelsons interferometer, because it would take the light longer to travel over one arm than the other arm. When the interferometer was rotated through 90°, the fringes would shift if the speed of light was not constant. In this most celebrated null experiment in the history of science, Michelson and Morley observed no changes in the fringes after many repetitions. The speed of light appears constant, regardless of the speed of its source, which was later explained by Einsteins theory of relativity.

## Interferometers

Interferometers such as Michelsons can be used for many types of measurements. As a spectrometer, they can be used to accurately measure the mirror #1 mounted on a motor, so it can be moved along the direction of the beam at a constant speed. As the mirror moves, a fringe at a point in the interference plane will appear as an alternating bright and dark band. The frequency of the changing fringes is related to the wavelength, and can be calculated to better than several parts in 100 billion.

### The Twyman-Green interferometer

Modifications to the Michelson interferometer were introduced in 1916 by the electrical engineer Frank Twyman (1876-1959) and A. Green for the purpose of testing optical instruments. If the element transmits light, like a prism or a lens, it is inserted between the beam splitter and mirror #1 in such a manner that the fringes that are observed become a measure of the elements optical quality. If the element to be tested is a mirror, and reflects light, it is substituted for mirror #1 altogether. Once again, the Twyman-Green interferometer fringes act as a map of irregularities of the optical element.

### The Mach-Zehnder interferometer

Another type of interferometer was introduced by L. Mach and L. Zehnder in 1891 (see Figure 2). light leaves the sources, and is divided by beam splitter #1. One half travels toward mirror #1, and is reflected. The other half is reflected from mirror #2. the beams are combined by beam splitter #2, and propagate to the detector, where interference is observed. By virtue of the fact that the beams are separated, the objects to be tested can be quite large. The Mach-Zehnder two

beam interferometer is used for observing gas flows and shock waves, and for optical testing. It has also been used to obtain interference fringes of electrons that exhibit wavelike behavior.

### Cyclic interferometers

Interference can occur if a beam is split, and one half travels in a clockwise path around the interferometer, while the other travels counterclockwise. Figure 3

shows the top view of a cyclic interferometer, named a Sagnac interferometer for its inventor, physicist Georges Sagnac (1869-1928). one half of the beam reflects off the beam splitter and travels from mirror #1, to mirror #2, to mirror #3, and again reflects off the beam splitter. The two halves interfere at the detector. The Sagnac interferometer is the basis for laser gyroscopes that were first demonstrated in 1963. They sense the interference pattern to determine the direction and the speed of rotation in a moving vehicle like an airplane or a spacecraft.

### The Fabry-Perot interferometer

In 1899, physicists Charles Fabry (18671945) and Alfred Perot (18631925) introduced an interferometer designed to produce circular interference fringes when light passes through a pair of parallel half-silvered mirrors. Figure 4 shows the Fabry-Perot interferometer used with a broad light source. When the plates are separated by a fixed spacer, the interferometer is called a Fabry-Perot etalon. The diameter of the fringes from the etalon is related to the wavelength, so it can be used as a spectrometer. If two beams of slightly different wavelength enter the etalon, the position of the overlap in fringes can be used to determine the wavelength to better than one part in 100,000. If the two plates of the Fabry-Perot interferometer are aligned parallel to each other, the device becomes the device becomes the basic laser resonant cavity, since only certain wavelengths will add constructively as they propagate between the mirrors.

### Wavefront splitting interferometry

Rather than splitting the amplitude of the beam by beam splitters, one part of the beam can be made to interfere with another in the manner of Lloyds mirror (see Figure 5). One half of the beam from the source propagates directly to the detector. The other half reflects off the mirror and interferes with the direct beam at the detector. Information about the surface of the mirror is contained in the fringes. The surface of crystals can be studied with fringes from x rays. The surface of a lake or Earths ionosphere can be studied using interference from radio waves.

### Wavefront shearing interferometry

A variation of the Mach-Zehnder interferometer, introduced by W. J. Bates in 1947, made it possible to measure the wavefront (phase) of a beam without an error-free reference wave. By rotating one beam splitter in the Mach-Zehnder configuration, an incoming beam is split into two, and one half is shifted (sheared). Overlapping these beams results in an interference pattern that is a measure of the slope, or tilt, of the wavefront. Shearing interferometers are used in optical testing and in astronomy for measuring the distortions of the atmosphere.

## Applications

The basic interferometer improves over the years as new technology appears. High-speed cameras and electronics, precise optics, and computers are brought together to make possible accurate interpretation of the fringes, as well as the extraction of new and exciting information.

### Stellar interferometry

Even though we cannot directly photograph and resolve the image of two stars close together, we can use interferometry to measure their separation. first proposed by the physicist Armand Fizeau (18191896)

in 1868, the method was first applied by Michelson and American astronomer Francis Pease (18811938) in 1920, and is commonly called Michelson stellar interferometry.

Light from two sources is collected by two telescopes that are a known distance apart. The light is filtered to restrict the wavelength, and then brought together. Each star exhibits a fringe pattern. The fringes will line up if the patterns of the two stars overlap. When the separation of the two telescopes is small, the fringes are visible. When the separation of the telescopes is exactly equal to the wavelength divided by twice the angle between the two sources, the fringes will disappear. By varying the separation of the telescopes and observing when the fringes disappear, the separation of the sources is calculated. In a similar way, a single remote star can be thought of as two halves that appear as point sources close together. By using stellar interferometry, the size of a star can be measured.

By placing an opaque screen with holes over the aperture of a telescope, each pair of holes will cause interference fringes. stellar interferometry over a number of simultaneous separations is called aperture plane interferometry.

Radio astronomers R. Hanbury Brown and R. Q. Twiss, the first to use stellar interferometry in the radio region, measured the size of the star sirius. Today, Very Long Baseline Interferometry links radio telescopes around the world to create interference fringes that can be used to measure stellar sizes in fractions of an arcsecond.

### Speckle interferometry

Invented by Antoine Labeyrie in 1970, speckle interferometry provides a method for large telescopes to see objects without being limited by the turbulence of the atmosphere. A star exposure for less than one hundredth of a second appears speckled, because light from all points of the telescope interferes with each other. The speckle is similar to the speckled pattern of red light that reflects off the glass of a supermarket price scanner.

Averaging many short exposures (or taking a long exposure) smears out the speckles because the atmosphere is constantly moving around. Information in the image, smeared out by the blur, is lost. Because individual speckles themselves contain information about the object, the speckle interferometer gathers many short exposures, and a computer processes them to extract the information. Many measurements have been made in the last quarter century. The size and surface features of asteroids and the planet Pluto have been determined by speckle interferometry. The size of the nearby star Betelguse has also been measured. The angular separation of binary stars, measured by this technique, leads astronomers to calculate the star masses and develop theories about the evolution of the universe.

### Holographic interferometry

Holography was invented by Dennis Gabor (19001979) in 1948. A hologram is recorded by splitting a light beam and letting half the beam scatter from an object while the other half travels undisturbed. The two beams combine on photographic film, where a complicated fringe pattern is formed. When light shines on the hologram, some of it will pass through the bright fringes, and some will be absorbed by the dark fringes. By observing the light from the hologram one reveals a three-dimensional replica of the original object.

Holographic interferometry is used to view small changes in an object. when two holograms, taken at

### KEY TERMS

Beam splitter A sheet of glass or plastic specially coated to reflect part of a beam of light and transmit the remainder.

Holography A technique for recording and displaying the three-dimensional image of an object.

Interference The interaction of two or more waves.

Propagation Movement of waves.

Spectrometer An instrument for determining radiant intensity of atomic spectra.

different times, of the same object are superimposed, fringes will reveal the difference between the two objects. It is possible to see slowly varying changes of a growing plant, or rapidly varying changes of a vibrating object such as the face of a violin. Today, holography is coming into use for high-capacity optical data storage systems. Holographic anti-counterfeiting elements, which cannot be copied using scanners and printers, are frequently attached to credit cards and other items.

## Resources

### BOOKS

Hariharan, P. Basics of Interferometry. 2nd ed. San Diego: Academic Press, 2006.

Lawson, Peter. Principles of Long-Baseline Stellar Interferometry. New York: Wiley-Interscience, 2006.

Newton, Isaac. Opticks. First printed, 1704. Reprint, New York: Dover, 1979.

### PERIODICALS

Morris, Mark R. Glimpsing Matter at the Brink. Science. 304 (2004): 689-692.

Robert K. Tyson

views updated

# Interferometry

Interferometry uses the principles of interference to determine properties about waves, their sources, or the wave propagation medium. Acoustic interferometry has been applied to study the velocity of sound in a fluid. Radio astronomers use interferometry to get accurate measurements of the position and properties of stellar radio sources. Optical interferometry is widely used to observe things without touching or otherwise disturbing them. Light beams are sent through various paths, and they combine at one observation region where interference fringes occur. Interpreting the fringes reveals information about optical surfaces, the precise distance between the source and the observer, spectral properties of light, or the visualization of processes such as crystal growth, combustion , diffusion , and shock wave motion .

## The Michelson-Morley experiment

The observation and explanation of interference fringes dates back to Robert Hooke (1635) and Isaac Newton (1642-1727), but the invention of interferometry is generally attributed to the American physicist Albert Michelson (1852-1931). The Michelson interferometer consists of two perpendicular arms with a half-silvered mirror (a beamsplitter) at the intersection (see Figure 1).

Each arm has a mirror at one end. Light from the source enters the interferometer along one arm, and is equally split at the beamsplitter. Half the light travels to mirror #1 and reflects back toward the beamsplitter. It passes through the beamsplitter and continues to the detector, which can be like a motion picture screen. The other half of the light first travels straight through the beamsplitter, reflects off mirror #2, and then returns to the beamsplitter, where it is reflected and sent to the detector. When the two beams combine at the detector, they interfere and produce a pattern of fringes that depends upon the path they traveled and the time it took them to travel this path.

In 1887, Michelson, along with the physicist Edward W. Morley (1838-1923), set out to determine if the speed of light was dependent on the speed of the observer. According to the accepted theory of the time, light had to propagate in a medium called the ether . The motion of the earth traveling through the ether would affect the fringe pattern on Michelson's interferometer, because it would take the light longer to travel over one arm than the other arm. When the interferometer was rotated through 90°, the fringes would shift if the speed of light was not constant. In this most celebrated null experiment in the history of science, Michelson and Morley observed no changes in the fringes after many repetitions. The speed of light appears constant, regardless of the speed of its source, which was later explained by Einstein's theory of relativity.

## Interferometers

Interferometers such as Michelson's can be used for many types of measurements. As a spectrometer, they can be used to accurately measure the mirror #1 mounted on a motor, so it can be moved along the direction of the beam at a constant speed. As the mirror moves, a fringe at a point in the interference plane will appear as an alternating bright and dark band. The frequency of the changing fringes is related to the wavelength, and can be calculated to better than several parts in 100 billion.

### The Twyman-Green interferometer

Modifications to the Michelson interferometer were introduced in 1916 by the electrical engineer Frank Twyman (1876-1959) and A. Green for the purpose of testing optical instruments. If the element transmits light, like a prism or a lens , it is inserted between the beam-splitter and mirror #1 in such a manner that the fringes that are observed become a measure of the element's optical quality. If the element to be tested is a mirror, and reflects light, it is substituted for mirror #1 altogether. Once again, the Twyman-Green interferometer fringes act as a map of irregularities of the optical element.

### The Mach-Zehnder interferometer.

Another type of interferometer was introduced by L. Mach and L. Zehnder in 1891 (see Figure 2). Light leaves the sources, and is divided by beamsplitter #1. One half travels toward mirror #1, and is reflected. The other half is reflected from mirror #2. The beams are combined by beamsplitter #2, and propagate to the detector, where interference is observed. By virtue of the fact that the beams are separated, the objects to be tested can be quite large. The Mach-Zehnder two-beam interferometer is used for observing gas flows and shock waves, and for optical testing. It has also been used to obtain interference fringes of electrons that exhibit wavelike behavior.

### Cyclic interferometers

Interference can occur if a beam is split, and one half travels in a clockwise path around the interferometer, while the other travels counterclockwise. Figure 3 shows the top view of a cyclic interferometer, named a Sagnac interferometer for its inventor, physicist Georges Sagnac (1869-1928). One half of the beam reflects off the beamsplitter and travels from mirror #1, to mirror #2, to mirror #3, and again reflects off the beamsplitter. The two halves interfere at the detector. The Sagnac interferometer is the basis for laser gyroscopes that were first demonstrated in 1963. They sense the interference pattern to determine the direction and the speed of rotation in a moving vehicle like an airplane or a spacecraft.

### The Fabry-Perot interferometer

In 1899, physicists Charles Fabry (1867-1945) and Alfred Perot (1863-1925) introduced an interferometer designed to produce circular interference fringes when light passes through a pair of parallel half-silvered mirrors . Figure 4 shows the Fabry-Perot interferometer used with a broad light source. When the plates are separated by a fixed spacer, the interferometer is called a Fabry-Perot etalon. The diameter of the fringes from the etalon is related to the wavelength, so it can be used as a spectrometer. If two beams of slightly different wavelength enter the etalon, the position of the overlap in fringes can be used to determine the wavelength to better than one part in 100,000. If the two plates of the Fabry-Perot interferometer are aligned parallel to each other, the device becomes the device becomes the basic laser resonant cavity, since only certain wavelengths will add constructively as they propagate between the mirrors.

### Wavefront splitting interferometry

Rather than splitting the amplitude of the beam by beamsplitters, one part of the beam can be made to interfere with another in the manner of Lloyd's mirror (see Figure 5). One half of the beam from the source propagates directly to the detector. The other half reflects off the mirror and interferes with the direct beam at the detector. Information about the surface of the mirror is contained in the fringes. The surface of crystals can be studied with fringes from x rays . The surface of a lake or the earth's ionosphere can be studied using interference from radio waves .

### Wavefront shearing interferometry

A variation of the Mach-Zehnder interferometer, introduced by W. J. Bates in 1947, made it possible to measure the wavefront (phase) of a beam without an error-free reference wave. By rotating one beamsplitter in the Mach-Zehnder configuration, an incoming beam is split into two, and one half is shifted (sheared). Overlapping these beams results in an interference pattern that is a measure of the slope, or tilt, of the wavefront. Shearing interferometers are used in optical testing and in astronomy for measuring the distortions of the atmosphere.

## Applications

The basic interferometer improves over the years as new technology appears. High-speed cameras and electronics , precise optics , and computers are brought together to make possible accurate interpretation of the fringes, as well as the extraction of new and exciting information.

### Stellar interferometry

Even though we cannot directly photograph and resolve the image of two stars close together, we can use interferometry to measure their separation. First proposed by the physicist Armand Fizeau (1819-1896) in 1868, the method was first applied by Michelson and American astronomer Francis Pease (1881-1938) in 1920, and is commonly called Michelson stellar interferometry.

Light from two sources is collected by two telescopes that are a known distance apart. The light is filtered to restrict the wavelength, and then brought together. Each star exhibits a fringe pattern. The fringes will line up if the patterns of the two stars overlap. When the separation of the two telescopes is small, the fringes are visible. When the separation of the telescopes is exactly equal to the wavelength divided by twice the angle between the two sources, the fringes will disappear. By varying the separation of the telescopes and observing when the fringes disappear, the separation of the sources is calculated. In a similar way, a single remote star can be thought of as two halves that appear as point sources close together. By using stellar interferometry, the size of a star can be measured.

By placing an opaque screen with holes over the aperture of a telescope , each pair of holes will cause interference fringes. Stellar interferometry over a number of simultaneous separations is called aperture plane interferometry.

Radio astronomers R. Hanbury Brown and R. Q. Twiss, the first to use stellar interferometry in the radio region, measured the size of the star Sirius. Today, "Very Long Baseline Interferometry" links radio telescopes around the world to create interference fringes that can be used to measure stellar sizes in fractions of an arcsecond.

### Speckle interferometry

Invented by Antoine Labeyrie in 1970, speckle interferometry provides a method for large telescopes to see objects without being limited by the turbulence of the atmosphere. A star exposure for less than one hundredth of a second appears speckled, because light from all points of the telescope interferes with each other. The speckle is similar to the speckled pattern of red light that reflects off the glass of a supermarket price scanner.

Averaging many short exposures (or taking a long exposure) smears out the speckles because the atmosphere is constantly moving around. Information in the image, smeared out by the blur, is lost. Because individual speckles themselves contain information about the object, the speckle interferometer gathers many short exposures, and a computer processes them to extract the information. Many measurements have been made in the last quarter century. The size and surface features of asteroids and the planet Pluto have been determined by speckle interferometry. The size of the nearby star Betelguse has also been measured. The angular separation of binary stars, measured by this technique, leads astronomers to calculate the star masses and develop theories about the evolution of the universe.

### Holographic interferometry

Holography was invented by Dennis Gabor (1900-1979) in 1948. A hologram is recorded by splitting a light beam and letting half the beam scatter from an object while the other half travels undisturbed. The two beams combine on photographic film, where a complicated fringe pattern is formed. When light shines on the hologram, some of it will pass through the bright fringes, and some will be absorbed by the dark fringes. By observing the light from the hologram one reveals a three-dimensional replica of the original object.

Holographic interferometry is used to view small changes in an object. When two holograms, taken at different times, of the same object are superimposed, fringes will reveal the difference between the two objects. It is possible to see slowly varying changes of a growing plant , or rapidly varying changes of a vibrating object such as the face of a violin.

## Resources

### books

Ditchburn, R.W. Light. New York: Dover, 1991.

Hariharan, P. Basics of Interferometry. San Diego: Academic Press, 1992.

Newton, Isaac. Opticks. First printed, 1704. Reprint, New York: Dover, 1979.

Smith, F.G., and J.H. Thomson. Opticks. New York: Wiley, 1988.

Steel, W.H. Interferometry. New York: Cambridge University Press, 1967.

Robert K. Tyson

## KEY TERMS

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Beamsplitter

—A sheet of glass or plastic specially coated to reflect part of a beam of light and transmit the remainder.

Holography

—A technique for recording and displaying the three-dimensional image of an object.

Interference

—The interaction of two or more waves.

Propagation

—Movement of waves.

Spectrometer

—An instrument for determining radiant intensity of atomic spectra.

views updated

# Interferometry

Interferometry is the process of making measurements by allowing sound, light, or other kinds of waves to interfere with each other. Interferometry is used for a large variety of purposes, such as studying the velocity of sound in a fluid, locating the position and properties of objects in space, determining the size and properties of objects without actually touching or otherwise disturbing them, and visualizing processes such as crystal growth, combustion (burning), diffusion (spreading), and shock wave motion.

## Principle of the interferometer

The interferometer was invented by German American physicist Albert A. Michelson (18521931) around 1881. The major features of Michelson's instrument are shown in Figure 1. Light from the source enters the interferometer along one arm and strikes a half-mirrored glass called a beam splitter. The light is split into two equal parts at the beam splitter. The first half reflects off the beam splitter and travels to mirror #1. The second half passes through the beam splitter to mirror #2.

The first beam of light reflects off mirror #1, passes back through the beam splitter, and continues to the detector. Meanwhile, the second beam reflects off mirror #2, returns to the beam splitter, and is also reflected to the detector.

What happens at the detector depends on the paths taken by the two beams. If they have both traveled exactly the same length, they will interfere with each other constructively. But if the distance taken by the two beams is different, an interference pattern will be formed. The kind of pattern produced, then, depends on the difference between the paths taken by the two beams of light.

## Words to Know

Beam splitter: A sheet of glass or plastic specially coated to reflect part of a beam of light and transmit the remainder.

Interference: The interaction of two or more waves.

Velocity: The rate at which the position of an object changes with time, including both the speed and the direction.

## Variations on the Michelson interferometer

In the hundred years since Michelson invented the interferometer, scientists have devised a number of variations on the original instrument. Most of these variations were designed to make special kinds of measurements. One example is the interferometer invented in 1891 by L. Mach and L. Zehnder. A top view of this instrument is shown in Figure 2.

Light leaves the source and is divided into two beams by beam splitter #1. One beam travels toward mirror #1 and is reflected toward beam splitter #2. The other beam travels toward mirror #2, where it is also reflected toward beam splitter #2. The two beams are then combined at beam splitter #2 and transmitted to the detector, where an interference pattern is produced. The Mach-Zehnder two-beam interferometer is used for observing gas flows and shock waves and for optical testing. It has also been used to obtain interference fringes of electrons that exhibit wave-like behavior.