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 Figure 1. The Michelson interferometer. Illustration by Hans & Cassidy. Courtesy of Gale Group. 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 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.

Figure 4. Fabry-Perot interferometer. Illustration by Hans & Cassidy. Courtesy of Gale Group.

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.

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 Figure 5. Wavefront splitting interferometer. Illustration by Hans & Cassidy. Courtesy of Gale Group. 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.