Interferometry

Interferometry is a technique which uses the interference of superimposed waves to extract information. Interferometry typically uses electromagnetic waves and is an important investigative technique in the fields of astronomy, fiber optics, engineering metrology, optical metrology, oceanography, seismology, spectroscopy, quantum mechanics, nuclear and particle physics, plasma physics, biomolecular interactions, surface profiling, microfluidics, mechanical stress/strain measurement, velocimetry, optometry, and making holograms.
Interferometers are devices that extract information from interference. They are widely used in science and industry for the measurement of microscopic displacements, refractive index changes and surface irregularities. In the case with most interferometers, light from a single source is split into two beams that travel in different optical paths, which are then combined again to produce interference; two incoherent sources can also be made to interfere under some circumstances. The resulting interference fringes give information about the difference in optical path lengths. In analytical science, interferometers are used to measure lengths and the shape of optical components with nanometer precision; they are the highest-precision length measuring instruments in existence. In Fourier transform spectroscopy they are used to analyze light containing features of absorption or emission associated with a substance or mixture. An astronomical interferometer consists of two or more separate telescopes that combine their signals, offering a resolution equivalent to that of a telescope of diameter equal to the largest separation between its individual elements.

Basic principles

Interferometry makes use of the principle of superposition to combine waves in a way that will cause the result of their combination to have some meaningful property that is diagnostic of the original state of the waves. This works because when two waves with the same frequency combine, the resulting intensity pattern is determined by the phase difference between the two waves—waves that are in phase will undergo constructive interference while waves that are out of phase will undergo destructive interference. Waves which are not completely in phase nor completely out of phase will have an intermediate intensity pattern, which can be used to determine their relative phase difference. Most interferometers use light or some other form of electromagnetic wave.
Typically a single incoming beam of coherent light will be split into two identical beams by a beam splitter. Each of these beams travels a different route, called a path, and they are recombined before arriving at a detector. The path difference, the difference in the distance traveled by each beam, creates a phase difference between them. It is this introduced phase difference that creates the interference pattern between the initially identical waves. If a single beam has been split along two paths, then the phase difference is diagnostic of anything that changes the phase along the paths. This could be a physical change in the path length itself or a change in the refractive index along the path.
As seen in Fig. 2a and 2b, the observer has a direct view of mirror M₁ seen through the beam splitter, and sees a reflected image '₂ of mirror M₂. The fringes can be interpreted as the result of interference between light coming from the two virtual images '₁ and '₂ of the original source S. The characteristics of the interference pattern depend on the nature of the light source and the precise orientation of the mirrors and beam splitter. In Fig. 2a, the optical elements are oriented so that '₁ and '₂ are in line with the observer, and the resulting interference pattern consists of circles centered on the normal to M₁ and M'₂. If, as in Fig. 2b, M₁ and '₂ are tilted with respect to each other, the interference fringes will generally take the shape of conic sections, but if '₁ and '₂ overlap, the fringes near the axis will be straight, parallel, and equally spaced. If S is an extended source rather than a point source as illustrated, the fringes of Fig. 2a must be observed with a telescope set at infinity, while the fringes of Fig. 2b will be localized on the mirrors.
Use of white light will result in a pattern of colored fringes. The central fringe representing equal path length may be light or dark depending on the number of phase inversions experienced by the two beams as they traverse the optical system.

History

The law of interference of light was described by Thomas Young in his 1803 Bakerian Lecture to the Royal Society of London. In preparation for the lecture, Young performed a double-aperture experiment in a water ripple tank. His interpretation in terms of the interference of waves was rejected by most scientists at the time because of the dominance of Isaac Newton's corpuscular theory of light proposed a century before.
The French engineer Augustin-Jean Fresnel, unaware of Young's results, began working on a wave theory of light and interference and was introduced to François Arago. Between 1816 and 1818, Fresnel and Arago performed interference experiments at the Paris Observatory. During this time, Arago designed and built the first interferometer, using it to measure the refractive index of moist air relative to dry air, which posed a potential problem for astronomical observations of star positions. The success of Fresnel's wave theory of light was established in his prize-winning memoire of 1819 that predicted and measured diffraction patterns. The Arago interferometer was later employed in 1850 by Leon Foucault to measure the speed of light in air relative to water, and it was used again in 1851 by Hippolyte Fizeau to measure the effect of Fresnel drag on the speed of light in moving water.
Jules Jamin developed the first single-beam interferometer in 1856. In 1881, the American physicist Albert A. Michelson, while visiting Hermann von Helmholtz in Berlin, invented the interferometer that is named after him, the Michelson Interferometer, to search for effects of the motion of the Earth on the speed of light. Michelson's null results performed in the basement of the Potsdam Observatory outside of Berlin, and his later more-accurate null results observed with Edward W. Morley at Case College in Cleveland, Ohio, contributed to the growing crisis of the luminiferous ether. Einstein stated that it was Fizeau's measurement of the speed of light in moving water using the Arago interferometer that inspired his theory of the relativistic addition of velocities.

Categories

Interferometers and interferometric techniques may be categorized by a variety of criteria:

Homodyne versus heterodyne detection

In homodyne detection, the interference occurs between two beams at the same wavelength. The phase difference between the two beams results in a change in the intensity of the light on the detector. The resulting intensity of the light after mixing of these two beams is measured, or the pattern of interference fringes is viewed or recorded. Most of the interferometers discussed in this article fall into this category.
The heterodyne technique is used for shifting an input signal into a new frequency range as well as amplifying a weak input signal. A weak input signal of frequency f₁ is mixed with a strong reference frequency f₂ from a local oscillator. The nonlinear combination of the input signals creates two new signals, one at the sum f₁ + f₂ of the two frequencies, and the other at the difference f₁ − f₂. These new frequencies are called heterodynes. Typically only one of the new frequencies is desired, and the other signal is filtered out of the output of the mixer. The output signal will have an intensity proportional to the product of the amplitudes of the input signals.
The most important and widely used application of the heterodyne technique is in the superheterodyne receiver, invented in 1917-18 by U.S. engineer Edwin Howard Armstrong and French engineer Lucien Lévy. In this circuit, the incoming radio frequency signal from the antenna is mixed with a signal from a local oscillator and converted by the heterodyne technique to a lower fixed frequency signal called the intermediate frequency. This IF is amplified and filtered, before being applied to a detector which extracts the audio signal, which is sent to the loudspeaker.
Optical heterodyne detection is an extension of the heterodyne technique to higher frequencies. While optical heterodyne interferometry is usually done at a single point it is also possible to perform this widefield.

Double path versus common path

A double-path interferometer is one in which the reference beam and sample beam travel along divergent paths. Examples include the Michelson interferometer, the Twyman–Green interferometer, and the Mach–Zehnder interferometer. After being perturbed by interaction with the sample under test, the sample beam is recombined with the reference beam to create an interference pattern which can then be interpreted.
A common-path interferometer is a class of interferometer in which the reference beam and sample beam travel along the same path. Fig. 4 illustrates the Sagnac interferometer, the fibre optic gyroscope, the point diffraction interferometer, and the lateral shearing interferometer. Other examples of common path interferometer include the Zernike phase-contrast microscope, Fresnel's biprism, the zero-area Sagnac, and the scatterplate interferometer.