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== 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 (not requiring a splitting aperture as the Arago interferometer did) 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 (the horse traffic in the center of Berlin created too many vibrations), 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 (or carrier frequency). 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 (1) shifting an input signal into a new frequency range as well as (2) amplifying a weak input signal (assuming use of an active mixer). A weak input signal of frequency f1 is mixed with a strong reference frequency f2 from a local oscillator (LO). 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 (superhet), 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 (LO) and converted by the heterodyne technique to a lower fixed frequency signal called the intermediate frequency (IF). 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 (visible) 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 TwymanGreen interferometer, and the MachZehnder 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.

=== Wavefront splitting versus amplitude splitting ===

==== Wavefront splitting inferometers ==== A wavefront splitting interferometer divides a light wavefront emerging from a point or a narrow slit (i.e. spatially coherent light) and, after allowing the two parts of the wavefront to travel through different paths, allows them to recombine. Fig. 5 illustrates Young's interference experiment and Lloyd's mirror. Other examples of wavefront splitting interferometer include the Fresnel biprism, the Billet Bi-Lens, diffraction-grating Michelson interferometer, and the Rayleigh interferometer.