Interferometry is an optical method that uses wave interference to measure distances, wavelengths, or other properties.Interferometry is a technique that uses the interference of coherent waves for precision measurements. By comparing the phases of superimposed waves, it is possible to detect changes on the order of a wavelength - in the optical range, this is fractions of a micron. It is widely used in metrology, astronomy (VLBI, astrometric interferometer), and fundamental physics.
Albert Michelson first used an interferometer in 1881 in an experiment to detect the ether; later (1887) with Edward Morley he conducted the famous experiment proving the constancy of the speed of light. In 1920, Michelson and Francis Pease measured the diameter of the star Betelgeuse using a stellar interferometer. The development of lasers in the 1960s made interferometry ubiquitous, and in 2015 LIGO discovered gravitational waves, which earned the Nobel Prize.
Two or more coherent beams are split, travel different optical paths, and recombine. The output intensity depends on the phase difference: I = I₁ + I₂ + 2√(I₁I₂) cos Δφ. The change in this pattern under controlled displacement allows calculation of the measured quantity. In heterodyne interferometry, the frequency of one beam is slightly shifted, and the signal is read out at the beat frequency. Sensitivity is limited by photon shot noise, and in gravitational-wave antennas additionally by quantum light noise and thermal noise. It is based on the principle of wave superposition and the constancy of the speed of light in a vacuum.
Used in fiber optics for interference-free data transmission and in gravitational-wave detectors like LIGO, which catch the trembling of space from black hole collisions.
The LIGO interferometer detects mirror displacements of 10⁻¹⁸ meter - that's a thousand times smaller than a proton, which is like measuring the distance to the nearest star with hair's breadth accuracy.
| F | variable | Fresnel number, dimensionless diffraction parameter — fresnel number |
| a | variable | Characteristic transverse size of aperture or obstacle — length metre |
| λ | variable | Wavelength of the wave — wavelength metre |
| L | variable | Propagation distance from aperture to observation plane — length metre |
| β | variable | spectral index of opacity |
| κ | variable | opacity (absorption coefficient) — opacity square metre per kilogram |
| ν | variable | frequency of radiation — frequency hertz |
| d/d log ν | operator | derivative with respect to the natural logarithm of frequency — logarithmic derivative |




















