# Interferometry
**Interferometry** is a family of measurement techniques that extract information from the superposition of two or more waves, most often light, by observing the fringes formed where the waves overlap. In a distance-measuring interferometer, each period of the interference signal corresponds to a change in measured distance of half a wavelength; interferometry ranks among the most sensitive forms of measurement available, reaching from optical benches to radio arrays, X-ray crystals, and beams of cold atoms.[1](https://iopscience.iop.org/article/10.1088/1681-7575/ac1456) • [2](https://academic.oup.com/book/46528)
| Key fact | Detail |
|---|---|
| Basic ruler | Each period of the interference signal corresponds to a distance change of half the wavelength; a red laser at λ ≈ 633 nm gives about 3 million interference-order oscillations per meter of travel[1](https://iopscience.iop.org/article/10.1088/1681-7575/ac1456) |
| Gravitational-wave precision | LIGO (4 km arms), Virgo and KAGRA (3 km arms) measure relative arm-length displacements of 10−18 m or smaller; the first detection in September 2015 reached a strain amplitude of 10−21 • [3](http://www.scholarpedia.org/article/Gravitational_Waves:_Ground-Based_Interferometric_Detectors) • [4](https://link.springer.com/article/10.1007/s41114-016-0002-8) |
| Phase sensitivity | Advanced LIGO demonstrated a phase noise spectral amplitude of 5 × 10−11 radian/√Hz around 150 Hz[3](http://www.scholarpedia.org/article/Gravitational_Waves:_Ground-Based_Interferometric_Detectors) |
| Astronomical resolution | Modern optical/IR interferometry reaches submilliarcsecond imaging and microarcsecond astrometry; CHARA operates baselines up to 330 m[5](https://www.annualreviews.org/content/journals/10.1146/annurev-astro-121622-045019) |
| Industrial metrology | Laser displacement interferometers measure linear positions with nanometre precision over distances of meters, the backbone of top-level length metrology[6](https://www.rp-photonics.com/interferometers.html) • [7](https://www.nist.gov/programs-projects/si-length-and-traceability) |
| Quantum enhancement | Advanced LIGO and Virgo reduced quantum shot noise by about 3 dB with squeezed light in the O3 run; Advanced LIGO achieved stable −6 dB squeezing in its fourth observing run[8](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.129.031101) • [9](https://opg.optica.org/abstract.cfm?uri=QSM-2025-QM2B.2) |
## Physical principles
An interferometer splits a wave into two or more paths and recombines them. Where the paths differ by an integer number of wavelengths the waves add; where they differ by half a wavelength they cancel. The observable is the pattern of bright and dark fringes, and its displacement measures the path difference. In a distance-measuring interferometer, each period of the changing signal corresponds to a change in distance by half the wavelength of the light used; with a typical red laser at λ ≈ 633 nm this means roughly 3 million oscillations per meter, so sub-wavelength changes are read out as fractions of a fringe.[1](https://iopscience.iop.org/article/10.1088/1681-7575/ac1456) A surface displacement d measured in reflection produces a wave aberration ΔW = 2nd, twice the geometric displacement because the light travels to the surface and back; the same displacement measured in transmission gives ΔW = (n₂ − n₁)d.[10](https://cdn.standards.iteh.ai/samples/iso/iso-tr-14999-2-2019/0f8a3391967041f0936b467373fd8649/iso-tr-14999-2-2019.pdf)
**Coherence sets the reach.** Fringe visibility depends on the mutual coherence of the two beams. The coherence length is the precision with which optical paths must be equalized for fringes to appear; for visible light with a spectral bandwidth Δλ of 1000 Å it is typically 2.5 microns.[11](https://ar5iv.labs.arxiv.org/html/1907.07443) Air turbulence makes counting integer interference-order changes practically impossible at larger distances, especially outdoors.[1](https://iopscience.iop.org/article/10.1088/1681-7575/ac1456)
The technique has deep roots. Stellar interferometry was proposed by Fizeau in 1868 and applied by Michelson to measure the angular diameters of Jupiter's moons in 1890–1891; Michelson, with Pease in 1921, made the first measurement of the angular size of a star beyond the Sun.[12](https://ar5iv.labs.arxiv.org/html/astro-ph/0307036) In 1888 Michelson and Morley's interferometer could measure 0.02 of a fringe, about 0.126 radian.[3](http://www.scholarpedia.org/article/Gravitational_Waves:_Ground-Based_Interferometric_Detectors)
## Interferometer configurations
A basic [Michelson interferometer](https://www.edgepedia.org/michelson-interferometer) consists of a light source, a beam splitter, two mirrors, and a photodetector recording the interference pattern.[13](https://www.ligo.caltech.edu/page/what-is-interferometer) The standard textbook configurations are treated as distinct two-beam designs: Michelson, Mach–Zehnder, and Sagnac, with Fizeau and Twyman–Green instruments under optical testing.[14](https://shop.elsevier.com/books/optical-interferometry-2e/hariharan/978-0-12-311630-7) Each suits a different task:
- **Michelson** is the topology of large gravitational-wave detectors, echoing the 1887 [Michelson–Morley experiment](https://www.edgepedia.org/michelson-morley-experiment) but using laser light for far higher accuracy.[4](https://link.springer.com/article/10.1007/s41114-016-0002-8)
- **Fizeau** interferometers are the standard workshop tool for testing the surface flatness of mirrors or the transmitted wavefront quality of lens systems, requiring high-quality reference optics such as transmission flats or spheres.[6](https://www.rp-photonics.com/interferometers.html)
- **Fabry–Pérot** arm cavities store many photons so that tiny phase shifts accumulate; gravitational-wave detector development progressed from simple Michelson interferometers through delay lines, Fabry–Pérot arm cavities, power recycling, and finally signal recycling.[4](https://link.springer.com/article/10.1007/s41114-016-0002-8)
- **Fiber-optic sensing** uses interferometric sensors for temperature, strain, pressure, and refractive index, categorized into four types: Fabry-Perot, Mach-Zehnder, Michelson, and Sagnac.[15](https://pmc.ncbi.nlm.nih.gov/articles/PMC3376629/)
## Detection techniques
**Homodyne versus heterodyne.** [Heterodyne detection](https://www.edgepedia.org/heterodyne-detection) mixes two slightly different optical frequencies so the signal appears as a modulation at an intermediate frequency, which can be filtered and counted electronically. Heterodyne He–Ne interferometers use the [Zeeman effect](https://www.edgepedia.org/zeeman-effect), with external magnetic fields splitting the laser line to generate frequency differences typically of 1 MHz to 3 MHz between orthogonally polarized waves.[1](https://iopscience.iop.org/article/10.1088/1681-7575/ac1456) Displacement interferometers often use heterodyne detection for direction sensing and noise immunity.[6](https://www.rp-photonics.com/interferometers.html) In radio and millimeter astronomy the same principle applies at the antenna level: the signal is heterodyned, the amplitude and phase of the electric field are recorded, and the signals from separate antennas are combined in a correlator, whereas optical interferometry usually combines the beams themselves before detection.[16](https://web-archives.iram.fr/IS/IS2002/html_2/node28.html)
**Surface testing methods.** [Phase-shifting interferometry](https://www.edgepedia.org/phase-shifting-interferometry) shifts the reference mirror in controlled steps and solves for the phase computationally, with error-correcting algorithms treated in the standard literature; white-light or coherence-scanning interferometry uses broadband low-coherence sources to profile rough surfaces and step heights without the phase ambiguity of monochromatic methods.[14](https://shop.elsevier.com/books/optical-interferometry-2e/hariharan/978-0-12-311630-7) • [6](https://www.rp-photonics.com/interferometers.html) The CSI and PSI methods are defined in [ISO 25178](https://www.edgepedia.org/iso-25178) part 6 (2010), and ISO/TR 14999-2:2019 gives fundamental explanations of interferometric measurement objects, hardware aspects, and evaluation methods for characterizing optical parts.[17](https://eprintspublications.npl.co.uk/5820/1/mgpg127.pdf) • [10](https://cdn.standards.iteh.ai/samples/iso/iso-tr-14999-2-2019/0f8a3391967041f0936b467373fd8649/iso-tr-14999-2-2019.pdf)
**Noise floors.** In gravitational-wave detectors, at signal frequencies above a couple of hundreds of hertz, sensitivity is limited by photon counting (shot) noise at the readout.[4](https://link.springer.com/article/10.1007/s41114-016-0002-8) Advanced LIGO is limited by seismic noise near 10 Hz, thermal noise from the suspension system and mirror coatings near 100 Hz, and shot noise above a few hundred hertz.[3](http://www.scholarpedia.org/article/Gravitational_Waves:_Ground-Based_Interferometric_Detectors) Vacuum noise entering the open input port of a beam splitter sets a shot-noise limit, which squeezed states of light can reduce.[6](https://www.rp-photonics.com/interferometers.html)
## By the numbers
[X-ray interferometry](https://www.edgepedia.org/x-ray-interferometry) serves as a picometre ruler for sub-nanometre displacement metrology, and combined optical and X-ray interferometry (COXI) provides a 1 mm long-range facility for calibrating displacement transducers.[1](https://iopscience.iop.org/article/10.1088/1681-7575/ac1456) LIGO's coated optics have surface figure and roughness of order 0.5 nm rms or better, and its metrology interferometer requires measurement repeatability of order 0.1 nm rms or better; in practice LIGO repeated measurements to 0.16 nm rms with a modified WYKO 6000 instrument, with thermal variation in the measurement space below 0.1 °C per day.[18](https://dcc.ligo.org/public/0003/E080508/002/E080508-v2_AdL_Metrology_IFO.pdf) At the other extreme, current optical stellar interferometers achieve angular resolution below 5 × 10−9 radians (1 milliarcsecond) while maintaining sub-micron optical stability over hundreds of meters of path.[12](https://ar5iv.labs.arxiv.org/html/astro-ph/0307036) Between these, Advanced LIGO demonstrated 5 × 10−11 radian/√Hz phase noise around 150 Hz, and the first detected gravitational wave reached a strain amplitude of 10−21.[3](http://www.scholarpedia.org/article/Gravitational_Waves:_Ground-Based_Interferometric_Detectors) • [4](https://link.springer.com/article/10.1007/s41114-016-0002-8)
## Applications
**Gravitational-wave detection.** The goal of interferometer design here is to store many photons in the arms so that tiny phase shifts induced by gravitational waves can accumulate and be detected.[4](https://link.springer.com/article/10.1007/s41114-016-0002-8) On September 14, 2015, shortly before Advanced LIGO's first official search and nearly 100 years after Einstein first postulated gravitational waves, LIGO's two interferometers achieved their first detection with a signal-to-noise ratio of 24.[19](https://www.caltech.edu/about/news/brief-history-ligo) LIGO operates two interferometers because each site experiences unique noise signatures, so continually comparing the data from the two sites is crucial to claiming a detection.[13](https://www.ligo.caltech.edu/page/what-is-interferometer)
**Length metrology and lithography.** [Laser interferometry](https://www.edgepedia.org/laser-interferometry) measures distances in terms of the wavelength of light and provides the backbone of top-level length metrology in industry and science.[7](https://www.nist.gov/programs-projects/si-length-and-traceability) Displacement interferometers are widely used in machine shops and lithography systems for measuring linear positions with nanometre precision over distances of meters.[6](https://www.rp-photonics.com/interferometers.html)
**Astronomical interferometry.** The GRAVITY instrument at the Very Large Telescope Interferometer, with four 8-m telescopes, reaches objects a thousand times fainter than earlier interferometers, and the CHARA array routinely offers baselines up to 330 m with six 1-m telescopes.[5](https://www.annualreviews.org/content/journals/10.1146/annurev-astro-121622-045019) These capabilities produced breakthrough results on the [Galactic Center](https://www.edgepedia.org/galactic-center), exoplanets, active galactic nuclei, young stellar objects, and stellar physics.[5](https://www.annualreviews.org/content/journals/10.1146/annurev-astro-121622-045019) Earlier interferometric work had already yielded precise stellar masses from spectroscopic binaries and resolved circumstellar disks and shells.[20](https://www.annualreviews.org/content/journals/10.1146.astro.39.1.353) In recent years interferometry has been used to make the first image of a black hole.[2](https://academic.oup.com/book/46528)
**Fiber sensing.** Fiber-optic interferometric sensors based on the four classic configurations measure temperature, strain, pressure, and refractive index where bulk optics are impractical.[15](https://pmc.ncbi.nlm.nih.gov/articles/PMC3376629/)
## How it compares across the spectrum
Optical and radio interferometry solve the same problem with different hardware. Optical interferometry typically reaches about 1 milliarcsecond resolution, whereas the Plateau de Bure millimeter interferometer reaches about 1 arcsecond and ALMA with extended baselines about 0.03 arcsecond, still about 30 times less resolved than optical.[16](https://web-archives.iram.fr/IS/IS2002/html_2/node28.html) The dominant noise also differs: millimeter interferometry is limited mainly by thermal noise, while optical interferometry contends with photon noise, detector read-out noise, background noise, and atmospheric turbulence.[16](https://web-archives.iram.fr/IS/IS2002/html_2/node28.html)
Matter waves extend the same mathematics to atoms. Atom interferometers are optimally sensitive to gravitational waves near 1 Hz, filling the frequency gap between terrestrial and space-borne laser interferometers, and atom interferometers have been used to test the equivalence principle of general relativity.[21](https://www.nature.com/articles/s41586-026-10617-1) • [22](https://arxiv.org/pdf/2008.05609)
## Recent developments
**The O4 observing run.** The fourth [LIGO–Virgo–KAGRA](https://www.edgepedia.org/ligo-virgo-kagra) observing run ran from May 2023 to November 2025, the longest data-taking period to date for the network, and produced an unprecedented number of gravitational-wave candidates announced in near real time for multi-messenger follow-up.[23](https://beta.iopscience.iop.org/article/10.1088/1742-6596/3177/1/012067/pdf)
**Squeezed light.** During the O3 run in 2019–2020, Advanced LIGO and Virgo mitigated quantum shot noise by about 3 dB via injected squeezed light, while GEO600 demonstrated a 6 dB reduction.[8](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.129.031101) In the fourth observing run, Advanced LIGO achieved stable −6 dB squeezing in phase quadrature, with modeling of frequency-dependent loss toward a −10 dB target.[9](https://opg.optica.org/abstract.cfm?uri=QSM-2025-QM2B.2) Researchers have also demonstrated the first 10 dB sensitivity enhancement of a shot-noise-limited tabletop Michelson interferometer using squeezed light with balanced homodyne detection, the scheme planned for the third-generation detectors [Einstein Telescope](https://www.edgepedia.org/einstein-telescope) and Cosmic Explorer.[8](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.129.031101) Looking further ahead, reflecting a squeezed beam from a detuned high-finesse filter cavity produces frequency-dependent squeezing that can simultaneously reduce shot noise at high frequencies and radiation pressure noise at low frequencies, a key planned upgrade combined with balanced homodyne readout.[24](https://dcc.ligo-wa.caltech.edu/public/0205/T2600053/001/IS%20white%20paper%20cover%20page%202026%20and%20WP%202025.pdf) In Advanced LIGO, Advanced Virgo, and KAGRA, the quantum behavior of light and of the mirrors' motion is predicted to interact within the same operating regime, so a careful quantum-noise analysis will be needed.[4](https://link.springer.com/article/10.1007/s41114-016-0002-8)
**Atom interferometry in space.** Investigators on the Cold Atom Lab aboard the [International Space Station](https://www.edgepedia.org/international-space-station) demonstrated high-visibility Mach–Zehnder atom interferometry in orbit, with interference fringes persisting for more than 150 ms during freefall, the first quantum matter-wave sensor in space.[25](https://www.nature.com/articles/s41467-024-50585-6) On the ground, the AION project tested a gradiometer configuration using strontium-87, combining atomic clock technology with atom interferometry; its prototype reached the standard quantum limit even in the presence of several radians of synthetic laser phase noise.[21](https://www.nature.com/articles/s41586-026-10617-1)
## References
1. [The new mise en pratique for the metre, Metrologia](https://iopscience.iop.org/article/10.1088/1681-7575/ac1456)
2. [Interference: The History of Optical Interferometry and the Scientists Who Tamed Light, Oxford Academic](https://academic.oup.com/book/46528)
3. [Gravitational Waves: Ground-Based Interferometric Detectors, Scholarpedia](http://www.scholarpedia.org/article/Gravitational_Waves:_Ground-Based_Interferometric_Detectors)
4. [Interferometer Techniques for Gravitational-Wave Detection, Living Reviews in Relativity](https://link.springer.com/article/10.1007/s41114-016-0002-8)
5. [Advances in Optical/Infrared Interferometry, Annual Review of Astronomy and Astrophysics](https://www.annualreviews.org/content/journals/10.1146/annurev-astro-121622-045019)
6. [Interferometers, RP Photonics Encyclopedia](https://www.rp-photonics.com/interferometers.html)
7. [SI Length and Traceability, NIST](https://www.nist.gov/programs-projects/si-length-and-traceability)
8. [10 dB Quantum-Enhanced Michelson Interferometer with Balanced Homodyne Detection, Physical Review Letters](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.129.031101)
9. [Advanced LIGO Quantum Noise in the Fourth Observing Run: Towards −10 dB Squeezing, Optica QSM 2025](https://opg.optica.org/abstract.cfm?uri=QSM-2025-QM2B.2)
10. [ISO/TR 14999-2:2019, Interferometric measurement of optical surfaces, Part 2](https://cdn.standards.iteh.ai/samples/iso/iso-tr-14999-2-2019/0f8a3391967041f0936b467373fd8649/iso-tr-14999-2-2019.pdf)
11. [Introduction to optical/IR interferometry: history and basic principles, arXiv 1907.07443](https://ar5iv.labs.arxiv.org/html/1907.07443)
12. [Optical Interferometry in Astronomy, arXiv astro-ph/0307036](https://ar5iv.labs.arxiv.org/html/astro-ph/0307036)
13. [What is an Interferometer? LIGO Lab, Caltech](https://www.ligo.caltech.edu/page/what-is-interferometer)
14. [Optical Interferometry, 2nd edition (Hariharan), Elsevier](https://shop.elsevier.com/books/optical-interferometry-2e/hariharan/978-0-12-311630-7)
15. [Interferometric Fiber Optic Sensors, Sensors](https://pmc.ncbi.nlm.nih.gov/articles/PMC3376629/)
16. [Optical versus millimeter radio interferometry, IRAM Summer School](https://web-archives.iram.fr/IS/IS2002/html_2/node28.html)
17. [NPL Good Practice Guide No. 127: Calibration of CSI and PSI](https://eprintspublications.npl.co.uk/5820/1/mgpg127.pdf)
18. [LIGO Instrument Requirements for Metrology Interferometer, E080508](https://dcc.ligo.org/public/0003/E080508/002/E080508-v2_AdL_Metrology_IFO.pdf)
19. [A Brief History of LIGO, Caltech](https://www.caltech.edu/about/news/brief-history-ligo)
20. [Optical Interferometry, Annual Review of Astronomy and Astrophysics](https://www.annualreviews.org/content/journals/10.1146.astro.39.1.353)
21. [A prototype differential atom interferometer for fundamental physics, Nature](https://www.nature.com/articles/s41586-026-10617-1)
22. [Matter-wave interferometry, arXiv 2008.05609](https://arxiv.org/pdf/2008.05609)
23. [The LIGO-Virgo-KAGRA Observing Run 4, J. Phys. Conf. Ser.](https://beta.iopscience.iop.org/article/10.1088/1742-6596/3177/1/012067/pdf)
24. [LIGO Instrument Science white paper 2026](https://dcc.ligo-wa.caltech.edu/public/0205/T2600053/001/IS%20white%20paper%20cover%20page%202026%20and%20WP%202025.pdf)
25. [Pathfinder experiments with atom interferometry in the Cold Atom Lab onboard the ISS, Nature Communications](https://www.nature.com/articles/s41467-024-50585-6)
---
*Topic: Encyclopedia › Physical world and mathematics › Physics › Classical physics › Waves and optics › Optical technologies and instruments › Interferometers and optical cavities › Interferometric configurations and techniques › Interferometry overview and principles*
*Initially written Sep 17, 2026 · Reviewed: Sep 17, 2026; Oct 15, 2026 · Edited: Oct 15, 2026 · Last review: Oct 15, 2026*
*Copyright 2026 EdgeChat AI, a subsidiary of Biostate AI.*
License: Edgepedia Community License 1.0, https://www.edgepedia.org/edgepedia/license