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Michelson interferometer

The Michelson interferometer is an optical instrument designed to measure lengths and displacements on the order of light wavelengths by exploiting the interference patterns produced when two beams of light are split, reflected along different paths, and recombined.^[1] It typically consists of a partially reflecting beam splitter that divides an incoming coherent light source—such as a laser—into two perpendicular paths, each terminating at a mirror that reflects the beam back to the splitter, where the beams interfere to form observable fringes on a detector.^[2] This setup allows for precise detection of path length differences as small as a fraction of a wavelength, making it invaluable for metrology and spectroscopy.^[3] Invented by American physicist Albert A. Michelson in 1881 while at the U.S. Naval Academy, the device was initially developed to test for the existence of the luminiferous ether by attempting to measure the Earth's motion through it via variations in light speed.^[4] Michelson's first interferometer used a light source from a slit illuminated by white light, a half-silvered mirror as the beam splitter, and adjustable mirrors to equalize path lengths, achieving sensitivities sufficient to detect shifts corresponding to ether drift but yielding null results that puzzled contemporaries.^[5] This invention built on earlier interferometric principles but introduced a practical, high-precision configuration that Michelson refined over subsequent years.^[6] The instrument gained prominence through its role in the 1887 Michelson-Morley experiment, conducted with chemist Edward W. Morley at Case Western Reserve University, which confirmed the null result and contributed to the eventual development of special relativity by Albert Einstein in 1905.^[7] Beyond foundational physics, the Michelson interferometer has found wide applications in measuring the standard meter in terms of light wavelengths (as Michelson did for the International Bureau of Weights and Measures in 1892-1893), Fourier transform spectroscopy for chemical analysis, and modern gravitational wave detection.^[6] In particular, the Laser Interferometer Gravitational-Wave Observatory (LIGO), operational since 2002 and featuring kilometer-scale arms, employs a power-recycled Michelson configuration to detect spacetime distortions from events like black hole mergers, earning the 2017 Nobel Prize in Physics for its creators Rainer Weiss, Barry Barish, and Kip Thorne.^[8]

History and Development

Invention by Albert A. Michelson

Albert A. Michelson, an American physicist born in 1852 in Prussia and educated at the U.S. Naval Academy, where he graduated in 1873 and later served as an instructor in physics and chemistry, sought to advance precision measurements in optics during the late 19th century.^[9] His early work focused on improving determinations of the speed of light, building upon the rotating mirror methods developed by French physicists Léon Foucault in 1850 and Hippolyte Fizeau in 1849, which had provided initial evidence for the wave nature of light but lacked sufficient sensitivity to detect subtle effects like potential ether drift relative to Earth's motion.^[4] Motivated by the prevailing hypothesis of a stationary luminiferous ether as the medium for light propagation, Michelson aimed to design an instrument capable of revealing any variation in light speed due to Earth's orbital velocity through this ether, expected to produce a measurable "ether wind" of about 30 km/s.^[5] In 1881, while on leave from the Naval Academy and studying in Europe, Michelson invented the interferometer during his time in Berlin, constructing the device with the help of opticians Schmidt and Haensch under the guidance of Hermann von Helmholtz at Friedrich Wilhelms University.^[9]^[5] He first tested it in April 1881 at the Astrophysical Observatory in Potsdam, Germany, where initial observations yielded a null result, indicating no detectable ether drift.^[5] The core design featured a half-silvered mirror serving as a beam splitter to divide an incoming light beam into two perpendicular paths, which were then reflected back by mirrors and recombined to produce interference fringes sensitive to path length differences. The instrument gained prominence through its refined application in the 1887 collaboration with chemist Edward W. Morley at the Case School of Applied Science in Cleveland, Ohio, where Michelson had taken a position in 1883 after resigning from the Navy.^[9] The apparatus was mounted on a massive stone slab floating in a mercury bath for smooth rotation and vibration isolation, with additional mirrors folding the beam paths to achieve effective lengths of up to 11 meters per arm, enhancing sensitivity to expected fringe shifts of about 0.4 wavelengths. One mirror was made adjustable on a floating platform to equalize paths precisely.^[4] The Michelson-Morley experiment produced a null result, detecting no ether drift and measuring any variation in light speed to be less than one-fortieth of the expected value, fundamentally challenging the ether hypothesis and contributing to the foundation of Einstein's special relativity in 1905. This work earned Michelson the 1907 Nobel Prize in Physics, the first for an American, specifically for his optical precision instruments and the metrological investigations enabled by the interferometer.^[6]

Key Experiments and Milestones

Following the null result of the original Michelson-Morley experiment, Dayton C. Miller, a successor to Michelson at Case School of Applied Science, conducted refined ether-drift measurements using an improved Michelson interferometer. Between 1921 and 1926, Miller performed experiments at Mount Wilson Observatory in California, where he reported detecting a small positive ether drift of about 10 km/s, particularly when the apparatus was oriented toward the constellation Dorado.^[10] These results were controversial due to inconsistencies with relativity and potential systematic errors, and they were later debunked in 1955 by Robert Shankland and colleagues, who attributed the fringe shifts to temperature gradients affecting the interferometer's optical components rather than an ether wind.^[10] In the 1920s, Albert A. Michelson advanced the interferometer's role in precision metrology by applying it to accurate measurements of light wavelengths, particularly the red line in the cadmium spectrum, which offered exceptional coherence for interferometric comparisons.^[11] This work built on his earlier 1893 determinations and culminated in the International Astronomical Union's 1925 adoption of the cadmium red radiation (at 643.8466 nm in air) as the international standard for wavelength measurements, enabling sub-micrometer accuracy in length standards.^[11] Michelson's cadmium-based interferometry directly influenced the 1960 redefinition of the meter by the General Conference on Weights and Measures, which specified it as 1,650,763.73 wavelengths of the krypton-86 orange-red line in vacuum, shifting from artifact prototypes to an invariant optical basis for enhanced stability and reproducibility.^[12] During World War II, the Michelson interferometer found applications in optical testing for military optics, including the evaluation of lens quality and surface flatness in precision instruments essential for aerial reconnaissance and gunnery systems.^[13] In the 1940s, adaptations of the instrument were developed to measure refractive indices of gases by observing interference fringe displacements caused by gas-filled paths in one arm, providing quantitative data on optical properties for atmospheric and industrial applications.^[11] Michelson's efforts in the 1920s also extended to improving ruling engines for producing high-quality diffraction gratings, which he ruled at the University of Chicago's Ryerson Laboratory and later at Mount Wilson Observatory.^[14] Between 1920 and 1934, his enhanced engine produced over 85 gratings up to 10 inches wide with groove densities exceeding 15,000 lines per inch, minimizing errors to angstrom levels and enabling advanced spectroscopic analysis of stellar spectra.^[14] These gratings linked the interferometer to broader spectroscopic uses by providing dispersed light sources for wavelength calibration in interferometric setups. By the 1950s, the Michelson interferometer had become a established standard in metrology at institutions like the National Bureau of Standards, routinely used for calibrating length artifacts with multi-wavelength sources including cadmium and mercury lines.^[15] Early concepts for integrating coherent light sources, foreshadowing the laser's 1960 invention, emerged in the late 1950s through proposals for stabilized interferometers to achieve even higher path-length resolutions in precision measurements.^[15]

Basic Configuration

Optical Components and Setup

The Michelson interferometer employs a beam splitter as its central component, typically a 50/50 partially reflecting mirror or cube that divides an incident light beam into two equal-intensity parts by reflecting and transmitting approximately half the light./03%3A_Interference/3.06%3A_The_Michelson_Interferometer) This setup originates from the 1887 apparatus designed by Albert A. Michelson and Edward W. Morley. The two resulting beams propagate along perpendicular arms to end mirrors: a fixed plane mirror in one arm and a movable plane mirror in the other, both positioned to reflect the beams back to the beam splitter for recombination./03%3A_Interference/3.06%3A_The_Michelson_Interferometer) To equalize the optical path lengths through glass in the beam splitter, a compensator plate—an unsilvered glass plate matching the beam splitter's thickness—is inserted in the fixed arm./03%3A_Interference/3.06%3A_The_Michelson_Interferometer) Light from a monochromatic source, such as a HeNe laser operating at 632.8 nm or a white light lamp filtered for narrow bandwidth, is directed onto the beam splitter at a 45-degree angle, with the recombined output directed to a detector or eyepiece.^[16]^[17] The entire assembly is mounted on a rigid base, often with vibration-isolating supports, and the arms are typically equal in length, adjustable via a micrometer-driven translation stage on the movable mirror to vary the path imbalance from 0 to several centimeters in visible wavelengths.^[18] Precise alignment is essential, with end mirrors adjusted to be perpendicular to their beam paths using kinematic mounts featuring tip-tilt screws for angular correction and linear stages for positional fine-tuning.^[16] Modern variants incorporate dielectric multilayer coatings on the beam splitter and mirrors to minimize absorption losses and enhance reflectivity across specific wavelengths.^[18]

Beam Paths and Interference Generation

In the Michelson interferometer, an incoming beam of light strikes a partially reflecting beam splitter, which divides it into two components of approximately equal intensity: one transmitted and one reflected.^[19] The transmitted beam propagates along the reference arm to a fixed mirror, undergoes reflection, and returns to the beam splitter along the same path, resulting in a total round-trip path length of $2L_1, where L_1 is the distance from the beam splitter to the fixed mirror./University_Physics_III_-Optics_and_Modern_Physics(OpenStax)/03%3A_Interference/3.06%3A_The_Michelson_Interferometer) Similarly, the reflected beam travels along the sample or delay arm to a movable mirror, reflects back, and returns to the beam splitter, yielding a round-trip path length of $2L_2, with L_2 being the distance to the movable mirror.^[19] This configuration allows precise control over the path difference by adjusting the position of the movable mirror.^[20] Upon returning to the beam splitter, the two beams recombine such that the component from the reference arm that is reflected overlaps with the component from the delay arm that is transmitted, and vice versa, forming two output beams./University_Physics_III_-Optics_and_Modern_Physics(OpenStax)/03%3A_Interference/3.06%3A_The_Michelson_Interferometer) One output beam is directed toward a detector for analysis, while the other returns toward the light source.^[19] The standard ray diagram illustrates this process: the input beam enters from the source port, splits at the beam splitter into two perpendicular paths leading to the fixed and movable mirrors, reflects back along the same paths, recombines at the beam splitter, and exits via the two output ports, often depicted with dashed lines for the reflected paths to emphasize the round trips.^[20] Interference arises from the coherent superposition of the two recombined beams, which occurs due to the optical phase difference introduced by the path length disparity \Delta L = 2(L_2 - L_1).^[19] For observable interference, the light source must exhibit both spatial coherence, ensuring the beams overlap precisely in the output plane, and temporal coherence, requiring the path difference to be within the coherence length of the source.^[21] In a balanced configuration, the arms are set to equal lengths (L_1 = L_2) to maximize interference visibility for symmetric measurements, whereas unequal arm lengths are employed in setups designed to probe material dispersion by introducing controlled imbalances.^[22]

Operating Principles

Fringe Formation and Visibility

In the Michelson interferometer, the two beams recombined at the beam splitter superpose to produce interference patterns known as fringes, observable under ideal conditions with monochromatic light.^[23] Constructive interference, resulting in bright fringes, occurs when the optical path length difference ΔL between the beams equals an integer multiple of the wavelength λ, i.e., ΔL = mλ where m is an integer (m = 0, ±1, ±2, ...). Destructive interference, producing dark fringes, happens when ΔL = (m + 1/2)λ.^[19]^[23] The resulting fringe pattern consists of linear fringes when observed in the far field with a collimated beam, alternating between bright and dark regions perpendicular to the direction of path difference variation.^[23] The intensity I of the interference pattern is given by

I = I_0 \left[1 + \cos\left(\frac{2\pi \Delta L}{\lambda}\right)\right],

where I_0 is the average intensity of the two beams, assuming equal amplitudes and perfect coherence. This equation predicts maximum intensity I_max = 2I_0 at constructive interference and minimum I_min = 0 at destructive interference.^[23] Fringe visibility V quantifies the contrast of the pattern and is defined as V = (I_max - I_min)/(I_max + I_min); for the ideal monochromatic case with equal beam intensities, V = 1, indicating maximum contrast.^[24] These fringes can be observed directly by eye through an eyepiece or on a viewing screen, or recorded using photodetectors or charge-coupled device (CCD) cameras for quantitative analysis; by scanning the position of the movable mirror and counting fringe shifts, the wavelength λ can be measured via ΔL = mλ, where ΔL = 2d is the optical path difference for mirror displacement d and the factor of 2 accounts for the round-trip path.^[19]^[23] In a stable setup, the instrument achieves high resolution, capable of measuring path differences to within λ/1000.^[25]

Effects of Source Bandwidth and Coherence

In the ideal case of monochromatic light, the Michelson interferometer produces high-contrast interference fringes across a wide range of path length differences, as derived from the basic fringe formation equation. However, real light sources possess finite spectral bandwidth, leading to partial coherence that degrades fringe visibility as the path length difference increases. The temporal coherence length l_c, which quantifies the maximum path difference over which stable interference can occur, is given by l_c = \frac{\lambda^2}{\Delta \lambda}, where \lambda is the central wavelength and \Delta \lambda is the spectral bandwidth./05%3A_Interference_and_coherence/5.05%3A_Temporal_Coherence_and_the_Michelson_Interferometer) Fringes remain visible only when the absolute path length difference |\Delta L| < l_c, beyond which the phase differences across wavelengths cause destructive superposition and fringe washout. For broadband sources like white light, where \Delta \lambda spans hundreds of nanometers, the coherence length is extremely short, typically on the order of 1–10 μm. In such cases, interference fringes rapidly diminish in visibility away from the central (zero-order) position, where all wavelengths constructively interfere to produce a sharp, achromatic white fringe; higher-order fringes appear colored due to wavelength-dependent phase shifts but quickly fade into uniform illumination. This effect arises because the superposition of multiple wavelengths with differing fringe spacings leads to overlapping patterns that average out the contrast. For sources with a Gaussian spectral profile, the fringe visibility V(\Delta L) decays quantitatively as V(\Delta L) = \exp\left( -\left( \frac{\pi \Delta L \Delta \nu}{c} \right)^2 \right), where \Delta \nu is the frequency bandwidth and c is the speed of light; this exponential form highlights the Gaussian envelope limiting observable interference to within the coherence length. To mitigate bandwidth-induced degradation and extend the effective coherence length, narrowband optical filters can be employed to reduce \Delta \lambda, or highly coherent sources such as lasers can be used, which offer l_c on the order of meters or more. It is essential to distinguish temporal coherence, governed by spectral bandwidth and affecting path-length-dependent interference, from spatial coherence, which depends on source size and influences beam overlap uniformity across the aperture.^[26] In the seminal 1887 Michelson-Morley experiment, a sodium lamp source with \Delta \lambda \approx 0.6 nm provided a coherence length of up to ~2 mm, allowing reliable fringe observation and adjustment over this range despite the apparatus's longer arm lengths.^[27]^[28]

Applications

Fourier Transform Spectroscopy

Fourier transform spectroscopy (FTS) utilizes the Michelson interferometer to measure the infrared spectrum of a sample by recording an interferogram and applying a Fourier transform to obtain the spectral intensity as a function of wavenumber. In this configuration, one mirror is mounted on a translation stage and scanned linearly over a maximum path length difference ΔL_max, typically ranging from a few centimeters to tens of centimeters depending on the desired resolution. The broadband light source, such as a globar for mid-infrared wavelengths, passes through the sample and enters the interferometer, where it is split into two beams that travel unequal paths before recombining. The resulting interferogram I(ΔL), which represents the intensity as a function of the path difference ΔL, encodes the spectral information in the time domain. The spectrum S(ν) is then recovered via the Fourier transform:

S(\nu) = \int_{-\infty}^{\infty} I(\Delta L) \exp(-i 2\pi \nu \Delta L) \, d\Delta L

where ν is the wavenumber in cm⁻¹.^[29]^[30] The interferometer is adapted for FTS with a rapidly oscillating or translating mirror driven by a servo-controlled mechanism to ensure precise and uniform motion, often at speeds of several centimeters per second to minimize atmospheric noise effects. A helium-neon (HeNe) laser provides a monochromatic reference beam that interferes within the same interferometer, generating evenly spaced fringes used to trigger the detector sampling at exact intervals corresponding to the laser wavelength (approximately 632.8 nm). This zero-crossing sampling ensures accurate digitization of the interferogram without aliasing, with the detector—typically a deuterated triglycine sulfate (DTGS) or mercury cadmium telluride (MCT) photoconductor—capturing the modulated infrared signal. The entire process is computer-controlled, with fast Fourier transform algorithms applied in real-time for spectral reconstruction.^[31]^[32] The spectral resolution δν in FTS is fundamentally limited by the maximum path difference, given by δν = 1 / ΔL_max, where both are expressed in consistent units (e.g., cm⁻¹ and cm). For instance, a maximum path difference of 2 cm yields a resolution of 0.5 cm⁻¹, sufficient to resolve closely spaced vibrational bands in molecular spectra. This high resolution, combined with the interferometer's ability to handle broadband sources, makes FTS ideal for mid-infrared spectroscopy (4000–400 cm⁻¹), where it identifies molecular functional groups through characteristic absorption bands, such as C-H stretches near 2900 cm⁻¹ or C=O stretches around 1700 cm⁻¹ in organic compounds. Compared to dispersive grating spectrometers, FTS offers two key advantages: the Fellgett (or multiplex) advantage, where all wavelengths are detected simultaneously, improving signal-to-noise ratio by the square root of the number of resolution elements for broadband or weak sources; and the Jacquinot (or throughput) advantage, arising from the slitless design that allows greater optical étendue and thus higher light collection efficiency, often by factors of 10–100.^[31]^[29]^[32] Commercial Fourier transform infrared (FTIR) spectrometers based on the Michelson design became available in 1969 with the introduction of the Digilab FTS-14, marking the transition from laboratory prototypes to routine analytical tools. These instruments revolutionized molecular spectroscopy in chemistry and materials science. In astronomy, Michelson-based FTS has been employed since the 1960s to study planetary atmospheres, providing high-resolution spectra of emission and absorption features in bodies like Venus and Jupiter, revealing trace gases such as CO₂ and CH₄ through their infrared signatures.^[33]

Optical Testing and Metrology

The Twyman-Green interferometer, a specialized variant of the Michelson interferometer, is widely employed in optical testing and metrology to evaluate the quality of optical components such as lenses, mirrors, and prisms for flatness, alignment, and wavefront aberrations.^[34] Developed in 1916 by English engineer Frank Twyman and chemist Arthur Green, this configuration uses a coherent laser source, typically a helium-neon laser at 632.8 nm, combined with a pinhole spatial filter to produce a clean, collimated beam that expands to illuminate the test optic.^[35] In the setup, the beam splitter divides the light into a reference arm with a flat mirror and a test arm where the optic under examination is inserted, allowing interference fringes to reveal deviations from ideal performance.^[36] Fringe patterns in the Twyman-Green interferometer provide direct visualization of optical errors: straight, equally spaced fringes indicate a flat surface or aberration-free wavefront, while distortions such as curvature or irregularities quantify defects, where each fringe deviation typically corresponds to a wavefront error on the order of λ/10 for high-precision assessments.^[36] The wavefront error δ can be calculated using the formula

\delta = \frac{N \lambda}{2 n}

where N is the fringe order count (deviation from straight fringes), λ is the wavelength, and n is the magnification factor of any beam expander in the system.^[37] This method achieves detection of surface irregularities down to 1 nm, enabling sub-wavelength precision essential for high-performance optics.^[38] For testing large optics where equal path lengths are impractical, the laser unequal path interferometer (LUPI) modifies the configuration with a short reference arm and a long test arm, accommodating path differences up to several meters while maintaining coherence with monochromatic laser illumination.^[37] This variant is particularly useful in semiconductor lithography for aligning large-scale optical systems, ensuring nanometer-level precision in reticle and wafer positioning.^[39] The Twyman-Green design has become a standard in the optics industry, adopted by manufacturers like Zeiss and Nikon for routine quality control of precision components.^[40]

Gravitational Wave Detection

The Michelson interferometer forms the core of advanced gravitational wave detectors like the Laser Interferometer Gravitational-Wave Observatory (LIGO), where passing gravitational waves induce minute differential changes in the lengths of the perpendicular arms. These waves, predicted by general relativity, cause spacetime strains h \approx 10^{-21} for detectable astrophysical sources such as merging black holes or neutron stars, resulting in arm length variations \delta L / L \approx h.^[41] The resulting phase shift in the recombined laser beams is given by \delta \phi = (4\pi L / \lambda) h, where L is the arm length and \lambda is the laser wavelength, allowing measurement of h through interference fringe shifts.^[42] LIGO employs a delayed Michelson configuration with 4 km-long arms incorporating Fabry-Pérot cavities to enhance light storage and effective path length, achieving power buildups of around 130 times the input for improved sensitivity.^[43] A continuous-wave Nd:YAG laser operating at 1064 nm serves as the light source, with input powers up to 125 W directed through power and signal recycling mirrors to boost circulating arm power to megawatts while optimizing the signal bandwidth.^[44] Power recycling reuses unused light to amplify the input, reducing shot noise at higher frequencies, while signal recycling reshapes the response to gravitational wave signals, narrowing the frequency band around 100 Hz for better strain sensitivity.^[45] Dominant noise sources include seismic vibrations at low frequencies (below 10 Hz), thermal noise from mirror suspensions and coatings around 10–100 Hz, and photon shot noise at higher frequencies above 100 Hz, all mitigated through advanced isolation systems and cryogenic cooling plans for future upgrades.^[46] The first direct detection of gravitational waves occurred on September 14, 2015 (GW150914), when LIGO observed a binary black hole merger at 410 Mpc, releasing energy equivalent to three solar masses in gravitational waves and confirming general relativity's predictions. This milestone was followed by GW170817 in 2017, a neutron star merger detected jointly by LIGO and Virgo, enabling multi-messenger astronomy through coincident electromagnetic observations of the kilonova and gamma-ray burst. By the end of the third observing run (O3) in 2020, the LIGO-Virgo network had confirmed over 50 events, rising to more than 90 by 2023; the fourth run (O4, started May 2023 and concluded November 2025) resulted in over 250 new detections, bringing the total to approximately 370 as of November 2025, including rare multi-messenger events like black hole-neutron star mergers.^[47] These observations, spanning the LIGO-Virgo-KAGRA collaboration, have mapped the stellar-mass black hole population and tested fundamental physics, with strain sensitivities reaching below $10^{-23} Hz^{-1/2} around 100 Hz in Advanced LIGO.^[48] To expand the global network, LIGO-India received final government approval in April 2023 for construction of a third detector identical to Advanced LIGO, targeting operation by the late 2020s, though site preparation advanced in 2025.^[49] This addition will improve sky localization for multi-messenger events and enhance detection rates by 30–50%, building on the strain sensitivity goal of $10^{-23} Hz^{-1/2} in the 30–800 Hz band.^[50]

Atmospheric and Space-Based Uses

The Michelson interferometer plays a key role in atmospheric monitoring through integration with direct-detection Doppler wind lidars (DD-DWLs), where it enables fringe imaging to measure wind speeds by analyzing Doppler-shifted backscattered light from ultraviolet laser pulses. In these systems, a field-widened Michelson interferometer (FW-FIMI) serves as the spectral analyzer, capturing interference fringes to derive radial wind velocities with high resolution, particularly for detecting wind shear in aviation corridors under clear-air conditions. This differential interferometry approach quantifies refractive index fluctuations in the atmosphere, which induce optical path delays and contribute to turbulence effects measurable via fringe shifts. The phase delay δφ arising from these fluctuations is given by

\delta \phi = \frac{2\pi}{\lambda} \int n \, ds,

where λ is the wavelength, n is the air refractive index, and the integral is along the light path ds.^[51]^[52]^[53] In space-based applications, the Michelson Doppler Imager (MDI) aboard NASA's Solar and Heliospheric Observatory (SOHO), launched in 1995, utilizes a Michelson interferometer to measure photospheric velocity Doppler shifts, enabling helioseismology studies of solar oscillations and interior dynamics through full-disk imaging. For atmospheric wind profiling from orbit, the European Space Agency's Aeolus mission (2018–2023) employed an interferometer backend in its ALADIN instrument to process lidar returns for global wind profiles, supporting weather forecasting and climate research; post-mission data from Aeolus has been assimilated into models to enhance precipitation and tropical cyclone predictions. Fringe tracking with Michelson configurations also supports adaptive optics in space telescopes, compensating for atmospheric phase errors to maintain coherent interferometry during stellar observations.^[54]^[55]^[56] Fiber-optic variants of the Michelson interferometer extend its utility to seismic monitoring, where they detect ground vibrations by measuring phase changes in light propagating through fiber loops, offering high sensitivity for broadband earthquake detection without polarization fading. These systems, often with passive demodulation, provide an alternative to traditional sensors for distributed sensing in remote or underwater environments, analogous to acoustic interferometry applications. In the 2020s, ongoing developments include pre-phase A studies for Michelson-based interferometers in follow-on missions like Aeolus-2, aimed at improved wind lidar performance for Earth observation.^[57]^[58]^[59]

Advanced Variants

Twyman-Green Interferometer

The Twyman-Green interferometer is a specialized variant of the Michelson interferometer designed for high-precision testing of optical components, such as lenses, prisms, and mirrors. Invented and patented in 1916 by Frank Twyman and Arthur Green, it was originally developed to evaluate the quality of prisms and microscope objectives by analyzing wavefront distortions.^[34] Unlike the standard Michelson setup, which typically uses a broadband source and point-like illumination, the Twyman-Green configuration employs a collimated laser beam that passes through a spatial filter—often a pinhole and lens combination—to produce a clean plane wave with minimal diffraction effects. The test optic is inserted in the transmission arm, allowing the interferometer to measure transmitted wavefront aberrations directly, while the reference arm maintains a flat or spherical reference wavefront.^[36] This design offers key advantages over the conventional Michelson interferometer, including superior temporal and spatial coherence from the monochromatic laser source, which enables sharper interference fringes and reduces sensitivity to environmental vibrations and diffraction artifacts.^[60] Quantitative analysis is achieved through phase-shifting interferometry, where a piezoelectric transducer introduces controlled phase steps in one arm, typically using a four-step (4-bucket) algorithm to compute detailed phase maps across the field. The phase map \phi(x,y) is derived from multiple intensity measurements I_k(x,y) at phase steps \delta_k (commonly 0, \pi/2, \pi, $3\pi/2) via the formula:

\phi(x,y) = \atan2\left( \sum_k I_k \sin \delta_k, \sum_k I_k \cos \delta_k \right)

This approach yields absolute phase values without manual fringe counting, facilitating automated error quantification.^[61] In applications, the Twyman-Green interferometer excels at testing aspheric surfaces, where null testing configurations use compensators—such as computer-generated holograms (CGHs) or partial null lenses—to cancel the aspheric deviation and produce a reference-like fringe pattern for direct error assessment. Wavefront errors extracted from the phase map are commonly decomposed into Zernike polynomials to identify and quantify aberrations like defocus, astigmatism, or higher-order terms, enabling precise surface figure correction. Modern digital implementations, incorporating charge-coupled device (CCD) cameras for fringe capture and processing, routinely achieve measurement accuracies of 0.01\lambda (where \lambda is the wavelength, typically 632.8 nm for He-Ne lasers), supporting sub-wavelength metrology in optical fabrication.^[62]

Step-Phase Interferometer

The step-phase interferometer, a variant of the Michelson interferometer, employs discrete phase shifts to facilitate high-speed, dynamic measurements of optical path differences. In this configuration, a piezoelectric transducer (PZT) attached to one of the mirrors introduces precise, known phase steps, typically in increments of 0, π/2, π, and 3π/2 radians, by displacing the mirror by fractions of the wavelength (e.g., λ/8 for a π/2 shift).^[63] This phase-stepping approach allows for the absolute retrieval of the phase difference without the 2π ambiguity inherent in continuous fringe counting, enabling robust phase extraction even in the presence of moderate noise or low fringe visibility.^[63] The phase information is derived from the recorded intensities at each step, where the interference pattern's modulation reveals the underlying phase shift. The retrieved phase Δφ, corresponding to the optical path difference ΔL, is given by

\Delta \phi = \frac{2\pi \Delta L}{\lambda},

computed via algorithms that analyze the intensity variations at the modulation frequency, such as the four-step arctangent method. Developed in the 1980s with advancements in digital processing and PZT control, this technique achieves sensitivities down to 1 nm displacement resolution at rates up to several kHz, making it suitable for transient events. Unlike standard Michelson setups relying on slow mechanical adjustments, the step-phase variant often incorporates acousto-optic or electro-optic modulators for rapid phase stepping, providing higher bandwidth for real-time applications.^[64] Key uses include vibration analysis, where it captures dynamic surface motions in engineering components, and real-time surface profiling for non-contact metrology in industrial quality control, such as inspecting machined parts or thin films.^[65] These capabilities stem from the method's ability to process sequential interferograms quickly, yielding quantitative displacement maps with sub-wavelength accuracy.^[65]

Phase-Conjugating and Modern Quantum Variants

Phase-conjugating variants of the Michelson interferometer employ nonlinear optical media, such as photorefractive crystals, to generate a phase-conjugate beam that reverses the wavefront phase distortions of the input light, enabling applications like adaptive optics and image processing.^[66] In this configuration, the interferometer's arms incorporate a nonlinear medium where four-wave mixing occurs, producing a backward-propagating wave that reconstructs the original wavefront with high fidelity.^[67] The process relies on degenerate four-wave mixing, where two pump beams and a probe beam interact in a χ^(3) medium, yielding a phase-conjugate field E_c \propto E_p^* |E_{\rm pump}|^2 through the third-order nonlinear polarization.^[68] A modern advancement is the fully symmetric dispersionless transmission-grating Michelson interferometer, introduced in 2020, which replaces traditional beam splitters with transmission gratings to minimize chromatic dispersion and achieve broadband operation across visible and near-infrared wavelengths.^[69] This design ensures high symmetry between interferometer arms, reducing phase instabilities and enabling stable interferometry for ultrafast pulse characterization without material-induced dispersion effects.^[69] In quantum applications, squeezed light injection into the dark port of the Michelson interferometer suppresses quantum shot noise below the standard quantum limit by replacing vacuum fluctuations with squeezed vacuum states, where noise in one quadrature is reduced at the expense of the orthogonal quadrature.^[70] This technique has been implemented in LIGO upgrades, achieving up to 3 dB of broadband noise reduction in the shot-noise-limited regime.^[71] Entanglement-enhanced variants further improve sensitivity by using entangled photon pairs or SU(1,1) nonlinear processes to surpass classical limits in precision metrology, enabling phase measurements with Heisenberg-limited scaling.^[72]^[73] Quantum optics implementations in the 2020s have demonstrated sub-shot-noise displacement sensitivities in Michelson interferometers, with up to 10 dB improvement through squeezed state interferometry in tabletop setups.^[74] These enhancements address limitations in classical interferometry and support applications in space missions, such as quantum gravimeters using atom-interferometric analogs of the Michelson design for inertial sensing in microgravity environments.^[75] Post-2020 developments include integration of quantum-enhanced Michelson principles into NIST sensors for precise optomechanical measurements, leveraging squeezed states for sub-quantum-limit detection.^[76] In LIGO's 2025 configuration, frequency-dependent squeezed vacuum states have reduced quantum noise below $10^{-23} strain/√Hz across the detection band, marking a key milestone in gravitational wave observatories (as of November 2025).^[77]

References

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[PDF] The Michelson Interferometer - UMD Physics
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What is an Interferometer? | LIGO Lab | Caltech
The configuration of a basic Michelson interferometer (seen at right) consists of a light source, a beam-splitter, two mirrors, and a photodetector (the black ...
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[PDF] Robert C. Youngquist The Michelson Interferometer
Aug 2, 2007 · The Michelson Interferometer consists of a light source that travels to a beam splitter and evenly splits the power of the source. Half the ...
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May 12, 2025 · In 1881, Michelson invented the interferometer, an instrument designed to detect minute differences in the speed of light traveling in ...
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This paper reviews briefly the history of the Michelson experiment, invented and performed for the first time in the Astrophysical Observatory Potsdam in 1881.
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Albert A. Michelson – Facts - NobelPrize.org
In the mid-1880s Albert Michelson developed an interferometer, which uses a semi-transparent mirror to divide up a beam of uniform light waves.
[7]
November 1887: Michelson and Morley report their failure to detect ...
Nov 1, 2007 · In 1887 Albert Michelson and Edward Morley carried out their famous experiment, which provided strong evidence against the ether.
[8]
https://www.ligo.caltech.edu/page/ligos-ifo
[9]
Albert A. Michelson – Biographical - NobelPrize.org
He performed early measurements of the velocity of light with amazing delicacy and in 1881 he invented his interferometer for the purpose of discovering the ...Missing: background | Show results with:background
[10]
https://einstein.caltech.edu/news/the-miller-rebuttal
[11]
[PDF] Interference methods for producing and calibrating end standards
Impetus for the use of light waves as standards of length developed from the classical measure- ments of Michelson and Benoit [1],1 who in 1893 determined the ...
[12]
[PDF] The Gauge Block Handbook
Despite the work of Michelson, the artifact standard was kept until 1960 when the meter was finally redefined in terms of the wavelength of light, specifically ...
[13]
[PDF] MITOCW | Lec 15 | MIT 2.71 Optics, Spring 2009
So in this talk really two types of interferometer-- the Michelson interferometer and the Mach-Zehnder interferometer. ... during the Second World War, where lots ...Missing: II | Show results with:II
[14]
[PDF] The Diffraction Gratings Laboratory - Mount Wilson Observatory |
Sep 1, 2017 · “Engines” capable of ruling hundreds of thousands of straight, parallel, equally spaced grooves within tolerances of only a few angstroms have.
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[PDF] Time Line for the Definition of the Meter
1925 The Michelson interferometer was in regular use at BIPM for measuring length. 1950 Cadmium 114, mercury 198, and krypton 86 were candidates to be a new.
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The Michelson Interferometer Experimental Setup - Newport
We offer a variety of motorized components including optical mirror mounts and translation stages. Every component is compatible with each other (and with ...
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[PDF] Michelson Interferometer
The basic Michelson interferometer setup uses any kind of beam splitter to divide one beam of light into two beams, each of them back-reflected to the beam ...
[18]
Optical Cage System Application: Michelson Interferometer
### Summary of Optical Components and Setup for Michelson Interferometer
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The Michelson Interferometer – University Physics Volume 3
Picture A shows a schematic drawing of the Michelson interferometer. Picture B is the planar. Because both beams originate from the same point on the source, ...
[20]
[PDF] Lab 6: Michelson Interferometer 1 Introduction 2 How it Works
One beam goes to a fixed mirror, and the other beam goes to a movable mirror. The beams are then re-combined on a viewing screen. Question 1: Does it matter ...
[21]
Michelson Interferometers - RP Photonics
Michelson interferometers are frequently used for highly precise distance measurements and sensing. They often achieve a resolution far better than 1 μm.
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Dispersion measurements with white-light interferometry
(b) The unbalanced Michelson interferometer is identical to that in (a) with the exception of an extra piece of glass (S) in one arm. D's, detectors.
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[PDF] Chapter 1 Optical Interferometry - Physics
The Michelson interferometer, shown in Fig. 1.1, is based on the interference of two beams: the initial light is split into two arms on a beam splitter, and ...
[24]
[PDF] Michelson Interferometry 1 Introduction - PhysLab
V = Imax - Imin. Imax + Imin. ,. (3) where Imax is the maximum intensity (bright fringe) and Imin is the minimum intensity (dark fringe). When the waves are ...
[25]
[PDF] Precision Interferometer Manual - UCSB Physics
NOTE: The preceding equipment includes everything needed for basic Michelson interferometry. You can pro- duce clear fringes and make precise measurements.
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[PDF] 1 Laboratory 8: Michelson Interferometer
The coherence length of the source may be increased by filtering out many of the wavelengths, which also reduces much of the available intensity! 1.1.3 ...
[27]
[PDF] On the Relative Motion of the Earth and the Luminiferous Ether (with ...
The relative motion of the earth and the luminiferous ether, by Albert A. Michelson, this Jour., III, xxii, 120. It may be mentioned here that the error was ...
[28]
Michelson interferometry with a diode laser - AIP Publishing
May 1, 2022 · Using his interferometer, Michelson was able to resolve very closely spectral lines, such as the sodium D-lines at 588.995 and 589.592 nm.11 ...
[29]
Fourier Transform Spectroscopy - RP Photonics
Fourier transform spectroscopy is a method where one computes an optical spectrum from raw data by applying a Fourier transform algorithm.
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4.27: The Michelson Interferometer and Fourier Transform ...
Jan 10, 2023 · A Michelson interferometer with a movable mirror in one arm is an essential element in Fourier Transform (FT) spectroscopy.
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FT-IR Spectroscopy - Newport
An FTIR is typically based on The Michelson Interferometer Experimental Setup; an example is shown in Figure 1. The interferometer consists of a beam splitter, ...
[32]
Principles of infrared spectroscopy (4) Advantages of FTIR ...
Sep 16, 2022 · FTIR spectroscopy involves the use of a Michelson interferometer. As shown in Fig. 9, a semi-transparent mirror is used, together with two ...
[33]
Fourier Spectroscopy of Planets - Science
Fourier Spectroscopy of Planets: Michelson interferometers have recently begun to produce remarkably fine infrared spectra of planets.Missing: astronomy | Show results with:astronomy
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Twyman-Green Interferometer - SPIE
The Twyman-Green interferometer was invented and patented in 1916 and was originally intended for testing prisms and microscope objectives.
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The Twyman Green Interferometer - AZoOptics
Aug 4, 2014 · It was invented and patented by the English electrical engineer Frank Twyman and the English chemist Arthur Green in 1916.
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[PDF] Testing Flat Surface Optical Components - The University of Arizona
The Twyman-Green and Fizeau give the same interferograms for testing surface flatness; the main advantages of the Twyman-Green are more versatility and it is a ...Missing: interpretation | Show results with:interpretation
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[PDF] Field Guide to - Interferometric Optical Testing
Mar 20, 2022 · With care, the Twyman-Green can provide high accuracy measurements; however, the test is expensive and subject to vibration and turbulence.<|control11|><|separator|>
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Tilted Wave Interferometer - SPIE
Jul 1, 2016 · The TWI is a modified Twyman-Green interferometer that can ... resolution better than 1 nm and a lateral resolution of several microns.”.
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Laser Interferometry | Precisioneers Group
Any distortions in the interference fringes indicate surface irregularities or optical defects, allowing for sub-nanometer accuracy in shape and flatness ...<|control11|><|separator|>
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µPhase ® - Fizeau/Twyman-Green Interferometer | TRIOPTICS
μPhase interferometers permit fast, high-precision measurements of the surface and wavefront deformation of reflective and transmitting components.Missing: Nikon | Show results with:Nikon
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[PDF] Interferometer Techniques for Gravitational-Wave Detection
Nov 18, 2015 · The main interferometer of an Advanced LIGO detector is based on a Michelson interferometer with arm cavities plus power and signal ...
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Interferometric gravitational wave detectors - Einstein-Online
All modern gravitational wave detectors are based on the principle of a Michelson interferometer. But how exactly does it work?
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[PDF] Advanced LIGO Optical Configuration and Prototyping Effort
The Fabry-Perot arms thus have a finesse of approximately 205, a cavity pole frequency of 91 Hz, and a power gain of 131. This parameter yields a shot-noise- ...
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LIGO 2 Reference Design
Fabry-Perot arm length, 4000 m. Laser wavelength, 1064 nm. Optical power at interferometer input, 125 W, 80 W. Power recycling factor, 16, 33. FP Input mirror ...
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[PDF] Advanced LIGO: The next generation of gravitational wave detectors
They will have recycling gain of 45 to increase optical power and lower high frequency quantum noise. In addition, there will be signal recycling cavities [3] ...
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Sensitivity and performance of the Advanced LIGO detectors in the ...
Sep 11, 2020 · Shot noise arises from statistical fluctuations in the arrival time of photons at the interferometer output. As the intracavity power is ...
[47]
LIGO-Virgo-KAGRA Announce the 200th Gravitational Wave ...
Mar 20, 2025 · Since the “advanced” era of gravitational wave detection began in 2015, the LVK network has now (as of March 19, 2025) recorded 290 GW events, ...
[48]
https://ui.adsabs.harvard.edu/abs/2016PhRvD..93k2004M/abstract
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India Approves Construction of Its Own LIGO
Apr 17, 2023 · The Indian government has granted the final approvals necessary for construction to begin on LIGO-India, a nearly identical version of the twin LIGO (Laser ...Missing: operational 2025 strain 23} Hz^ 1/2}
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LIGO-India - IndIGO
... 10-23 Hz-1/2 in the frequency range between 30 to 800 Hz. The design would be identical to that of the Advanced LIGO detectors that are being commissioned ...Missing: operational 2025 strain
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Aeronautics Application of Direct-Detection Doppler Wind Lidar - MDPI
For our application, we opted for a field-widened Michelson interferometer (see Figure 3) for fringe imaging (FW-FIMI) for several reasons, inter alia, the ...
[52]
Windspeed determination from a near-field, UV, direct-detection ...
Feb 26, 2025 · Windspeed determination from a near-field, UV, direct-detection Doppler wind lidar based on Michelson interferometer fringe imaging. Philippe ...Missing: shear | Show results with:shear
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Doppler Wind Lidar From UV to NIR: A Review With Case Study ...
Doppler wind lidar (DWL) uses the optical Doppler effect to measure atmospheric wind speed with high spatial-temporal resolution and long detection range ...
[54]
The solar oscillations investigation: Michelson Doppler imager
The Solar Oscillations Investigation (SOI) developed the Michelson Doppler Imager (MDI) to investigate the properties of the solar interior using the tools ...Missing: SDO | Show results with:SDO
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https://ui.adsabs.harvard.edu/abs/1995SoPh..162..129S/abstract
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Aeolus / formerly ADM (Atmospheric Dynamics Mission) - eoPortal
Jul 10, 2024 · November 12, 2019: Aeolus has improved weather forecasts through its innovative wind profile observations using Doppler wind lidar technology.<|separator|>
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New Methods to Seismic Monitoring: Laboratory Comparative Study ...
The proposed solution uses a Michelson fiber-optic interferometer designed without polarization fading and with operationally passive demodulation technique ...
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Fiber-based interferometer for seismic detection - SPIE Digital Library
Oct 4, 2024 · Michelson Interferometry. A Michelson interferometer can be used to detect fibre length changes in the following way. For convenience, we define ...
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Aeolus-2 instrument: the new Doppler wind LIDAR
Jul 28, 2025 · This is used for wind speed measurements from aerosols at lower altitudes (typically few km) in the Planetary Boundary Layer (PBL) as well as ...
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Twyman–Green Interferometers – optical surface inspection
Twyman–Green interferometers, named after Frank Twyman and Arthur Green, are interferometers which are used for characterizing optical surfaces.Missing: invention 1916
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[PDF] Direct Phase Measurement Interferometry and Optical Testing
High measurement accuracy (>1/1000 fringe, fringe following only 1/10 fringe). • Rapid measurement. • Good results with low contrast fringes.
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Testing aspheric surfaces with computer-generated holograms
Various interferometric methods can be used for testing aspheric surfaces with high accuracy. Using a partially compensating lens in a Twyman-Green ...
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[PDF] Part 9 Phase Shifting Interferometry Classical Analysis of ...
High measurement accuracy (>1/1000 fringe, fringe following only 1/10 fringe). • Rapid measurement. • Good results with low contrast fringes.Missing: seminal paper
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Michelson interferometer for phase shifting interferometry with a ...
The most common phase shifter consists of a mirror displaced by a piezoelectric transducer (PZT) controlled by voltage. In practice, the most significant errors ...
[65]
Interferometric Dynamic Measurement: Techniques Based on High ...
In 1996, de Lega and Jacquot [19] proposed the object-induced temporal phase changes where a piezoelectric transducer (PZT) with the driven frequency of 80 Hz ...
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Phase‐conjugate Michelson interferometers for all‐optical image ...
of optical waves through the nonlinear interaction of laser radiation with various media is four-wave mixing, a process which is formally analogous to ...
[67]
Doppler-free phase-conjugate reflection - Optica Publishing Group
1 Schematic for reflection from a moving PCM using four-wave mixing. · 2 Phase-conjugate Michelson interferometer with frequency-shifted input beam. · 3 Optical ...
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[PDF] Chapter 3 Degenerate Four Wave Mixing - VTechWorks
The field amplitude of the wave generated by the nonlinear polarization is proportional to A. A A and is the phase conjugate of A . 3.1.2 Wave-equations for ...
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Fully symmetric dispersionless stable transmission-grating ...
Dec 1, 2020 · Here, we present and characterize a transmission grating-based Michelson interferometer, which is practically dispersion-free, has intrinsically ...
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[PDF] Squeezed Light Techniques for Gravitational Wave Detection
Jul 6, 2012 · ➢ Shot noise in a Michelson interferometer is due to vacuum ... ➢ Phase squeezing reduces shot noise. Amplitude fluctuations in the ...
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A gravitational wave observatory operating beyond the quantum ...
Sep 11, 2011 · The injection of squeezed vacuum states into GEO 600 leads to a broadband noise reduction of up to 3.5 dB (black to red trace) in the shot-noise ...
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Entanglement-enhanced quantum metrology: From standard ...
Jul 2, 2024 · Entanglement-enhanced quantum metrology explores the utilization of quantum entanglement to enhance measurement precision.
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Quantum Enhancement of Phase Sensitivity for the Bright-Seeded ...
Dec 19, 2018 · SU(1,1) interferometers, based on nonlinear optical processes, potentially offer better phase sensitivity than traditional instruments.
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10 dB Quantum-Enhanced Michelson Interferometer with Balanced ...
Jul 15, 2022 · We report on the first successful 10 dB sensitivity enhancement of a shot-noise limited tabletop Michelson interferometer via squeezed light in the fundamental ...
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WG Q.1: Quantum gravimetry in space and on ground - IAG - Geodesy
The goal of this WG is to elaborate the major benefit and most promising applications of atom interferometry for gravimetry and inertial sensing in space and ...
[76]
[PDF] Designing sensors with tensioned Silicon Nitride micromechanical ...
Chapter 2 overviews the physics of the Michelson interferometer in the context of quantum- limited measurement of the motion of a micromechanical resonator ...
[77]
Squeezing the quantum noise of a gravitational-wave detector ...
Sep 19, 2024 · Squeezed vacuum was injected at the output port of the interferometer to reduce quantum noise (20). The LIGO squeezer generates frequency- ...
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Thermal Noise Measurement Below the Standard Quantum Limit
Sep 21, 2025 · Later, with the injection of squeezed light, quantum noise in the LIGO detector was suppressed 3 dB below the SQL, first with the ...<|control11|><|separator|>