The Optics of LIGO
High-precision optics enabled detection of gravitational waves.
Albert Einstein’s general theory of relativity predicted that massive, accelerating bodies in deep space, such as supernovae or orbiting black holes, emit huge amounts of energy that radiate throughout the universe as gravitational waves. Although Einstein did not propose how these “ripples in space-time” could be detected, the high-precision optical technology to do so now exists.
A century after Einstein formulated his theory, the twin Laser Interferometer Gravitational-Wave Observatories (LIGO) in the US, 3000 km apart in Louisiana and Washington state, measured the first direct evidence of his theory by recording gravitational-wave signal GW150914.
The signal detected on 14 September 2015 is believed to have been produced by two black holes coalescing 1.3 billion light years away.
A second signal detected on 26 December came from the merger of two other black holes.
At the heart of the LIGO discoveries lies fused silica optics with figure quality and surface smoothness refined to enable measurement of these incredibly small perturbations. Their design is an important part of LIGO’s story.
“Most impressive are [the optics’] size combined with surface figure, coating uniformity, monolithic suspensions, and low absorption,” says Daniel Sigg, a LIGO lead scientist at the California Institute of Technology (Caltech).
LIGO’s optics system amplifies and splits a laser beam down two 4-km-long orthogonal tubes. The two beams build power by resonating between reflective mirrors, or “test masses,” suspended at either end of each arm. This creates an emitted wavelength of unprecedented precision.
When the split beam recombines, any change in one arm’s path length results in a fringe pattern at the photodetector. For GW150914, this change was just a few times 10–18 meters.
But the entire instrument is subject to vibrations and environmental noise that reduces sensitivity. A noise plot shows the actual strain on the instruments at all frequencies, which must be distinguished from gravity-wave signals. The optics themselves contribute to the noise, which basically includes thermal noise and the quality factor, or ‘Q,’ of the substrate.
“If you ping a wine glass, you want to hear ‘ping’ and not ‘dink,’” explains GariLynn Billingsley, LIGO optics manager at Caltech. “If it goes ‘dink’, the resonance line is broad and the entire noise increases. But if you contain all the energy in one frequency, you can filter it out.” That’s the Q of the mirrors.
Further, if the test-mass surfaces did not allow identical wavelengths to resonate in both arms, it would result in imperfect cancellation when the beam recombines. And if non-resonating light is lost, so is the ability to reduce laser noise. Perhaps most problematic, the optics’ coatings contribute to noise due to stochastic particle motion. Stringent design standards ameliorate these problems.
In 1996, scientists comprising the LIGO Scientific Collaboration invited manufacturers and labs to demonstrate their ability to meet the specifications required by LIGO’s optics. Australia’s Commonwealth Scientific and Industrial Research Organisation (CSIRO) won the contract.
“It was a combination of our ability to generate large surfaces with excellent flatness, combined with very low microroughness,” says Chris Walsh, now at University of Sydney, who supervised the overall CSIRO project for the so-called Advanced LIGO. “It requires enormous expertise to develop the polishing process to get the necessary microroughness (0.2-0.4nm RMS) and surface shape simultaneously.”
Master optician Achim Leistner led the work, with Bob Oreb in charge of metrology. (The two were part of the CSIRO team that received the 2012 SPIE Technology Achievement Award.) Leistner pioneered the use of a Teflon lap, which provides a very stable surface that matches the desired shape of the optic during polishing and allows for controlled changes. “We built the optics to a specification that was different to anything we’d ever seen before,” Walsh adds.
Even with high-precision optics and a thermal compensation system that balances the minuscule heating of the mirror’s center, the Advanced LIGO was not expected to detect gravity waves. Advanced LIGO, begun in 2010 and completing its first observations on 12 January 2016, offers a tenfold increase in design sensitivity due to upgrades that address the entire frequency range.
“Very simply, we have better seismic isolation at low frequencies; better test masses and suspension at intermediate frequencies; and higher powered lasers at high frequencies,” says Michael Landry, a lead scientist at the LIGO-Hanford observatory.
At low frequencies, mechanical resonances are well understood. At high frequencies, radiation pressure and laser ‘shot’ noise dominate. But at intermediate frequencies (60-100 Hz), scattered light and beam jitter are difficult to control.
“Our bucket is lowest here. And there are other things we just don’t know,” adds Landry. “The primary thermal noise, which is the component at intermediate frequency that will ultimately limit us, is the Brownian noise of the coatings.”
To improve signal-to-noise at intermediate frequencies, Advanced LIGO needed larger test masses (340-mm diameter). California-based Zygo Extreme Precision Optics won the contract to polish them.
“We were chosen based on our ability to achieve very tight surface-figure, roughness, radius of curvature, and surface-defect specifications simultaneously,” says SPIE member John Kincade, managing director of Zygo’s Extreme Precision Optics unit. The test masses required a 1.9-km radius of curvature, with figure requirements as stringent as 0.3nm RMS.
After super polishing to extremely high spatial frequency, ion-beam figuring fine tunes the curvature by etching the surface several molecules at a time. This allows reliable shape without compromising on ability to produce micro-roughness over large surfaces.
Dielectric coatings deposited on the high-precision surfaces determine their optical performance. CSIRO and the University of Lyon Laboratoire des Matériaux Avancés shared the contract to apply molecule-thin alternating layers of tantalum and silica via ion-beam sputtering.
Katie Green, project leader in CSIRO’s optics group, says “the thickness of the individual layers are monitored as they’re deposited. Each coating consists of multiple layers of particular thicknesses, with the specific composition of the layers varying depending on how the optic needs to perform in the detector.”
Additionally, gold coatings around the edges provide thermal shielding and act as an electrostatic driver.
LIGO’s next observation run is scheduled to begin in September. And after Advanced LIGO reaches its design sensitivity by fine-tuning current systems, further upgrades await in the years 2018-2020 and beyond.
“One question is how you reduce the thermal noise of the optics, in particular their coatings. But coating technologies make it hard to get more than a factor of about three beyond Advanced LIGO’s noise level,” Landry says.
Operating at cyrogenic temperatures is one possibility. But “fused silica becomes noisy at cold temperatures, and you need a different wavelength laser to do this,” according to Billingsley. Another way of increasing the sensitivity at room temperature is to use 40-km-arm-length interferometers.
Other optics-related systems reduce noise. Advanced LIGO’s test masses are suspended on fused silica fibers, creating monolithic suspension that reduces thermal noise and raises the system’s resonant frequency compared with Advanced LIGO.
“The Q of that system is higher so an entire band shrinks,” Landry says. “That means opening up more space at lower frequencies, where binary black holes are.”
Studying the interactions of those black holes and of exploding neutron stars is one of the main goals of scientists in the nascent field of gravitational-wave astronomy. They hope to use information from LIGO and other gravitational-wave detectors across the globe to make more precise measurements of how much dark energy exists in the universe and how fast the universe is expanding.
They also hope the study of general relativity via gravitational waves will help them learn more about gravitons, the particle believed to carry the gravitational force, just as the photon carries the electromagnetic force.
More information on LIGO and the discovery of gravitational waves: spie.org/ligo.
–Rachel Berkowitz is a US-based freelance science writer. An earlier version of this article appeared previously in the SPIE Newsroom.
Numerous technical articles in the SPIE Digital Library and elsewhere cover the development of optical technologies involved with gravitational wave astronomy.
The manufacture and testing of the core optical substrates for the Laser Interferometer Gravitational-Wave Observatory (LIGO) at Australia’s Commonwealth Scientific and Industrial Research Organisation (CSIRO) are described in a proceedings paper from 1999. Among the authors are Chris Walsh, Achim Leistner, and Bob Oreb. See dx.doi.org/10.1117/12.369187
GariLynn Billingsley is coauthor of a paper on LIGO optics presented at SPIE Laser Damage 2001. See: dx.doi.org/10.1117/12.461689
A technical document describing the Advanced LIGO instruments was published in March 2015 in the journal Classical and Quantum Gravity. See arxiv.org/abs/1411.4547
A preprint of a paper describing the configuration and sensitivity of the LIGO detectors during its operation from September 2015 to January 2016 is available at arxiv.org/pdf/1604.00439v1.pdf
Daniel Sigg, a senior scientist at the California Institute of Technology working on the Laser Interferometer Gravitational-Wave Observatory (LIGO) in Washington State, will give a plenary talk at SPIE Optics + Photonics Tuesday 30 August.
In the wake of the US LIGO’s first-ever detection of a gravitational wave, the Indian government in February granted in-principle approval for another instrument in a network of gravitational-wave detectors placed strategically across the globe.
“This is the step that we’ve been waiting for,” said David Reitze, executive director of the Laser Interferometer Gravitational-Wave Observatory (LIGO) Lab at California Institute of Technology. “It will allow funding for the LIGO-India project to begin and commence a number of critical path activities toward getting a detector built in India,” he said.
The US National Science Foundation funds the two US observatories that detected the first two gravitational waves. The two LIGOs were conceived, built, and are operated by Caltech and Massachusetts Institute of Technology.
When completed, LIGO India will join the Virgo detector in Italy, GEO600 in Germany, and other facilities that together help scientists pin down the locations and sources of gravitational waves coming from space. Japan is also building a large-scale gravitational telescope, KAGRA, near the Super-Kamioka Observatory.
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