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Optical Design & Engineering

High-precision optics enable LIGO's new view of the universe

The first detection of a gravitational wave depended on large surfaces with excellent flatness, combined with low microroughness and the ability to mitigate environmental noise.

15 April 2016, SPIE Newsroom. DOI: 10.1117/2.2201604.01
LIGO test mass

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 these "ripples in spacetime" may travel billions of light years, Einstein never thought the technology would exist that would allow for their detection on Earth.

But a century later, the technology does exist at the Laser Interferometer Gravitational-Wave Observatory (LIGO). Measurements from two interferometers, 3000km apart in Louisiana and Washington State, have provided the first direct evidence of Einstein's theory by recording gravitational-wave signal GW150914, determined to be produced by two black holes coalescing 1.2 billion light years away. At the heart of the discovery 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.

Image of black hole coalescence data

The black hole coalescence was detected as an upward-sweeping 'chirp' from 35 to 300Hz, which falls in the detectors' mid-frequency range that is plagued by noise from the optics. Left and right images show data from Hanford and Livingston observatories. Click to enlarge. (Caltech/MIT/LIGO Laboratory)

"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 Caltech.

LIGO's optics system amplifies and splits a laser beam down two 4km-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.

Reducing noise sources at each frequency improves interferometer sensitivity. Green shows actual noise during initial LIGO science run. Red and blue (Hanford, WA and Livingston, LA) show noise during advanced LIGO's first observation run, during which GW150914 was detected. Advanced LIGO's sensitivity goal (gray) is a tenfold noise reduction from initial LIGO.

Reducing noise sources at each frequency improves interferometer sensitivity. Green shows actual noise during initial LIGO science run. Red and blue (Hanford, WA and Livingston, LA) show noise during advanced LIGO's first observation run, during which GW150914 was detected. Advanced LIGO's sensitivity goal (gray) is a tenfold noise reduction from initial LIGO. Click to enlarge. (Caltech/MIT/LIGO Laboratory)

But the entire instrument is subject to 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 most 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'. 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," explains GariLynn Billingsley, LIGO optics manager at Caltech. 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, a program invited manufacturers to demonstrate their ability to meet the specifications required by initial LIGO's optics. Australia's Commonwealth Science 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 the University of Sydney, who supervised the overall CSIRO project. "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. 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," adds Walsh.

Even with high-precision optics and a thermal compensation system that balances the minuscule heating of the mirror's center, initial LIGO was not expected to detect gravity waves. Advanced LIGO, begun in 2010 and completing its first observations when GW150914 was detected, 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.

Image of Advanced LIGO test mass

Advanced LIGO test mass suspended in the interferometer. (Caltech/MIT/LIGO Laboratory)

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 (340mm 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 John Kincade, Zygo's Extreme Precision Optics managing director. The test masses required a 1.9km 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.

Image of Advanced LIGO input test mass champion data

Advanced LIGO input test mass champion data. Zygo achieved figuring accuracy to 0.08nm RMS over the critical 160mm central clear aperture, and sub-nanometer accuracy on the full clear 300mm aperture of many other samples. Click to enlarge. (Zygo Extreme Precision Optics)

Dielectric coatings deposited on the high-precision surfaces determine their optical performance. CSIRO and the University of Lyon Laboratoire des Materiaux Avances 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 drive.

LIGO's next observation run is scheduled to begin in September 2016. 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," says Landry.

One possibility is operating at cyrogenic temperatures. 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 40km-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 initial LIGO. "The Q of that system is higher so an entire band shrinks. That means opening up more space at lower frequencies, where binary black holes are," says Landry.

Image of aerial view of the LIGO-Hanford observatory

Aerial view of the LIGO-Hanford observatory. (Caltech/MIT/LIGO Laboratory)

In the 17th century, Galileo pointed a telescope to the sky and pioneered a novel way of observing the universe. Now, LIGO's detection of GW150914 marks another new era of astronomy. As advances in glass lenses enabled Galileo's discoveries, so have state-of-the-art optics made LIGO's discoveries possible. And with astronomy's track record of developing new generations of optical devices, both the astrophysical and precision optics communities are poised for an exciting future.

Rachel Berkowitz is a freelance science writer based in Washington State.