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A Ring of Light and Time

The world's largest precision ring laser sits beneath Christchurch, and is part of research attracting worldwide interest.

Geoffrey E Stedman

Thirty metres below Christchurch's Cashmere Hills is an unlikely setting for a facility investigating highly precise measurements of the Earth's rotation, but that is where the world's largest precision ring laser can be found.

The cavernous ex-army command post, built during the last war, provides the vibration-free, temperature-controlled environment necessary to operate the highly sensitive ring laser.

Ring lasers are used as gyroscopes to sense absolute rotation, and along with accelerometers (which measure linear acceleration) are the core of the modern aircraft inertial guidance systems used in Boeing 767s and other aircraft.

The principles are simple. Consider two runners racing in opposite directions around a looped track. They pass each other once. If they are equally fast, they arrive together back at the start/finish line.

Think of say 10 such runners, who at the start are spaced out evenly round the track in pairs, with the members of each pair running in opposite directions. When the race is under way, each runner passes another going the opposite way at the point where a track official ("marker") embodies the starting position for a team-mate.

Racing Light Beams

Now replace each set of runners by a light beam of a known wavelength travelling in the appropriate direction. There is no risk of jostling -- the runners share the same path, going through each other. A standing wave pattern is formed: the starting positions of the multi-runner race become nodes or dark points where the oppositely directed light beams cancel each other out; midway between these are the antinodes, where the light amplitudes reinforce each other to form a bright point. The racetrack becomes a necklace of beads of light and dark.

It's not a necklace which can be seen, as the beads of light measure less than a micron -- a thousandth of a millimetre -- across. The Canterbury ring laser uses four mirrors to direct the beams around a one-metre-square racetrack. The laser is a helium-neon one, where the light beams have an individual wavelength of 633 nanometres (0.000000633 m). The distance and wavelength and the way they interact within the device produces a necklace of 12.6 million beads.

Suppose we give one set of runners a blatant handicap: let the markers at the various start/finish points around the race track agree to jog slowly clockwise once the race begins. The clockwise racers have to run further to get to their finish. Every anticlockwise runner will beat her clockwise partner to the finish. The points where runners pass no longer match the positions of the markers.

When the ring laser is rotated, say clockwise, the necklace of light stays as far as possible at rest in the original unrotated frame of reference, because that is the frame where both beams share the same speed, c. The nodes and antinodes, in trying to "stay still", appear in the rotating frame to snake in an anticlockwise direction around the light path. Each mirror, acting as a marker, now sees a sequence of nodes and antinodes moving past. The combined beam changes from light to dark as every bead of the necklace passes by, and generates a voltage in a detector. This makes a ring laser an absolute sensor of rotation.

The Earth's rotation is big enough to show up in the Canterbury ring laser, with each of the 12.6 million beads passing each mirror each day as the Earth turns. That works out to be 146 beads at any mirror, or beats, per second. Adjustments for the size and shape of the ring laser, plus the latitude of its location, result in a beat frequency of 68 hertz.

If such a signal is played through a sound system, you hear a reassuringly deep bass note, about 2.5 octaves below middle C. At Cashmere, the deep bass sound echoes through our cave and, as we work, we can tell not only that the Earth is rotating, but how well the laser is working from the pitch and timbre of the sound.

If we touch a corner of the ring and push it very gently clockwise, the pitch of the note rises before it falls, telling us that we are in the Southern Hemisphere.

Drag Problems

Some smaller ring lasers have already been used to detect the Earth's rotation, but they needed a special trick. Aviation ring gyros have a triangular light path, with a perimeter of only 20 centimetres or so. This reduces the beat frequency induced by the Earth's rotation, compared to that in the Canterbury ring laser, so that one bead takes four seconds or so to get past a mirror. Even with the best mirrors in the world (99.999% reflectance say), the beads tend to stay away from the absorbing parts of the ring -- the "bad" spots which have only say 99.99% reflectance. As a result, the beads tend to get dragged by the bad spots on the mirrors in their rotational motion. If the dragging is fully effective, the beat signal disappears and the two counter-rotating beams lock.

Aviation gyros have to fight this tendency hard in order to be sufficiently sensitive. Commercial firms during the 1970s and early 1980s solved this "lock-in" problem by developing a technique of gently shaking the ring with piezoelectric transducers so as to prevent the beads from "sticking" at the mirrors. The full details are still proprietary or military secrets.

The Canterbury ring is unique in being unlocked by the Earth rotation alone. It can do this because it has sufficiently good mirrors, made by the world's best manufacturer, and the laser's large area means that the Earth rotation signal frequency (68 Hz) is sufficiently high.

We have to be scrupulous about cleanliness, however. And we are also sensitive to everything else. When we ran the experiment at the University of Canterbury, the wind rocking the building was quite enough to cancel the Earth rotation effect and make the ring lock on every swing of the building. Hence one major reason for using the mammoth Cashmere cavern -- we are on bedrock basalt there.

The other reason is that once underground, temperature fluctuates much less, the distance travelled by the beams and the amount of light beads which form vary less, and dragging of the beads become less important. Even in the cave and with the ring mirrors mounted on a block of low-expansion ceramic glass, however, the bead numbers and thus beat frequency changes every 20 minutes or so as the temperature of the room drifts by a fraction of a degree.

The signal from the ring can be analysed for its harmonic content. The ring signal sounds like an over-deep tuba; the harmonics have amplitudes in geometric progression. Since the beads of the necklace tend to avoid bad spots on the mirror as they move past, there is a jerkiness in the necklace motion which gives an impure sound and also lowers, or "pulls", the frequency below 68 Hz. A full investigation of these phenomena is under way at Canterbury as a study in fundamental research which has not been undertaken before.

Plotting a typical waveform and its frequency (Fourier) spectrum shows the Earth rotation signal and its harmonics as signal peaks above a base signal. A trained ear can pick out the extra effects in the audio signal. The signal peaks are clearly defined as the Earth is a particularly reliable rotator, its rotation rate varying by only one part in 108 or so on second-to-hour timescales. This is below the level of detection of our ring.

One justification for the Canterbury ring has been its success as a feasibility study for an even bigger ring of four metres square. This will be able to measure highly accurately the variation in Earth rotation. Such measurements could provide information about what is happening in the Earth's interior. Until our research, it had been thought that large rings were impractical. The go-ahead for German collaboration on the larger ring has been given, and a second-generation ring, with an area similar to the present one but with much more robust construction, is to be built in Germany and the US and then installed at Cashmere.

In fact we find it possible to detect the position of the Earth signal peak to better than five microhertz. This is the origin of our claim for exceptional precision -- we are able to detect a frequency difference (or wavelength, or colour difference) which is a minute fraction (10-20) of the laser frequency itself (474 terahertz). It turns out that we are detecting very near the sensitivity limit imposed by quantum mechanics in such a system. The size of photons, or particles of light, in energy terms and in particular the rate at which the beams lose energy and need to replenish their photons, limits how accurately one can create and measure any such frequency.

Detecting Quakes

The signal plots also reveal very weak signals which are produced by extra ground rotational effects, conspicuous even 30 metres underground in the cavern. At almost any point on Earth, one can "see" the effects of earth motion with such a sensitive instrument. The ground twists as well as moves with a period of a few seconds, thanks to wave motion at the coasts of the continents.

We are investigating this further with the aim of assessing the ring's potential for seismic rotation detection. Rotational movement in earthquakes causes more damage than linear movement, but to date there has been no simple way to measure it. The ring laser could provide one way of doing this.

We were unexpectedly successful in detecting local rotational effects from the Los Angeles earthquake of January 17th. The linear motion was detected by conventional seismometers in Wellington at 01:45 on January 18th, 14 minutes after leaving Los Angeles. Local rotation associated with this gave a clearly detected change in angle of the ring laser at 01:47. We're still investigating this and other possibilities of the ring laser.

Professor Geoffrey Stedman is in the Department of Physics and Astronomy at Canterbury University.