Large Laser Gyroscopes for Monitoring Earth Rotation

Objectives

Today, Earth rotation parameters are routinely obtained using the geodetic space techniques VLBI (Very Long Baseline Interferometry), SLR (Satellite Laser Ranging), GPS (Global Positioning System) und DORIS (Doppler Orbitography by Radiopositioning Integrated on Satellite). Technical progress over the last decades resulted in a precision of recently 0.01 milliseconds in length of day and 0.1 milliarcseconds in pole coordinates. The common principle is the relative measurement of rotation by observing reference points, stars or satellites, outside the rotating Earth. All these techniques require global networks and structures for the observation and data handling, which are coordinated by the international services IVS, ILRS, IGS and IDS.

The absolute measurement of rotation using inertial rotation sensors is a completely different approach. Mechanical gyros measuring the coriolis force are by far not sensitive enough to detect Earth rotation variations. Instruments measuring the centrifugal acceleration as a part of the total gravity vector, gravimeters and tiltmeters, are basically sensitive to Earth rotation variations, but even the excellent resolution of superconducting gravimeters of 10-11 g is not sufficient to resolve short-period Earth rotation variations. In contrast, laser gyroscopes use the Sagnac effect, whereas the small wavelength of the laser light allows an extreme high resolution. An adequate sensitive laser gyroscope attached to the Earth gives us instantaneous access to the spin of the Earth and the orientation of its axis. For the determination of the complete rotation vector, three linear independent laser gyroscopes are required.

The basic goals of laser gyroscopes for Earth rotation monitoring are:

It is not expected that laser gyroscopes will ever reach the excellent long-term stability of the geodetic space techniques. However, the increasing interesting short-time range is poorly covered by these techniques. Furthermore ring laser measurements are continuous, while VLBI and SLR usually have a resolution of one day, with gaps of some days.


Principle of Operation

Ring lasers are inertial rotation sensors using the Sagnac effect, which is the frequency splitting of two counter-rotating laser beams due to rotation (Sagnac 1913). A minimum of three mirrors form a closed light path in a ring resonator. The resonator cavity is filled with the laser medium, a helium/neon gas mixture. The plasma is excited at one location by an alternating electrical field generating two counter-propagating laser beams. When this assembly is rotating, the (also rotating) observer sees a frequency difference between the co-rotating and the counter-rotating beam being proportional to the rotation rate. This beat frequency or Sagnac frequency delta_f is described by the Sagnac formula for active resonators:

enclosed area
perimeter (beam path length)
optical wavelength
normal vector to A
rotation vector

The task is to measure the frequency of the optical interference pattern, which is roughly 12 magnitudes below the optical frequency, with a relative precision of 10-9.

Ring laser G: principle of operation
Ring laser G: principle of operation (click to enlarge)

A horizontally installed ring laser being rigidly attached to the Earth measures the projection of the Earth rotation vector onto the laser plane normal vector. Considering the orientation the inner product between the rotation and the normal vector can be expressed as:

where phi is the geographic latitude and delta_N and delta_E are small angular variations towards North and East, respectively. When using one ring laser alone, one can not distinguish between variations of the rotation rate and angular variations between the ring laser and the rotation axis.


History of Development

After theoretical investigations have shown that large ring lasers have basically the potential to detect Earth rotation variations (Rotgé et al. 1986, Höling 1990), the Forschungsgruppe Satellitengeodäsie (FGS) decided in 1990 to develop a large ring laser for Earth rotation monitoring. At this time the feasibility of big laser gyroscopes was demonstrated at the University of Canterbury in Christchurch, New Zealand (Stedman et al. 1993). This "Canterbury Ring" (C-I) spanned an area of roughly 0.75 m2 and obtained a beat frequency of nearly 71 Hz. It was the first ring laser that unlocked due to Earth rotation. Locking means that both laser beams show the same frequency and thus no Sagnac signal due to weak coupling. The mechanical design of this instrument did not allow routine measurements over long periods of time.(see also http://www.phys.canterbury.ac.nz/research/laser/ring_c1.shtml)

Ring laser C-I
Ring laser C-I

Basing on these experiences and in close cooperation with the ring laser team at the University of Canterbury and Oklahoma State University, the Forschungseinrichtung Satellitengeodäsie (FESG) of the TU Munich and the Bundesamt für Kartographie und Geodäsie (BKG) developed a ring laser of similar size specially designed for long-term stability. This prototype called C-II has been constructed and build by the company Carl Zeiss in Oberkochen (Germany). The key technologies were the application of the glass ceramic Zerodur as the base material for geometric stability and the optical contacting to obtain a perfect vacuum seal. Zerodur is a material with extrem small thermal expansion and was provided by the Schott company. Since 1997 the C-II is in operation close to the C-I installation site in the Cashmere Cavern, Christchurch. It shows the expected Sagnac frequency of 79,4 Hz and its ability for long-term operation. However, the size of 1 m2 is too small to resolve changes in Earth rotation. The main problem with small rings is the coupling between both laser beams due to backscatter, which is strongly reduced with increasing size. Backscatter makes the instrument extremly sensitive to perimeter changes, caused e.g. by varying air pressure. By operating C-II under constant air pressure, the signal sensitivity (minimum in the Allan deviation plot) could be reduced from 1 x 10-5 down to 5 x 10-7 relative to the Earth rotation rate at a sample length of 700 s. A detailed description of the C-II and its properties is given in Schreiber (2000). (see also http://www.phys.canterbury.ac.nz/research/laser/ring_c2.shtml)

Ring laser C-II
Ring laser C-II (click to enlarge)

After the basic technologies for the construction of a large ring laser for Earth rotation monitoring has been tested successfully, one important question remained: Is is physically possible to operate a large ring laser in monobeam mode? This has not been clear, because with increasing size, the frequency spacing between two longitudinal modes (free sprectral range) decreases and thus the maximum allowed optical power. To ensure the feasibility, a large but simple constructed ring laser of 3.5 m x 3.5 m size has been realized on a vertical concrete wall in the Cashmere Cavern (Rowe et al. 1999, Schreiber 2000). This second prototype called G-0 had first light in 1998 showing the expected Sagnac frequency of 288 Hz. The results of the C-II and G-0 Experiments ensured that no basic physical or technical problems make the realization of a monolithic 4 m x 4 m ring laser impossible.

The contract with the company Carl Zeiss for the construction of the ring laser G was signed in September 1998. After "first light" in June 2001, the official opening was held in October 2001.


G Ring Laser

Technical Concept

The large ring laser G is like C-II made of Zerodur, but in a semi-monolithic construction. Four bars are rigidly attached to a base plate forming the edges of a square with 4 m side length. The coefficient of thermal expansion is 1.4 10-8 K-1 for the base plate and -1.7 10-8 K-1 for the bars, resulting in a total coefficient of less than 1 10-8 K-1. The four mirrors and their mirror holders are attached at the face sides of the bars by molecular adhesion. This technique ensures a stable vacuum seal. Once surveyed and attached, the mirrors can never be readjusted. The only possibility to slightly affect the beam path is the adjustment of the gain tube. The mirrors are of extreme quality, only losses of few ppm are allowed to reduce backscattering to a uncritical level. They are slightly concave with a radius of 4 m to keep the laser beam in line. The laser medium, a Helium/Neon gas mixture with a pressure of few hPa, is excited in a Pyrex gain tube by an alternating electrical field to maintain the lasing process. The optical beam power is continuously monitored and kept constant by a feedback loop steering the excitation power. At one mirror the transmitted fraction of each of the laser beams is separated and interfered at the beam combiner, where the interference signal is converted to an electrical frequency by a photomultiplier or a PIN diode.

Ring laser G
Ring laser "G" (click to enlarge)

Data Acquisition

For the precise measurement of the obtained Sagnac frequency of approx. 348.6 Hz, two different techniques are used. At the software-based AR-2 method the Sagnac signal is digitized at a sampling rate of 1000 Hz and the obtained sine wave is bandpass filtered and numerically fitted by an autoregression algorithm (AR-2). This is done for data chunks of different length, i.e. 3 s (hires file), 30 s (dat file), and 1800 s (sagnac file). In these files, additional operation parameters like optical beam power, backscatter phase or signal amplitudes are stored. The second method is a hardware-based frequency determination. A specially designed period counter ('Canterbury Counter') performs a precise frequency measurement by integration over 30 minutes.

A faster but less precise data acquisition line for monitoring seismic waves is sampling the Sagnac frequency using a commercial time interval counter (SR 620) and a frequency demodulator. The demodulator is a proprietary development and converts frequency variations into an analog voltage. This signal together with the signals from a co-located standard seismometer (Lennartz 3D/20s) are sampled with a rate of 20 Hz.


Installation and Environment

The "G" ring laser is operating at the Fundamentalstation Wettzell (Bavaria). It is resting on a polished granite table being embedded in a 90 t concrete monument. The monument is attached to a massive 2.7 m diameter concrete pillar, which is founded on crystalline bedrock 10 m below the former surface. A system of concrete rings and isolation material shield monument and pillar from lateral deformations and heat flow. The instrument is protected against external influences in a subsurface installation, where a passive thermal stability is reached by a 2 m alternating layer of styrofoam and wet clay, and a 4 m earth mound. A lateral entrance tunnel with 5 isolating doors and a separate control room minimize thermal perturbations. After 2 years of thermal adaptation, the average temperature reached 12.2 deg with seasonal variations of less than 0.6 deg.

Underground lab
Schematic section through the "G" underground lab (click to enlarge)

Despite huge efforts concerning the stability of the foundation, tilts due to ground deformations of thermoelastic or hydrologic origin cannot be avoided in the µrad level. Tilts in N-S direction considerably affect the measured Earth rotation signal and have to be monitored. For this purpose a set of six specially designed platform tiltmeters (type Lippmann) are arranged on the ring laser body. The high resolution of these vertical pendulums and the excellent environmental conditions allow the detection of signals in the nanorad level. Five of these instruments, being aligned in N-S, E-W and diagonal directions, are subject to a 40 s lowpass filter and record one sample every 13 s. One N-S aligned instrument records at 20 Hz without being lowpass filtered. Different environmental parameters like temperatures at different locations, air humidity, air pressure, and groundwater level are recorded once per minute.

6 Tiltmeters on ring laser "G" (click to enlarge) Tiltmeter section (click to enlarge)

Resolution and Stability

According to the Sagnac formula, the scale factor increases with the ring laser size. On the other hand, the resolution is physically limited by shot noise of the laser light. The shot noise level can be estimated using information about the resonator quality, as measured in a ringdown experiment, and the measured optical power (see Schreiber, 2000). This results in a recent maximum sensitivity of 9 10-11 rad s-1 Hz-0.5. In order to reach a resolution of 10-9 of the Earth rotation rate or 7.3 10-14 rad s-1, an integration time of 420 hours is required. This can currently not be reached due to instrumental drifts.

A proper tool to estimate the stability of a ring laser is the Allan variance (sigma2) or Allan deviation (sigma). It describes the variance of a timeseries segment in relation to the length of the segment:

where fk and fk+1 are two subsequent data samples and n is the number of samples in the considered segment. This representation also helps identifying noise processes (white noise, 1/f noise, ..), which occur in a double logarithmic scale as straight lines with different slopes. The resolution of the "G" ring in the short-period range up to 5000 s is limited by white noise, probably shot noise, showing a characteristic slope of t-0.5 in the double logarithmic Allan deviation plot. After a minumum close to 2 hours the Allan deviation increases as a consequence of signal and instrumental drift. When periodic signals like the effect of Earth tides and diurnal polar motion are removed, the minimum in the Allan deviation shifts to 10-8 for data segment lengths of 3 hours.

Allan deviation plot
Allan deviation of 3 large ring lasers operating in Christchurch (C-II, UG) and Wettzell (G)

 

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Letzte Änderung: 23.11.2005