Time and Frequency Division

Technical Highlights

• Quantum Limits to Measurement and A Quantum Computer. In earlier experiments, the Ion Storage Group observed what can be called "quantum projection noise." In spectroscopy, this source of noise is caused by the statistical fluctuations in the measured number of absorbers (atomic ions in this case) which are observed to undergo the transition of interest. This was the first observation of this noise source in spectroscopy, and the Group developed and confirmed theory that describes it.

  Having reached this noise floor, John Bollinger, Wayne Itano, and Dave Wineland of the Group then proposed a method for using quantum-mechanically correlated states to reduce the noise below this level. The promise of this method was sufficiently high that a program aimed at realizing the concept was initiated. Their approach involved the development of a linear ion trap capable of storing one-dimensional "strings" of ions along the trap axis. As this work progressed, I. Cirac and P. Zoller from the University of Innsbruck proposed using an identical configuration to produce a quantum computer. The synergism of these two disparate projects, an atomic frequency standard and a quantum computer, is extremely high. In fact, the work that needs to be done to prove the quantum-computer idea will lead quite naturally to the reduced-noise frequency standard, so work on these two projects is now being pursued concurrently.

  In the first phase of the computer project, Chris Monroe, Dawn Meekhof, Brian King, Wayne Itano, and Dave Wineland of this Division have demonstrated the operation of a two-bit "controlled-NOT" quantum logic gate, a fundamental building block of a quantum computer. The two quantum bits are stored in the internal and external degrees of freedom of a single trapped ion which is first laser-cooled to the zero-point energy. This gate is a simplified version of the Cirac/Zoller scheme. Although this minimal system is not useful for computation, it illustrates the basic operations necessary for, and the problems associated with, constructing a large scale quantum computer.

  The interest in this subject stems from the fact that certain problems can be more efficiently solved on a quantum computer than on a classical computer. In particular, a quantum computer should be able to factorize large numbers very efficiently. This is of interest, because the security of many data encryption schemes relies on the inability of classical computers to factorize large numbers. (D.J. Wineland)
• Development of Future Generations of Atomic Frequency Standards. Two projects within the Physics Laboratory are aimed at the development of dramatically improved frequency standards. In Boulder, John Miller, Dana Berkeland, Jim Bergquist, Wayne Itano, and Dave Wineland have developed a linear ion trap system that can be used to demonstrate both microwave and optical frequency standards. The ion being used for both the microwave and optical standards is ¹⁹⁹Hg⁺. Trapping of ions eliminates the first-order Doppler shift and laser cooling reduces the second-order Doppler shift to a very low value. Since observation times can be extremely long, linewidths can be very narrow. For this system, fundamental systematic uncertainties are known to nearly one part in 10¹⁸. Of course, other technical problems may limit performance short of this goal, but an uncertainty in the vicinity of 10^-16 should be achievable for the microwave transition. Images of long strings of ions have now been observed and a preliminary test of the microwave frequency standard should occur within the next year.
  
  A second standard is being developed in a collaboration between Bill Phillips and Steve Rolston of the Atomic Physics Division in Gaithersburg and Bob Drullinger, Fred Walls, David Lee, and Jon Shirley of the Time and Frequency Division in Boulder. This standard, called an atomic fountain standard, operates by launching laser-cooled cesium atoms vertically through a microwave cavity; then, under the influence of gravity, they fall back through the same cavity. The atoms move more slowly than those in an atomic beam standard, so the Doppler shifts are much lower. Furthermore, the long observation time results in a narrower linewidth. This standard should operate with an uncertainty of better than 10^-15, and has the advantage of using the same time-defining transition as is used in present cesium-beam standards. This standard is in a much earlier phase of development, but preliminary operation should be demonstrated within the year. (J.C. Bergquist and R.E. Drullinger
• Rabi Pedestal Shifts as a Diagnostic Tool in Primary Frequency Standards. Jon Shirley, David Lee, and Bob Drullinger of this Division, in collaboration with Daniel Rovera of the Laboratoire Primaire du Temps et des Fréquences in Paris, have developed a new method for evaluating certain systematic frequency shifts in primary cesium frequency standards. They use a digital servo system to measure the frequency offset between the Rabi pedestal and the Ramsey fringe for all seven of the components of the hyperfine transition observed in a cesium-beam standard. Measurement of the dependence of each of these shifts on microwave power enables them to separate three distinct causes: Rabi pulling, cavity pulling, and magnetic field inhomogeneity.

  The method was used to evaluate these three shifts for NIST-7, NIST's new optically pumped cesium-beam frequency standard. The method indicates a shift due to magnetic-field inhomogeneity of 2 × 10^-15, a shift due to cavity pulling of 6 × 10^-15, and a shift due to Rabi pulling of less than 1 × 10^-16. One advantage of the method is that it requires frequency measurements no better than 1 × 10^-11 to evaluate these exceedingly small frequency biases. This work is part of a continuing effort to find additional independent methods for measuring each of the systematic errors in NIST-7. The shifts measured in this manner are consistent with previous measurements using other methods, and add confidence to the NIST-7 uncertainty statement which is now 5 × 10^-15.

  This and other new evaluation methods hold the potential for further improvement, perhaps by as much as a factor of five. This means that the original goal of an improvement of a factor of ten could be extended to a factor of one hundred, producing the largest performance advance for any frequency standard constructed at NIST. These advances give NIST a more comfortable margin over commercial frequency standards which are now approaching uncertainties of 1 × 10^-13. (R.E. Drullinger
• Observation of a Schrödinger Cat State. In recent experiments, Chris Monroe, Dawn Meekhof, Brian King, and Dave Wineland generated a "Schrödinger cat-like" state of matter at the single atom level. In 1935 Schrödinger developed a thought experiment where a cat is placed in a quantum superposition of being dead and alive (correlated with a single radioactive atom which has and has not decayed, respectively). The state of the system is represented by an entangled quantum mechanical wavefunction involving a superposition of the two different states. This situation of course defies our sense of reality, where we only observe live or dead cats and we expect that there exist only live and dead cats independent of our observation. This is a classic illustration of the conflict between the existence of quantum superpositions and our real world experience of observation and measurement. Although superposition states such as Schrödinger cat states appear to be absent from the macroscopic world, there is great interest in the creation of "Schrödinger cat-like" states in mesoscopic systems (systems having both microscopic and macroscopic features and hence bridge the gap between the quantum and classical worlds). These types of experiments may provide an interesting proving ground in the controversial theory of quantum measurement.
  
  In their experiments, a single laser-cooled and trapped ⁹Be⁺ ion is prepared in a quantum superposition of two separate localized positions correlated with different internal states of the ion. This state is prepared by applying several pulses of laser radiation, which "entangle" the internal (electronic) and external (motional) states of the ion. They verify the superposition by detecting the quantum mechanical interference between the localized wavepackets. Of critical importance in these experiments is the high level of control of the motion of the ion, from the initial laser-cooling to the zero-point of energy to the excitation to higher-energy coherent states of motion in the harmonic potential. (C. Monroe
• Improvements in the AT1 Time Scale. Tom Parker, Jim Gray, and Judah Levine have implemented a number of improvements in the AT1 time scale allowing the Division to more accurately realize UTC in real time. Over the last 280  days, UTC(NIST) has been held within 50 ns of the international UTC maintained by the BIPM. This provides a more accurate time scale for dissemination to high-end users in the United States, and improves the quality of input data to the BIPM on the frequency of the primary-frequency standard, NIST-7.

  

  Figure 1. NIST time scale performance. This plot of UTC - UTC(NIST) covers the period from Modified Julian Date (MJD) 48989 to 50049. The time constant for steering to international UTC is apparent in the oscillations. The BIPM feedback of offsets between UTC and UTC(NIST) occurs between 1 and 2 months after data is provided to the BIPM.

  The key improvements involve the addition of new commercial hydrogen masers and cesium-beam standards to the scale and the development of new reset procedures in the AT1 algorithm. The drift rate of the scale was reduced from 1 × 10^-16/day to 3 × 10^-17/day. The level of random fluctuations of AT1 were also reduced by a factor of 2 to 2 × 10^-15 at 100 days. These improvements, shown in Figure 1, continue a long history of world leadership in time scale operation. Further improvements are expected as two additional masers are added to the scale in 1996. (T. Parker
• Two-Way Satellite Time and Frequency Transfer (TWSTFT). Christine Hackman, Tom Parker, Steve Jefferts, and Victor Zhang have advanced NIST's TWSTFT capability through three separate projects. In the first, an empirical method was developed for correcting for effects of unevenly spaced data. Two-way time transfer data is typically taken three days per week. Traditional analysis methods, based on evenly spaced data, could not properly account for the noise in the unevenly spaced data, thus limiting knowledge of the uncertainty in the measurements. In a second project, a complete analysis was made of the time transfer noise between averaging times of 1 s and 100  days. This first-ever analysis indicated a time variance, σ_x(τ), of 100 ps at an averaging time of 100 s and 1 ns with averaging of 1 day clearly establishing the value of the method. Finally, improved automation of analysis of the TWSTFT data was implemented saving substantial staff effort in routine handling of the large amount of data involved. (T. Parker
• Multi-Channel GPS Receivers for Time Transfer. Judah Levine of NIST, Al Gifford of the U.S. Naval Observatory, and Tom Bartholomew of The Analytical Sciences Corporation are collaborating on the characterization of time transfer using multi-channel GPS receivers. These receivers make simultaneous observations of eight GPS satellites and support dual-wavelength observations which can be used to estimate the satellite-receiver delay associated with the ionosphere. Variations in ionospheric delay are important contributors to the uncertainty in using GPS time transfer to compare separated clocks. The current method used by NIST for time transfer involves simultaneous "common-view" observations of the same satellite by different observers, and subsequent careful processing of many observations to remove common-mode delay errors. This new work seeks to use a simpler "melting-pot" algorithm for the time transfer process.
  
  The current experiments are being carried out between NIST and the Naval Observatory. Making use of the same type of receivers, the group also plans to make measurements between NIST and NASA's Jet Propulsion Laboratory using carrier-phase observations. Such measurements are potentially more accurate, but pose a challenge in resolving the carrier-phase ambiguity, that is in determining that both sites have identified the same cycle of the carrier and that this identification does not slip during the observation period. (J. Levine
• Telecommunications Synchronization. Marc Weiss is leading efforts to integrate synchronization concepts developed by the telecommunications industry and by the time-and-frequency community. As part of this effort, NIST has now sponsored four (annual) workshops on synchronization with attendance growing to more than 60 participants per year, mostly from U.S. industry. These workshops grew out of earlier NIST work on synchronization interface standards. The first one was held to familiarize the industry with NIST-developed methods for characterizing synchronization systems. NIST became involved when it was asked by the industry to assist in developing more useful timing measures. The very rapid success of this venture along with the rapid acceptance of the measures as national and international standards cemented a working relationship that has stimulated the continuation of the workshop into something that more nearly represents a conference on telecommunications synchronization.
  
  In a related project, Steve Jefferts and Marc Weiss are developing a measurement system for determining the phase noise introduced by optical fiber (SONET) links used to transmit synchronization signals. The measurement system, operated in a loop-back mode, exhibits stabilities below 50 ps at an averaging time of 5000. This work responds to growing international interest in actually using the network to transmit timing signals for use within the network. (M.A. Weiss
• Fundamental Limits on the Frequency Stabilities of Crystal Oscillators. Fred Walls of NIST and John Vig of the U.S. Army Research Laboratory have recently published a review of the instabilities in precision bulk-acoustic-wave (BAW) quartz crystal oscillators. This is the most comprehensive review of this topic in the literature. Their examination of the fundamental limits on achievable frequency stabilities and the degree to which these fundamental limits have been approached provide researchers with a road map for improving the performance of oscillators. Highlights of their study include thermodynamic limits to temperature stability, the limits imposed by noise generated in the electronic sustaining stage, the effects of static and dynamic temperature fluctuations, and the possible role of background ionizing radiation on long-term frequency drift. They conclude their study with a discussion of the ideal resonator and suggest a levitation method for suspending a resonator so as to eliminate (or minimize) the non-ideal effects of resonator suspensions. (F.L. Walls
• Voltage Noise in Chemical Cells. Chadwick Boggs and Alan Doak, both students at the University of Colorado, along with Fred Walls of this Division have recently reported measurements of voltage noise on a variety of chemical cells. Chemical cells have often been used in electronics for their low current drift, isolation of a particular circuit from other circuits, and low voltage noise. While it is clear that voltage noise on these cells is small, actual values for the voltage noise have not been reported, so there has been little evidence suggesting that one type of cell might be better than another.

  This work was made possible by the development of a cross-correlation measurement system capable of measuring voltage noise below -200 dBV/Hz. The method involves two parallel measurement channels. Because the measurement noises in these two channels are completely independent, a cross-correlation of the outputs of the two channels effectively rejects the measurement noise while recovering the noise on the device under test.

  Nickel-cadmium cells exhibited the lowest noise of all cells tested over the frequency range from 1 Hz to 60 kHz. An AA-size nickel-cadmium cell showed a noise of -205 dBV/Hz at 10 kHz. This noise level is consistent with the Johnson noise produced by the 0.2 Ω internal resistance of the cell. The study involved nickel-cadmium, alkaline, lithium, and mercury cells. A general conclusion of the study was that the dominant broadband noise process in cells is the Johnson noise arising from the internal resistance. This clearly indicates that larger capacity batteries with lower internal resistance should produce lower voltage noise. The voltage noise was found to be independent of bias current suggesting that shot noise is not significant. The results of this study should provide guidance in electronics applications demanding the lowest possible levels of voltage noise. (F.L. Walls
• A 100 MHz Timing Distribution Amplifier. Fred Walls of NIST, in collaboration with Marco Siccardi, Stephania Römisch, and Andrea De Marchi of the Politecnico de Torino in Italy, have developed a 100 MHz frequency distribution amplifier that can support highly advanced timing measurements, even at the performance levels of the next generations of atomic frequency standards. Typical timing distribution system use 5 MHz or 10 MHz signals, but, due to the sensitivity of currently available phase detectors to both temperature and rf amplitude, much better timing performance can be achieved at 100 MHz.
  
  The amplifier provides five outputs for one input and exhibits signal isolation of better than 100 dB. The 1/f noise added by the amplifier stages is extremely low, -163 dBc/Hz at 10 Hz. In addition, a very good match to 50 Ω at both the input and output reduces the voltage standing wave ratio thus minimizing the phase errors that accompany signal reflection. (F.L. Walls
• An Improved Variance for Characterizing Oscillators. Dave Howe has developed an improved variance, closely related to the Allan variance, that provides increased confidence level at long averaging time. This is important because the long-term data, requiring longer measurement time, is the most costly to obtain. As the method is adopted, manufacturers of oscillators can expect to either reduce measurement time or increase measurement accuracy.
  
  The improvement follows from the simple observation that the procedure for the Allan variance, sometimes called the two-sample variance, measures only frequency variations with an odd symmetry at and near the longest averaging time resulting in a bias. This work constructs a three-sample variance of even symmetry and combines this result with the two-sample variance in order to minimize the bias and thus improve the confidence interval. The process bears a similarity to the method of complex demodulation used in signal processing. The gain in measurement confidence depends on the noise type involved. For white phase-modulation noise, the improvement for the longest averaging time in a data set can be better than an order of magnitude. The improvement is significant, but not quite as dramatic, for higher order noise processes. (D.A. Howe
• Upgraded Time Broadcasts from WWVB. The Services Group has embarked on a major renovation and enhancement of the time broadcasts from radio station WWVB located north of Fort Collins, Colorado. These broadcasts are attractive for a number of applications because receivers and their antennas can be particularly simple, small, and inexpensive, and because signal reception within buildings is feasible. However, the presently available signal strength has been marginal, particularly in areas along the U.S. east coast. One of the key objectives of this effort is to resolve this problem by increasing signal strength by at least 6 dB. This will provide U.S. industry options for new products serving both high-end timing applications and consumer needs.
  
  A key roadblock to this project has been the very high cost of new transmitters. This difficulty was overcome when the Navy agreed to provide NIST with three spare high-power transmitters which they had in storage. Purchased new, these transmitters would have cost NIST more than $1M. Installation of the transmitters requires substantial engineering modifications at the site. These include new transmission lines to antennas, new impedance matching networks, and modified interfacing to the transmitters. The present plan is to complete installation and modifications in about a year. (D.W. Hanson)
• Algorithm for Improving Time Dissemination Through Networks. In a collaborative effort, Judah Levine along with David Mills of the University of Delaware and Greg Woods of the National Center for Atmospheric Research have developed an algorithm that is now in use for disseminating time signals through the INTERNET. The algorithm separates the noise in the calibration channel from the noise in the clock itself and adjusts parameters of the algorithm to optimize performance. The concept used is an application of an earlier patent (granted to NIST) on a "Smart-Clock" concept for maintaining synchronization of a remote clock to a master clock with a minimal number of transmissions. The NIST-patent concept was developed by Dave Allan, Dick Davis, Judah Levine, and Marc Weiss. Their system permits time servers to be located anywhere on the INTERNET and minimizes variabilities introduced by long network paths. A new version of the algorithm is under development. It will improve characterization of the network delays. (J. Levine
• Diode-Laser Wavelength Standard for Absolute Distance Measurement Delivered. A major milestone in a collaboration between two NIST Laboratories which share responsibility in the realization of the meter as the international standard of length was achieved when a tunable diode laser primarily developed by one as a wavelength reference standard was delivered to the other. Both Laboratories contributed to the design and both will characterize the laser for use in absolute-distance interferometry, the shared goal of collaboration. While the Manufacturing Engineering Laboratory has responsibility for providing U.S. industry with practical access to the meter as the international standard of length, now defined in terms of the length of path an electromagnetic wave travels in an interval of time, the Physics Laboratory has responsibility for providing access to the second as the international standard of time, in part via laser wavelength reference standards. The diode laser for this project has been co-developed by Michelle Stephens and Leo Hollberg of the Physics Laboratory, who carried out the major task of creating a tunable laser from a commercial diode, with contributions from Lowell Howard and Jack Stone of the Manufacturing Engineering Laboratory on the design of the mechanical laser-cavity tuning structure. By comparison with commercial visible-light lasers, the one being co-developed at NIST can sweep either ten times farther than those with comparable rate or 100 times faster than those with a comparable range. With its unique ability to continuously and rapidly sweep its central wavelength near 680 nm over a range of 2 nm at a rate of 10 Hz, the laser will allow development of an absolute-distance interferometry system which can overcome the limitations of present displacement interferometry systems for an uninterrupted beam. With the new interferometer system being developed, absolute distance between the reflectors of the interferometer can be measured directly rather than requiring the position of one reflector to be physically translated over the distance to be measured. (M. Stephens and L. Howard
• Wavenumber Standards for the Infrared. The International Union of Pure and Applied Chemistry (IUPAC) working group on "Unified Wavenumber Standards" has recently issued a set of recommendations for high resolution wavenumber standards for the infrared. Joe Wells and Ken Evenson of NIST and Art Maki formerly of NIST (now at University of Washington) served on this working group. A large share of the measurements cited in the recommendations were made at NIST. The objective of this work is the improvement of calibrations of high resolution infrared spectra where measurements have traditionally been more precise than accurate. The group's recommendation of a large set of accurately measured spectral lines covers the range from about 4 to about 7000 cm^-1. (K.M. Evenson
• Observation of Laser Oscillation Without Population Inversion. In a recent collaboration with scientists from Texas A&M University and Russia's Lebedev Institute of Physics, Leo Hollberg and Hugh Robinson of this Division have demonstrated laser oscillation without population inversion (LWI). Collaborators at Texas A&M included A.S. Zibrov, M.D. Lukin, D.E. Nikonov, and M.O. Scully. V.L. Velichansky of the Lebedev Institute also participated in the work. The experiments, carried out at NIST, followed the surprising theoretical prediction that, in a V-type configuration of energy levels, atomic coherence can result in gain without population inversion. A strong driving field on one transition has a significant effect on a second transition that shares the same ground state as the driven transition. Related coherence effects had already been observed, but this was the first demonstration of actual lasing without inversion.

  The experiments were carried out in a rubidium cell using only 25 mW of drive power from simple diode lasers. Measurements showed that the observed laser oscillation occurred without population inversion, and that it was the presence of the coherent drive-laser radiation that produced the conditions necessary for oscillation. Earlier, the group reported cw amplification without inversion in the same system, but more efficient containment of photons was needed before the system would oscillate.

  The work has possible practical implications. In particular it suggests the possibility that short wavelength lasers (in the ultraviolet region and beyond) might be feasible. While the work described here involved laser oscillation at a wavelength not too far from the wavelength of the drive laser, there is now the clear possibility that the same approach could be used to produce laser oscillation at much shorter wavelengths, far removed from the wavelength of the drive laser. Experiments to test this possibility are in progress. (L. Hollberg
• High Resolution Spectroscopy Supporting Atmospheric Chemistry Studies. The diode-laser systems developed for use with optical and microwave frequency standards are also proving useful for spectroscopic detection of molecular species important in the chemistry of the upper atmosphere. With NOAA's atmospheric scientists sharing adjacent facilities, a collaboration on the application of these lasers to their measurement problems has been natural. The most notable recent success is a collaboration between NOAA scientists and Rich Fox of NIST on the detection of NO₃. This radical plays a key role in nighttime atmospheric chemistry, interacting for example with molecules involving chlorine. NO₃ dissociates in sunlight. Their recently reported measurements quantify NO₃ reactions with other key species providing input to atmospheric models.

  NO₃ has a strong electronic absorption band at 662 nm that can be reached with commercial red diode lasers. In these experiments a solitary diode laser is used to detect the time-dependent concentration of NO₃ in a cell. Good detection sensitivity is achieved with direct absorption measurements. The interaction path is increased using reflected multiple passage of the laser beam through the cell.

  In addition, they have frequency doubled the light from infrared diode lasers to produce precisely tunable blue light that can be used to detect other important atomic and molecular resonances. For example, laser light at 425 nm, generated by this technique, has been applied to the high-sensitivity detection of the IO molecule. Both NO₃ and IO play important roles in determining the concentration of ozone in the atmosphere. (R. Fox
• 30 THz Mixing Experiments Using High-T_c Josephson Junctions. Eric Grossman, Leila Vale, and David Rudman of the Electromagnetic Technology Division of EEEL along with Ken Evenson and Lyndon Zink of this Division recently published a paper describing their experiments on high-frequency mixing in high-T_c Josephson junctions. They directly observed second-order difference frequencies from 10 MHz to 12.8 GHz between two CO₂ laser lines near 30 THz. Applying a third microwave signal to the junction, they observed laser difference frequencies up to 27 GHz. This is the first observation of Josephson mixing at CO₂ frequencies in high-T_c junctions. The hope is that these devices can be further developed to provide simpler means for synthesizing and measuring optical signals at arbitrary frequencies.
  
  The devices studied were thin-film YBa₂Cu₃O_7-δ superconductor-normal-superconductor junctions fabricated in EEEL's Boulder facilities. The dc-bias dependence of the difference signal, as well as other evidence, suggests two distinct mixing mechanisms: hot-electron mixing in the junction banks at high dc bias, and bolometric Josephson mixing at low dc bias. The latter mixing mechanism is superior for third and higher-order mixing products. (K.M. Evenson
• Improved CO₂ Laser. Ken Evenson, using a new grating produced by a local Boulder optical manufacturer, has developed a CO₂ laser which oscillates on about 250 lines with a maximum power output of 40 W. Most CO₂ lasers will oscillate on only about 80 lines. The laser uses a grating to couple power out of the laser in zero order. The new laser promises to be an excellent infrared frequency and wavelength standard as well as a source of radiation for pumping far-infrared lasers.

  

  Figure 2. Output of the new CO₂ laser as a function of wavelength. This plot was made by scanning the grating angle to select the various laser lines. The wavelength of the shortest wavelength at the left of the figure is 9.2 µm and the longest wavelength at the right is 11.4 µm. The various overlapping bands are identified above the figure.

  Three years ago, Evenson developed a ribbed laser tube which greatly increased the grating resolution of the laser cavity. This provided a substantial improvement in laser performance, because the ribbed structure reduces or eliminates modes associated with radiation bouncing off the walls of the tube. The latest improvement is a direct result of the improved grating which couples out 3% of the power over the region from 9 µm to 11.5 µm. The new grating, with 150 lines/mm, was developed by a local optical manufacturer in direct response to NIST requirements and was tested and proven at NIST. Figure 2 shows the laser output as the grating angle is scanned to select the various laser lines. The laser has a mirror separation of 2.67 m and a diameter of 16.3 mm. (K.M. Evenson
• Measurement and Interpretation of Tidal Tilts. In a recent publication based on her PHD dissertation, Mary Kohl of the University of Colorado and her advisor, Judah Levine of this Division, describe a new method for using simultaneous tilt measurements at different depths to estimate the secular strain rate. Such measurements may be useful in understanding earthquake dynamics. The new measurements are potentially more accurate than those provided by strainmeters at the same locations. While most borehole strainmeter installations are permanent, tilt instruments can be removed for repair or moved to other locations at relatively low cost. In their work, they show that earth tides can provide a continuous calibration of the instrument, since these are of known amplitude. (J. Levine)