Accurate Frequency Measurements Research Articles

Single-Atom Optical Clock with High Accuracy

For the past 50 years, atomic standards based on the frequency of the cesium ground-state hyperfine transition have been the most accurate time pieces in the world. We now report a comparison between the cesium fountain standard NIST-F1, which has been evaluated with an inaccuracy of about 4 x 10(-16), and an optical frequency standard based on an ultraviolet transition in a single, laser-cooled mercury ion for which the fractional systematic frequency uncertainty was below 7.2 x 10(-17). The absolute frequency of the transition was measured versus cesium to be 1,064,721,609,899,144.94 (97) Hz, with a statistically limited total fractional uncertainty of 9.1 x 10(-16) the most accurate absolute measurement of an optical frequency to date.

Phase statistics in non-Gaussian scattering

Amplitude weighting can improve the accuracy of frequency measurements in signals corrupted by multiplicative speckle noise. When the speckle field constitutes a circular complex Gaussian process, the optimal function of amplitude weighting is provided by the field intensity, corresponding to the intensity-weighted phase derivative statistic. In this paper, we investigate the phase derivative and intensity-weighted phase derivative returned from a two-dimensional random walk, which constitutes a generic scattering model capable of producing both Gaussian and non-Gaussian fluctuations. Analytical results are developed for the correlation properties of the intensity-weighted phase derivative, as well as limiting probability densities of the scattered field. Numerical simulation is used to generate further probability densities and determine optimal weighting criteria from non-Gaussian fields. The results are relevant to frequency retrieval in radiation scattered from random media.

Milliarcsecond-Scale Spectral Properties and Jet Motions in M 87

Abstract We have combined high resolution VLBI Space Observatory Programme (VSOP) data at 1.6 and 4.8 GHz with Very Long Baseline Array (VLBA) data at higher frequencies and with similar resolutions to study the spectral properties of the core of M 87 with milliarcsec resolution. The VSOP data allows a more accurate measurement of the turnover frequency, and hence more reliable determination of associated physical parameters of the source. Comparison of the images with previously published images yields no evidence for significant motions of components in the parsec-scale jet. In addition, the brightness temperatures obtained from modelfits to the core are well below the inverse Compton limit, suggesting that the radio emission we are observing is not strongly Doppler boosted.

Design and Analysis of Association Studies using Pooled DNA from Large Twin Samples

Evidence is mounting that multiple genes are involved in complex traits and that these each account for very small proportions of the overall phenotypic variance. Association studies of many markers in 1000s of individuals will be required to identify such genes. A number of large twin cohorts have already been collected and provide a valuable resource for carrying out studies that are robust to the effect of population stratification. Technologies based on microarrays will soon allow 1.000,000 SNPs to be typed at one time, however financial considerations prevent most researchers from using these approaches to genotype all individuals. Recently, microarrays have been shown to give accurate allele frequency measurements in pooled DNA samples and provide a simple way to select the best markers for individual genotyping. This drastically reduces the cost and workload of large scale association studies. One limitation of this methodology relates to the analytical procedures which have only been developed to allow comparison of two pools e.g. case/control pools. In this paper we use meta-regression to analyze pooled DNA data allowing the allele frequency in each pool to be related to the average quantitative phenotypic measure of the individuals whose DNA were used to construct the pools. Alongside this we describe a technique that can be used to determine the power for such studies. We present results from some preliminary investigations of different pooling strategies that can be applied to large twin samples and demonstrate that the method retains a large proportion of the power available from individual genotyping.

Identification of disease causing loci using an array-based genotyping approach on pooled DNA

BackgroundPooling genomic DNA samples within clinical classes of disease followed by genotyping on whole-genome SNP microarrays, allows for rapid and inexpensive genome-wide association studies. Key to the success of these studies is the accuracy of the allelic frequency calculations, the ability to identify false-positives arising from assay variability and the ability to better resolve association signals through analysis of neighbouring SNPs.ResultsWe report the accuracy of allelic frequency measurements on pooled genomic DNA samples by comparing these measurements to the known allelic frequencies as determined by individual genotyping. We describe modifications to the calculation of k-correction factors from relative allele signal (RAS) values that remove biases and result in more accurate allelic frequency predictions. Our results show that the least accurate SNPs, those most likely to give false-positives in an association study, are identifiable by comparing their frequencies to both those from a known database of individual genotypes and those of the pooled replicates. In a disease with a previously identified genetic mutation, we demonstrate that one can identify the disease locus through the comparison of the predicted allelic frequencies in case and control pools. Furthermore, we demonstrate improved resolution of association signals using the mean of individual test-statistics for consecutive SNPs windowed across the genome. A database of k-correction factors for predicting allelic frequencies for each SNP, derived from several thousand individually genotyped samples, is provided. Lastly, a Perl script for calculating RAS values for the Affymetrix platform is provided.ConclusionOur results illustrate that pooling of DNA samples is an effective initial strategy to identify a genetic locus. However, it is important to eliminate inaccurate SNPs prior to analysis by comparing them to a database of individually genotyped samples as well as by comparing them to replicates of the pool. Lastly, detection of association signals can be improved by incorporating data from neighbouring SNPs.

Dual-mode CO2-laser/microwave-sideband spectrometer with broadband and saturation dip detection for CH3OH

This work reports dual-mode operation of a broadly tunable CO2-laser/microwave-sideband spectrometer employing a Cheo waveguide modulator and a CO2 laser that can operate on hot and sequence band lines as well as low- and high-J regular band lines. The spectrometer has a broadband scanning mode at Doppler-limited resolution for spectral searching and assignment, and a narrow-band sub-Doppler mode for precision measurements. In broadband mode, a 6.7–18.5 GHz (∼0.4 cm−1) window can be covered for each sideband in a single microwave sweep with a tracking Fabry–Perot etalon filter under computer control. In sub-Doppler mode, saturation-dip spectra are obtained at sub-MHz resolution with absolute frequency measurement accuracy of the order of ±200 kHz. The instrumental performance is demonstrated via spectra of the C–O stretching fundamental vibrational band of methanol. Doppler-limited broadband scans have been recorded with good signal-to-noise ratio in both the low- and high-J regions of the 9.6-μm-CO2 laser band, while narrow-band sub-Doppler scans have permitted clean separation of very close-lying lines in the CH3OH spectrum. The measurement precision is confirmed for several CH3OH transition systems through closure of combination loops. Our results illustrate the wide coverage and excellent resolution obtainable with CO2-sideband infrared laser radiation in a broadly tunable and convenient infrared source with high potential for spectroscopic applications.

Resonance ultrasound spectroscopy with laser-Doppler interferometry for studying elastic properties of thin films

We propose an advanced method to determine the elastic-stiffness coefficients C ij of thin films using resonance ultrasound spectroscopy (RUS). It uses free-vibration resonance frequencies of a film/substrate layered solid and derives inversely the film’s C ij from the resonance frequencies. We develop a piezoelectric tripod consisting of two pinducers and one support to place the specimen on it and measure the resonance frequencies with high enough accuracy. Furthermore, we achieve mode identification by measuring deformation distributions on the vibrating specimen surface using laser-Doppler interferometry. Accurate measurements of frequencies and correct mode identification are the keys for deducing reliable C ij of the film. We applied this technique to copper thin films deposited of Si substrates. The resulting film’s C ij are considerably smaller than the bulk’s C ij and show anisotropy between the out-of-plane direction and in-plane direction.

Improvement of estimation accuracy of the central frequency of narrow-band process in FFT processor

Several algorithms are suggested making it possible to improve the estimation accuracy of the central frequency in a narrow-band process. The algorithms can be used in the fast Fourier transform processor during signal detection. Analytical formulas of correction for several weight functions (windows) are derived. An interpolation algorithm for improvement of such estimation for arbitrary windows is developed. The gain in accuracy of central frequency measurement for various methods and weight functions is defined.

Developments of Optical Frequency Standards for Wavelength-division-multiplexing (WDM) Optical Fiber Communication Systems

We have developed optical frequency standards for wavelength-division-multiplexing (WDM) optical communication systems based on absorption lines of acetylene molecules in the 1.5 μm region. We developed acetylene-stabilized diode lasers using a Doppler-free saturation absorption of acetylene as a frequency reference. We also developed an accurate frequency measurement sysytem in the 1.5 μm region and the absolute optical frequency of an acetylene line was measured with an uncertainty of 12 kHz. As a result, the acetylene optical frequency standard can be used as an accurate absolute frequency reference for the calibration of optical instruments used in the WDM systems.

Atomic-resolution measurements with a new tunable diode laser-based interferometer

We develop a new implementation of a Michelson interferometer designed to make measurements with an uncertainty of less than 20 pm. This new method uses a tunable diode laser as the light source, with the diode laser wavelength continuously tuned to fix the number of fringes in the measured optical path. The diode laser frequency is measured by beating against a reference laser. High-speed, accurate frequency measurements of the beat frequency signal enables the diode laser wavelength to be measured with nominally 20-pm accuracy for the measurements described. The new interferometer design is lightweight and is mounted directly on an ultra-high vacuum scanning tunneling microscope capable of atomic resolution. We report the simultaneous acquisition of an atomic resolution image, while the relative lateral displacement of the tip along the sample distance is measured with the new tunable diode laser Michelson interferometer. © 2004 Society of Photo-Optical Instrumentation Engineers.

Estimation of a Brillouin power spectrum distribution based on an iterative weighted least mean square method

AbstractA fiberoptic strain sensor is being developed that exploits the fact that the difference between the central frequency of Brillouin scattering, which is a type of back scattering that occurs in optical fibers, and the incident light frequency depends on the strain of the optical fiber. The measurement of the central frequency of the Brillouin scattering requires an estimation of the power spectrum distribution of the Brillouin scattering. An improvement in distribution estimation accuracy can potentially improve both the accuracy of central frequency measurements and the precision of strain measurements. Focusing on the problem of the power spectrum distribution of the Brillouin scattering, this paper proposes a weighted repetition least mean square algorithm. The paper also examines the stability of the proposed repetition algorithm and demonstrates the effectiveness of the proposed approach through simulations. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 1, 87(1): 72–80, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecja.1183

International Photolysis Frequency Measurement and Model Intercomparison (IPMMI): Spectral actinic solar flux measurements and modeling

The International Photolysis Frequency Measurement and Model Intercomparison (IPMMI) took place in Boulder, Colorado, from 15 to 19 June 1998, aiming to investigate the level of accuracy of photolysis frequency and spectral downwelling actinic flux measurements and to explore the ability of radiative transfer models to reproduce the measurements. During this period, 2 days were selected to compare model calculations with measurements, one cloud‐free and one cloudy. A series of ancillary measurements were also performed and provided parameters required as input to the models. Both measurements and modeling were blind, in the sense that no exchanges of data or calculations were allowed among the participants, and the results were objectively analyzed and compared by two independent referees. The objective of this paper is, first, to present the results of comparisons made between measured and modeled downwelling actinic flux and irradiance spectra and, second, to investigate the reasons for which some of the models or measurements deviate from the others. For clear skies the relative agreement between the 16 models depends strongly on solar zenith angle (SZA) and wavelength as well as on the input parameters used, like the extraterrestrial (ET) solar flux and the absorption cross sections. The majority of the models (11) agreed to within about ±6% for solar zenith angles smaller than ∼60°. The agreement among the measured spectra depends on the optical characteristics of the instruments (e.g., slit function, stray light rejection, and sensitivity). After transforming the measurements to a common spectral resolution, two of the three participating spectroradiometers agree to within ∼10% for wavelengths longer than 310 nm and at all solar zenith angles, while their differences increase when moving to shorter wavelengths. Most models agree well with the measurements (both downwelling actinic flux and global irradiance), especially at local noon, where the agreement is within a few percent. A few models exhibit significant deviations with respect either to wavelength or to solar zenith angle. Models that use the Atmospheric Laboratory for Applications and Science 3 (ATLAS‐3) solar flux agree better with the measured spectra, suggesting that ATLAS‐3 is probably more appropriate for radiative transfer modeling in the ultraviolet.

SOLAR SHORT-PERIOD OSCILLATIONS EXCITED BY A SMOOTH FORCE

The basic objective of helioseismology is to determine the structure and the dynamics of the Sun by analysing the frequency spectrum of the solar oscillations. Accurate frequency measurements provide information that enables us to probe the solar interior structure and the dynamics. Therefore the frequency of the solar oscillation is the most fundamental and important information to be extracted from the solar oscillation observation. This is why many efforts have been put into the development of accurate data analysis techniques, as well as observational efforts. To test one's data analysis method, a realistic artificial data set is essential because the newly suggested method is calibrated with a set of artificial data with predetermined parameters. Therefore, unless test data sets reflect the real solar oscillation data correctly, such a calibration is likely incomplete and a unwanted systematic bias may result in. Unfortunately, however, commonly used artificial data generation algorithms insufficiently accommodate physical properties of the stochastic excitation mechanism. One of reason for this is that it is computaionally very expensive to solve the governing equation directly. In this paper we discuss the nature of solar oscillation excitation and suggest an efficient algorithm to generate the artificial solar oscillation data. We also briefly discuss how the results of this work can be applied in the future studies.

Accurate frequency measurement of a submillimeter wave gyrotron output using a far-infrared laser as a reference

Accurate measurement of gyrotron frequency has been carried out by using a far-infrared (FIR) molecular laser as a reference. Highly stable operation of a FIR laser enables us to make the resolution of frequency measurement so precisely that both the frequency width Δf and the frequency fluctuation level δf can be studied within the accuracy of 1 kHz or less. When our submillimeter wave gyrotron operates in cw mode, the observed frequency width Δf is around 2 kHz and the fluctuation level δf 10 kHz. Such an accurate measurement is a useful tool for development of high quality gyrotrons with stable frequency.

Nonresonant corrections for the hydrogen atom

The nonresonant (NR) corrections are estimated for the 1s–2p one-photon and for the 1s–2s two-photon resonances in the hydrogen atom. These corrections depend on the measurement process and set the limit for the accuracy of atomic frequency measurements. With the measurement process accepted in recent experiments the NR contribution for the 1s–2s transition energy can reach 10–3 Hz while the experimental inaccuracy is quoted to be ±46 Hz. PACS Nos.: 31.30Jv, 12.20Ds, 06.20Jr, 31.15-p

Nonresonant corrections to the1s−2stwo-photon resonance for the hydrogen atom

The nonresonant (NR) corrections are estimated for the most accurately measured two-photon transition 1s-2s in the hydrogen atom. These corrections depend on the measurement process and set a limit for the accuracy of atomic frequency measurements. With the measurement process adopted in the modern experiments the NR contribution for 1s-2s transition energy can reach 10^{-3} Hz while the experimental inaccuracy is quoted to be +/- 46 Hz.

Absolute frequency measurement of the 4355-nm ^171Yb^+-clock transition with a Kerr-lens mode-locked femtosecond laser

We have measured the frequency of the $6s^2S_{1/2} - 5d^2D_{3/2}$ electric-quadrupole transition of $^{171}$Yb$^+$ with a relative uncertainty of $1\times 10^{-14}$, $\nu_{Yb}$ = 688 358 979 309 312 Hz $\pm$ 6 Hz. A femtosecond frequency comb generator was used to phase-coherently link the optical frequency derived from a single trapped ion to a cesium fountain controlled hydrogen maser. This measurement is one of the most accurate measurements of optical frequencies ever reported, and it represents a contribution to the development of optical clocks based on an $^{171}$Yb$^+$ ion standard.

Analysis of frequency measurement of power signals with varied amplitudes

AbstractFrequency is one of the most important operating parameters of a power system. Thus accurate frequency measurement plays a key role in understanding the system performance and developing effective control strategies. So far various approaches have been proposed. However, one important area, which has been neglected, is what is the effect of varied signal amplitudes on these approaches. Starting with the traditional definition of frequency, this paper analyses the basic requirements for frequency measurement, and presents new concepts for various frequency definitions. The difference between actual frequency and measured frequency by various approaches is discussed in detail. Postprocessing approach is proposed to improve the accuracy of the measurement.

Optimal Masks for Low-Degree Solar Acoustic Modes.

We suggest a solution to an important problem in observational helioseismology of the separation of lines of solar acoustic (p) modes of low angular degree in oscillation power spectra by constructing optimal masks for Doppler images of the Sun. Accurate measurements of oscillation frequencies of low-degree modes are essential for the determination of the structure and rotation of the solar core. However, these measurements for a particular mode are often affected by leakage of other p-modes arising when the Doppler images are projected on to spherical harmonic masks. The leakage results in overlapping peaks corresponding to different oscillation modes in the power spectra. In this Letter, we present a method for calculating optimal masks for a given (target) mode by minimizing the signals of other modes appearing in its vicinity. We apply this method to time series of 2 yr obtained from the Michelson Doppler Imager instrument on board the Solar and Heliospheric Observatory space mission and demonstrate its ability to reduce efficiently the mode leakage.

A new method for instantaneous power system frequency measurement using reference points detection

Abstract An accurate power system frequency measurement is difficult due to the presence of unwanted noise including higher-order harmonics, dc component and random noise. An algorithm that creates unique reference points in a sinusoidal signal corrupted by unwanted noise is introduced in this paper and used for precise instantaneous frequency measurement. The reference points are determined using symmetry features of the power signal. They are used to measure time between each two consecutive cycles and further to determine signal frequency. The algorithm that determines reference points employs two main features important for precise frequency measurement: a ‘correlation’ feature to remove the random noise effect, and a modified ‘symmetry detection’ feature to generate a single reference point at a unique location (time instance) in each cycle. The method is aimed at frequency relays for load shedding application.