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Statistics of Atomic Frequency Standards
Abstract
A theoretical development is presented which results in a relationship between the expectation value of the standard deviation of the frequency fluctuations for any finite number of data samples and the infinite time average value of the standard deviation, which provides an invariant measure of an important quality factor of a frequency standard. A practical and straightforward method of determining the power spectral density of the frequency fluctuations from the variance of the frequency fluctuations, the sampling time, the number of samples taken, and the dependence on system bandwidth is also developed. Additional insight is also given into some of the problems that arise from the presence of "flicker noise" (spectrum proportional to |ω|<sup>-1</sup>) modulation of the frequency of an oscillator. The theory is applied in classifying the types of noise on the signals of frequency standards made available at NBS, Boulder Laboratories, such as: masers (both H and N<sup>15</sup>H 3 ), the cesium beam frequency standard employed as the U. S. Frequency Standard, and rubidium gas cells. "Flicker noise" frequency modulation was not observed on the signals of masers for sampling times ranging from 0.1 second to 4 hours. In a comparison between the NBS hydrogen maser and the NBS III cesium beam, uncorrelated random noise was observed on the frequency fluctuations for sampling times extending to 4 hours; the fractional standard deviations of the frequency fluctuations were as low as 5 parts in 10<sup>14</sup>.
... The AVAR method assesses the noise coefficients and characteristic noises of inertial sensors, such as acceleration ramp AccR (Rate Ramp RR), velocity random walk VRW (Angle Random Walk ARW), quantization noise, sinusoidal noises, exponentially correlated (Markov) noise, bias instability BI, and acceleration random walk AccRW (Rate Random Walk RRW) [12][13][14][15]. ...
... Angle random walk ARW (or velocity-VRW) with white frequency modulation noise, is a high frequency noise that has a correlation time that is less than the sample time. At the sensor output, ARW is represented as white noise [14,15]. ...
This article deals with power supply linear and switching regulators commonly used in various applications for stabilizing an output voltage and ensuring a necessary power input to the load. It describes their basic parameters, performances, advantages, and disadvantages according to their topologies. We design a measurement chain for efficiency evaluation based on power monitors INA219 connected to an embedded system, Arduino UNO. Measurements were focused on evaluation linear regulators MA7805, LM317, switching regulators SZBK07, LM2575, SCW05B-05, and XH-M401. The resulting efficiency of linear and switching regulators was analyzed and errors in the measurement chain were evaluated. The second contribution is an innovative way of carrying out regulator noise estimation using a fast Allan variance method, focused on white noise and flicker noise (bias instability). The main contribution is employing a fast Allan variance method algorithm that dramatically decreases computation time by up to 11 s for 72 million measured (or generated) samples. It enables the analysis of large data sets of various physical quantities (for example, regulator output voltages).
... This task can be performed in advance using the Allan variation method, which initially was applied for characterizing the stability of atomic clocks [7]. Later, it was widely used for IMU analysis [8,9] and even adopted as an IEEE standard, though just for fiber optic and laser gyros [10,11]. ...
... To analyze the noise characteristics of the sensors, the so-called Allan deviation (ADEV) slope method was used. The ADEV analysis method, originally formulated by David W. Allan in the 1960s [7], has evolved with the introduction of ADEV slopes, enhancing its capability to provide insights into IMU sensor noise characteristics across various time scales. The Overlapped Allan Deviation (OADEV) analysis method offers a refined approach to understanding the noise and stability characteristics of IMU sensors. ...
Inertial measurement units (IMUs) are key components of various applications including navigation, robotics, aerospace, and automotive systems. IMU sensor characteristics have a significant impact on the accuracy and reliability of these applications. In particular, noise characteristics and bias stability are critical for proper filter settings to perform a combined GNSS/IMU solution. This paper presents an analysis based on the Allan deviation of different IMU sensors that correspond to different grades of micro-electromechanical systems (MEMS)-type IMUs in order to evaluate their accuracy and stability over time. The study covers three IMU sensors of different grades (ascending order): Rokubun Argonaut navigator sensor (InvenSense TDK MPU9250), Samsung Galaxy Note10 phone sensor (STMicroelectronics LSM6DSR), and NovAtel PwrPak7 sensor (Epson EG320N). The noise components of the sensors are computed using overlapped Allan deviation analysis on data collected over the course of a week in a static position. The focus of the analysis is to characterize the random walk noise and bias stability, which are the most critical for combined GNSS/IMU navigation and may differ or may not be listed in manufacturers’ specifications. Noise characteristics are calculated for the studied sensors and examples of their use in loosely coupled GNSS/IMU processing are assessed. This work proposes a structured and reproducible approach for working with sensors for their use in navigation tasks in combination with GNSS, and can be used for sensors of different levels to supplement missing or incorrect sensor manufacturers’ data.
... It is notable that the estimation of each clock's drift captures only the frequency error of the clock at a single point in time. The frequency error of the clock on each platform will also tend to randomly walk over time depending on the frequency stability of the clock, as described by the Allan variance [35]. To overcome this shortcoming, the synchronization algorithm will need to be run periodically to capture the frequency drift of the clocks over time. ...
... Broadcast frequency reference pulses amongst all platforms pairwise using either (17) or (31) for s j (τ j ) Each platform computes the received frequency valuesf α i, j andf β i, j if using two-tone technique using the FFT and sinc NL-LS If using single-tone with exchange, each platform exchanges all values off α i, j /f α,d i, j with all other platforms Solve forα i andf d i, j , if applicable, using (23), (29), or (35) ...
To continue improving the performance of modern communications and radar remote sensing systems, the implementation of distributed radio frequency (RF) systems has become an increasingly active area of research. One major obstacle to implementing such a distributed network is achieving highly accurate synchronization of all RF electrical states – time, carrier phase, and carrier frequency – as without such synchronization, coherent operation amongst all systems in the network is impossible. Many techniques for achieving synchronization are not accurate enough for application in RF phase and frequency synchronization and thus cannot be applied in such networks. Others are hardware-based, making them difficult to apply to legacy systems. Moreover, many synchronization procedures require external references for establishing synchronization of one or more of the RF electrical states, limiting their application to scenarios where such external references are unavailable. Finally, many techniques are not tolerant of relative motion between platforms, making them less useful for systems such as distributed synthetic aperture radar (SAR) systems. In this paper, an RF synchronization procedure is proposed. Though its intended application is distributed radar sensor networks, it is applicable to any distributed network requiring RF coordination, such as distributed RF communication systems. The technique is capable of achieving synchronization of time, carrier phase, and carrier frequency, and can do so without external references or additional hardware. Moreover, the technique is scalable to large networks and is capable of compensating for relative motion-induced synchronization errors. The proposed technique is validated in simulations for a wide variety of operating conditions, and a three-sensor distributed SAR simulation is provided to demonstrate the effectiveness of the proposed technique in a mobile distributed radar scenario.
... In a common-clock experiment, two or more GNSS receivers are supplied with a common reference frequency, resembling the perfect setup for analyzing the impact of errors such as tropospheric delay, since the ground truth is provided by an optical fiber link. The link instability is computed and assessed using different Allan variances depending on the proposed application [11][12][13]. Relative frequency instability of GNSS-based links can reach the range of 10 −17 over 20-30 days averaging time in terms of modified Allan deviation (MDEV) [14,15]. We use the same measure of instability in this report. ...
... The LAMBDA method is used to fix the float ambiguitiesN 1 , where integer search estimator is applied [30,31]. The fixed ambiguitiesŇ 1 , and their variance-covariance matrices, are used afterwards to compute the tropospheric fixed solution as shown by equation (11). Then we apply both parameters correcting the IF WL fixed solution to compute the IF final fixed solution by compensating the offsets between the computed relative tropospheric segments to estimate the receiver clock differences as mentioned in equation (12): ...
Realizing a clock-based geodetic network with a relative uncertainty level of 10^-18 has been a significant objective for the scientific community. This network can be utilized for realizing more accurate geodetic reference frames and for testing the fundamental laws of physics, such as the theory of relativity. Typically, optical fibers are connecting optical clocks in such a network. For the last decades, Global Navigation Satellite Systems (GNSSs) have built a trustful and easy-setup method for frequency and time transfer. However, recently optical fiber link networks showed better frequency instability. In this study, we investigate the limits of GNSS-based frequency transfer links with the help of an optical fiber link as ground truth. Therefore, we analyze the GNSS data acquired in a dedicated common-clock experiment over a 52 km baseline. We focus on developing two algorithms to estimate the receiver clock differences, hence the frequency instability. These are the single difference (SD) approach with ambiguity fixing as a common view technique, and precise point positioning as an all in-view technique. We discuss the frequency instability achieved by the optical fiber link as well. We evaluate further the performance by computing the modified Allan deviation for both cases. The results show that the ambiguity-fixed solution of SD-CV improves the relative frequency instability via GNSS to reach the order of 3–5 · 10^-17 at one day averaging time. In the optical fiber link, which is the basis of the common clock setup, the round-trip instability shows better performance for all averaging times.
... There are many statistics used to estimate frequency stability. One o mon metrics is the Allan deviation [38]. Another parameter determining f ity is a dimensionless quantity defined as the ratio of frequency fluctuati nal frequency. ...
... There are many statistics used to estimate frequency stability. One of the most common metrics is the Allan deviation [38]. Another parameter determining frequency stability is a dimensionless quantity defined as the ratio of frequency fluctuations to the nominal frequency. ...
In this paper, we explore several widely available software-defined radio (SDR) platforms that could be used for locating with the signal Doppler frequency (SDF) method. In the SDF, location error is closely related to the accuracy of determining the Doppler frequency shift. Therefore, ensuring high frequency stability of the SDR, which is utilized in the location sensor, plays a crucial role. So, we define three device classes based on the measured frequency stability of selected SDRs without and with an external rubidium clock. We estimate the localization accuracy for these classes for two scenarios, i.e., short- and long-range. Using an external frequency standard reduces the location error from 20 km to 30 m or 15 km to 2 m for long- and short-range scenarios, respectively. The obtained simulation results allowed us to choose an SDR with appropriate stability. The studies showed that using an external frequency standard is necessary for minimizing SDR frequency instability in the Doppler effect-based location sensor. Additionally, we review small-size frequency oscillators. For further research, we propose two location sensor systems with small size and weight, low power consumption, and appropriate frequency stability. In our opinion, the SDF location sensor should be based on the bladeRF 2.0 micro xA4 or USRP B200mini-i SDR platform, both with the chip-scale atomic clock CSAC SA.45s, which will allow for minor positioning errors in the radio emitters.
... The long term stability of an atomic clock is quantified by the Allan deviation σ y (τ ) [78] characterizing the fluctuations of fractional frequency deviations y = ω/ω 0 averaged over τ ≫ T . In a dead-time free scenario, the Allan deviation is well approximated by ...
The use of correlated states and measurements promises improvements in the accuracy of frequency metrology and the stability of atomic clocks. However, developing strategies robust against dominant noise processes remains challenging. We address the issue of decoherence due to spontaneous decay and show that Greenberger-Horne-Zeilinger (GHZ) states, in conjunction with a correlated measurement and nonlinear estimation strategy, achieve gains comparable to fundamental bounds for ensembles of up to 40 atoms. This result is surprising since GHZ states do not provide any enhancement under dephasing noise compared to the standard quantum limit of uncorrelated states. The gain arises from a veto signal, which allows for the detection and mitigation of errors caused by spontaneous emission events. Through comprehensive Monte-Carlo simulations of atomic clocks, we demonstrate the robustness of the GHZ protocol.
... Классическая вариация Аллана AV AR в применении к серии измерений y i , i = 1, . . . , n определяется как (Allan, 1966) AV AR = 1 2(n − 1) ...
Pulkovo Observatory has been operating a permanent GNSS station PULK since 2002. This paper presents the results of preliminary analysis of the changes in the errors in the coordinates of the station over time, primarily after replacement of the receiver or antenna. Two accuracy estimates were applied: the formal error of the daily coordinate estimates and the noise component of the PULK coordinate series. In the first case, the median estimate was used, in the second, the Allan variance. As a result, it turned out that two receiver replacements in the first years of operation led to a noticeable decrease in the formal coordinate error, whereas subsequent receiver replacements, as well as both antenna replacements, showed no noticeable changes in this error. The magnitude of the noise component of the coordinate series did not change much during the entire observation period.
... The measurement of precision and power consumption of an autonomous atomic clock is thus sufficient to determine whether it might be modelled as a Markov jump process as considered here and in Ref. [65], or whether coherences need to be taken into account. In the context of clocks, the statistical error is quantified by the Allan variance [73], which in our notation corresponds to Var[N (t )]. The relative uncertainty √ Var[N (t )]/ N (t ) = F/( Ṅ t ) decays with the averaging time t, until statistical errors reach the same level as systematic uncertainties. ...
We analytically derive universal bounds that describe the tradeoff between thermodynamic cost and precision in a sequence of events related to some internal changes of an otherwise hidden physical system. The precision is quantified by the fluctuations in either the number of events counted over time or the waiting times between successive events. Our results are valid for the same broad class of nonequilibrium driven systems considered by the thermodynamic uncertainty relation, but they extend to both time-symmetric and asymmetric observables. We show how optimal precision saturating the bounds can be achieved. For waiting-time fluctuations of asymmetric observables, a phase transition in the optimal configuration arises, where higher precision can be achieved by combining several signals.
Published by the American Physical Society 2024
... For F322W2, we find that the noise is generally ∼20-30% above the photon noise limit, while F444W is ∼2-10% above the photon noise limit. Visual examination of the Allan variance plots (Allan 1966) for both observations show no evidence for residual red noise. ...
We report observations of the atmospheric transmission spectrum of the sub-Neptune exoplanet GJ 3470 b taken using the Near-Infrared Camera (NIRCam) on JWST. Combined with two archival HST/WFC3 transit observations and fifteen archival Spitzer transit observations, we detect water, methane, sulfur dioxide, and carbon dioxide in the atmosphere of GJ 3470 b, each with a significance of >3-sigma. GJ 3470 b is the lowest mass -- and coldest -- exoplanet known to show a substantial sulfur dioxide feature in its spectrum, at $M_{p}$=11.2${\,{\rm M}_{\oplus}}$ and $T_{eq}$=600$\,$K. This indicates disequilibrium photochemistry drives sulfur dioxide production in exoplanet atmospheres over a wider range of masses and temperatures than has been reported or expected. The water, carbon dioxide, and sulfur dioxide abundances we measure indicate an atmospheric metallicity of approximately $100\times$ Solar. We see further evidence for disequilibrium chemistry in our inferred methane abundance, which is significantly lower than expected from equilibrium models consistent with our measured water and carbon dioxide abundances.
... Hence, the width choice is critical for photothermal sensing. Fig. 3d displays the Allan deviation (AD) for a string (green solid curve) [54]. All the acquired AD have been compared with the theoretical model, accounting for the transfer functions (27) of the PLL and SSO tracking schemes [33,49]. ...
Nanomechanical photothermal sensing has significantly advanced single-molecule/particle microscopy and spectroscopy, and infrared detection through the use of nanomechanical resonators that detect shifts in resonant frequency due to photothermal heating. However, the relationship between resonator design, photothermal sensitivity, and response time remains unclear. This paper compares three resonator types - strings, drumheads, and trampolines - to explore this relationship. Through theoretical modeling, experimental validation, and finite element method simulations, we find that strings offer the highest sensitivity (with a noise equivalent power of 280 fW/Hz$^{1/2}$ for strings made of silicon nitride), while drumheads exhibit the fastest thermal response. The study reveals that photothermal sensitivity correlates with the average temperature rise and not the peak temperature. Finally, the impact of photothermal back-action is discussed, which can be a major source of frequency instability. This work clarifies the performance differences and limits among resonator designs and guides the development of advanced nanomechanical photothermal sensors, benefiting a wide range of applications.
... Auto baseline characterisation was disabled throughout the characterisation period. Then the Allan variance (Allan, 1966) was determined to assess the stability and noise characteristics of the measurements over different averaging timescales. Due to the potentially lower aerosol loading from the airborne measurements compared to the 3422 C. Yu et al.: Characterising particle SSA with a modified CAPS monitor ground-based measurements, the Allan variance approach is useful to assess the stability of the A2S2 as modified. ...
Atmospheric aerosols impact the Earth's climate system directly by scattering and absorbing solar radiation, and it is important to characterise the aerosol optical properties in detail. This study reports the development and validation of an airborne dual-wavelength cavity-attenuated phase-shift (CAPS) single monitor, named A2S2 (Aerosol Absorption Spectral Sizer), based on the commercial CAPS single-scattering albedo monitor (CAPS-PMSSA; Aerodyne), to simultaneously measure the aerosol optical scattering and extinction at both 450 and 630 nm wavelengths. Replaced pressure and temperature sensors and an additional flow control system were incorporated into the A2S2 for its utilisation on board research aircraft measuring within the troposphere. The evaluation of A2S2 characteristics was performed in the laboratory and included the investigation of the signal-to-noise ratio, validation of performance at various pressure levels, optical closure studies and intercomparing with the currently validated techniques. The chamber experiments show that the A2S2 can perform measurements at sample pressures as low as 550 hPa and at sample temperatures as high as 315 K. Based on the Allan analysis results, we have evaluated that the minimum detection limit of the measurements shows that the measurements have a limit accuracy of ∼ 2 Mm−1 at 450 nm and ∼ 1 Mm−1 at 630 nm for 1 Hz measurements of both scattering coefficients (σsca) and extinction coefficients (σext). The optical closure study with size-selected polystyrene latex (PSL) particles shows that the truncation error of the A2S2 is negligible for particles with particle volume diameter (Dp) < 200 nm, while, for the larger sub-micrometre particles, the measurement uncertainty of A2S2 increases but remains less than 20 %. The average factors to correct the truncation error are 1.13 and 1.05 for 450 and 630 nm, respectively. A simplified truncation correction, dependent on the scattering Ångström exponent (SAE), was developed to rectify truncation errors of the future A2S2 field measurement data. The σsca and σext measured by the A2S2 show good agreement with the concurrent measured results from the nephelometer and the CAPS particle extinction monitor (CAPS-PMex). The absorption coefficient (σabs) derived through the extinction-minus-scattering (EMS) method by the A2S2 also corresponds with the results obtained from the aethalometer. The A2S2 was successfully deployed during an aircraft measurement campaign (Atmospheric ChemistRy Of the Suburban foreSt – ACROSS) conducted in the vicinity of Paris and the surrounding regions. The average SSA measured during the entire ACROSS flight campaign is 0.86 and 0.88 at 450 and 630 nm, respectively, suggesting that light-absorbing organic aerosols play a significant role. The average SAE and absorption Ångström exponent (AAE) varied due to measurements in various pollution conditions. The results presented in this study indicate that the A2S2 instrument is reliable for measuring aerosol σsca and σext at both blue and red wavelengths, and it stands as a viable substitute for future airborne evaluations of aerosol optical properties.
... Part of this excess long-wavelength white noise is probably the result of the impact of background noise, as these limits only considered the stellar photon noise. Although neither of our NIRCam observations show evidence for residual red noise in their Allan variance plots 68 , several of our MIRI/LRS channels do show moderate amounts of residual red noise. Following the β error-inflation method developed in ref. 69, we computed β, the ratio of the median value of our Allan variance plots at 15-23-min timescales (around the approximately 19-min transit ingress/egress duration of WASP-107b) to the value expected for white noise and multiplied our transmission spectra uncertainties by this amount. ...
Interactions between exoplanetary atmospheres and internal properties have long been proposed to be drivers of the inflation mechanisms of gaseous planets and apparent atmospheric chemical disequilibrium conditions¹. However, transmission spectra of exoplanets have been limited in their ability to observationally confirm these theories owing to the limited wavelength coverage of the Hubble Space Telescope (HST) and inferences of single molecules, mostly H2O (ref. ²). In this work, we present the panchromatic transmission spectrum of the approximately 750 K, low-density, Neptune-sized exoplanet WASP-107b using a combination of HST Wide Field Camera 3 (WFC3) and JWST Near-Infrared Camera (NIRCam) and Mid-Infrared Instrument (MIRI). From this spectrum, we detect spectroscopic features resulting from H2O (21σ), CH4 (5σ), CO (7σ), CO2 (29σ), SO2 (9σ) and NH3 (6σ). The presence of these molecules enables constraints on the atmospheric metal enrichment (M/H is 10–18× solar³), vertical mixing strength (log10Kzz = 8.4–9.0 cm² s⁻¹) and internal temperature (>345 K). The high internal temperature is suggestive of tidally driven inflation⁴ acting on a Neptune-like internal structure, which can naturally explain the large radius and low density of the planet. These findings suggest that eccentricity-driven tidal heating is a critical process governing atmospheric chemistry and interior-structure inferences for most of the cool (<1,000 K) super-Earth-to-Saturn-mass exoplanet population.
... Part of this excess longwavelength white noise is likely due to the impact of background noise as these limits only considered the stellar photon noise. While neither of our NIRCam observations show evidence for residual red-noise in their Allan variance plots 70 , several of our MIRI/LRS channels do show moderate amounts of residual rednoise. Following the β error inflation method developed by ref. 71 , we computed β, the ratio of the median value of our Allan variance plots at 15-23 minute timescales (around WASP-107b's approximately 19minute transit ingress/egress duration) to the value expected for white noise, and multiplied our transmission spectra uncertainties by this amount. ...
Interactions between exoplanetary atmospheres and internal properties have long been hypothesized to be drivers of the inflation mechanisms of gaseous planets and apparent atmospheric chemical disequilibrium conditions. However, transmission spectra of exoplanets has been limited in its ability to observational confirm these theories due to the limited wavelength coverage of HST and inferences of single molecules, mostly H$_2$O. In this work, we present the panchromatic transmission spectrum of the approximately 750 K, low-density, Neptune-sized exoplanet WASP-107b using a combination of HST WFC3, JWST NIRCam and MIRI. From this spectrum, we detect spectroscopic features due to H$_2$O (21$\sigma$), CH$_4$ (5$\sigma$), CO (7$\sigma$), CO$_2$ (29$\sigma$), SO$_2$ (9$\sigma$), and NH$_3$ (6$\sigma$). The presence of these molecules enable constraints on the atmospheric metal enrichment (M/H is 10--18$\times$ Solar), vertical mixing strength (log$_{10}$K$_{zz}$=8.4--9.0 cm$^2$s$^{-1}$), and internal temperature ($>$345 K). The high internal temperature is suggestive of tidally-driven inflation acting upon a Neptune-like internal structure, which can naturally explain the planet's large radius and low density. These findings suggest that eccentricity driven tidal heating is a critical process governing atmospheric chemistry and interior structure inferences for a majority of the cool ($<$1,000K) super-Earth-to-Saturn mass exoplanet population.
... The Allan variance time-domain analysis method was created by David Allan in the 1960s to assess oscillators' frequency and phase stability 15 . This approach has gained widespread recognition from IEEE for its ability to analyze gyroscope and accelerometer parameters due to similarities between these devices and oscillators. ...
Spectrum feature extraction plays a crucial role in identifying seismic events and calculating structural response parameters. However, the criteria for identifying effective modal components in Variational Mode Decomposition (VMD) are not well-defined, resulting in inaccurate spectrum feature extraction. To address this issue, we propose a novel spectrum feature extraction method that combines Allan variance, VMD, and power spectral density (PSD). Firstly, VMD is applied to filter noise components from triaxial accelerometer observations and add effective signals. Secondly, PSD is utilized to extract three groups of seismic frequencies (tri-axial accelerometers). Finally, the Allan method is introduced to identify the group of accelerometer observations with the highest reliability as the vibration frequency caused by the seismic excitation. We validate the effectiveness of our method by analyzing a Mw 2.6 micro-seismic event that occurred in Huairou, Beijing in 2022. The result shows that our proposed method accurately extracts spectrum features of the Great Wall. Specifically, the seismic excitation vibration frequencies at four monitoring stations were found to be 26.95 Hz, 12.89 Hz, 12.89 Hz, and 12.5 Hz. These findings underscore our method's utility in evaluating the Great Wall's structural response to seismic loading, which has significant implications for the conservation and protection of heritage structures.
... kHz in the PL mode. At a given acquisition time (τ), Allan deviation [44] (σ d ) was calculated by ...
Precise distance metrology and measurements play an important role in many fields of scientific research and industrial manufacture. Dual-comb laser ranging combines sub-wavelength ranging precision, large non-ambiguity range, and high update rate, making it the most promising candidate in precise distance metrology and measurements. However, previous demonstrations of dual-comb ranging suffer from short working distances, limited by the decoherence of lasers in interferometric schemes or by the low sensitivity of the photodetectors in response to the sparse echo photons. Here, we propose and demonstrate time-of-flight laser ranging with dual-comb nonlinear asynchronous optical sampling and photon counting by a fractal superconducting nanowire single-photon detector, achieving ranging precision of 6.2 micrometers with an acquisition time of 100 ms and 0.9 micrometers with an acquisition time of 1 s in measuring the distance of an outdoor target approximately 298 m away.
... The Allan variance of MEMS-IMU measurement data is mainly related to the following five noise terms: QN, ARW, BI, rate random walk (RRW), and rate ramp (RR) [18]. ...
The error characteristics of a typical commercial MEMS-IMU were analyzed. Using 15 ICM-42688 sensors, a 3*5 MEMS-IMU array was designed, and a weighted data fusion method based on Allan variance for the MEMS-IMU array was proposed. This effectively reduces the random measurement errors of the MEMS-IMU, providing a data foundation for the precise measurement of motion and attitude of robots, vehicles, aircraft, and other systems under low-cost conditions. The text describes a measurement method for non-stationary motion attitudes of sports vehicles based on adaptive Kalman-Mahony. Specifically, it first uses adaptive Kalman filter on array sensor data to calculate the measurement noise in real-time and adaptively adjust the filtering gain. Then, it determines the compensation coefficient of the accelerometer to the gyroscope angular velocity based on the motion state of the vehicle, and solves the attitude through complementary filtering to obtain the motion attitude quaternion. Finally, it converts it into the roll angle, pitch angle, and yaw angle of the sports vehicle. Experimental results show that the proposed MEMS-IMU array weighted data fusion method based on Allan variance has significant advantages over traditional single MEMS-IUM methods and traditional average weighting methods in reducing sensor angle random walk and zero drift instability. The proposed adaptive Kalman-Mahony attitude measurement method also shows a significant improvement in the accuracy of non-stationary motion attitude measurement compared to traditional methods.
... Under these conditions, the potential signal averaging times, ensuring spatial resolution finer than tens of meters, will not exceed a few seconds. Figure 6 illustrates the dependence of the Allan deviation [45] for the signal acquired at a distance of 50 m from the scattering surface on the accumulation time, alongside its comparison with the corresponding dependency for white noise, presented on a double logarithmic scale. Signal stability on time scales of less than tens of seconds, caused by the open path analytical channel optical system, is deemed optimal for the expected device applications. ...
Enhancement of methane emission measurement techniques is necessary to address the need for greenhouse gas emissions monitoring. Here we introduce a gas analyzer designed for remote sensing of atmospheric methane aboard unmanned aerial vehicles. This device employs the wavelength modulation spectroscopy approach and quadrature detection of laser radiation scattered from the underlying surface. Our results demonstrate that the observed correlation between various signal attributes and the distance to the surface, where laser radiation scatters, aligns with analytical expectations. Calibrations proved that the instrument provides reliable methane measurements up to 120 meters while being lightweight and power efficient. Notably, this device outperforms its competitors at altitudes exceeding 50 meters, which is safer for piloting.
... The Allan variance (AVAR) is chosen to quantify the phase noise due to its sensitivity to patterns within the fluctuation scales rather than the absolute value of the signal. The AVAR is defined as [63] (C1) where N is the time series length, T is the interval between each data sample, τ is delay time between each variance estimate, and y k is the kth fractional frequency over the delay time τ : y k = t k +τ t k y (t)dt = ...
The creation of underwater optical turbulence is driven by density variations that lead to small changes in the water’s refractive index, which induce optical path length differences that affect light propagation. Measuring a laser beam’s optical phase after traversing these turbulent variations can provide insight into how the water’s turbulence behaves. The sensing technique to measure turbulent fluctuations is a self-heterodyne beatnote enhanced by light’s orbital angular momentum (OAM) to obtain simultaneous optical phase and amplitude information. Experimental results of this method are obtained in a water tank that creates a thermally driven flow called Rayleigh–Bénard (RB) convection. The results show time-varying statistics of the beatnote that depend on the incident OAM mode order and the strength of the temperature gradient. Beatnote amplitude and phase power spectral densities are compared to analytic theory to obtain estimates of the turbulent length scales using the Taylor hypothesis that include mean flow speed, turbulent strength, and length scales, and flow dynamics due to intermittency in the RB process.
... The precisions of the three analyzers were characterized in two ways. First, the instruments' inlets were overflowed using a ZA source for 24 h and precision was calculated via an Allan-Werle curve (Allan, 1966), as in prior instrument characterization studies (Shutter et al., 2019;Glowania et al., 2021). Results are shown as the solid lines in Fig. 4. The G2307 achieves precisions of 0.09, 0.05, and 0.03 ppb for integration times of 5, 20, and 60 min. ...
Current formaldehyde (HCHO) measurement networks rely on the TO-11A offline chemical derivatization technique, which can be resource intensive and limited in temporal resolution. In this work, we evaluate the field performance of three new commercial instruments for continuous in situ formaldehyde monitoring: the Picarro cavity ring-down spectroscopy G2307 gas concentration analyzer and Aeris Technologies' mid-infrared absorption Pico and Ultra gas analyzers. All instruments require regular drift correction, which is accomplished through instrument zeroing using dinitrophenylhydrazine (DNPH)-coated cartridges, Drierite, or molecular sieves, while heated Hopcalite failed to remove all incoming HCHO. We show that a modified precision estimate accounting for regular instrument zeroing results in values of 0.09, 0.20, and 0.22 ppb at a 20 min integration time for the G2307, Ultra, and Pico, respectively. After applying standard addition and dynamic dilution calibrations, all instruments agreed within 13 % and were well correlated with each other (all r ≥ 0.90). TO-11A HCHO observations resulted in a normalized mean bias of −58 % compared to co-located Picarro G2307 measurements (r=0.62, slope = 0.38, int = 0.07 ppb HCHO). Using a 6-month deployment period in the Atlanta metropolitan area, we determined that the Picarro G2307 and Aeris units have sufficient accuracy and precision to capture the Atlanta spatial HCHO gradient. We find that midday HCHO concentrations have decreased by 22.3 % since 1999 in the city's urban core, and DNPH measurements at a nearby Photochemical Assessment Monitoring Station (PAMS) site show a greater decrease of 53 %.
... Allan variance [36] is a time-domain analysis technique commonly used for analyzing random errors in data collected by accelerometers under static conditions. Here, the Allan variance curve was used to analyze the denoising effects of the RLMD-SE-TFPF methods, as shown in Figure 14. ...
MEMS accelerometers are significantly impacted by temperature and noise, leading to a considerable compromise in their accuracy. In response to this challenge, we propose a parallel denoising and temperature compensation fusion algorithm for MEMS accelerometers based on RLMD-SE-TFPF and GRU-attention. Firstly, we utilize robust local mean decomposition (RLMD) to decompose the output signal of the accelerometer into a series of product function (PF) signals and a residual signal. Secondly, we employ sample entropy (SE) to classify the decomposed signals, categorizing them into noise segments, mixed segments, and temperature drift segments. Next, we utilize the time-frequency peak filtering (TFPF) algorithm with varying window lengths to separately denoise the noise and mixed signal segments, enabling subsequent signal reconstruction and training. Considering the strong inertia of the temperature signal, we innovatively introduce the accelerometer’s output time series as the model input when training the temperature compensation model. We incorporate gated recurrent unit (GRU) and attention modules, proposing a novel GRU-MLP-attention model (GMAN) architecture. Simulation experiments demonstrate the effectiveness of our proposed fusion algorithm. After processing the accelerometer output signal through the RLMD-SE-TFPF denoising algorithm and the GMAN temperature drift compensation model, the acceleration random walk is reduced by 96.11%, with values of 0.23032 g/h/Hz for the original accelerometer output signal and 0.00895695 g/h/Hz for the processed signal.
... signal to calibrate the gravimeter, we determined that the acceleration sensitivity of the device is 15 μGal= ffiffiffiffiffiffi Hz p [29]. Allan deviation is a useful technique to investigate the stability of a device [31]. Figure 3 shows the experimental data in the time domain and the corresponding Allan deviation. ...
The precise measurement of the gravity of Earth plays a pivotal role in various fundamental research and application fields. Although a few gravimeters have been reported to achieve this goal, miniaturization of high-precision gravimetry remains a challenge. In this work, we have proposed and demonstrated a miniaturized gravimetry operating at room temperature based on a diamagnetic levitated micro-oscillator with a proof mass of only 215 mg. Compared with the latest reported miniaturized gravimeters based on microelectromechanical systems, the performance of our gravimetry has substantial improvements in that an acceleration sensitivity of 15 μGal/Hz and a drift as low as 61 μGal per day have been reached. Based on this diamagnetic levitation gravimetry, we observed Earth tides, and the correlation coefficient between the experimental data and theoretical data reached 0.97. Some moderate foreseeable improvements can develop this diamagnetic levitation gravimetry into a chip size device, making it suitable for mobile platforms such as drones. Our advancement in gravimetry is expected to facilitate a multitude of applications, including underground density surveying and the forecasting of natural hazards.
... Uncertainties in manometric mole fractions are based on the accuracy of the manometers (MKS Baratron) used to prepare the mixtures. Allan variance decreases at early times of the measurement due to the domination of thermal noise until reaching its minimum value at around 10 s [42], and later increases due to laser intensity fluctuations [41]. ...
A mid-infrared laser-based sensor is designed and demonstrated for trace detection of benzene, toluene, ethylbenzene, and xylene isomers at ambient conditions. The sensor is based on a distributed feedback inter-band cascade laser emitting near 3.29 µm and an off-axis cavity-enhanced absorption spectroscopy configuration with an optical gain of 2800. Wavelength tuning and a deep neural network (DNN) model were employed to enable simultaneous and selective BTEX measurements. The sensor performance was demonstrated by measuring BTEX mole fractions in various mixtures. At an integration time of 10 s, minimum detection limits of 11.4, 9.7, 9.1, 10, 15.6, and 12.9 ppb were achieved for benzene, toluene, ethylbenzene, m-xylene, o-xylene, and p-xylene, respectively. The sensor can be used to detect tiny BTEX leaks in petrochemical facilities and to monitor air quality in residential and industrial areas for workplace pollution.
... The Allan deviation [13] of the CsIII clock used, as determined by the reference, receiver was calculated. It renders bellow the specification limit of the 5071A clock (see to Fig. 1), which verifies the setup of the reference receiver. ...
A comparison between low-cost single-frequency and dual-frequency Global Navigation Satellite System (GNSS) receiver timing modules is presented, focusing on their suitability for time transfer applications. The study uses a zero-length baseline measurement approach to assess their performance and highlights the advantages of dual-frequency receivers. The clock comparison residuals between these low-cost devices and a reference receiver are analyzed. In particular, it is shown that the use of averages longer than 200s can effectively mitigate the quantization error inherent in pulse per second outputs of the timing modules. The results showcase sub-nanosecond time deviation instabilities between the reference receiver and the dual-frequency timing module. In contrast, the single-frequency module exhibits time deviations of 3.3ns at a one-day averaging interval. This research provides insights into the selection and utilization of GNSS timing modules for time transfer applications, where such modules can serve as attractive, cost-effective alternatives for applications requiring moderate accuracy.
... The Allan variance and/or deviation [44] is a statistical approach commonly used for noise identification and analysis in evaluating the frequency stability of crystal oscillators. The method has also been widely used to determine the intrinsic noise of inertial sensors, such as accelerometers and gyroscopes [45]. ...
This study involved synchronous observations of electromagnetic (EM) fields at both ground level (+ 22 m above sea level) and a depth of − 848 m within the Huainan Underground Laboratory, China. The primary objective was to assess how an underground environment influences the temporal and spatial variations in EM fields. A conductive cover acts as a low-pass filter as expected, resulting in the attenuation of high-frequency (> 1 Hz) EM fields in the underground laboratory. Specifically, these fields were attenuated by factors ranging from approximately 10-100 times compared to ground level fields. To analyze the data, a digit low-pass filter with a 1-Hz cutoff frequency was applied consistently to both ground and underground datasets. Notably, the underground data exhibited significantly lower levels of contamination from background noise. Additionally, the Allan variance analysis suggested favorable conditions for long-term stable observations in an underground environment. Ground level data exhibited diurnal disturbance noise associated with human activities, a characteristic absent in the underground data. In conclusion, our study suggests that employing a comprehensive approach that combines digital filtering and attenuation suppression holds the potential to yield cleaner EM fields when compared to traditional ground observations. These findings carry valuable implications for EM field research, highlighting the benefits of conducting observations in underground settings to enhance data quality and stability.
... Allan deviation plot has also been used to analyze the stability of the optical fiber-tip PTI gas sensor. Allan-Werle deviation analysis [12,13] was conducted with the noise data over a period of 2 hours, as shown in Fig. 4a. The result given in Fig. 4b shows that the NEC goes down to ~0.4 ppm C2H2 when the integration time is 440 s, which corresponds to a NEA of ~4.2×10 -7 cm -1 . ...
We report a miniature fiber-optic photothermal gas sensor based on a Fabry-Pérot
microcavity directly 3D μ-printed on the end-face of a standard single-mode optical fiber. A
detection limit of 0.4 parts-per-million for acetylene is demonstrated
... These contour plots offer an alternative representation of the minimum frequency fluctuation detectable by the device, which is more typically calculated using a single-mode Allan deviation; this is a measure of frequency stability involving the standard deviation of the differences of time-averaged fractional frequencies. 21 Importantly, the gap between samples required for the jump is automatically incorporated into this bootstrapping calculation, in contrast with the Allan deviation, which requires careful modification of the standard formula. The window length (the size of X and Y) can be fixed by choosing the value that minimizes the volume of these frequency fluctuation contours in N-dimensional space. ...
Recent years have seen explosive growth in miniaturized sensors that can continuously monitor a wide variety of processes, with applications in healthcare, manufacturing, and environmental sensing. The time series generated by these sensors often involves abrupt jumps in the detected signal. One such application uses nanoelectromechanical systems (NEMS) for mass spectrometry, where analyte adsorption produces a quick but finite-time jump in the resonance frequencies of the sensor eigenmodes. This finite-time response can lead to ambiguity in the detection of adsorption events, particularly in high event-rate mass adsorption. Here, we develop a computational algorithm that robustly eliminates this often-encountered ambiguity. A moving-window statistical test together with a feature-based clustering algorithm is proposed to automate the identification of single-event jumps. We validate the method using numerical simulations and demonstrate its application in practice using time-series data that are experimentally generated by molecules adsorbing onto NEMS sensors at a high event rate. This computational algorithm enables new applications, including high-throughput, single-molecule proteomics.
... Allan variance (AV) is a time-domain signal analysis method originally developed for oscillator stability studies [46][47][48]. Later, it was also adapted to analyze the stochastic drift properties of inertial sensors [23, [49][50][51]. ...
MEMS (micro-electro-mechanical system) gyroscopes and accelerometers are used in several applications. They are very popular due to their small size, low price, and accessibility. The design of MEMS accelerometers enables the measurement of vibrations, with frequencies from tenths of hertz to even 1 kHz. MEMS gyroscopes can be applied to measure angular rates, and indirectly also angular oscillations with frequencies similar to accelerometers. Despite significant stochastic errors, MEMS sensors are used not only in popular domestic appliances (e.g., smartphones) but also in safety-critical units, such as aeronautical attitude and heading reference systems (AHRSs). In engineering, methods of stochastic properties analysis are important tools for sensor selection, verification, and the design of measurement algorithms. In this article, three methods used for the analysis of stochastic properties of sensors are presented and comparative analyses are shown. The applied measurement frequencies (1 kHz) were much higher than those typically found in MEMS sensor applications. Additionally, an exemplary analysis of temperature drift frequency, as well as the possibility for the synthesis of complementary filter parameters with the use of the described methods, is shown. Assessment of the stochastic properties of MEMS accelerometers and gyroscopes was performed under both constant and variable temperature conditions (during warm-up after switching on) with the use of classic methods, such as power spectral density (PSD) and Allan variance (AV), as well as the less known but very promising generalized method of wavelet moments (GMWM).
... In order to go beyond the analysis of the noise power spectral density, we extract information from the feedback loop by analyzing the Allan deviation of the laser fractional frequency. Although the Allan deviation is still limited by amplitude noise for integration times below 3 ms, The Allan deviation of an oscillator's fractional frequency is a measure of its frequency instability [38]. We can extract the fractional frequency of the laser from the error signal as the latter is proportional to the frequency fluctuations of the laser, which allows it to be used to characterize the laser's short-term instability [39][40][41], as shown in Fig. 6 by the overlapping Allan deviation [42] of the laser's fractional frequency for averaging times ranging from 2.5 µs to 0.6 s. ...
We report laser frequency stabilization by the combination of modulation transfer spectroscopy and balanced detection of a relatively weak hyperfine transition of the R(158)25-0 line of molecular iodine (¹²⁷I2), which is used as a new frequency reference for laser trapping and cooling of ¹⁷⁴Yb on the ¹S0 − ³P1 transition. The atomic cloud is characterized by time-of-flight measurements, and an on-resonance optical depth of up to 47 is obtained. We show laser noise reduction and characterize the short-term laser frequency instability by the Allan deviation of the laser fractional frequency. The minimum measured value is 3.9 ×10⁻¹³ at 0.17 s of averaging time.
The International Celestial Reference Frame (ICRF) plays an important role in astronomy and geodesy. The realization of ICRF is based on the position of thousands of quasars observed using the Very-Long Baseline Interferometry (VLBI) technique. Better quality of ICRF is achieved when the position of the quasars is stable. In this study, we aim to analyze the stability of one of the quasars in ICRF called 4C31.61 (2201+315). We performed VLBI data analysis by using Vienna VLBI and Satellite Software (VieVS) to get the position of the quasar. We also used the data of the quasar’s position from the Paris Observatory Geodetic VLBI Center. We examined the stability of the quasar position by using the Allan standard deviation technique. We found that the quasar 4C31.61 (2201+315) has a stable position with the dominance of white noise across the majority of time scales.
In quantum technologies, it is essential to understand and exploit the interplay of light and matter. We introduce an approach creating and maintaining the coherence of four oscillators: a global microwave reference field, a polarization-gradient traveling-wave pattern of light, and the spin and motional states of a single trapped ion. Our method employs a UV light pattern capable of achieving a gigahertz-modulation bandwidth, here demonstrated in the megahertz regime, allowing for stroboscopic tracking of dynamic changes in phase space. We achieve noise floors of 1.8(2)nm for position and 8(2)zNµs for momentum observables, superresolving variations on timescales ≲100 ns. The implications of our findings contribute to enhancing quantum control and metrological applications.
Physics is living an era of unprecedented cross-fertilization among the different areas of science. In this perspective review, we discuss the manifold impact that state-of-the-art cold and ultracold-atomic platforms can have in fundamental and applied science through the development of platforms for quantum simulation, computation, metrology and sensing. We illustrate how the engineering of table-top experiments with atom technologies is engendering applications to understand problems in condensed matter and fundamental physics, cosmology and astrophysics, unveil foundational aspects of quantum mechanics, and advance quantum chemistry and the emerging field of quantum biology. In this journey, we take the perspective of two main approaches, i.e., creating quantum analogues and building quantum simulators, highlighting that independently of the ultimate goal of a universal quantum computer to be met, the remarkable transformative effects of these achievements remain unchanged. We wish to convey three main messages. First, this atom-based quantum technology enterprise is signing a new era in the way quantum technologies are used for fundamental science, even beyond the advancement of knowledge, which is characterised by truly cross-disciplinary research, extended interplay between theoretical and experimental thinking, and intersectoral approach. Second, quantum many-body physics is unavoidably taking center stage in frontier’s science. Third, quantum science and technology progress will have capillary impact on society, meaning this effect is not confined to isolated or highly specialized areas of knowledge, but is expected to reach and have a pervasive influence on a broad range of society aspects: while this happens, the adoption of a responsible research and innovation approach to quantum technologies is mandatory, to accompany citizens in building awareness and future scaffolding. Following on all the above reflections, this perspective review is thus aimed at scientists active or interested in interdisciplinary research, providing the reader with an overview of the current status of these wide fields of research where cold and ultracold-atomic platforms play a vital role in their description and simulation.
Optical fiber sensor emerges as a highly promising technology for trace gas detection due to their high sensitivity, remote capability, and immunity to electromagnetic interference. However, the state‐or‐the‐art fiber‐optic gas sensors typically use lengthy optical fibers as gas absorption cells or coatings with functional materials to achieve more sensitive gas detection, which poses challenges such as slow response and/or poor selectivity, as well as limitations on their use in confined spaces. Here, an ultraminiature optical fiber‐tip photothermal gas sensor via direct 3D micro‐printing of a Fabry‐Pérot cavity on the end face of a standard single‐mode optical fiber is reported. It enables not only direct interaction between light and gas molecules at the fiber output but also remote interrogation through an interferometric read‐out scheme. With a low‐finesse microcavity of 66 µm in length, a noise equivalent concentration of 160 parts‐per‐billion acetylene gas is demonstrated with an ultra‐fast response time of 0.5 s. Such a small high‐performance photothermal gas sensor offers an approach to remotely detecting trace gases for a myriad of applications ranging from in‐reactor monitoring to medical diagnosis.
Ammonia (NH3) toxicity, stemming from nitrification, can adversely affect aquatic life and influence the taste and odor of drinking water. This underscores the necessity for highly responsive and accurate sensors to continuously monitor NH3 levels in water, especially in complex environments, where reliable sensors have been lacking until this point. Herein, we detail the development of a sensor comprising a compact and selective analyzer with low gas consumption and a timely response based on photoacoustic spectroscopy. This, combined with an automated liquid sampling system, enables the precise detection of ammonia traces in water. The sensor system incorporates a state-of-the art quantum cascade laser as the excitation source emitting at 9 μm in resonance with the absorption line of NH3 located at 1103.46 cm–1. Our instrument demonstrated detection sensitivity at a low ppm level for the ammonia molecule with response times of less than 60 s. For the sampling system, an ammonia stripping solution was designed, resulting in a prompt full measurement cycle (6.35 min). A further evaluation of the sensor within a pilot study showed good reliability and agreement with the reference method for real water samples, confirming the potential of our NH3 analyzer for water quality monitoring applications.
Time and frequency measurement is among the most widely used types of measurement. Data on the exact time and the national time scale is in great demand among a variety of consumers, from commercial power metering systems, where the required synchronization accuracy is a few seconds, to space navigation systems, which require synchronization at the level of nanoseconds. In addition, consumer requirements for the accuracy of time and frequency measurement, as well as the efficiency of obtaining frequency and time data, are steadily increasing, which entails the need to modernize the means of reproducing, maintaining, and disseminating time and frequency units and the time scale. In order to meet the modern requirements of consumers for the accuracy of time and frequency measurement, technical means of reproducing, maintaining, and disseminating units have been introduced into GET 1‑2022 State Primary Standard for time and frequency units and the national time scale, which allow the contribution of GET 1‑2022 to the Coordinated Universal Time (UTC) to be significantly increased. The authors provide a brief overview of the composition of GET 1‑2022, perform a comparative analysis of the contribution of national time standards from different countries to UTC, as well as carry out an analysis of frequency instability and time scale shifts in the considered standards relative to UTC. It is shown that from September 2022 to March 2023, the contribution of GET 1‑2022 to UTC increased significantly and exceeded that of the standard of the U.S. Naval Observatory; presently, the contributions of these standards are comparable. According to such indicators as frequency instability and average contribution to UTC, the atomic standards comprising GET 1‑2022 are significantly superior to similar instruments included in the national standards of other countries. The national coordinated time scale of the Russian Federation UTC(SU) was found to be one of the best national UTC realizations, while the national atomic time scale TA(SU) holds the leading position in terms of stability among the time scales realized by leading foreign time laboratories.
In recent years, fiber-based frequency dissemination has attracted widespread attention. A phase-locked loop (PLL) on the transmitter side (TX) is used to compensate for the phase noise caused by the environmental disturbance (PNE). However, the phase noise caused by transfer delay (PNT) cannot be suppressed. A clean PLL on the receiver side (RX) is used to improve the phase noise of the received signal. Consequently, the performance of PLLs on both sides significantly impacts the phase noise of the final recovered signal. Empirical configurations of PLL parameters often fail to achieve optimal results. In this paper, a phase noise control method is proposed and demonstrated. Through analyzing the PNT, PNE, and phase noise margin of the recovered signal, we optimally configure the PLL parameters at the TX and RX. In this way, the PNT is effectively suppressed and the compensation capability for the PNE is evaluated. By comparing the anthropogenic noise in different environments and the compensation capability of the system, this analysis can provide a reference for the construction of large-scale time-frequency networks.
This work conducts a thorough comparison between two temperature compensation methods for resonant MEMS sensors, i.e. (1) a newly proposed in-situ temperature compensation technique based on a multiple parameter decoupling (MPD) using a single resonant MEMS sensor subject to blue-sideband excitation (BSE), and (2) the prevailing method utilizing a temperature sensor, which, in this work, is a resonant thermometer in close vicinity of the sensor. Experimental results show that the MPD-based in-situ temperature compensation method offers better noise performance, long-term stability (4-fold at 1000s integration time) and application simplicity, compared to the compensation method using an additional thermometer, affirming that the proposed subject is of considerable potential for true in-situ temperature compensation for high-precision resonant MEMS sensors.
Complex architectures for wireless communications, digital electronics and space-based navigation interlink several oscillator-based devices such as clocks, transponders and synthesizers. Estimators characterizing their stability are critical for addressing the impact of random fluctuations (noise) on the overall system performance. Manufacturers typically specify this as an Allan/Hadamard Variance (AVAR/HVAR) profile in the
time
domain. However, stochastic processes constituting the noise are more thoroughly described in the
frequency
domain by the power spectral density function (PSD). Both are second-moment measures of the time series, but it is only possible to translate unambiguously
from
the PSD
to
the AVAR/HVAR, not vice versa, except in the case of a single noise type, a rather unrealistic case. This note presents an analytical method to generate an approximated PSD expressed as a set of power-laws defined in specific intervals in the frequency domain, starting from an AVAR/HVAR expressed as a set of power-laws in the time domain. The proposed algorithm is straightforward to implement, applicable to all noise types (and combinations thereof) and can be self-validated by reconstructing the corresponding AVAR/HVAR by direct computation. Coupling with well-established algorithms relying on the PSD for power-law noise generation [18], the ensuing method encompasses the capability for generating multi-colored noise in end-to-end simulations, as demonstrated hereby for NASA’s Deep Space Atomic Clock. We also report on the limitations of the algorithm and analytical expressions of the continuous version of the algorithm.
Optical absorption spectroscopy is a widely used method for gas detection, with many different applications in physics, chemistry, biology, environmental science, etc. Recent developments in mid‐infrared supercontinuum sources have opened up new possibilities for trace gas detection in these research fields. Supercontinuum sources have a wide spectral range (spectral coverage of a lamp), a high light intensity, and a high spatial coherence (directionality of a laser). The wide coverage enables to detect gases in complex gas mixtures, while the directionality allows a long path length through the gas sample, thereby improving the sensitivity for specific gases. After a short historical overview and background on the generation of supercontinuum light, attention is focused on the combination of supercontinuum sources, gas cells, and spectroscopic detection systems, to achieve an optimal detection limit and selectivity for gasses. The main methods for improving the signal‐to‐noise ratio ( SNR ) and detection sensitivity of gases are discussed. Applications are described with examples of the detection of gaseous pollutants in the atmosphere, postharvest physiology, and plasmas analysis.
We report a miniature fiber-optic photothermal gas sensor based on a Fabry-Pérot microcavity directly 3D µ-printed on the end-face of a standard single-mode optical fiber. A detection limit of 0.4 parts-per-million for acetylene is demonstrated.
Measurement of time and frequency is one of the most widespread types of measurements, information on the exact value of time, on the national time scale is extremely in demand by a wide variety of consumers, ranging from commercial electricity metering systems, where the required synchronization accuracy is a few seconds, to space navigation systems that impose requirements on synchronization at the level of units of nanoseconds. At the same time, consumer requirements for the accuracy of time and frequency measurements, as well as for the efficiency of obtaining time-frequency information, are steadily growing, which entails the need to modernize the means of reproducing, storing and transmitting units of time, frequency and time scale. To meet modern consumer requirements for the accuracy of time and frequency measurements, technical means of reproduction, storage and transmission of units have been introduced into the State primary standard of units of time, frequency and national time scale GET 1-2022, allowing to significantly increase the contribution of GET 1-2022 to the formation of the coordinated universal timescale UTC. A brief overview of the composition of GET 1-2022 is given, a comparative analysis of the contribution of time standards to the formation of the UTC timescale is carried out, as well as an analysis of the shifts of the time scales of the standards relative to UTC and the instability of the frequency standards. It is shown that from September 2022 to March 2023, the contribution of GET 1-2022 to the formation of the UTC increased significantly and exceeded that of the US Naval Observatory standard, and currently the contributions of these standards are comparable. In terms of frequency instability and average contribution to the formation of UTC, the atomic standards of GET 1-2022 are significantly superior to similar standard instruments from other countries. It has been established that the national coordinated time scale UTC(SU) is one of the best national implementations of UTC, and the national atomic time scale TA(SU) occupies a leading position among the time scales of leading foreign time laboratories in terms of instability.
This article provides an overview of laser-based absorption spectroscopy applications and discusses the parameter space and requirements of laser systems for each of these applications, with a special emphasis on frequency comb systems. We walk the reader through the basics of laser absorption spectroscopy, review common line-broadening mechanisms as fundamental challenges to precision spectroscopy, look into established solutions, introduce frequency-comb-based absorption spectroscopy, and suggest a novel approach to broadband precision spectroscopy in the mid-infrared spectral region based on a combination of broadband high-power ultra-stable optical frequency combs, crystalline supermirror technology, and an instrumental line-shape-free measurement technique. We conclude after an introduction of noise sources and their implications for precision measurements with an in-depth discussion and overview of the current state-of-the-art laser and optical parametric frequency conversion technologies.
A cross-correlation technique for measuring the very short-term (milliseconds to seconds) properties of stable oscillators is described. Time-dependent functions representing signals from two separate oscillators are led to a function multiplier where the instantaneous product of the functions is made. The oscillators are either set to a given phase relation or allowed a small relative drift so that a slow beat frequency is observed. Short-term fluctuations superimposed upon the slow beat signal from the multiplier output will represent the instantaneous phase difference between the oscillators when the inputs are in quadrature. When the inputs are in and out of phase, the fluctuations represent amplitude fluctuations. The time averaging function is determined by a filter having a rectangular pass band from nearly zero frequency to a cutoff frequency v c . The mean square frequency deviation measured in a bandwidth ω c is obtained by differentiating, filtering, squaring, and averaging the signal from the function multiplier data being taken when the input signals are in quadrature. Mean square averages of amplitude and phase averaged over various bandwidths ω c may be obtained by bypassing the differentiator. Sample data from measurements on hydrogen masers are presented, and the effect of thermal noise is seen to be the major factor limiting the short-term frequency stability of the signals.
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Precision quartz oscillators have three main sources of noise contributing to frequency fluctuations: thermal noise in the oscillator, additive noise contributed by auxiliary circuitry such as AGC, etc., and fluctuations in the quartz frequency itself as well as in the reactive elements associated with the crystal, leading to an f<sup>-1</sup>type of power spectral density in frequency fluctuations. Masers are influenced by the first two types of noise, and probably also by the third. The influence of these sources of noise on frequency fluctuation vs. averaging time measurements is discussed. The f<sup>-1</sup>-spectral density leads to results that depend on the length of time over which the measurements are made. An analysis of the effects of finite observation time is given. The characteristics of both passive and active atomic standards using a servo-controlled oscillator are discussed. The choice of servo time constant influences the frequency fluctuations observed as a function of averaging time and should be chosen for best performance with a given quartz oscillator and atomic reference. The conventional methods of handling random signals, i.e., variances, autocorrelation, and spectral densities, are applied to the special case of frequency and phase fluctuations in oscillators, in order to obtain meaningful criteria for specifying oscillator frequency stability. The interrelations between these specifications are developed in the course of the paper.
Since most systems that generate atomic time employ quartz crystal oscillators to improve reliability, it is essential to determine the effect on the precision of time measurements that these oscillators introduce. A detailed analysis of the calibration procedure shows that the third finite difference of the phase is closely related to the clock errors. It was also found, in agreement with others, that quartz crystal oscillators exhibit a "flicker" or |ω|<sup>-1</sup>type of noise modulating the frequency of the oscillator. The method of finite differences of the phase is shown to be a powerful means of classifying the statistical fluctuations of the phase and frequency for signal generators in general. By employing finite differences it is possible to avoid divergences normally associated with flicker noise spectra. Analysis of several cesium beam frequency standards have shown a complete lack of the |ω|<sup>-1</sup>type of noise modulation.
08-64-01. See also, P. Karta-schoff Shot-effect influence on the frequency of an oscillator Definition and Measurement of Short-Term Frequency Stability, locked to an atomic beam resonator The am-Van Sostrand. monia beam maser as a standard of frequency
- L S R H Switzerland
Switzerland, Rapport L.S.R.H. 08-64-01. See also, P. Karta-schoff, " Shot-effect influence on the frequency of an oscillator Definition and Measurement of Short-Term Frequency Stability, locked to an atomic beam resonator, 1964 Proc. Symp. on the [IO] A. A. Vuylsteke, Elements of Maser Themy. Princeton, N. 1.: Ill] J. A. Barnes, D. \X7. Allan, and A. E. Wainwright, " The am-Van Sostrand. monia beam maser as a standard of frequency, " IRE Trans. on Instrumentation, vol. 1-11, pp. 26-30, June 1962.