Allan Variance Research Articles

Miniaturization study on helmholtz-based photoacoustic cell for PAS-based trace gas detection

In this study, the acoustic behavior and gas flow noise in a Helmholtz photoacoustic cell were simulated and optimized to study the influence of the cell dimensions and buffer structure. Numerical analysis using finite element analysis and experimental validation were performed in this study. A spindle-type photoacoustic cell with a resonator volume of 0.5 mL and buffer volume of 0.4 mL was selected for CH4 detection. Besides its strong photoacoustic enhancement, the spindle-type buffer structure has the best ability to eliminate flow noise compared to the other buffer structures. A linearity of 0.9992 was achieved over a wide concentration range of 0–10000 ppm in the CH4 measurement experiment. The 1σ equivalent detection limit for a response time of 10 s was measured to be 0.49 ppm. Allan deviation analysis indicated that a minimum detection limit of 17.9 ppb can be achieved by extending the integration time to 4760 s.

Modelling inertial measurement unit error parameters for an unmanned air vehicle

This paper demonstrates a study that focuses on the modeling, design, and realization of an Inertial Measurement Unit (IMU) component for the use of Unmanned Aerial Vehicles (UAV). The experimental data is obtained by multiple flights conducted by the realized UAV (Teknofest–SEMRUK team UAV). The structure is remodeled for increasing the accuracy, and performance of the UAV after the conducted flights. Noise parameters are estimated throughout the Allan variance analysis. MEMS technology-based capacitive-type accelerometers and gyroscopes are preferred. This paper also discusses the error types and compares the real data with the modeled simulation data. Systematic errors of the inertial sensors are simulated according to their datasheet parameters. Sensor filters and noise are modeled and they are also implemented in the simulation. Simulation results and UAV measurements are compared to observe the efficiency of modeling. A complementary filter is presented and combined with a magnetometer, accelerometer, and gyroscope to obtain the ultimate design. The comparison showed a satisfactory agreement among the complementary filter measurements and UAV measurements in the stable position and the results presented.

Optical frequency dissemination via 103-km urban fiber link with remote passive phase stabilization.

In this paper, we propose a technique for a fiber-based optical frequency dissemination system with remote passive phase noise cancellation. At the remote site, a 1×2 fiber pigtailed acousto-optic modulator (AOM) with two diffraction order outputs (0 and -1 order) is employed as the phase-compensated device, the undesired phase noise of fiber link introduced by environmental perturbations are passively canceled at remote sites. Different from other existing schemes, the proposed technique harnesses the benefits of remote radio frequency (RF) independence and low-temperature sensitivity in this noise-suppression configuration. Consequently, the system noise floor of the proposed optical frequency dissemination system achieves 9.44 × 10-21 without requiring a precise remote RF reference, and the phase-temperature coefficient is reduced to about 2 fs/K. A real-world experiment is conducted over a noisy round-trip 103 km urban fiber link. After being passively compensated, we demonstrate a fractional frequency instability of 1.57 × 10-14 at the integration time of 1 s and scales down to 3.96 × 10-20 at 10,000 s in terms of modified Allan deviation. The frequency uncertainty of the retrieved light after transferring through this noise-compensated fiber link relative to that of the input light achieves 1.80 × 10-18. This work demonstrates the system's capability to disseminate the ultra-stable optical frequency standards and is a significant step towards realizing multi-node dissemination of the state-of-the-art optical clock signal with remote noise compensation via a tree-like topology fiber network.

Simultaneous measurement of 13C-,18O-, and 17O- isotopes of CO2 using a compact mid-infrared hollow waveguide gas sensor

A compact gas sensor has been developed for the first time employing a quantum cascade laser (QCL) with a central wavelength of 4.32 μm, combined with direct absorption spectroscopy technology and a hollow waveguide. The sensor could measure the concentrations of four isotopic molecules (16O12C16O, 18O12C16O, 16O13C16O, and 17O12C16O) in CO2 gas simultaneously, thereby obtaining the relative isotope ratios of δ13C, δ18O, and δ17O. By adjusting the incident light path, the anomalous absorption peaks in the system have been effectively suppressed, and a compact feedback function generator has been integrated to ensure control of the laser output wavelength to eliminate the loss of measurement precision caused by wavelength fluctuations. Under the two conditions of free-running and wavelength-controlled, a standard CO2 sample with a concentration of 5 % was measured continuously. The results showed that under wavelength-controlled conditions, the precision of the four isotopic molecule concentration measurements was improved by a minimum of 1.8 times, and the measurement precision could be further improved after filtering. According to the Allan variance analysis, the detection precision for δ13C, δ18O, and δ17O were 0.7 ‰, 0.62 ‰, and 1.58 ‰, respectively, at the optimal integration time of 98 seconds. This study has the potential for respiratory diagnosis to detect simultaneously the values of δ13C, δ18O, and δ17O in exhaled samples.

Влияние смены оборудования пулковской ГНСС-станции PULK на результаты наблюдений

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.

Erratum to “Thin-Film Silicon MEMS for Dynamic Mass Sensing in Vacuum and Air: Phase Noise, Allan Deviation, Mass Sensitivity and Limits of Detection”

Erratum to “Thin-Film Silicon MEMS for Dynamic Mass Sensing in Vacuum and Air: Phase Noise, Allan Deviation, Mass Sensitivity and Limits of Detection”

A frequency servo SoC with output power stabilization loop technology for miniaturized atomic clocks

A frequency servo system-on-chip (FS-SoC) featuring output power stabilization technology is introduced in this study for high-precision and miniaturized cesium (Cs) atomic clocks. The proposed power stabilization loop (PSL) technique, incorporating an off-chip power detector (PD), ensures that the output power of the FS-SoC remains stable, mitigating the impact of power fluctuations on the atomic clock's stability. Additionally, a one-pulse-per-second (1PPS) is employed to synchronize the clock with GPS. Fabricated using 65 nm CMOS technology, the measured phase noise of the FS-SoC stands at −69.5 dBc/Hz@100 Hz offset and −83.9 dBc/Hz@1 kHz offset, accompanied by a power dissipation of 19.7 mW. The Cs atomic clock employing the proposed FS-SoC and PSL obtains an Allan deviation of 1.7 × 10−11 with 1-s averaging time.

Microcontroller Based Evaluation of Voltage Regulators Efficiency and Their Noise Performance Estimation by Fast Allan Variance Method

Microcontroller Based Evaluation of Voltage Regulators Efficiency and Their Noise Performance Estimation by Fast Allan Variance Method

Perovskite photodetector-based laser absorption spectroscopy for gas detection

A gas detection method based on CH3NH3PbI3 (MAPbI3) and poly (3,4-ethylenedioxythiophene): poly (4-styrene sulfonate) (PEDOT:PSS) composite photodetectors (PDs) is proposed. The operation of the PD primarily relies on the photoelectric effect within the visible light band. Our study involves constructing a gas detection system based on tunable diode laser spectroscopy (TDLAS) and MAPbI3/PEDOT:PSS PD, and O2 was selected as the target analyte. The system has achieved a minimum detection limit (MDL) of 0.12% and a normalized noise equivalent absorption coefficient (NNEA) of 8.83 × 10−11 cm-1⋅W⋅Hz-1/2. Furthermore, the Allan deviation analysis results indicate that the system can obtain sensitivity levels as low as 0.058% over an averaging time of 328 seconds. This marks the first use of MAPbI3/PEDOT:PSS PD in gas detection based on TDLAS. Despite the detector's performance leaves much to be desired, this innovation offers a new approach to developing spectral based gas detection system.

Spectrum feature extraction method combining Allan variance, VMD, and PSD

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.

Transferring time and frequency signal through phase compensated telecommunication fibres

Precise time and frequency signal transfer over White Rabbit Precision Time Protocol (WRPTP) based underground optical fibre link has been experimentally demonstrated for its potential enhancement and better signal integrity. In order to prove its advantages in practical applications, the time synchronization performance of WRPTP-based underground telecommunication optical fibre links have been examined in controlled environment conditions as well as in varying ambient conditions. Under controlled environment conditions, time synchronization has been achieved within ± 100 ps uncertainty but variation in ambient conditions degrades the stability as well accuracy of the time transfer link. The introduction of active phase variation compensation enhances the accuracy by ∼ 66 % of the WRPTP-based underground time transfer link. The link’s instability in terms of Modified Allan deviation reaches to 2.0 E -15 from 7.5 E -15 at 4096 s of integration time which indicate that dynamic phase variation compensation improves the stability of WRPTP-based time transfer link under varying ambient conditions.

Quasi-distributed quartz enhanced photoacoustic spectroscopy sensing based on hollow waveguide micropores.

In this Letter, a quasi-distributed quartz enhanced photoacoustic spectroscopy (QEPAS) gas sensing system based on hollow waveguide micropores (HWGMP) was reported for the first time, to the best of our knowledge. Three micropores were developed on the HWG to achieve distributed detection units. Three self-designed quartz tuning forks (QTFs) with low resonant frequency of 8.7 kHz were selected as the acoustic wave transducer to improve the detection performance. Compared with micro-nano fiber evanescent wave (FEW) QEPAS, the HWGMP-QEPAS sensor has advantages such as strong anti-interference ability, low loss, and low cost. Acetylene (C2H2) was selected as the target gas to verify the characteristics of the reported sensor. The experimental results showed that the three QTFs almost had the same sensing ability and possessed an excellent linear concentration response to C2H2. The minimum detection limits (MDLs) for the three QTFs were determined as 68.90, 68.31, and 66.62 ppm, respectively. Allan deviation analysis indicated that the system had good long-term stability, and the MDL can be improved below 3 ppm in an average time of 1000 s.

Method for measuring non-stationary motion attitude based on MEMS-IMU array data fusion and adaptive filtering

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.

Transient long-range distance measurement by a Vernier spectral interferometry

Rapid and long-range distance measurements are essential in various industrial and scientific applications, and among them, the dual-comb ranging system attracts great attention due to its high precision. However, the temporal asynchronous sampling results in the tradeoff between frame rate and ranging precision, and the non-ambiguity range (NAR) is also limited by the comb cycle, which hinders the further advancement of the dual-comb ranging system. Given this constraint, we introduce a Vernier spectral interferometry to improve the frame rate and NAR of the ranging system. First, leveraging the dispersive time-stretch technology, the dual-comb interferometry becomes spectral interferometry. Thus, the asynchronous time step is unlimited, and the frame rate is improved to 100 kHz. Second, dual-wavelength bands are introduced to implement a Vernier spectral interferometry, whose NAR is enlarged from 1.5 m to 1.5 km. Moreover, this fast and long-range system also demonstrated high precision, with a 22.91-nm Allan deviation over 10-ms averaging time. As a result, the proposed Vernier spectral interferometry ranging system is promising for diverse applications that necessitate rapid and extensive distance measurement.

A Faraday laser locked to 87Rb D2 line

We present a single-frequency Faraday laser utilizing a 5-Torr-Ar-mixed 85Rb atomic filter as a frequency-selecting element, and lock it to 87Rb D2 line via modulation transfer spectroscopy (MTS). The wavelength of the free-running Faraday laser fluctuated between 780.2457 and 780.2470 nm, which was limited within the ultra-narrow transmission bandwidth (700 MHz) of the atomic filter. When the Faraday laser was stabilized to 87Rb 52S1/2 F = 2 → 52P3/2 F′ = 3 hyperfine transition line, the output wavelength of the laser was approximately 780.24602 nm, and the fractional frequency Allan deviation measured by residual error signal arrived at 2.87 × 10−14 at 1 s, then reached 1.25 × 10−14 at 100 s. The laser system is easy to be locked to 87Rb D2 line within the current range of laser diode (LD) from 75 to 140 mA, which has the potential to achieve a “turnkey” systems and is suitable for laser-pumped rubidium atomic clocks and laser-cooling experiments.

High-Sensitivity Differential Helmholtz Photoacoustic System Combined with the Herriott Multipass Cell and Its Application in Seed Respiration.

A highly sensitive photoacoustic detection system using a differential Helmholtz resonator (DHR) combined with a Herriott multipass cell is presented, and its implementation to sub-ppm level carbon dioxide (CO2) detection is demonstrated. Through the utilization of erbium-doped optical fiber amplifier (EDFA), the laser power was amplified to 150 mW. Within the multipass cell, a total of 22 reflections occurred, contributing to an impressive 33.6 times improvement in the system sensitivity. The normalized noise equivalent absorption coefficient (NNEA) was 8.64 × 10-11 cm-1·W·Hz-1/2 [signal-to-noise ratio, (SNR) = 1] and according to the Allan variance analysis, a minimum detection limit of 500 ppb could be achieved for CO2 at 1204 s, which demonstrates the long-term stability of the system. The system was applied to detect the respiration of rice and upland rice seeds. It is demonstrated that the system can monitor and distinguish the respiration intensity and respiration rate of different seeds in real time.

Multiple-access ultrastable frequency dissemination based on optical frequency combs via a fiber link.

We demonstrate an optical fiber-based, multiple-access frequency transmission using two optical frequency combs. The experimental results using the Allan deviation analysis show that with the phase compensation technique, the frequency instabilities at the remote site are 8.7 × 10-15/1 s and 1.0 × 10-17/103 s, and at the accessing node along the fiber link, the frequency instabilities are 6.9 × 10-15/1 s and 1.1 × 10-17/103 s. Similarly, the power spectral density of phase noise was analyzed in the frequency domain. These experimental results demonstrate that the compensation scheme improved the performance by two to three orders of magnitude. Thus, the proposed frequency transmission technique has potential application for disseminating ultrastable frequency references in the optical fiber network.

Long-wave infrared pulsed external-cavity QCL spectrometer using a hollow waveguide gas cell

A spectrometer built using an external cavity pulsed quantum cascade laser is described. The spectrometer has a tuning range from 10 – 13 µm (1,000 – 769 cm−1) and is designed to target volatile organic compounds (VOCs) which often exhibit water-free molecular absorption within the region. The spectrometer utilizes a hollow silica waveguide gas cell which has an internal volume of a few millilitres, a fast response time (∼1 s), and is advantageous when only low sample volumes, similar to the cell volume, are available. Propane is used as a test gas because it is easy to handle, and its spectral profile is comparable to VOCs of interest. Its absorption in the region is primarily within the ν21 band which spans from 10.55 – 11.16 µm (948 – 896 cm−1). Spectral measurements at a range of concentrations show good linearity and an Allan deviation of absorbance values recorded over a 100-minute period indicates a minimum detectable absorbance of 3.5×10−5 at an integration time of 75 s.

MEMS Gyroscope Temperature Compensation Based on Improved Complete Ensemble Empirical Mode Decomposition and Optimized Extreme Learning Machine.

Herein, we investigate the temperature compensation for a dual-mass MEMS gyroscope. After introducing and simulating the dual-mass MEMS gyroscope's working modes, we propose a hybrid algorithm for temperature compensation relying on improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), sample entropy, time-frequency peak filtering, non-dominated sorting genetic algorithm-II (NSGA II) and extreme learning machine. Firstly, we use ICEEMDAN to decompose the gyroscope's output signal, and then we use sample entropy to classify the decomposed signals. For noise segments and mixed segments with different levels of noise, we use time-frequency peak filtering with different window lengths to achieve a trade-off between noise removal and signal retention. For the feature segment with temperature drift, we build a compensation model using extreme learning machine. To improve the compensation accuracy, NSGA II is used to optimize extreme learning machine, with the prediction error and the 2-norm of the output-layer connection weight as the optimization objectives. Enormous simulation experiments prove the excellent performance of our proposed scheme, which can achieve trade-offs in signal decomposition, classification, denoising and compensation. The improvement in the compensated gyroscope's output signal is analyzed based on Allen variance; its angle random walk is decreased from 0.531076°/h/√Hz to 6.65894 × 10-3°/h/√Hz and its bias stability is decreased from 32.7364°/h to 0.259247°/h.

Analysis of short-term polarization stability using Allan variance

The application of Allan variance to characterize the stability of optical signals affected by stochastic polarization fluctuations and the identification of the underlying power law noise processes is explored. Allan variance can ease the comparison regarding polarization stability of optical systems affected by polarization noise and define a near-optimum integration interval to reveal trends. Examples of the application of Allan variance to optical systems with stable polarization conditions show that white noise and random walk terms can be observed. Additionally, experiments show that the three Stokes parameters can exhibit different statistical behaviors in the Brownian-noise regime. Allan analysis can easily be used to define, in real-time systematically, the denoising strategy in polarization-based sensing and for the optimization of polarization-sensitive optical systems instead of the conventional approach relying on heuristics or information criteria.