Spectroscopic techniques are increasingly used for field laser applications in industry and research. Under field conditions complex gas sensors cannot be considered as stable and therefore drift characterization is a key issue to distinguish between sample data and sensor drift. In this paper the history of von Neumann’s two-sample variance and Allan variance stability investigations in the field of frequency metrology and the relationship to wavelet analysis are reviewed. The concept has been used to characterize accuracy and precision of spectroscopic data in the time domain and practical guidelines for the interpretation of σ/τ plots are presented. Two topics relevant for spectroscopic measurements are discussed: First, the optical fringe effect, which is present in any spectrometer, limits the precision and accuracy of spectroscopic measurements by forming time dependent background structures superimposed to the signal under investigation. The two-sample variance is used to characterize optical etalons and long-term drift using σ/τ plots. Second, the short-term instrument stability characteristic in the presence of atmospheric turbulence is discussed. This is important for laser-based gas monitors measuring the turbulent transport of trace gases between the biosphere and the atmosphere using the eddy-covariance technique. It will be shown how the spectral characteristics of turbulence in the Kolmogorov inertial subrange can be identified in the time domain and how the effect of optical fringes can be separated from atmospheric signals.

Accuracy and precision of laser spectrometers for trace gas sensing in the presence of optical fringes and atmospheric turbulence

The advent of quantum cascade lasers has provided matured continuously tunable solid state laser sources emitting from mid-infrared to terahertz wavelengths. Such sources, used as local oscillators, offer the practical prospect of aircraft, high altitude platform, and satellite deployment of compact and shot noise limited heterodyne radiometers for Earth observation and astronomy. A ground-based prototype of a quantum cascade laser heterodyne radiometer operating in the mid-infrared has been developed and is presented. The instrument design and concepts are described, together with evaluation of the instrument in the laboratory and during field measurements of atmospheric ozone. In this study the best performance achieved by the prototype quantum cascade laser heterodyne radiometer was a signal-to-noise ratio of three times the theoretical shot-noise limit. The prototype has allowed the main sources of excess noise to be identified as residual optical feedback in the local oscillator optical path and a lack of mechanical and thermal stability in the local oscillator collimation system. Instrument improvements are currently being implemented and enhanced performance is expected in the near future.

Ground-based prototype quantum cascade laser heterodyne radiometer for atmospheric studies

We present the connection of two programmable Josephson arrays generating synchronous waveforms to measure impedance ratios?the Josephson two-terminal-pair impedance bridge. This approach is more flexible than conventional bridges at the same level of uncertainty. The Josephson bridge can measure over a wider frequency range, over a wider range of impedance ratios than conventional two-terminal-pair bridges. Furthermore, the phase angle between the two impedances can take any value. As a first application, we present measurements of a 1?:?1 resistance ratio at the 10?k? level in the frequency range between 25?Hz and 10?kHz. The uncertainties are better than a few parts in 108 and hence comparable to those of conventional impedance bridges. Quantization at up to 10?kHz was confirmed by varying the bias current of the Josephson arrays, resulting in constant resistance ratios within the measurement resolution.

https://iopscience.iop.org/article/10.1088/0026-1394/47/4/011/pdf

The Josephson two-terminal-pair impedance bridge

Stochastic errors characterize the performance of inertial sensors and indicate the potential improvements of the device. Accurate modeling of these errors can enhance the performance of inertial navigation system. The simplest and generally adopted method to model stochastic errors of inertial sensor is the normal nonoverlapped Allan variance, but its estimation accuracy decreases in long cluster time. The fully overlapping Allan variance improves the estimation accuracy in long cluster time very much, while the traditional total variance based on maximal-overlapping cluster samples further increases the estimation accuracy in long cluster time greatly. However, with these two methods, better estimation is achieved at the expense of much longer computation time. Besides, the computation burden for large dataset and many variance data points is extremely large, while the inertial sensors need large dataset with many variance data points to fully characterize their stochastic errors. This is because the correlation time for some stochastic error is very long (e.g., the correlation time is 3 h for rate random walk), and the Allan variance curve of some stochastic error is very complicated (e.g., sinusoidal noise). Consequently, the fully overlapping Allan variance and the traditional total variance are not suitable for inertial sensor stochastic error modeling. This paper proposes a not fully overlapping Allan variance which has similar estimation accuracy to fully overlapping Allan variance, and whose calculation time is greatly reduced relative to fully overlapping Allan variance. Then, the not fully overlapping concept is integrated to that of total variance to further improve the estimation accuracy in long cluster time with respect to Allan variance, and the calculation time of total variance is greatly reduced as well. This method enables high accuracy and high computational efficiency of Allan variance analysis at the same time, especially for large dataset and many variance data points analysis. Finally, the proposed methods are applied to 12-hour static data of gyroscopes and accelerometers from a position and orientation system, and their advantages are demonstrated.

Not Fully Overlapping Allan Variance and Total Variance for Inertial Sensor Stochastic Error Analysis

Gyro north finders have been widely used in maneuvering weapon orientation, oil drilling and other areas. This paper proposes a novel Micro-Electro-Mechanical System (MEMS) gyroscope north finder based on the rotation modulation (RM) technique. Two rotation modulation modes (static and dynamic modulation) are applied. Compared to the traditional gyro north finders, only one single MEMS gyroscope and one MEMS accelerometer are needed, reducing the total cost since high-precision gyroscopes and accelerometers are the most expensive components in gyro north finders. To reduce the volume and enhance the reliability, wireless power and wireless data transmission technique are introduced into the rotation modulation system for the first time. To enhance the system robustness, the robust least square method (RLSM) and robust Kalman filter (RKF) are applied in the static and dynamic north finding methods, respectively. Experimental characterization resulted in a static accuracy of 0.66° and a dynamic repeatability accuracy of 1°, respectively, confirming the excellent potential of the novel north finding system. The proposed single gyro and single accelerometer north finding scheme is universal, and can be an important reference to both scientific research and industrial applications.

A Novel MEMS Gyro North Finder Design Based on the Rotation Modulation Technique.

When analyzing nanovoltmeter measurements, stochastic serial correlations are often ignored and the experimental standard deviation of the mean is assumed to be the experimental standard deviation of a single observation divided by the square root of the number of observations. This is justified only for white noise. This paper demonstrates the use of the power spectrum and the Allan variance to analyze data, identify the regimes of white noise, and characterize the performance of digital and analog DC nanovoltmeters. Limits imposed by temperature variations, 1/f noise and source resistance are investigated.

Using the Allan variance and power spectral density to characterize dc nanovoltmeters

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Using the Allan variance and power spectral density to characterize dc nanovoltmeters