Low Measurement Uncertainty Research Articles

Bayesian weak lensing tomography: Reconstructing the 3D large-scale distribution of matter with a lognormal prior

We present a Bayesian reconstruction algorithm that infers the three-dimensional large-scale matter distribution from the weak gravitational lensing effects measured in the image shapes of galaxies. The algorithm is designed to also work with non-Gaussian posterior distributions which arise, for example, from a non-Gaussian prior distribution. In this work, we use a lognormal prior and compare the reconstruction results to a Gaussian prior in a suite of increasingly realistic tests on mock data. We find that in cases of high noise levels (i.e. for low source galaxy densities and/or high shape measurement uncertainties), both normal and lognormal priors lead to reconstructions of comparable quality, but with the lognormal reconstruction being prone to mass-sheet degeneracy. In the low-noise regime and on small scales, the lognormal model produces better reconstructions than the normal model: The lognormal model 1) enforces non-negative densities, while negative densities are present when a normal prior is employed, 2) better traces the extremal values and the skewness of the true underlying distribution, and 3) yields a higher pixel-wise correlation between the reconstruction and the true density.

Micro-displacement reconstruction using a laser self-mixing grating interferometer with multiple-diffraction.

In this paper, we demonstrated an improved laser self-mixing grating interferometer (SMGI) with auto-collimation design which can avoid the disturbance from the light feedback of the zero-order diffraction beam. In order to obtain higher optical subdivision, SMGI with multiple-diffraction is implemented. Both theoretical analysis and experimental work show that the proposed system for displacement measurement can achieve high sensitivity and low measurement uncertainty. Using the proposed system, different forms of micro-displacement signals applied on the target (grating) have been reconstructed with accuracy of a few nanometers. The work presented in this paper provides a good way to achieve robust and high precision measurement with compact system configuration.

The use of the photogrammetric method for measurement of the repose angle of granular materials

The paper addresses a vitally important issue of precise determination of the angle of repose of granular materials. For calculation of the said angle, a photogrammetric 3D coordinate measurement method has been proposed. With the view of method verification, 600 independent measurement results were obtained, based on which the angle of repose of examined plant granular materials (triticale) was determined with a statement of the associated measurement uncertainty. The conducted analysis has shown that the proposed method is useful and capable of low (as for biological materials) measurement uncertainty congruent with the requirements of automated systems, and as such may be helpful in laying down the standard specification for measuring of the angle of repose, using coordinate metrology.

Comparison between matrix method, equation method and full air-buoyancy correction method for dissemination of microgram weights

Over the past 9 years since 2007, there has been growing interest in the field of small weight measurement, like determination of sensitivity property of microbalance. This drives the requirement for more accurate small weight measurement down to microgram level. NMIs researched on the microgram from manufacture, material and shape, storage and holding method, measurement equipment and weighing scheme. Subdivision comparison is commonly adopted and matrix method (MM) is used to solve the measurement Eq.. In this paper, the density of test and standard weight rather than the volume were adopted in MM. Details on how to use this method based on Matlab software were presented. Then the comparison between MM, Eqution method (EM) and full air-buoyancy correction method (FACM) were made. Differences between these three methods were analyzed and evaluation results were given out. Experiment showed that EM and FACM were of the same relative uncertainty, but MM had lower measurement uncertainty than EM and FACM.

Leak-Rate-Quantification Method for Gas Pressure Seals with Controlled Pressure Differential

An enhancement to the pressure-decay leak-rate method with mass-point analysis solved deficiencies with the standard method. By adding a control system, a constant gas pressure differential across the test article was maintained. As a result, the desired pressure condition was met at the onset of the test, and the mass leak rate and measurement uncertainty were computed in real time. Data acquisition and control systems were programmed to automatically end the test when specified criteria were met. Typically, the test was stopped when a specified level of measurement uncertainty was attained. Using silicone O-ring test articles, the enhanced method was compared with the standard method that permitted the downstream pressure to be nonconstant atmospheric pressure. Two example cases were presented: one case had a low leak rate, whereas the second leak rate was three orders of magnitude higher. The two methods recorded comparable leak rates, but the enhanced method resulted in significantly lower measurement uncertainty, statistical variance, and test duration. Utilizing this enhancement in leak-rate quantification, projects will realize reduced cost and schedule, improved test results, and easier interpretation between data sets.

EMPRESS: A European Project to Enhance Process Control Through Improved Temperature Measurement

A new European project called EMPRESS, funded by the EURAMET program ‘European Metrology Program for Innovation and Research,’ is described. The 3 year project, which started in the summer of 2015, is intended to substantially augment the efficiency of high-value manufacturing processes by improving temperature measurement techniques at the point of use. The project consortium has 18 partners and 5 external collaborators, from the metrology sector, high-value manufacturing, sensor manufacturing, and academia. Accurate control of temperature is key to ensuring process efficiency and product consistency and is often not achieved to the level required for modern processes. Enhanced efficiency of processes may take several forms including reduced product rejection/waste; improved energy efficiency; increased intervals between sensor recalibration/maintenance; and increased sensor reliability, i.e., reduced amount of operator intervention. Traceability of temperature measurements to the International Temperature Scale of 1990 (ITS-90) is a critical factor in establishing low measurement uncertainty and reproducible, consistent process control. Introducing such traceability in situ (i.e., within the industrial process) is a theme running through this project.

A new low-uncertainty measurement of the 31Si half-life

Half-life values are widely used in nuclear chemistry to model the exponential decay of the activity of radionuclides. The analysis of existing half-life data values reveals a general lack of information on the performed experiments and, in a few cases, an almost complete absence of uncertainty budgets. This is the situation for 31Si, the radionuclide produced via neutron capture reaction recently used to quantify trace amounts of 30Si in a sample of the 28Si-enriched material produced for the determination of the Avogadro constant. In particular, the now recommended 157.36(26) min value is the weighted average of ten data acquired between the 40s and the 90s and published without a detailed discussion of the uncertainty budget. In order to improve the 31Si half-life value we carried out repeated observations of the 31Si decay rate via γ-ray spectrometry measurements. This paper reports the result we obtained, including details of the experiment and the evaluation of the uncertainty.

Two Thermoeconomic Diagnosis Methods Applied to Representative Operating Data of a Commercial Transcritical Refrigeration Plant

In order to investigate options for improving the maintenance protocol of commercial refrigeration plants, two thermoeconomic diagnosis methods were evaluated on a state-of-the-art refrigeration plant. A common relative indicator was proposed for the two methods in order to directly compare the quality of malfunction identification. Both methods were applicable to locate and categorise the malfunctions when using steady state data without measurement uncertainties. By introduction of measurement uncertainty, the categorisation of malfunctions became increasingly difficult, though depending on the magnitude of the uncertainties. Two different uncertainty scenarios were evaluated, as the use of repeated measurements yields a lower magnitude of uncertainty. The two methods show similar performance in the presented study for both of the considered measurement uncertainty scenarios. However, only in the low measurement uncertainty scenario, both methods are applicable to locate the causes of the malfunctions. For both the scenarios an outlier limit was found, which determines if it was possible to reject a high relative indicator based on measurement uncertainty. For high uncertainties, the threshold value of the relative indicator was 35, whereas for low uncertainties one of the methods resulted in a threshold at 8. Additionally, the contribution of different measuring instruments to the relative indicator in two central components was analysed. It shows that the contribution was component dependent.

Recent Advances in Synthetic Calibrations of Multi Junction Solar Cells and their Corresponding Component Cells

Precise calibrations of primary reference standards for Multi Junction Solar Cells are crucial for the exact characterization of photovoltaic devices for space applications. To complement the established but rarely performed atmospheric calibration campaigns via balloon flights a reliable laboratory based, synthetic, calibration method is desirable. Differential spectral responsivity measurements are an established calibration method for solar cells in terrestrial application. Here it is shown that such synthetic calibrations can also be performed with lowest measurement uncertainties on Component Cells but also on whole Multi Junction Solar cell devices.

Single-shot low coherence pointwise measuring interferometer with potential for in-line inspection

Low-coherence-interferometry (LCI) is a well-known optical metrology technique which offers high resolution and a low measurement uncertainty. For the inspection of dynamic and fast processes, single-shot point sensors can show their full capability. Therefore, a new approach of an interferometer is presented, allowing an single-shot acquisition of a LCI signal. The presented concept is based on tilted wavefronts to generate a spatial modulated interferogram. Using a three faceted mirror (TFM) in the reference path, a virtual field point is generated leading to a tilted planar reference wavefront in the pupil plane of the telecentric objective lens. Three mirror surfaces, which are diamond milled out of a monolithic copper cube, are applied to guarantee a stable TFM geometry, resulting in an invariant reference field point position.

Improvement of the detection efficiency calibration and homogeneity measurement of Si-SPAD detectors.

BackgroundSilicon single-photon avalanche diodes (Si-SPADs) are the most used devices for measuring ultra-weak optical radiant fluxes in many quantum technology fields, such as quantum optics, quantum communication, quantum computing, etc. In all these fields, the detection efficiency is the main parameter, which has to be accurately known for achieving reliable measurements. In this paper we present the improvements performed on the setup described in López et al. (J Mod Opt 62:S21–S27, 2015) for determining the detection efficiency of Si-SPAD detectors with a low measurement uncertainty. The improvement arises from the precise alignment of the Si-SPAD detector and the low deviation reached between the total calculated filter transmission and the individual filter transmission measurements (≤0.05%) performed with an integrating sphere with attached Si-photodiode as standard detector.Results The relative standard uncertainty of the Si-SPAD detection efficiency measurement achieved is now as low as ~0.16%. Furthermore, the investigation of the detection efficiency homogeneity of two commercial Si-SPAD detectors from different manufacturers and with different sensor diameters is also presented. The obtained homogeneity is ≤2.2% within a region of diameter of 40 μm.ConclusionsThe detailed analysis presented in this paper shows the potential for achieving low measurement uncertainties for Si-SPAD detector calibration even in the low photon flux range. The low uncertainties are only to be realized for reproducible measurement conditions, i.e. in specific for equal beam sizes and beam shapes and well as for an irradiation of equal active areas of the detector. This, however, will be difficult to obtain when measurements are performed at different national metrology institutes.

The role of measurement uncertainty in the conformity assessment of the chemical composition of feeds

Official feed inspection has been directly related to the dispersion of the measures achieved by control laboratories, which can be due to several analytical techniques, calculation models and estimation approaches. The present study aims to demonstrate the importance of calculating the measurement uncertainty (MU) in the analysis of the chemical composition of several feedingstuffs, in order to avoid making wrong decisions due to incomplete measures. Samples of feedingstuffs (n=690), collected from 321 establishments, were analyzed. Complete measurements were compared to the labeling information declared by the processor. Animal feeds and mineral mixtures were the most frequent non-compliant samples and, among them, crude protein (n=94), calcium (n=50) and phosphorus (n=40) were the most frequent violations. Method performance was assessed in terms of in-house precision and recovery and by international proficiency testing. MU was calculated by using a bottom-up approach, combined with random effects inherited from the performance evaluation. A top-down approach based on the interlaboratory deviation was also carried out. The MU values calculated by the combined bottom-up approach were mostly lower than those calculated by interlaboratory experimental data. This latter approach overestimated the MU in most results, becoming inadequate. Titrimetric and spectrometric methods presented the higher and the lower MU among all techniques, respectively. A detailed study of the MU plays a key role in the conformity assessment of feedingstuffs, because the use of complete measures avoided 314 wrong decisions taking and prevented the disposal of approximately 1,000,007tons of animal feed.

A novel gas divider using nonlinear laminar flow

Gas dividers are important in emissions measurement since they continuously and accurately mix two gases to create a known gas concentration that is needed in the multi-point calibration of gas analyzers. A novel gas divider was designed using nonlinear laminar flow induced from the density change along the capillary channels due to the high-pressure drop (relative to the inlet gas pressure). The minor losses from entrance and exit effects can be ignored due to the high pressure loss from Hagen-Poiseuille's law relative to the minor losses. Small diameter wires inside of a tube were used to create capillary channels through which gas could flow. The gas divider, using nonlinear laminar flow, showed lower measurement uncertainty at high (90%) dilution levels than using linear laminar flow due to the higher-pressure drop at the same volumetric flow rates. Experiments showed the expected gas concentration from using the gas divider to be within 2% of the measured gas concentrations.

Whispering Gallery Mode Thermometry.

This paper presents a state-of-the-art whispering gallery mode (WGM) thermometer system, which could replace platinum resistance thermometers currently used in many industrial applications, thus overcoming some of their well-known limitations and their potential for providing lower measurement uncertainty. The temperature-sensing element is a sapphire-crystal-based whispering gallery mode resonator with the main resonant modes between 10 GHz and 20 GHz. In particular, it was found that the WGM around 13.6 GHz maximizes measurement performance, affording sub-millikelvin resolution and temperature stability of better than 1 mK at 0 °C. The thermometer system was made portable and low-cost by developing an ad hoc interrogation system (hardware and software) able to achieve an accuracy in the order of a few parts in 109 in the determination of resonance frequencies. Herein we report the experimental assessment of the measurement stability, repeatability and resolution, and the calibration of the thermometer in the temperature range from −74 °C to 85 °C. The combined standard uncertainty for a single temperature calibration point is found to be within 5 mK (i.e., comparable with state-of-the-art for industrial thermometry), and is mainly due to the employed calibration setup. The uncertainty contribution of the WGM thermometer alone is within a millikelvin.

Sea ice density measurements. Methods and uncertainties

Sea ice density is an important engineering and geophysical parameter. However, it lacks a standard method of measurement. In this paper, we show that the hydrostatic weighing method is the best available method that can capture the natural variation of the ice density throughout the ice thickness below the water line. The hydrostatic weighing method has a lower measurement uncertainty (0.2%) in comparison with the most common mass/volume method, which has an uncertainty of 4% when applied to ice samples with lengths and diameters of ~70mm. The density of first-year level ice below the waterline measured by the hydrostatic weighing method in the present study lies in a range of 894–921kgm−3. The density of rafted multiyear ice and the ice above the waterline had a wider range, 863–929kgm−3.

Quantitative Analysis of Pemel and PEMFC Electrode Drying

The establishment of a fully renewable energy system is predicated on the use of hydrogen as a fuel. Polymer electrolyte membrane (PEM-) water electrolyzers for its generation and (PEM-) fuel cells for its reconversion will be essential components of such a system. In order for this to be economically feasible, however, their costs have to be reduced. The quantity of expensive materials utilized for the construction of cells, including platinum, iridium or titanium must be reduced and overall efficiency increased. The efficiency of these devices is a function of the electrochemical processes that take place in the electrodes and is inseparably tied to their structure. The structure can be affected by controlling various steps in the manufacturing progress. Aside from the chemical composition of the wet coat (consisting of the supported catalyst, Nafion®, solvents and additives) the drying plays a significant role during the self-organization progress in the catalyst layer. Therefore, the drying aspect is one of the main focuses of interest. Nowadays the most commonly used catalyst-containing dispersions in the manufacturing of membrane electrode assemblies (MEAs) are based on a mixture of organic solvents. In order to clarify the drying process a test rig was constructed. By using a gas phase infrared spectrometer the drying can be monitored by analyzing the waste gas. The set up enables a wide range of conditions in terms of the temperature and the type of drying gas and its preloading. Furthermore, the contact time between the drying gases with the coated layer is adjustable. As various substances differ in their boiling points a different drying rate is observed for each organic component inside the electrode layer. Consequently, the physical and chemical parameters of the solvent mixture which evaporates during the drying step change dramatically over time. The test rig gives time-resolved information about the selectivity of drying, and the drying rates of the single mixture components in general. The measurement system provides accurate and consistent results. The low measurement uncertainty (< 2% rel.) offers an ideal tool for observing slight modifications during the drying progress.

An Eight-Channel 4.5-ps Precision Timestamps-Based Time Interval Counter in FPGA Chip

We present the design, operation, and test results of a new integrated time interval (TI) counter that provides high resolution (1.9 ps), low measurement uncertainty (below 4.5-ps rms in advanced measurement modes), and wide measurement range (above 1 h, easily extendable). Fundamental for the counter, TI measurements are simultaneously performed in eight independent channels, while the advanced configuration of input channels improves either the precision (up to 3 ps) or the measurement speed (up to $91.2 \times 10^{6}$ registered events/s). The functional flexibility and high speed are achieved based on the timestamp (TS) principle that makes possible registering on the common time scale events appearing at counter inputs and then measuring the time intervals between any registered events. The high precision is obtained by employing two-stage inner interpolation with an eight-phase clock in the first stage of interpolation and an equivalent time coding delay line in the second one. The time counter is integrated in a single, cost-effective field programmable gate array chip manufactured in a 28-nm CMOS process.

Measurement of the Inhomogeneity in Type B and Land–Jewell Noble-Metal Thermocouples

Inhomogeneity is the largest contributor to uncertainty in temperature measurements made with thermocouples, and the knowledge of inhomogeneity is essential if low-uncertainty measurements are required. Inhomogeneity is a particular problem for long-term applications at temperatures near or above 1500 $$^{\circ }\hbox {C}$$ , where pairs of alloyed noble-metal thermocouples must be used and the alloy components and potential contaminants become very mobile and cause large deviations in the Seebeck coefficient. While changes in inhomogeneity are a known and well-studied problem in noble-metal alloys at temperatures below 1100 $$^{\circ }\hbox {C}$$ , the effects are not well quantified at higher temperatures. This paper reports the first detailed measurements of inhomogeneity in a number of Type B and Land–Jewell thermocouples exposed to either short-term calibration up to 1600 $$^{\circ }\hbox {C}$$ or long-term in situ measurements for a period of approximately 3000 h at 1600 $$^{\circ }\hbox {C}$$ . The inhomogeneity is measured in a high-resolution scanner operating over the range from 600 $$^{\circ }\hbox {C}$$ to 900 $$^{\circ }\hbox {C}$$ . The results show that drifts of between 0.2 % and 0.6 % can be expected for reversible crystallographic and oxidation effects, whereas drift caused by irreversible contamination effects can be expected to be between 0.6 % and 1.1 %. It is also shown that the deviations in emfs caused by irreversible homogeneities in these thermocouples scale approximately linearly with temperature. This scalability allows uncertainties assessed at one temperature, to be extrapolated to other temperatures. Additionally it is shown that a preconditioning anneal at 1100 $$^{\circ }\hbox {C}$$ should be applied both before and after calibration to remove undesirable crystallographic and rhodium-oxidation effects.

Calculating Measurement Uncertainty of the “Conventional Value of the Result of Weighing in Air”

Abstract:The conventional value of the result of weighing in air is frequently used in commercial calibrations of balances. The guidance in OIML D-028 for reporting uncertainty of the conventional value is too terse. When calibrating mass standards at low measurement uncertainties, it is necessary to perform a buoyancy correction before reporting the result. When calculating the conventional result after calibrating true mass, the uncertainty due to calculating the conventional result is correlated with the buoyancy correction. We show through Monte Carlo simulations that the measurement uncertainty of the conventional result is less than the measurement uncertainty when reporting true mass.

Metrological multispherical freeform artifact

Precisely known artifacts are required to characterize the accuracy of asphere and freeform measuring instruments. To this end the best knowledge of the surface characteristics in conjunction with a low measurement uncertainty are necessary. Because this is a challenging task for typical freeform surfaces used in optical systems, the concept of “metrological” artifacts is introduced. We have developed a multispherical freeform artifact for performance tests of tactile touch probe and contact-free optical measuring systems. The measurement accuracy of the complete form and the deviation from calibrated spherical sections can thus be determined. The radius calibration of multiple spherical sections is performed with an extended radius measuring procedure by interferometry. Evaluated surface forms of different measuring methods and the radii determined can be compared to each other. In this study, a multispherical freeform specimen made of copper, with two differing radii, has been measured by two optical measuring methods, a full field measuring tilted-wave interferometer and a high accuracy cylinder coordinate measuring machine with an optical probe. The surface form measurements are evaluated and compared, and the radii determined are compared to the results of a radius measurement bench.