Design and optimization of the calibration procedure for a miniaturized Fourier transform spectrometer

This paper presents a Fourier transform infrared (FT-IR) spectrometer calibration procedure based on an unusual source made from a spectrally selective surface. An alternative solution to the usual calibrators has been developed to cope with the tight mass budget of an instrument devoted to Mars surface exploration. The designed system has proved effective, in terms of achievable radiometric accuracy, despite the drawbacks due to the significant reflectivity of the sources. The proposed procedure is a standard "two-source" approach in which both cold and hot sources are thermally controlled surfaces, similar to an optical solar reflector, associated to a filament lamp. Such a system allows the required signal to be achieved in the 2-25 l m instrument wavelength range. Source optimization was performed using, as a cost function, the computed radiometric uncertainty, while the required absolute accuracy of the instrument was imposed as the optimization constraint.     

A gamma-ray spectrometer system for fusion applications

A NaI scintillator spectrometer system for the measurement of gamma-ray spectra in tokamak discharges has been developed and installed on the Frascati Tokamak Upgrade. Two NaI scintillators are viewing the plasma at two different angles with respect to the equatorial plane. The main features of the spectrometer system (energy range: 0.3–23 MeV) and of the unfolding technique used to restore physical spectra from the pulse-height distributions are described: a method of solution with regularisation for matrix equations of large size, allowing to process count distributions with significant statistical noise, has been developed. A dedicated software, portable to any platform, has been written both for the acquisition and the analysis of the spectra. The typical gamma-ray spectra recorded in hydrogen and deuterium discharges, also with additional heating, are presented and discussed; two components have been observed: (a) thick-target bremsstrahlung gamma-rays produced by runaway electrons hitting the inconel poloidal limiter and/or the vessel; and (b) neutron capture gamma-rays generated in the detector shielding and tokamak structures. The maximum energy resulting from the bremsstrahlung spectra is in agreement with the runaway energy predicted by a test particle model of runaway electron dynamics.     

A simple method of estimating the position of a germanium gamma-ray detector crystal within its spectrometer housing using common gamma-ray calibration sources requiring the suppression of coincidence summing losses

A simple method of estimating the distance between the front face of the spectrometer housing and the germanium crystal of a gamma-ray detector is described. The activity (A) of small (10 μCi) gamma-ray point sources is measured over a range of distances (d) from the detector housing front face. A graph of d versus $\text{(A)}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$ gives the effective penetration depth into the crystal. Results of measurements on both planar and coaxial detectors using sources emitting photons over a range of energies (14–1332 keV) are presented. The success of the method depends on suppressing counting losses due to true coincidence summing of gamma and/or X-ray photons emitted in cascade by many gamma-ray sources. To achieve this, a 1.5 mm brass plate was placed in front of the detector to give high attenuation of all radiation below about 40 keV. The results of this study are relevant both to an understanding of the effective penetration depth of photons in germanium crystals and to the elimination of bias in detector efficiency measurements using common laboratory sources.     

A least squares finite element formulation for elastodynamic problems

A residual finite element formulation is developed in this paper to solve elastodynamic problems in which body wave potentials are primary unknowns. The formulation is based on minimizing the square of the residuals of governing equations as well as all boundary conditions. Since the boundary conditions in terms of wave potentials are neither Dirichlet nor Neumann type it is difficult to construct a functional to satisfy all governing equations and boundary conditions following the variational principle designed for conventional finite element formulation. That is why the least squares technique is sought. All boundary conditions are included in the functional expression so that the satisfaction of any boundary condition does not become a requirement of the trial functions, but they should satisfy some continuity conditions across the interelement boundary to guarantee proper convergence. In this paper it is demonstrated that the technique works well for elastodynamic problems; however, it is equally applicable to any other field problem.     

Development of a portable high-energy neutron spectrometer

The design of a portable high-energy (20-800 MeV) neutron spectrometer based on CsI or BaF2 is described. The particle discrimination properties of these scintillators allow the light-ion spallation products (p, d, t and alpha) from neutron interactions to be identified uniquely. One or more of the resulting pulse-height spectra can be unfolded to reveal the incident neutron spectrum. Dosimetric quantities can then be calculated based on the unfolded spectrum. Due to the high stopping power of these scintillators, modest-sized crystals are suitable for this application. Combined with advances in electronics, a lightweight instrument capable of on-line particle discrimination with a real-time display of neutron-induced count rate is feasible. Preliminary experimental data are presented, and the importance of validating MCNPX-generated response functions is discussed. A brief discussion on future work follows.     

A least squares procedure for the evaluation of multiple generalized stress intensity factors at 2D multimaterial corners by BEM

Detailed characterization of linear elastic stress states at corners and crack tips requires knowledge of the stress singularity orders, the characteristic angular functions and the generalized stress intensity factors (GSIF). Typically a high accuracy is found in the literature for the evaluation of the stress singularity orders and characteristic angular functions (numerically computed from analytical expressions in most cases). Nevertheless, GSIF values, evaluated by means of a numerical model using FEM or BEM and usually by postprocessing the results, are often reported with a lower level of confidence. A robust procedure is presented in this work for the evaluation of the GSIF at multimaterial corners. The procedure is based on a simple least squares technique involving stresses and/or displacements, computed by BEM, at the neighborhood of the corner tip. A careful verification of the robustness and accuracy of the procedure using a few benchmark problems in the literature has been carried out. Applications of the procedure developed to the evaluation of GSIFs appearing at corners in metal-composite adhesive lap joints are presented.     

Partial least squares regression calibration for determining wax content in processed flax fiber by near-infrared spectroscopy

The quality of flax fiber in the textile industry is closely related to the wax content remaining on the fiber after the cleaning process. Extraction by organic solvents, which is currently used for determining wax content, is very time consuming and produces chemical waste. In this study, near-infrared (NIR) spectroscopy was used as a rapid analytical technique to develop models for wax content associated with flax fiber. Calibration samples (n=11) were prepared by manually mixing dewaxed fiber and isolated wax to provide a range of wax content from 0 to 5%. A total of fourteen flax fiber samples obtained after a cleaning process were used for prediction. Principal component analysis demonstrated that one principal component is enough to separate the flax fibers by their wax content. The most highly correlated wavelengths were 2312, 2352, 1732, and 1766 nm, in order of significance. Partial least squares models were developed with various chemometric preprocessing approaches to obtain the best model performance. Two models, one using the entire region (1100-2498 nm) and the other using the selected wavelengths, were developed and the accuracies compared. For the model using the entire region, the correlation coefficient (R2) between actual and predicted values was 0.996 and the standard error of prediction (RMSEP) was 0.289%. For the selected-wavelengths model, the R2 was 0.997 and RMSEP was 0.272%. The results suggested that NIR spectroscopy can be used to determine wax content in very clean flax fiber and that development of a low-cost device, using few wavelengths, should be possible.     

A pixilated design of high pressure xenon gamma-ray spectrometer

A pixilated anode design of a high pressure xenon gamma-ray spectrometer is investigated. This design is composed of a single planar cathode and four anode pixels embedded in the center of a “non-collecting” anode plate. This design removes the Frisch grid which can suffer from excessive micro-phonics in real-world applications. To investigate the energy resolution of this design, the charge collecting efficiency and waveform of induced charge on each anode were calculated via tracking electron cloud drifting.     

A least squares method for fitting head fields by parametricequations

Models of magnetic recording systems generally require the field of the record head to be calculated. In the interests of speed a simple, but accurate, analytic expression is desirable. In this paper the method of minimization of squared residuals is used to obtain parameters defining a parametric approximation to the head field. As an example parameters are obtained which give best fits to finite pole tip head fields produced by conformal mapping. It is found that a good set of parameters is obtained by separately characterizing the infinite pole length head field and correction terms due to the outer pole edges evaluated at the medium surface. The same method could be used to fit measured data or fields obtained using numerical models     

A traceable calibration procedure for MEMS-based load cells

Characterizing the mechanical properties of materials and biological systems at the nanoscale requires accurate measurement of forces on the order of μN and less. Due to the scale of the measurements and size of the instrumentation, calibration of nanoscale devices presents a new challenge in metrology. In order to ensure accuracy of results, traceable calibrations must be performed on nanoscale instrumentation. Our group recently developed a novel MEMS-based high resolution load cell with force resolution on the order of μN. This paper reports on a simple method for traceably calibrating our device using dead weights that could be generalized to other MEMS-based load cells. In this article, fabrication of a MEMS load cell is detailed and we compare our calibrated force–displacement curves to a non-linear theoretical prediction, revealing errors as great as 29%.     

CHELSI: a portable neutron spectrometer for the 20-800 MeV region

CHELSI is a CsI-based portable spectrometer being developed at Los Alamos National Laboratory for use in high-energy neutron fields. Based on the inherent pulse shape discrimination properties of CsI(Tl), the instrument flags charged particle events produced via neutron-induced spallation events. Scintillation events are processed in real time using digital signal processing and a conservative estimate of neutron dose rate is made based on the charged particle energy distribution. A more accurate dose estimate can be made by unfolding the 2D charged particle versus pulse height distribution to reveal the incident neutron spectrum from which dose is readily obtained. A prototype probe has been assembled and data collected in quasi-monoenergetic fields at The Svedberg Laboratory (TSL) in Uppsala as well as at the Los Alamos Neutron Science Center (LANSCE). Preliminary efforts at deconvoluting the shape/energy data using empirical response functions derived from time-of-flight measurements are described.     

A procedure for calculating the characteristics of a dispersed phase in a mist flow on rewetting

The mechanisms involved in the formation of a range of droplets over a nonwetted region in a reflooded preliminarily heated channel are considered. A scheme is suggested for determining the droplet size.Moscow Power Engineering Institute, Moscow. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 65, No. 2, pp. 159–163, August, 1993.     

A two-level partial least squares system for non-invasive blood glucose concentration prediction

In this study, we propose and demonstrate a novel two-Level Partial Least Squares (2L-PLS) architecture for non-invasive blood glucose concentration measurement. A total of 290 Near-Infrared (NIR) spectroscopy readings from six laser diodes with discrete wavelengths of between 1500 nm and 1800 nm are obtained together with blood glucose concentration readings collected via Oral Glucose Tolerance Test (OGTT) experiments from a healthy volunteer over 4 days. While the conventional approach to predicting the blood glucose concentrations is to use a single Partial Least Squares (PLS) or non-linear PLS model, these systems do not achieve a high level of accuracy. As such, a 2L-PLS system consisting of one PLS model at the first level and three at the second level is proposed to enhance the prediction accuracy. A non-linear 2L-PLS system based on the same structure is also investigated in this study. The proposed 2L-PLS systems show improvements of 10 to 12% in the number of predictions that fall below a 5% error margin as compared to single-level PLS systems.     

A least squares approach to principal component analysis for interval valued data

Principal Component Analysis (PCA) is a well-known technique, the aim of which is to synthesize huge amounts of numerical data by means of a low number of unobserved variables, called components. In this paper, an extension of PCA to deal with interval valued data is proposed. The method, called Midpoint Radius Principal Component Analysis (MR-PCA), recovers the underlying structure of interval valued data by using both the midpoints (or centers) and the radii (a measure of the interval width) information. In order to analyze how MR-PCA works, the results of a simulation study and two applications on chemical data are proposed.     

Application of latent root regression for calibration in near-infrared spectroscopy. Comparison with principal component regression and partial least squares

Several analytical applications of spectroscopy are based on the assessment of a linear model, linking laboratory values to spectral data. Among various procedures, the following three methods have been used, i.e. principal component regression (PCR), partial least squares (PLS) and latent root regression (LRR). These methods can be applied in order to tackle the high collinearity commonly observed with spectral data. A collection of 99 near-infrared spectra, each including 351 data points, was used for the comparison of the 3 methods. The dependent variable was the specific production of pelleting. The spectral collection was divided into 49 and 50 observations for calibration and validation, respectively. The main elements of comparison were the minimum error observed on the verification set, the number of regressors introduced in the models and the stability of the errors around the minimum values. The minimum errors were 3.29, 3.13 and 3.07 for PCR, PLS and LRR, respectively. LRR required a large number of regressors in order to obtain the minimum error. Nevertheless, it gave very stable results, and the errors were not markedly increased when an arbitrary large number of regressors was introduced into the LRR model.     

A general approach of least squares estimation and optimal filtering

The least squares method allows fitting parameters of a mathematical model from experimental data. This article proposes a general approach of this method. After introducing the method and giving a formal definition, the transitivity of the method as well as numerical considerations are discussed. Then two particular cases are considered: the usual least squares method and the Generalized Least Squares method. In both cases, the estimator and its variance are characterized in the time domain and in the Fourier domain. Finally, the equivalence of the Generalized Least Squares method and the optimal filtering technique using a matched filter is established.     

Temporal sensitivity of the wavelength calibration of a photodiode array spectrometer

Subtle differences in the relationship between wavelength and pixel on photodiode array spectrometers contribute to difficulties in transferring calibrations from one instrument to another and may even introduce errors on a single instrument over time. To quantify the level of drift that might be expected in photodiode instruments, we calibrated the wavelength scale of two Zeiss MMS-1 photodiode spectrometers weekly over a 12-month period. We found no evidence of drift in the wavelength calibration. The wavelength calibration was consistent within 0.03 nm over at least 150 days and better than 0.1 nm over the year. To provide context for the wavelength accuracy, we applied small perturbations to wavelength in two partial least squares (PLS) models. We found that wavelength perturbations introduced a linear increase in bias of about 7%/nm (for example, a 1-nm perturbation shifted fruit dry matter prediction from 14% to 21%) in a kiwifruit dry-matter model and about 3.6 °C/nm in an Intralipid temperature model. By including small wavelength perturbations in the training sets, we were able to reduce this error to less than 1.7%/nm and 0.2 °C/nm in the dry-matter and temperature models, respectively. These results suggest that the wavelength scale of photodiode instruments can be very stable. However, in light of the high sensitivity of the PLS models we examined, we recommend testing and, where possible, mitigating the sensitivity of PLS models to small wavelength shifts.     

A weighted total least squares estimator for multivariable systemswith nearly maximum likelihood properties

The aim of the present paper is to develop a parametric estimator for linear time-invariant multivariable systems with nearly maximum likelihood properties. The estimator is based on the total least squares (TLS) method. It can be seen as an “optimally” weighted iterative generalized TLS (GTLS) estimator, combining the nice asymptotic properties of the maximum likelihood (ML) method with the global minimization property of the GTLS estimator