Numerical differentiation of experimental data: local versus global methods

In the context of the analysis of measured data, one is often faced with the task to differentiate data numerically. Typically, this occurs when measured data are concerned or data are evaluated numerically during the evolution of partial or ordinary differential equations. Usually, one does not take care for accuracy of the resulting estimates of derivatives because modern computers are assumed to be accurate to many digits. But measurements yield intrinsic errors, which are often much less accurate than the limit of the machine used, and there exists the effect of “loss of significance”, well known in numerical mathematics and computational physics. The problem occurs primarily in numerical subtraction, and clearly, the estimation of derivatives involves the approximation of differences. In this article, we discuss several techniques for the estimation of derivatives. As a novel aspect, we divide into local and global methods, and explain the respective shortcomings. We have developed a general scheme for global methods, and illustrate our ideas by spline smoothing and spectral smoothing. The results from these less known techniques are confronted with the ones from local methods. As typical for the latter, we chose Savitzky-Golay-filtering and finite differences. Two basic quantities are used for characterization of results: The variance of the difference of the true derivative and its estimate, and as important new characteristic, the smoothness of the estimate. We apply the different techniques to numerically produced data and demonstrate the application to data from an aeroacoustic experiment. As a result, we find that global methods are generally preferable if a smooth process is considered. For rough estimates local methods work acceptably well.     

A grid procedure applied to the determination of parameters of a kinetic process

A fitting procedure for one trap and one recombination centre kinetic model is described here. The procedure makes use of a grid in the parameters space obtained by changing each parameter back and forth and calculating robust cost functions on the surfaces of this grid. The lengths of the changes are determined empirically. The best set of parameters is calculated by the projection on the grid surface with smallest cost function. The fitting procedure applied to the fit of one, two and three parameters of the kinetic model is analyzed. In all cases the optimization procedure shows reliable fitting within a feasible interval of processing time.     

PIXE-PIGE analysis of Carolingian period glass from Slovenia

Glass artifacts excavated from the Late Roman and Carolingian period site at Bašelj Slovenia were analyzed by the combined PIXE-PIGE method using a proton beam in air. The results show that the majority of objects and glass ingots were made of traditional Roman, natron-type glass. Increased titanium and other impurities were found indicating that the glass had been recycled several times. As the composition of the ingots was similar to the other objects, a possibility exists of a secondary glass workshop in the local vicinity. The typologically and stratigraphically dated objects confirm that the Roman glassmaking continued in the area of Eastern Alps well into the 9th century.     

Effects of 80 KeV proton radiation on the optical properties and microstructure of type-GG17 glass as rubidium lamp envelope

Effect of 80 KeV proton radiation with fluences of 10¹⁴-2 × 10¹⁶ protons/cm² on the optical properties and microstructure of type-GG17 borosilicate glass as a candidate material for rubidium spectra lamp envelope was investigated. The change in microstructure before and after proton radiation was evaluated by means of UV-vis-NIR spectroscopy, X-ray photoelectron spectroscopy (XPS) and positron annihilation lifetime spectrometer (PALS). The experimental results show that under radiation of 80 KeV some broken Si-O bonds were induced and thus the number of non-bridge oxygen (NBO) increased. These irradiation-induced defects caused the degeneration of optical property and loosened glass structure which accelerates rubidium diffusion into lamp envelop.     

A novel method for focus assessment in atomic resolution STEM HAADF experiments

Analysis of the Fourier components of through-focal images in scanning transmission electron microscopy with a high angle annular dark field detector is used to assess illumination defocus values. The method is based on a least squares fitting of the peculiar dependence of Fourier components of the high angle annular dark field image on defocus. The validity of the method has been checked against simulations and experiments obtaining a good level of accuracy on the defocus measurement (δf=2 nm) for simulated specimen thickness up to 40 nm. The difference between simulated and experimental Fourier coefficients for large defoci can be used to estimate the specimen thickness at least up to 30 nm but with decreasing precision for larger thickness.     

Iterative regularization method for lidar remote sensing

In this paper we present an inversion algorithm for ill-posed problems arising in atmospheric remote sensing. The proposed method is an iterative Runge-Kutta type regularization method. Those methods are better well known for solving differential equations. We adapted them for solving inverse ill-posed problems. The numerical performances of the algorithm are studied by means of simulations concerning the retrieval of aerosol particle size distributions from lidar observations.     

Micro-PIXE-RBS methods highlighting the influence of phosphorus on the in vitro bioactivity of sol-gel derived glass particles in the SiO2-CaO-P2O5 system

Ion beam analysis methods were used to characterize the interface of bioactive glasses with surrounding biological fluids. Glass particles in the SiO₂-CaO and SiO₂-CaO-P₂O₅ compositions were made by sol-gel processing and soaked in biological fluids for periods up to 4 days. The surface changes were characterized using PIXE-RBS, which are efficient methods for multielemental analysis and accurate trace elements quantification. Elemental maps of major and trace elements were obtained at a micrometer scale and revealed the bone bonding ability of the materials. Glass particles are quickly coated with a thin calcium phosphate-rich layer containing traces of magnesium. After a few days, SiO₂-CaO-P₂O₅ glass particles are entirely changed into calcium phosphates, whereas SiO₂-CaO particles exhibit a different behavior: the previously Ca-P enriched periphery has been dissolved and glass particles consist of a silicate network. Calculation of the Ca-P atomic ratios at the glass/biological fluids interface provides us with an explanation for this: an enduring apatitic phase seems to be formed at the periphery of SiO₂-CaO-P₂O₅ glass particles. Presence of phosphorus in the glass matrix thus has an influence on the amplitude and the kinetics of reaction of the bioactivity process. It might result in an improved chemical bond with living tissues.     

Multidimensional nuclear spectra compression using fast adaptive Fourier-based transforms

In the paper a class of fast adaptive Fourier-based transforms were used for spectroscopic data compression. These transforms are based on adaptive modification of the Cooley-Tukey's signal flow graph. The adaptive versions of the cosine, cosine-Haar and cosine-Walsh transform of various degrees were taken as a base for the experiments. The transform kernels are modified according to reference vectors representing a given class of processed data. The results obtained using these transforms for γ-γ ray coincidence spectra compression are presented and compared with the results obtained by use of classical transforms. Both classical and adaptive transforms can be used for off-line as well as for on-line compression.     

Materials and processing of vacuum components for the high-intensity proton beam accelerator, J-PARC

The Japan Proton Accelerator Research Complex (J-PARC) project of the proton beam accelerator, involving a 400-MeV linac, a 3-GeV rapid-cycling synchrotron and a 50-GeV synchrotron, started in 2002. Materials used as vacuum components, such as electroformed copper, titanium, stainless steel and alumina ceramics, were examined from the point of view outgassing and electrical breakdown. The mechanical characteristics of a hydro-formed titanium bellows and a quick-disconnect flange system were also investigated.     

International Atomic Energy Agency intercomparison of ion beam analysis software

Ion beam analysis (IBA) includes a group of techniques for the determination of elemental concentration depth profiles of thin film materials. Often the final results rely on simulations, fits and calculations, made by dedicated codes written for specific techniques. Here we evaluate numerical codes dedicated to the analysis of Rutherford backscattering spectrometry, non-Rutherford elastic backscattering spectrometry, elastic recoil detection analysis and non-resonant nuclear reaction analysis data. Several software packages have been presented and made available to the community. New codes regularly appear, and old codes continue to be used and occasionally updated and expanded. However, those codes have to date not been validated, or even compared to each other. Consequently, IBA practitioners use codes whose validity, correctness and accuracy have never been validated beyond the authors’ efforts. In this work, we present the results of an IBA software intercomparison exercise, where seven different packages participated. These were DEPTH, GISA, DataFurnace (NDF), RBX, RUMP, SIMNRA (all analytical codes) and MCERD (a Monte Carlo code). In a first step, a series of simulations were defined, testing different capabilities of the codes, for fixed conditions. In a second step, a set of real experimental data were analysed. The main conclusion is that the codes perform well within the limits of their design, and that the largest differences in the results obtained are due to differences in the fundamental databases used (stopping power and scattering cross section). In particular, spectra can be calculated including Rutherford cross sections with screening, energy resolution convolutions including energy straggling, and pileup effects, with agreement between the codes available at the 0.1% level. This same agreement is also available for the non-RBS techniques. This agreement is not limited to calculation of spectra from particular structures with predetermined parameters, but also extends to extracting information from real data. In particular, we have shown data from an Sb implanted sample where the Sb fluence was certified with an uncertainty of 0.6%. For this sample, and using SRIM03 stopping powers for 1.5 MeV ⁴He in Si, the codes were able to extract the Sb fluence with an average 0.18% deviation from the certified value and a 0.11% agreement between the codes. Thus IBA is a suitable technique for accurate analysis where traceability is critical. These results confirm that available IBA software packages are, within their design limitations, consistent and reliable. The protocol established may be readily applied to validate future IBA software as well.