Application of Bayesian Super-Resolution to Spectroscopic Data for Precise Characterization of Spectral Peak Shape

The number of data points of digitally recorded spectra have been limited by the number of multichannel detectors employed, which sometimes impedes the precise characterization of spectral peak shape. Here we describe a methodology to increase the number of data points as well as the signal-to-noise (S/N) ratio by applying Bayesian super-resolution in the analysis of spectroscopic data. In our present method, first, the hyperparameters for the Bayesian super-resolution are determined by a virtual experiment imitating actual experimental data, and the precision of the super-resolution reconstruction is confirmed by the calculation of errors from the ideal values. For validation of the super-resolution reconstruction of spectroscopic data, we applied this method to the analysis of Raman spectra. From 200 Raman spectra of a reference Si substrate with a data interval of about 0.8 cm−1, super-resolution reconstruction with a data interval of 0.01 cm−1 was successfully achieved with the promised precision. From the super-resolution spectrum, the Raman scattering peak of the reference Si substrate was estimated as 520.55 (+0.12, −0.09) cm−1, which is comparable to the precisely determined value reported in previous works. The present methodology can be applied to various kinds of spectroscopic analysis, leading to increased precision in the analysis of spectroscopic data and the ability to detect slight differences in spectral peak positions and shapes.

BraggNN: fast X-ray Bragg peak analysis using deep learning

X-ray diffraction based microscopy techniques such as high-energy diffraction microscopy (HEDM) rely on knowledge of the position of diffraction peaks with high precision. These positions are typically computed by fitting the observed intensities in detector data to a theoretical peak shape such as pseudo-Voigt. As experiments become more complex and detector technologies evolve, the computational cost of such peak-shape fitting becomes the biggest hurdle to the rapid analysis required for real-time feedback in experiments. To this end, we propose BraggNN, a deep-learning based method that can determine peak positions much more rapidly than conventional pseudo-Voigt peak fitting. When applied to a test dataset, peak center-of-mass positions obtained from BraggNN deviate less than 0.29 and 0.57 pixels for 75 and 95% of the peaks, respectively, from positions obtained using conventional pseudo-Voigt fitting (Euclidean distance). When applied to a real experimental dataset and using grain positions from near-field HEDM reconstruction as ground-truth, grain positions using BraggNN result in 15% smaller errors compared with those calculated using pseudo-Voigt. Recent advances in deep-learning method implementations and special-purpose model inference accelerators allow BraggNN to deliver enormous performance improvements relative to the conventional method, running, for example, more than 200 times faster on a consumer-class GPU card with out-of-the-box software.

Application of Bayesian Super-Resolution to Spectroscopic Data for Precise Characterization of Spectral Peak Shape

The number of data points of digitally recorded spectra have been limited by the number of multi-channel detectors employed, which sometimes inhibits the precise characterization of spectral peak shape. Here we describe a methodology to increase the number of data points as well as the signal-to-noise (S/N) ratio by applying Bayesian super-resolution in the analysis of spectroscopic data. In our present method, first the hyperparameters for the Bayesian super-resolution are determined by a virtual experiment imitating actual experimental data, and the precision of the super-resolution reconstruction is confirmed by the calculation of errors from the ideal values. For validation of the super-resolution reconstruction of spectroscopic data, we applied this method to the analysis of Raman spectra. From 200 Raman spectra of a reference Si substrate with a data interval of about 0.8 cm-1, super-resolution reconstruction with a data interval of 0.01 cm-1 was successfully achieved with the promised precision. From the super-resolution spectrum, the Raman scattering peak of the reference Si substrate was estimated as 520.55 (+0.12, -0.09) cm-1, which is comparable to the precisely determined value reported in previous works. The present methodology can be applied to various kinds of spectroscopic analysis, leading to increased precision in the analysis of spectroscopic data and the ability to detect slight differences in spectral peak positions and shapes.

Equatorial aberration for powder diffraction data collected by continuous-scan integration of a silicon strip X-ray detector

The application of continuous-scan integration to collect X-ray diffraction data with a Si strip X-ray detector (CSI-SSXD) introduces additional effects on the peak shift and deformation of peak shape caused by the equatorial aberration. A deconvolutional method to correct the effects of equatorial aberration in CSI-SSXD data is proposed in this study. There are four critical angles related to the effects of spillover of the incident X-ray beam from the specimen face in the CSI-SSXD data. Exact values of cumulants of the equatorial aberration function are efficiently evaluated by 4 × 4 point two-dimensional Gauss–Legendre integral. A naïve two-step deconvolutional method has been applied to remove the effects of the first and third-order cumulants of the equatorial aberration function from the observed CSI-SSXD data. The performance of the algorithm has been tested by analyses of CSI-SSXD data of three LaB6 powder specimens with the widths of 20, 10, and 5 mm, collected with a diffractometer with the goniometer radius of 150 mm.

Screening Coarse Airborne Dust for Lead-Rich Phase Occurrence during Characterisation of Particle Mineralogy, Chemistry and Provenance: Application to Deposits in the Vicinity of an Integrated Steelworks

A method has been developed to screen large numbers (~103–104 per sample) of coarse airborne dust particles for the occurrence of Pb-rich phases, together with quantification of the particles’ mineralogy, chemistry, and inferred provenance. Using SEM-EDS spectral imaging (SI) at 15 kV, and processing with the custom software PARC, screening of individual SI pixels is performed for Pb at the concentration level of ~10% at a length-scale of ~1 µm. The issue of overlapping Pb-Mα and S-Kα signal is resolved by exploiting peak shape criteria. The general efficacy of the method is demonstrated on a set of NIST particulate dust standard reference materials (SRMs 1649b, 2580, 2584 and 2587) with variable total Pb concentrations, and applied to a set of 31 dust samples taken in the municipalities surrounding the integrated steelworks of Tata Steel in IJmuiden, the Netherlands. The total abundances of Pb-rich pixels in the samples range from none to 0.094 area % of the (total) particle surfaces. Overall, out of ca. 92k screened particles, Pb was found in six discrete Pb-phase dominated particles and, more commonly, as superficial sub-particles (sub-micron to 10 µm) adhering to coarser particles of diverse and Pb-unrelated provenance. No relationship is apparent between the samples’ Pb-rich pixel abundance and their overall composition in terms of particle provenance.