An Optimized Deconvolution Algorithm for Energy-Dispersive X-ray Spectroscopy

Quantitative analysis in energy-dispersive X-ray spectroscopy (EDS) commonly comprises of three steps—qualitative analysis, k-ratio extraction, and matrix correction. The accuracy of both the qualitative analysis and k-ratio extraction is strongly influenced by characteristic peaks overlapping in the acquired spectrum. Qualitative analysis errors caused by overlaps can be corrected manually by a skilled spectroscopist or with an external knowledge of the approximate composition. Any k-ratio extraction errors generated by peak overlaps must be mitigated through peak deconvolution. A generally accepted method for deconvolving peak intensities in EDS spectra is the so-called Filter-Fit method described in [1]. The Filter-Fit method eminence emerges from its capability to mitigate slowly varying background caused by bremsstrahlung radiation along with the possibility to deconvolve characteristic emission peak shapes. The Filter-Fit method requires three parameters—namely, upper lobe length, lower lobe length, and region of interest. In most cases, the upper and lower lobe are chosen either as a constant value or calculated from the energy resolution of the detector. The region of interest is set specifically for the element and line family. The presented work aims to find optimal parameters of the Filter-Fit method. To achieve this goal, a database of characteristic X-ray event counts, similar to the k-ratio database proposed in [2], is iteratively compiled (containing 1600 spectra so far). In comparison to k-ratio database, the main advantage of an event counts database is that it does not require any prior knowledge about the chemical composition of the sample. Moreover, by investigating counts directly, performance under some non-analytical conditions can be evaluated, e.g., presence of sum peaks, incomplete charge collection (ICC) effects, and short acquisition times (< 0.1 s). Although non-analytical conditions can be almost completely mitigated for the purpose of accuracy, they are inevitable for recently popular techniques of chemical mapping and standardless analysis. These popular techniques lower the knowledge threshold so much that every EDS hardware or software manufacturer must address them and related issues. Currently, the database consists of roughly 10% peer-reviewed EDS spectra and approximately 500 extracted characteristic X-ray event counts deduced by means of proper spectra modeling. Figure 1 provides an example of a model decomposition of the unresolved Si K peak to characteristic events, a model of ICC effect from [3], and a bremsstrahlung model from [4]. Other cases, like the overlapping peaks of Fe Kα and Mn Kβ require information about line weights, which is strongly influenced by uncertainties of such values. Worse, exact modeling for the cases of Ti and V L-lines is almost impossible due to the ambiguity of conventional optimizers and uncertainty of required physical constants. However, a k-ratio database should give great insight for such cases, preferably confirmed by measurements of wavelength-dispersive X-ray spectroscopy. Results shown in this work (see Figure 2) will provide better understanding of deconvolution algorithms performance, namely how parameters of Filter-Fit method influence accuracy of characteristic X-ray events extraction. This information can be further exploited in analysis of k-ratio extraction and full chemical quantification. An example of peak shape features that are often found on modern detectors after long term use. Vertical hatching depicts errors introduced by fitting only a Si Kα line and omitting the presence of well-resolved Si Kβ line. Horizontally hatched area shows deviation from gaussian shapes resulting from ICC caused by photon-induced damage to the detector. a) differences caused by individual Filter-Fit parameters shown on unknown (Albite) and reference spectra (quartz, corundum), b) intensities extracted by individual Filter-Fit parameters.