Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms
Advances in Dynamic Analysis PIXE imaging: Correction for spatial variation of pile-up components
Introduction
Quantitative analysis in nuclear microscopy using proton induced X-ray emission (PIXE) demands accurate treatment of the various spectrum components including elemental line-shapes, continuum background, the effects of detector artefacts such as escape peaks and incomplete charge-collection tailing, and pulse pile-up. In the case of a PIXE spectrum from a point analysis, methods have been developed to fit these components, in order to extract a measure of the concentrations of the elemental components. Two of the software packages developed for this purpose, GeoPIXE [1], [2] and GUPIX [3], build on the pioneering work of Johansson et al. [4] aimed at establishing PIXE as a quantitative tool.
Pile-up corresponds to random-coincidence summing of pulse heights. Even with some form of pile-up rejection in place (electronic or on-demand beam-switching), which reject pulses with partial time-overlap, pile-up events that fall within the timing resolution τ of the pile-up rejector (∼100–300 ns for solid-state X-ray detectors and electronic rejection) go un-rejected. Provided that τ is small compared to the pulse shaping time (typically 4–15 μs), the pile-up sum-peaks appear at energies given by the sum of the contributing line energies. Hence, the intensity of pile-up is in proportion to the product of line intensities in the PIXE spectrum, and occurs at energies corresponding to pair-wise summing of the intense lines in the spectrum. Johansson et al. incorporated this effect in calculating pile-up line intensities for an effective “pile-up element” in PIXE spectrum fitting, which included a binomial probability factor reflecting the number of ways of combining element lines [5]. Ryan et al. extended this approach to higher order pile-up, which follows a multinomial distribution, and incorporated it into GeoPIXE spectrum fitting to pile-up of second order (i.e. pile-up of three pulses) [1].
The preceding treatment assumes that line intensities do not vary in time, beyond random statistical fluctuations. However, during PIXE imaging using a finely focussed proton beam and a scanning nuclear microprobe, the intensities of lines may vary from pixel to pixel, reflecting the changing concentrations of elements. Therefore, the sum-peak components, or line relative intensities, of a “pile-up element” may change from pixel to pixel. Then, if the spectrum corresponds to the integral across all or a portion of the image area, the pile-up element line intensities will not follow in general the product of line intensities in this spectrum.
The spatial variation in the nature of the “pile-up element” is a non-linear effect, related to the product of X-ray intensities for the dominant elements in each pixel and may lead to serious errors in the images of elements with lines that overlap with pile-up lines. The magnitude of these errors may vary from ppm to many wt% depending on the overlap of element lines of interest with the pile-up lines and the count rates of the lines giving rise to the pile-up. However, both matrix and these pile-up effects are related to composition variation. Hence, it should be possible to determine all these in a self-consistent fashion. The purpose of this paper is to describe recent extensions to the GeoPIXE method to tackle pile-up effects in both spectra and images, and to illustrate their application to major and trace element microanalysis in geology using high-resolution data from the CSIRO scanning nuclear microprobe [6].
Section snippets
The Dynamic Analysis method for PIXE imaging
The Dynamic Analysis (DA) matrix transform provides a method to generate real-time quantitative elemental PIXE images [7], [8], [9]. The method builds a matrix transform of the form, [9]where the DA matrix Γ is used to map spectrum vector S onto concentration vector C; Q is the integrated beam charge or fluence. In real-time imaging, each event picks out a column of the Γ matrix containing increments to make to each elemental image, thus accumulating images in ppm-charge units [9].
Point analysis spectra
In the case of a spectrum from a PIXE point analysis, the pile-up element relative intensities can be calculated to first order using the product of line intensities,where the sum runs over all lines i and j and so counts i ≠ j twice, which obviates the need for a binomial factor. In practice in GeoPIXE, the resulting list of pile-up lines is sorted in energy order, and histogrammed to merge lines separated by less than 60 eV. Then the list
Calculation and removal of pile-up effects in images
There are two common approaches to elemental imaging: (1) estimation of spatial distribution based on an energy window set on a major line for an element, and (2) using the DA matrix projection to unfold quantitative elemental concentration from the overlapping contributions of other elements, background and pile-up (with some restrictions). Both approaches can be influenced by pile-up features in the spectrum. An energy window may include pile-up lines, which may lead to artefacts in images
Tests and examples in geology
PIXE images of a sulphide mineral assemblage (dominated by pyrite (FeS2) with minor sphalerite (ZnS)) associated with gold exploration, generated using the DA method, are shown in Fig. 1. The spatial variation of the dominant major elements Fe, Zn and As are quite distinct, with the As concentrated on the rims of the pyrite grains (high Fe areas) and Zn concentrated in a separate phase with a small area (and hence high count rates). The PIXE spectrum integrated over this image area is shown in
Conclusions
A treatment is described where the spatial variation of the intensity and spectral make-up of pile-up contributions, which vary quadratically with dominant line intensities, can be successfully calculated for spectra and images collected using PIXE and the nuclear microprobe. This enables accurate fitting of spectra corresponding to a sum over an image area, and the subtraction of pile-up related effects in elemental images. These procedures have been incorporated into the GeoPIXE software for
Acknowledgments
The authors wish to thank Gary Cripps for his role in the development of the Nuclear Microprobe.
References (12)
- et al.
Nucl. Instr. and Meth. B
(1990) - et al.
Nucl. Instr. and Meth. B
(1989) - et al.
Nucl. Instr. and Meth.
(1970) - et al.
Nucl. Instr. and Meth. B
(2001) - et al.
Nucl. Instr. and Meth. B
(1993) - et al.
Nucl. Instr. and Meth. B
(1995)
Cited by (25)
Elemental mapping of large samples by external ion beam analysis with sub-millimeter resolution and its applications
2018, Nuclear Instruments and Methods in Physics Research, Section B: Beam Interactions with Materials and AtomsMicro-PIXE characterisation of uranium occurrence in the coal zones and the mudstones of the Springbok Flats Basin, South Africa
2017, Nuclear Instruments and Methods in Physics Research, Section B: Beam Interactions with Materials and AtomsCitation Excerpt :Complexity of elemental distribution, in particular presence of small pyrite grains visible on the left side of mapped area in sample 3.01 (Fig. 1), as well as very high concentration of calcium in the carbonate cleats, required careful and detailed processing of the obtained maps and spectra. Maps were corrected for pulse pile-up related artefacts, as described by Ryan et al. [9]. Fig. 3 shows that, after correction, the uranium map based on L-lines shows significant reduction of artefacts in the region dominated by presence of microscopic pyrite grains.
Improved Dynamic Analysis method for quantitative PIXE and SXRF element imaging of complex materials
2015, Nuclear Instruments and Methods in Physics Research, Section B: Beam Interactions with Materials and AtomsCitation Excerpt :The result converges quickly (e.g. 2–3 iterations) to provide better quantitative concentrations in each pixel [1]. Methods have also been developed to correct for pileup effects in images related to the product of the intensity of strong spectral lines [3]. However, this approach does not correct for changing relative X-ray line intensities or background components.
PIXE and the nuclear microprobe: Tools for quantitative imaging of complex natural materials
2011, Nuclear Instruments and Methods in Physics Research, Section B: Beam Interactions with Materials and AtomsCitation Excerpt :The treatment of each pixel in isolation with initially assumed yields tends to oversimplify the sample and analysis problem. Correction of images have been developed to (i) account for changing sample composition across an image that introduce errors in the initially assumed yields Yj (see below), (ii) correct for complex pile-up effects in images produced by changes in pile-up lines across an image reflecting changing major peak count-rates in each pixel spectrum [102], and (iii) correct for edge effects in images near grain boundaries of different composition, which produces changes in absorption of excited X-rays from depth on their way to the detector [103]. The resulting images more accurately portray detailed element concentration distribution.
Investigation of the mouse cerebellum using STIM and μ-PIXE spectrometric and FTIR spectroscopic mapping and imaging
2011, Nuclear Instruments and Methods in Physics Research, Section B: Beam Interactions with Materials and AtomsCitation Excerpt :In order to reduce low energy X-rays and to prevent scattered protons from entering the detector, a 100-μm Mylar foil was placed in front of the detector. The μ-PIXE data were analysed using GeoPIXE software [8,9] and elemental maps were extracted from the data. These elemental maps were used to calculate average elemental concentrations in the different tissue types by integration over a larger region.
- 1
Rio Tinto Technical Services, 1 Research Ave., Bundoora VIC 3083, Australia.