Improved Dynamic Analysis method for quantitative PIXE and SXRF element imaging of complex materials

doi:10.1016/j.nimb.2015.08.021

Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms

Volume 363, 15 November 2015, Pages 42-47

https://doi.org/10.1016/j.nimb.2015.08.021 Get rights and content

Abstract

The Dynamic Analysis (DA) method in the GeoPIXE software provides a rapid tool to project quantitative element images from PIXE and SXRF imaging event data both for off-line analysis and in real-time embedded in a data acquisition system. Initially, it assumes uniform sample composition, background shape and constant model X-ray relative intensities. A number of image correction methods can be applied in GeoPIXE to correct images to account for chemical concentration gradients, differential absorption effects, and to correct images for pileup effects. A new method, applied in a second pass, uses an end-member phase decomposition obtained from the first pass, and DA matrices determined for each end-member, to re-process the event data with each pixel treated as an admixture of end-member terms. This paper describes the new method and demonstrates through examples and Monte-Carlo simulations how it better tracks spatially complex composition and background shape while still benefitting from the speed of DA.

Introduction

The complexity of natural material and the demands of research applications provide strong motivation for the development of quantitative trace and major element imaging capabilities exploiting X-ray fluorescence data generated using finely focussed ion and X-ray beams. Methods have been developed at the CSIRO aimed at efficient quantitative imaging using particle induced X-ray emission (PIXE) and synchrotron X-ray fluorescence (SXRF) and made available in the GeoPIXE software package. Central to these methods is the Dynamic Analysis (DA) method for spectral deconvolution and image reconstruction from event data. This computationally fast method uses a matrix transform approach, relying on linear combinations of spectral terms, to project both quantitative images [1] and variance estimates [2].

However, the method assumes that PIXE and SXRF model yields and X-ray relative intensities, for lines from each element, remain constant across an image area. In many samples the composition can display significant spatial contrasts, which means that yields and to a lesser extent relative intensities both vary. In addition, the shape of underlying background components also can vary spatially. A method was previously reported that corrects images for the effects of spatial composition complexity on PIXE yields [1]. It relies on decomposition of pixel composition into end-member phase components, for each of which yields have been calculated. The method estimates yields for the admixture of phases in each image pixel and iteratively corrects images based on the new yields. 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. Errors in X-ray relative intensities can lead to errors in the deconvolution of overlapping element components in some samples. For many regions extracted from PIXE image event data, the reconstructed spectra show some discrepancies compared to the PIXE spectrum. The aim of this work was to develop a new method to provide more accurate quantitative element images. The new method makes use of an analysis of region spectra that sample areas approaching the end-members in composition, in order to not only better calculate yields for each end-member, but also to exploit the calculated X-ray relative intensities and build a picture of the changing background shape in each phase to better approximate changing spectral complexity. This new “multi-phase DA” (MPDA) method has been implemented in the GeoPIXE program.

Section snippets

The DA method

The DA method is based on the expression of a linear least-squares fit to a PIXE or SXRF spectrum as the solution of a set of simultaneous equations, written in matrix form [4], and re-arranged into the form of a matrix transformation of the spectrum to elemental concentration vector [1], [5], [6], [7]. This transformation can be applied to each event in turn, and can also be implemented as a lookup table operation for real-time imaging in a data acquisition system [8], [9]. In GeoPIXE, the

Extension to detector arrays

The method represents an evolution from a simple fundamental parameters approach. The simple approach assumes a small solid-angle detector where take-off angle variation across the detector is negligible and ‘generic’ theoretical yields can be pre-calculated into a library based on sample composition and structure (e.g. thickness) and beam energy for an ideal, unit solid-angle detector and combined with specific experimental details. These details include integrated beam charge Q, detector

Image construction

When imaging, each detected event in spectrum bin e selects a column Γ_ke from the DA matrix. This suggests a convenient strategy to accumulate elemental images M_k in concentration-fluence units by simply incrementing each image k for each event (at x,y) by Γ_ke [1] and image variance V_k by Γ_ke² [2]. These images can be directly interrogated for average concentrations 〈C_k〉 in a region (and their uncertainties 〈δC_k〉), both on-line during data collection or off-line, by reference to the beam

The multi-phase DA method

The earlier yield correction method development [1] demonstrated that element images can be decomposed into phase maps. Representative regions of images can be selected that approach the end-member phase composition. Spectra extracted from these regions provide an approximation of the shape of spectral features such as background in the end-member phases. A full GeoPIXE fit to each end-member spectrum, coupled with calculation of PIXE or SXRF yields for the end-member composition, in principal

Spectrum reconstruction

Regions of pixels can be selected in GeoPIXE using geometric shapes, spline curves or through fields selected on element-element association plots. In order to display the equivalent of a fit overlay on the PIXE or SXRF spectrum extracted for a region, GeoPIXE reconstructs the spectrum based on the concentration of elements in the region and the pure element spectra pure_kj: $overlay = Q \cdot \sum_{kj} \cdot f_{k} \cdot Y_{kj} \cdot C_{kj} \cdot {pure}_{kj}$

Now with MPDA, this scheme is modified to form an average over the phase contributions:

Monte-Carlo tests

Monte-Carlo tests were used to test the MPDA algorithm’s ability to cope with spatially changing composition and its effects on yields, X-ray relative intensities and background. The following example illustrates the results for background shape. Simulated PIXE image data (20 × 20 pixels; ∼10⁵ events) were generated using a model with simple geometric spatial distributions of phases based on the elements As, Sr, Pb and Sn with the PIXE model peaks superimposed on background shapes chosen with

Geological application

The new MPDA method was applied to refine the element PIXE imagery from a study of element zonation through the walls of “black smoker” chimneys associated with submarine volcanic activity [14], [15]. Minerals dissolved within conductively heated hydrothermal fluids reach the cooler sea water causing rapid precipitation forming tall chimneys. These black smokers may form base- and precious-metal-rich massive sulphide ore deposits. These deposits potentially form valuable mineral resources both

Conclusions

The DA method in the GeoPIXE software enables fast spectral deconvolution and the projection of overlap and background subtracted element images orders of magnitude faster than fitting individual pixel spectra. It can be applied in real-time when embedded in a data acquisition system. However, the approximation implicit in DA, of uniform sample composition and constant yields across the image area, can lead to errors in cases of strong spatial composition contrasts. While a method to correct

Acknowledgments

The authors wish to thank Dave Belton and Chris Yeats for providing the black smoker PIXE data example, the CSIRO Mineral Research Flagship for continued support of GeoPIXE development and David Jamieson and Roland Szymanski for their support and hosting of the CSIRO Nuclear Microprobe on the University of Melbourne Pelletron accelerator.

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Improved Dynamic Analysis method for quantitative PIXE and SXRF element imaging of complex materials

Abstract

Introduction

Section snippets

The DA method

Extension to detector arrays

Image construction

The multi-phase DA method

Spectrum reconstruction

Monte-Carlo tests

Geological application

Conclusions

Acknowledgments

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