Quantitative Imaging using Dynamic Analysis

Dynamic Analysis is a method for projecting quantitative major and trace element images from PIXE and SXRF event data-streams obtained using proton and X-ray microprobes, such as the CSIRO-GEMOC Nuclear Microprobe. The method un-mixes full elemental spectral signatures to produce images that strongly reject artefacts due to overlapping elements, detector effects (such as escape peaks and tailing) and background. The images are also quantitative, stored in ppm-charge/flux units.

Typical PIXE Spectrum Components
The spectrum on the left is a typical PIXE spectrum for a Nuclear Microprobe (NMP) scan over an area of silicate and carbonate minerals. The yellow curve shows the data, the red is a fit to it and the blue shows the background estimation.

Even in this rather simple spectrum there are numerous element overlaps. The figure shows the pure element line-shapes (elemental signatures) just for the 10-20 keV interval. In this range there are 11 overlapping elements. Only the Sr Ka is relatively free of interference.

The spectrum can be least-squares fitted rather accurately, using these elemental signatures. The red curve shows the fit using the CSIRO GeoPIXE II software package.

The peak areas in the spectrum can be thought of as linear combinations of the elemental signatures. We could solve the resulting set of linear simultaneous equations, expressed as a matrix equation, to obtain elemental concentrations. This could be done by matrix inversion. The inverse matrix would then become a transform from peak area to elemental concentration.

Using this matrix, every X-ray event can then be transformed as it occurs to build pure element images, free of overlap artefacts, in real-time. See the references (Ryan, 2000, 2001) and (Ryan and Jamieson, 1993; Ryan et al., 1995) for more information. The extension to SXRF is outlined elsewhere (Ryan et al., 2005). 

The Dynamic Analysis approach
The Dynamic Analysis method takes this idea one step further, by building a matrix to transform from counts in each channel of the spectrum to contributions to elemental concentration. These functions are part of GeoPIXE II.

Dynamic Analysis PIXE Images
The spectrum above corresponds to the total PIXE spectrum for a scan over a melt inclusion trapped in clinopyroxene, and the images to the right are the elemental distribution images projected using Dynamic Analysis. (The original images are 560x512 pixels; these have been scaled down for the www.)

The images show very distinct distributions for these elements, with no evidence for artefacts that would mix them. For example, there is no hint of a false Rb signal due to the overlap of Br Kb on Rb Ka, although this would necessarily be weak as the average concentration of Br is only 2.6 ppm.

However, Sr at 543 ppm (average) would normally pose a problem for Zr imaging (average 14 ppm), with conventional imaging which uses simple energy windows on peaks, as the Sr Kb overlaps with Zr Ka and is about 10 times stronger. Despite this, the Dynamic Analysis method has projected a Zr image free of artefacts due to Sr overlap.

Beyond this simple illustration, the Dynamic Analysis method has been tested rigorously using known synthetic targets with severe multi-element overlaps, and performs very well in all cases tested. These results are published elsewhere (Ryan, 2000)(Ryan et al., 1995).

Another good example is the imaging of trace elements in sulfides.