Developments in numerical treatments for large data sets of XPS images

Empirical data include signal with superimposed variations in intensity of an unwanted nature. These signal fluctuations are of particular interest in XPS measurements when the data are partitioned into both spatial and energy collection bins. In separating signals into a data cube with axes of energy and displacement in x and y, this division creates many more data binning locations than is typical of spectroscopy or classical imaging-type measurements resulting in only small numbers of counts per data bin. Under these circumstances, errors can easily dominate the signal of interest. It is usually assumed that pulse counted data have Poissonian statistics, so that the magnitude of the noise is proportional to the square root of the number of counts. When data are distributed throughout a 3D cube, the counts per voxel are typically low and any random errors can cause deviation from the expected Poisson distributed intensities, which has consequences for data treatment. This paper shows how raw intensities from 3D data sets can be preprocessed to recover a pseudo-Poisson behaviour, which allows principal component analysis with prior data scaling to be used to process the data. Data acquired from crystal formations on photosensitive films based on titanium clusters are used to demonstrate these techniques. Copyright (c) 2016 John Wiley & Sons, Ltd.