Processing *

An XPS spectrum represents an envelope that is derived from many unresolved peaks. The relative intensity of these peaks may vary as a function of the kinetic energy imparted to the electrons being recorded as well as the magnification of the electron optics (lens mode/pass energy). In addition, the position of the peaks may differ from the expected value due to a combination of instrument energy calibration and charging effects on the sample. Casa XPS therefore provides a number of processing options that assist in understanding the data envelope and allow adjustments to the spectrum so as to compensate for analysis variables.

The processing options are available from the "Options" main menu item or from the main toolbar button shown in Figure 1.

Figure 1. Main toolbar processing options.

Data smoothing may be performed using a range of Savitzky-Golay algorithms or by weighted averaging the data using a set of weights that are a normalised Gaussian distribution.

Smoothing algorithms should always come with a statistical health warning. Smoothing can seriously affect your curve fitting! The act of fitting synthetic peaks is, not only, the best form of smoothing but also makes assumptions about the distribution of errors within the data as well as the statistical independence of the measurements. Smoothing the data before curve fitting invalidates these assumptions.

A Savitzky-Golay filter is derived by approximating the data with a polynomial of degree less than or equals to the chosen number of 2n + 1 channels. The coefficients for the selected polynomial are determined in the linear-least-squares sense and the datum at the centre of the 2n + 1 channels is replaced by the value for the polynomial at that point.

To perform a smoothing operation using Savitzky-Golay, it is necessary to select the degree of the polynomial and the width of the data-channels over which the approximation is to be made.

Gaussian smoothing merely needs the width of the data-channels to be used when averaging the spectrum.

Differentiation of spectra is also achieved using the Savitzky-Golay polynomial. This is appropriate since noise interference would cause problems to an algorithm used for analytical functions, and so the implied smoothing operation involved in Savitzky-Golay differentiation, would explicitly be required with other techniques.

The parameters used in differentiation are, therefore, identical to those for smoothing the data. To get a feel for what was actually done to the spectrum during the differentiation procedure, a smooth operation with the same parameters, applied to the original spectrum can provide an insight into the shape of the data that produced the derivative.

A more novel use of the Savitzky-Golay polynomial is in calculating the integral for a spectral range. Integration by any means has implied smoothing involved since it is essentially an averaging process. However, when noise is involved there is little benefit in using sophisticated Newton-Cotes or other quadrature methods, as these generally involve forcing a function to take on the data values at the corresponding nodes. The virtue of putting a quadratic through three points containing noise is somewhat doubtful. Integrating the data using a least-squares fit of a quadratic to more than three points seems better, however from a practical perspective, if there is a significant difference between these two operations, then there’s trouble somewhere!

To summarise, integration is performed using the Savitzky-Golay polynomial in which a quadratic is used to approximate 5 data channels. From a Users point of view, integration is performed by pressing the apply button on the "Integration" property page.

A spectral line may appear at an energy position that is not the expected value for a transition. The reason for this may be due to spectrometer calibration or sample charging, however, for presentation purposes, the energy scale can be adjusted using parameters on the "Calibration" property sheet. Two values can be entered, the record position of the line and the required energy for the peak. On pressing the "Apply" button a shift is computed and the display is updated. Note that if preferred, the spectrum can be shifted by an amount by setting the measure value to zero and entering the required shift in energy into the field for the true energy.

A spectrum recorded on a particular instrument represents only the electrons as a function of kinetic energy that the instrument was capable of sampling. The transmission characteristics for an instrument are important if the spectra are used to quantify the chemical composition of a sample. This extends even as far as calculating the background for the data, where techniques presented by Tougaard can be only applied after accounting for such variations in the intensity.

The "Intensity Calibration" property page allows the intensity to be adjusted using a function of a constant power of the energy. The same page on the "Processing" dialog window allows the inclusion of a relative transmission function to be specified.

The VAMAS file format does not specify how the transmission function for an instrument can be incorporated with the data, however CasaXPS does allow the use of a second corresponding variable per VAMAS block, to define the transmission behaviour for the instrument. This is particularly important when a single relative sensitivity factor (R.S.F) is used to quantify results from a range of magnifications and pass energies. Without first correcting for the differences due to operating modes of the instrument, a single R.S.F. would not yield consistent quantification results for the same sample.

If a valid corresponding variable index is specified, the act of calibrating the intensity modifies the data by dividing the raw spectrum by the indicated transmission function.

Each VAMAS file data-block can be processed using any of the available options. The "Processing History" property page provides the means of viewing the operations that have been applied to the data. Further, the processing may be reversed entirely or selectively. The "Reset" button removes all the processing operations and restores the data to that originally supplied in the VAMAS file. Alternatively, by selecting a set of lines within the scrolled list, then pressing the "Apply Selection" button, the indicated set of processing operations are performed on the original data. Thus the previous processing history is replaced by only those actions selected prior to pressing the button.

Processing for a block of data can be globally applied to a set of VAMAS blocks. Select these blocks within the browser view, then right click on the corresponding display view to reveal a dialog window for propagating operations such as curve fitting and processing. Choose the required actions then press the "Apply" button. A second window appears showing the progress of the propagation and offers a "Stop" button. If the "Stop" button is pressed, the propagation will terminate following the completion of the current action. Note that some actions, for example curve fitting, may take a significant period of time to complete.

Not all actions for processing the data may be applicable to all the selected blocks. To prevent, for example, the energy calibration for the current block from being propagated to other blocks, the history item can be flagged so that it is not propagated along with other appropriate actions.

To exclude a processing operation from a propagate action, select the item in the history list, then press the button labelled "Propagate Flag". The entry in the list for the selected processing option will change to indicate that the flag for propagating the action is false. Repeat the procedure to remove the exclusion.