Data processing

Data processing is a necessary prerequisite for data analysis, and therefore separate from the latter. The main effort in spectroscopy is usually not recording the raw data, but processing and analysing those data in order to answer the questions that triggered the measurements in the first place.

Processing steps can be categorised further. The following is an attempt to do that for cw-EPR data and to summarise how to properly record and (post-)process cw-EPR data. For more authoritative answers, you may as well have a look into the EPR literature, particularly the “EPR Primer” by Chechik/Carter/Murphy and the book on quantitative EPR by the Eatons.

Corrections

When analysing cw-EPR data, usually, a series of simple correction steps is performed prior to any further analysis. This is particularly important if you plan to compare different datasets or if you would like to compare your spectra with those from the literature (always a good idea, though).

• Magnetic field correction

  Usually, the magnetic field in an EPR measurement needs to be determined by measuring a field standard in the identical setup, as the actual magnetic field at the sample will usually differ from the field set in the software.

  Appropriate magnetic field correction becomes particularly important if you are interested in absolute g values of your sample, e.g. to compare it to literature data or quantum-chemical calculations and to get ideas as to where the unpaired spin may predominantly reside on (in terms of nuclear species).

• Microwave frequency correction

  Comparing datasets is only possible in a meaningful manner if they are either corrected for same frequency, or their magnetic field axes converted into a g axis.

• Microwave phase correction

  Usually, cw-EPR spectra are not recorded with quadrature detection, i.e., with both, absorptive and dispersive signal components. However, using the Hilbert transform, one can reconstruct the dispersive signal (imaginary component) and correct the phase of the microwave source this way.

• Baseline correction

  However careful measurements are performed, baselines are quite often encountered. There are two different kinds of baseline that need to be corrected in different ways. Drifts can usually be handled by fitting and afterwards subtracting a (low-order) polynomial to the data.

  Particularly for low-temperature data, weak signals, and large magnetic field sweep ranges, the signal originating from the resonator itself, usually termed “resonator background”, can become quite dramatic. Here, usually the only viable way is to record the empty resonator (or alternatively or additionally the signal of an otherwise empty tube) independently under as much identical conditions as possible compared to recording the signal of the actual sample (but with slightly broader field range to compensate for different microwave frequency). Afterwards, you will subtract this dataset (empty resonator or empty tube, i.e. resonator background signal) from the signal of the actual sample.

Algebra

Comparing datasets often involves adding, subtracting, multiplying or dividing the intensity values by a given fixed number. Possible scenarios where one wants to multiply the intensity values of a cw-EPR spectrum may be comparing spectra resulting from a single species from those of known two species, different (known) concentrations and alike. Other possible situations are normalisation to same number of scans or same receiver gain, as necessary particularly for data recorded with older spectrometers. For details, see below (towards the end of the section on normalisation).

Of course, dividing the intensity of the spectrum by the maximum intensity is another option, however, this would be normalisation to maximum (not always a good idea, usually normalising to area or amplitude is better), and this is handled by a different set of processing steps (see below).

Note

This type of simple algebra is quite different from adding or subtracting datasets together. Whereas simple algebra really is a one-liner in terms of implementation, handling different datasets involves ensuring commensurable axis dimensions and ranges, to say the least.

Normalisations

Normalising data to some common characteristic is a prerequisite for comparing datasets among each other.

There is a number of normalisations that are common for nearly every kind of data, as there are:

• Normalisation to maximum

  Simply divide the intensity values by their maximum

  Often used as a very simple “normalisation” approach. Depends highly on the situation and focus of the represenntation, but usually, other methods such as normalisation to amplitude or area, are better suited.

• Normalisation to minimum

  Simply divide the intensity values by their minimum

  The same as for the normalisation to maximum applies here. Furthermore, normalising to the minumum usually only makes sense in case of prominent negative signal components, as in first-derivative spectra in cw-EPR spectroscopy.

• Normalisation to amplitude

  Divide the intensity values by the absolute of the difference between maximum and minimum intensity value

  Usually better suited as a simple normalisation than the naive normalising to maximum or minimum described above. However, it strongly depends on what you are interested in comparing and want to highlight.

• Normalisation to area

  Divide the intensity values by the area under the curve of the spectrum

  Not as easy as it looks like for first-derivative cw-EPR spectra, as here, you are usually interested in normalising to the same area ( i.e., integral of the curve) of the absorptive (zeroth-derivative or zeroth harmonic) spectrum.

  At least given appropriate measurement conditions (no saturation, no line bradening due to overmodulation, proper phasing), the cw-EPR signal intensity should be proportional to the number of spins in the active volume of the resonator/probehead. Therefore, with all crucial experimental parameters directly affecting the signal strength being equal (microwave power, modulation amplitude), normalising to same area should be the most straight-forward way of comparing two spectra in a meaningful way.

  Bear in mind, however, that spectra with strongly different overall line width will have dramatically different minima and maxima, making comparison of this kind sometimes less meaningful.

Besides these rather general ways of normalising spectra (although described above particularly with cw-EPR data in mind), there are some other normalisations more particular to cw-EPR spectroscopy:

• Normalisation to same number of scans

  Some spectrometers (probably only older ones) did usually sum the intensity for each scan, rather than afterwards dividing by the number of scans, making comparison of spectra with different number of scans quite tricky.

  Make sure you know exactly what you do before applying (or not applying) such normalisation if you would like to do some kind of (semi-)quantitative analysis of your data.

• Normalisation to same receiver gain

  The preamplifiers in the signal channel (as the digitising unit in cw-EPR spectrometers is usually called) have usually a gain that can be adjusted to the signal strength of the actual sample. Of course, this setting will have a direct impact on the intensity values recorded ( usually something like mV).

  Comparing spectra recorded with different receiver gain settings therefore requires the user to first normalise the data to the same receiver gain setting. Otherwise, (semi-)quantiative comparision is not possible and will lead to wrong conclusions.

  Note on the side: Adjusting the receiver gain for each measurement is highly recommended, as setting it too high will make the signal clip and distort the signal shape, and setting it too low will result in data with (unnecessary) poor signal-to-noise ratio.

Handling 2D datasets

2D datasets in cw-EPR spectroscopy, huh? Well, yes, more often than one might expect in the beginning. There are the usual suspects such as power sweeps and modulation amplitude sweeps, each varying (automatically) one parameter in a given range and record spectra for each value.

There are, however, other types of 2D datasets that are quite useful in cw-EPR spectroscopy. Some vendors of EPR spectrometers offer no simple way of saving each individual scan in a series of accumulations. However, this may sometimes be of interest, particularly as a single “spike” due to some external event or other malfunctioning may otherwise ruin your entire dataset, however long it might have taken to record it. Therefore, one way around this limitations is to perform a 2D experiment with repeated field scans, but saving each scan as a row in a 2D dataset.

Generally, there are at least two different processing steps of interest for 2D datasets:

• Projection along one axis

  Equivalent to averaging along that axis

  If recording multiple scans of one and the same spectrum for better signal-to-noise ratio, but saving each scan individually within a row of a 2D dataset, this is the way to get the dataset with improved signal-to-noise ratio originally intended.

  May as well be used for rotation patterns, i.e., angular-dependent measurements, if there turns out to be no angular dependence in the data. In this case, at least you save the measurement time by having a dataset with clearly better signal-to-noise ratio than initially intended.

• Extraction of a slice along one dimension

  Having a 2D dataset, we may often be interested in only one slice along one dimension.

  Typical examples would be comparing two positions of the goniometer (zero and 180 degree would be an obvious choice) or slices with similar parameters for different datasets.

More complicated and probably more involved processing of 2D datasets would be to (manually) inspect the individual scans and decide which of those to average, e.g. in case of one problematic scan in between, be it due to external noise sources or spectrometer problems.

Working with multiple datasets

Comparing multiple datasets by plotting them in one and the same axis is a rather simple way of handling multiple datasets. However, usually, you would like to perform much more advanced operations on multiple datasets, such as adding and subtracting one from the other.

May sound pretty simple at first, but is indeed rather demanding in terms of its implementation, as internally, you need to check for quite a number of things, such as commensurable axes and ranges. Furthermore, as soon as the axes do not share a common grid, you need to interpolate the data.

Particularly in EPR spectroscopy, each measurement will have a unique microwave frequency for which the data were recorded. Therefore, to combine the numerical values of two datasets (subtract, add, average), you will first need to correct them for same microwave frequency. This will generally result in different field axes for different datasets. Furthermore, some vendors like to record data with non-equidistant field axes as well, making handling of those datasets additionally messy.

• Subtract a dataset from another dataset

  Ensure the datasets are compatible in terms of their axes (dimension, quantity, unit, common area of values), subtract the common range of values and return only the subtracted (i.e., usually truncated) dataset.

  A common use case for subtracting a dataset from another would be a resonator background signal independently recorded, or some other background signal such as the “glass signal” (from impurities in the glass tube you’ve used).

  Other, more advanced applications may involve subtracting the spectrum of a single species from that of a spectrum consisting this and other species. However, in such case be aware of the fact that the spectrum containing more than one species may not be a simple superposition of the spectra of the two independent species.

• Add a dataset to another dataset

  Ensure the datasets are compatible in terms of their axes (dimension, quantity, unit, common area of values), add the common range of values together and return only the summed (i.e., usually truncated) dataset.

• Average two datasets

  Ensure the datasets are compatible in terms of their axes (dimension, quantity, unit, common area of values), average the common range of values together and return only the averaged (i.e., usually truncated) dataset.

  A common use case if you performed several independent measurements of the same sample (with otherwise similar/comparable parameters) and would like to average for better signal-to-noise.