Which Background Acquisition/Analysis Method is Best?

[Probeman]

I was recently having a discussion with a colleague about how one decides which background correction method one should utilize for a given element in a given analytical situation. That is, should one use the traditional off-peak method? Or perhaps the mean atomic number (MAN) method, or the multi-point background (MPB) for the background correction? In Probe for EPMA one has a choice of three different background acquisition methods as seen here:



The short answer of course is: it depends. Because the optimum background acquisition method depends on so many different considerations. Is the element a major element, a minor element or a trace element?  How complex is the elemental matrix (can one find off-peak background positions that are not interfered with)? Is acquisition time important?  How much sensitivity does one require.? How important is accuracy for this element and at what level?  How many different phases are to be examined and how much does their average atomic number vary (which of course changes the continuum intensity)?  Should we use the same background correction in the standards and the unknowns?  Are we performing point analyses or X-ray mapping?  How long should we integrate the background? How sensitive is the sample to beam damage?

And then there are options for the background analysis method, which are separate from the background acquisition method (e.g., using MAN background corrections for off-peak acquired elements).

In this topic we can discuss these different considerations for selecting the optimum background correction method for the elements and samples in question. First we should start with a quick summary of the three (or four, depending on how one counts them) background correction methods in Probe for EPMA.

1. Traditional off-peaks

The off-peak background correction is where the analyst (usually) specifies two spectrometer positions (usually) on either side of the emission peak, and the software interpolates the background intensity under the peak from these off-peak positions.

This is the only background correction method available in the JEOL or Cameca software and is often a reasonable choice for the analyst, but it does require that there are no spectral interferences on these off-peak positions for optimum accuracy. In addition the off-peak method requires additional time to position the spectrometer at each of these off-peak measurement positions, and of course it also requires a certain amount of integration time at each of these on-peak positions. For major and some minor elements the amount of off-peak integration time can usually be somewhat less than the on-peak integration time, but it depends on the peak to background ratio, though the ideal off-peak integration time can be calculated according to this expression:



In this example, the on-peak count rate is 1000, the off-peak count rate is 50 and the on-peak count time is 20 seconds. Because the peak to background ratio is relatively high in this example, the background intensity is statistically less critical and therefore only about 4.5 seconds of off-peak integration time (or 2.2 seconds for each off-peak position) is required to provide equivalent statistics for the net intensity calculation.

Of course as one approaches a peak to background ratio of 1.0 (the limiting value for a trace element at zero concentration), the integration time of the off-peak positions needs to be equal to the on-peak integration time.

The advantage of the off-peak method is that it is a direct measurement of the continuum, but we still depend on the accuracy of the off-peak interpolation which may be affected not only by other emission peaks, but also by the long tails of the emission peak, curvature of the continuum (especially at low spectrometer positions), and continuum artifacts such as absorption edges from our detectors and samples.

2. Mean Atomic Number or MAN background corrections

MAN background corrections are based on modeling Kramer's Law, which states that the continuum is a function of the average atomic number of the sample. When acquiring samples using the MAN method, no off-peak measurements are necessary as only the on-peak intensities are measured. Though they can also be acquired for subsequent comparisons of MAN vs. off-peak as described here:

https://probesoftware.com/smf/index.php?topic=4.msg9953#msg9953

To perform the MAN correction, one usually acquires on-peak intensities on standards that *do not* contain the element in question, but the standards cover a range of average atomic number that covers the range of average atomic number in the unknown (and standard!) samples.  For example, the primary standards for Si, Al, Ca and Fe might be SiO2, Al2O3, diopside (CaMgSi2O6) and magnetite (Fe3O4). The standards chosen for the Si Ka MAN calibration might be Al2O3 and magnetite (if the magnetite is pure).  While the Al Ka MAN calibration could utilize SiO2, diopside and magnetite (again if the diopside and magnetite do not contain Al. And so on for the Ca Ka and Fe Ka MAN background calibration. Note that the acquisition of these primary and MAN standards can combined as both primary and MAN standards can utilize the same standard acquisition.

The advantage of the MAN background method is that because no off-peaks are acquired, not only does one save considerable time, but also there is no possibility for off-peak interferences. This is be very helpful in cases where the backgrounds are complex and/or have continuum artifacts.  In addition, because the MAN method produces a highly precise determination of background using multiple standards, the sensitivity of MAN corrected elements is roughly 40% more precise than the off-peak method. For those interested, this claim is discussed in detail in this paper:

https://epmalab.uoregon.edu/publ/A%20new%20EPMA%20method%20for%20fast%20trace%20element%20analysis%20in%20simple%20matrices.pdf

The disadvantage of the MAN is trace element accuracy, which is roughly limited to 100 to 200 PPM accuracy for silicates and oxides. But as described in the above paper, this accuracy question can be addressed (in many cases) by utilizing a so called "blank" standard.  By application of a blank correction (using a suitable blank material), one can obtain an accuracy *equal* to one's measurement precision. An amazing claim, but true.

One other consideration is that if one utilizes the MAN background method for all elements in one's acquisition setup, then there is no need to perform wavescans of the sample, to check for off-peak interferences. This could save significant setup and acquisition time.

3. Multi-Point Background or MPB corrections

The MPB method is an extension of the off-peak method where instead of acquiring two off-peak positions, one acquires additional off-peak measurements so that one has 3 or more off-peak measurements. In Probe for EPMA one can have up to 18 off-peak positions on each side of the peak, for a total of 36 off-peak background measurements when using the MPB method!

The immediate advantage of the multi-point background method is that one can fit the background measurements to a *curve*, usually exponential but also polynomial which can provide a more accurate interpolation of the intensity under the peak.  The disadvantage of the MPB is that it requires more time, but this is offset by the fact that because the MPB method allows one to (automatically or manually) remove off-peak measurements that are interfered with, one can perform a very cursory wavescan prior to acquisition, and in fact one can even skip the wavescan acquisition completely.

For details on the MPB method please see this paper:

https://www.proquest.com/openview/208992e799d48f657d3508a6ef11ca1c/1

4. Multi-Point Background or MPB corrections using "Shared Off-Peak Backgrounds"

A popular alternative MPB method (when acquiring more than one element per spectrometer!), is to acquire normal off-peak backgrounds, and then have Probe for EPMA scan for these extra backgrounds and utilize them *as though* they had been acquired using the MPB method.  So if one acquires two elements on PET sp2, then one would have 4 MPB measurements to fit for the background for each of these two elements.  If one has three elements on the same spectrometer, one would have 6 MPB measurements for all three elements.   Obviously one has to be careful regarding interpolation across absorption edges, just as one must with traditional off-peak measurements. Here is a discussion for the "shared" background method:

https://probesoftware.com/smf/index.php?topic=9.msg2666#msg2666

Next we can discuss what factors one might consider in choosing the best background method for a given element, in a given matrix, for a desired sensitivity and accuracy at some specified beam condition. Please feel free to chime in with you own experiences and observations.

[Probeman]

In the above post we discussed the various background methods available in Probe for EPMA (traditional off-peak, Mean Atomic Number and Multi-Point Backgrounds). In this post we will start discussing various considerations for selecting one background type over another, given specific analytical situations.  Let's start by listing some factors in our decisions:

A. Acquisition time (many analysis points vs. only a few analysis points)

Although using the MAN background method saves about half the acquisition time per point, if one is only planning a few dozen analyses it might not be worth the time and effort to acquire an MAN curve. On the other hand, if one acquires all elements using MAN curves, there is no need to acquire wavescans to check for off-peak background interferences or absorption edges. However once one is acquiring more than a few dozen point analyses, the MAN background begins to save considerable acquisition time (and provides better precision than off-peak methods). Note also that because a standard can be acquired once and utilized both as a primary standard and an MAN standard,the amount of acquisition time required for the MAN curve can be only a few minutes.

B. Availability of pure standards (for MAN curve generation)

However, if one is going to utilize the MAN background method, it really helps to have a number of pure standards covering a range of Z-bar (average atomic number) that includes the standards and the unknown samples under consideration. But usually the analyst can find a few pure oxides (or even pure elements or metals) that can be utilized for the MAN curves. Ideally one would like three or more standards for each analyzed element (that do not contain the element in question). However, alternatively one can utilize impure standards (and even standards containing the element!) and acquire off-peak backgrounds on the standards, and utilize MAN backgrounds for the unknown samples, by utilizing the "interpolated" MAN below) as described here:

https://probesoftware.com/smf/index.php?topic=987.0

This method allows the user to acquire off-peak backgrounds on ones standards, and then use the *interpolated* off-peak intensity for constructing the MAN correction curve. This interpolated MAN curve can then be applied to unknown samples acquired using the MAN background method.

C. Complex or curved backgrounds or with many over-lapping peaks (e.g., REE analysis)

Samples with very curved and/or complex backgrounds require additional considerations. The multi-point background (MPB) method, first described by Mike Jercinovic and Julien Allaz, allows the user to specify more than one off-peak background positions on each side of the emission line for a more accurate determination of the background intensity under an emission line.  This is especially useful for highly curved backgrounds at low sin thetas, or when the sample is highly heterogeneous and/or there are no ideal places to measure the off-peak backgrounds.

The MPB method does require more time for acquisition of the additional backgrounds, but provides enormous flexibility in fitting the background subsequent to acquisition. Think of it like acquiring a high precision (but very sparse) wavescan, at the same time as the unknown acquisition!  This background method allows one to skip tedious wavescans on multiple samples and yet provides a highly accurate background determination.

The MAN method can also be considered for such complex background situations, but this partly depends on the standards available for the MAN curve.

D. High accuracy trace element analysis (is there a suitable blank standard available)

Regardless of whether one utilizes the off-peak, MAN or MPB method for background acquisition, the use of a blank sample ensures that one trace element accuracy is *equal *to the measurement precision as described here:

https://probesoftware.com/smf/index.php?topic=29.msg387#msg387

A blank sample is of course a standard with a matrix that is roughly similar to the sample in question, but which contains a *zero* concentration of the element in question, and is acquired as an unknown sample, using the *same* acquisition method as the unknown samples, to which it will be applied. By a zero concentration we mean a concentration lower than the instrument is capable of detecting. So for an EPMA instrument, generally any concentration below 1 PPM can be considered a "blank" level. I still refer to Mike Jercinovic's admonition: "If you can't measure something, then see if you can measure nothing... because, if you can't measure nothing, then you can't measure anything."

Of course the blank correction in Probe for EPMA can also utilize standards with a known non-zero concentration of the element in question. But then we come back to problems with using trace element standards (with a non-zero concentration of the element). Specially we shouldn't be using trace element standards because we really don't know the trace concentration of an element. Is the concentration 100 PPM or is it 110 PPM, and more importantly, how do we know? Yes, we can use another method such as ICP-MS and get an average of the trace element, but then how well do we know that the trace element is homogeneous at the micro-scale? Of course the irony is that most techniques (such as ICP-MS) run a "blank" sample to determine zero anyway. So why don't we just do the same thing on the EPMA using a blank standard?

E. Beam sensitive materials (TDI vs. short count times)

If time is of the essence because our sample is very beam sensitive, then the MAN method can be helpful to limit the beam exposure of the sample.

In fact even when using the MPB method Mike Jercinovic, Julien Allaz and Karsten Goemann will often utilize the Nth point background method, where the first point is a "sacrificial" point utilized simply to determine the background intensity. Which is then applied to each subsequent point assuming that the sample is relatively homogeneous.  More details on the Nth point method is here:

https://probesoftware.com/smf/index.php?topic=806.msg8036#msg8036

Writing this reminds me of the old ARL SEMQ EPMA instrument we had at Berkeley which had 4 fixed monochromators (Si, Fe, Ca, Al) and 4 tunable spectrometers, so using the MAN background method we could acquire 8 elements in 10 seconds. Which was very useful for measuring alkali rich glasses.

F. Average Z of standards and unknowns (high Z materials = high continuum intensities)

Finally there is the issue of average atomic number or average Z or Z-bar.  As we know from Kramer's Law, the continuum intensity is proportional to the average Z of the material. In silicates and oxides (and many mineral glasses) this usually means a range of Z-bar from 10 to 20. E.g., MgO, Al2O3 and SiO2 are about 10, TiO2 is around 16 and MnO and Fe2O3 are around 20. So if you have pure standards like these, it is very easy to acquire an MAN curves suitable for almost all oxides, silicates and glasses.

Using MAN backgrounds in such materials we usually see accuracies around 100 to 200 PPM or better. And of course with a blank standard/sample even better than that.

However, as we look at materials with higher Z-bars, the continuum intensity increases and our P/B tends to go down, meaning that the accuracy of the background correction becomes even more critical. While this is true for all background measurement methods, the advantage of the MAN method remains that one is directly measuring the continuum at the emission line position so no interpolation (or extrapolation) from off-peak measurements is necessary. Therefore there are no issues with off-peak interferences, peak tails or absorption edges.

On the other hand, the availability of pure high Z standards for calibrating the MAN curve becomes the dominant question for high Z samples. And while the MAN curve is not affected by off-peak interferences, it most certainly is affected by *on-peak* interferences. Luckily, whether these "interferences" observed in our MAN curves is due to an actual on-peak interference, or a (previously unspecified) amount of the element in the standard, we can simply apply the rule of thumb that "background is (by definition) generally the lowest intensity we can measure". So if we see a high intensity outlier in our MAN curves, we can simply reject that intensity and re-fit the MAN curve. Here are some examples of "outliers" in MAN curves:

https://probesoftware.com/smf/index.php?topic=4.msg499#msg499

And here are some examples of a few of these high Z-bar MAN curves are seen here:

https://probesoftware.com/smf/index.php?topic=4.msg5136#msg5136

And once again, remember that one can obtain accuracy in the MAN method equal to one's precision simply by apply a suitable blank standard/sample to the analyses. This becomes especially important the higher the Z-bar of ones samples.

Of course one can also utilize a "mixture" of background acquisition methods. For example, acquire the major elements using MAN backgrounds, and traces using a higher beam current and off-peak backgrounds. What are your own thoughts regarding the selection of background methods?

[sem-geologist]

Interesting... title of the subject is Which Background Acquisition/Analysis Method is Best?, but then it is demonstrated that "it depends"  .
I probably am going to trigger everyone here. I am not PfE user and still use vendors original software (Cameca Peaksight). MAN and multi-point methods are not available for me. I look to MAN curiously, and that could be kind of a selling point to me as that could solve some analytical problems we sometimes come over. The "multi-point"... ghm... from my point of view is completely overdone, dangerous, extremely error-prone, completely useless method... it mimics beloved "democracy" - the majority wins, even if those are interfered positions and one of rejected outliers is the only correct position (if there is any correct at all).

So what is my ultimate the best of the best background method?
Don't laugh. It is single off-peak with precise slope.
Saves analytical time? ✅
Good for very precise trace analysis? ✅
Resilient against modelling/extrapolating background across absorption edge(s)? ✅
Possible to do right without WDS scanning of unknown (other time save)? ✅
No magic or hard to comprehend mathematical models, it is clear what it is doing? ✅

Well, honestly it would be a miracle to do it correctly with current vendor software tools as it requires to know the precise, interference-free (or in majority of cases the least interfered position) off-peak position and slope, which would be correct across multitude of blind standards. Vendor software is a bit blind in that direction. This however can be easily done with right additional software (attention: self-advertising) which can plot (overlay) multitude of WDS scans of high concentration standards revealing the least interfered positions, and making it possible to find the universal off-peak position and slope for all possible element combinations for the given mineral species (fortunately nature has mercy on probers, and 40+ element-bearing minerals are rare).
Yeah sure MAN curves looks nice, and probably it takes care also of spectral artefacts (particularly annoying on LPET's) without any knowledge about those... probably. But with my WDS plotting workflow and single off-peak precise slope method I exactly know what is offending my precise measurement, and most of times I can come up with some additional last-man-stand option to minimize or eliminate it (i.e. do combined-analytical conditions and analyse the troublesome element with lower voltage, which would completely eliminate 2nd order peaks and artefacts of interfering elements, which PHA can't do).

Few additional things to consider. As I do lots of REE-bearing mineral analyses (some comes with 40+ elements i.e. fergusonite) I often get to situation where there is no interference-free off-peak position (I have trouble with finding a single position for background, and now just try to imagine how the "multi-point" would be dealing with the problem... pfff...). Everyone mentions that it is not good idea to measure background on peak tails... but my situation forced me to re-investigate the possibility to ignore that superstition. I had tried that on few elements, with different concentrations, and as far the off-peak position (and slope!) is kept exactly at the same position as standard measurement there is no any visible biases depending from concentration. There is some caveats: satellite peaks, but those are directly scaled down to the peak we are measuring, and so far influence of those to measurement is much lesser (or insignificant) than interference of off-peak position with lines of other element. The only obvious requirement for this to work is the correct slope - the slope which is correct on blind standards, albeit it looks completely out-of-mind for real standard clearly pointing to position above base line of the measured peak. The secret of that is that k-ratios do not care if we deal with absolute heights or relative heights of peak as far we keep consistent per element. With measuring peak with off-peak at flank of peak we no more measure absolute height, but relative height, and that requires that all measurements would be done at exactly same off-peak position and slope as for standard.
The drawback can be in some statistical calculations of measurement (significantly lower peak/background ratio for standard can mess up the std_dev estimation and det.lim. calculations by some of formulas)

Honorable mentions, which as far I saw PfS screenshots and follow this forum clearly is not taken into consideration.
2 point off-peak from same side (most often positive side to get away with absorption edges) with extrapolation under peak, both exponential and linear.
Same side background position is mentioned in Cameca Peaksight manual. The advantage is that it is easier to setup, and can work with simple minerals. It is possible to abuse it to solve tricky situations (i.e. U Ma measurement and solving Ar K edge problem). However, when single side off-peak parameters are found it obsoletes that method.

[John Donovan]

So what is my ultimate the best of the best background method?
Don't laugh. It is single off-peak with precise slope.

I won't laugh... isn't it wonderful that we live in a world where there are so many different opinions!   

It is in light of this reality that we offer so many background correction methods in our Probe for EPMA software. Everybody gets exactly what they want!  Including one side off-peak slope backgrounds with user defined slope coefficients.