Hi Jakub,
Please understand that there is nothing extraordinary about using the MAN background correction. My guess is that, at least for geologists who utilize the software, the MAN correction is used almost all the time, at least for the major and minor elements (note that one can utilize a mix of MAN and off-peak elements for any given sample setup). The reason for it being utilized so often, is that the MAN correction saves so much time time (and improves precision) on major, and even minor elements, where very small accuracy errors in the MAN calibration curve, are generally smaller than the precision of the peak intensity measurement.
For typical geological samples with K emission lines and low to moderate average Z materials, this is usually the case. In my experience with typical silicates and oxides, the MAN background correction is accurate down to 200-300 PPM, even without a blank correction. The use of the MAN correction with higher Z matrices and high Z emission lines is still an area of active investigation. But maybe a little "MAN" history would be appropriate here...
The very first rationale for the MAN considerably preceded my own initiation to EPMA, and was invented to deal with EPMA instruments which utilized fixed monochromaters for commonly measured elements. For example, on my first EPMA instrument, which I inherited at UC Berkeley in the 1980s, it had 4 fixed monochromaters (for Si, Fe, Ca and Al), and 4 tunable spectrometers for another 4 elements. The reason of course being that fixed monochromaters *cannot* be de-tuned for the off-peak measurement! So people came up with the idea of utilizing a calibration curve of standards which did not contain the elements of interest, for the background correction for these "fixed" spectrometers. Which meant of course that using the MAN correction, we could measure 8 elements in 10 seconds! This was very useful as you might imagine for beam sensitive materials.
Since then the MAN background correction has been significantly improved and as my Amer. Min. 2016 paper showed, the MAN background correction can even be utilized for improving sensitivity for trace elements. Basically this results in a 40% or more improvement in detection limits, in 1/2 the acquisition time, because only the on-peak intensity is measured. And of course, of interest to you, one automatically avoids off-peak interferences, because there are no off-peak measurements when using the MAN correction! In addition, interpolation issues with non-linear backgrounds and/or absorption edges simply disappear with the MAN method because, again, only the on-peak position is utilized.
But even though the MAN method can result in better accuracy than off-peak methods when such off-peak issues are present, the main caveat for the MAN method remains accuracy (at least at trace levels), because we are not performing a direct measurement of the continuum on the sample. Therefore for ultimate accuracy, the MAN method is commonly combined with the so-called "blank" correction. The blank correction works well for relatively simple matrices where suitable (usually synthetic) blank samples can be obtained, e.g., quartz, zircon, pyrite, TiO2, Fe2O3, Fe3O4, etc. Of course for complex materials, zero blanks may be difficult to obtain. But it is also of interest to note that the blank correction as implemented in Probe for EPMA, can be applied to non-zero blank samples, so there is that option.
Now having said all that, the remaining practical difficulties of the MAN method is obtaining pure standards that do not contain the element of interest. As you pointed out in the linked post, many standards have not been properly characterized for trace elements. For example, I have two synthetic zircons, one appears to have a couple hundred PPM more phosphorus than the other. I have heard from many colleagues that utill they started utilizing the MAN method, they had not realized how contaminated some of their standard materials were. On the other hand, the MAN method can teach us quite a lot that we didn't already know about our standards!
Just as a small aside, Ben Hanson at Dow Corning came up with a really crazy idea for the MAN method, which is to utilize the *off-peak* interpolated intensities for the MAN calibration curve, or "offset MAN" as he called it, as described here:
https://probesoftware.com/smf/index.php?topic=987.msg6447#msg6447"Crazy as a fox" as they say! The reason he requested this because he found that many of his standards weren't as pure as he thought they were. I thought it was a good idea for another reason: sometimes I've wanted to utilize the MAN method for oxygen analysis, and it's difficult to find standards that don't contain even trace oxygen (since we live in an ocean of oxygen)! Whatever.
It boils down to this: almost without exception, the lowest intensity one can measure (by definition!) is the background. Yes, there are possible sample and/or detector absorption edges and "holes" in the background continuum due to secondary Bragg diffraction (e.g, the hole in the continuum seen in FeS2 near the Au Ma position and in some PET crystals at the Ti Ka position, though there is still some debate about this), but these are fairly rare. So in general, any standards that fall above the general trend of the MAN calibration curve are either from contamination (from the element being present), or an interference from another analytical peak.
The general strategy at the user level is to simply remove those (higher intensity) offending standards from fit of the MAN curve. Now because you are conducting a bit of a research project here with your high Z materials, you are interested in exactly what is causing these outliers in the MAN calibration curve. And that is great and you should pursue this line of inquiry because it is interesting and helpful for greater understanding of the details.
As to particular difficulties with high Z matrices, the main difficulty is due to the fact that the P/B ratios are worse for high Z matrices since from Kramers Law we know that we produce more continuum in higher Z materials. Second, when analyzing high Z emission lines, we are generally restricted to L or even M emissions and these are also typically lower P/B than K emissions. So combined this means that the calibration of the MAN curve is even more critical for high accuracy work in high Z materials, especially at low concentrations.
That said, there are advantages to using the MAN method even in complex high Z materials, as has been pointed out (no off-peak interferences and no interpolation). But I think other approaches such as the MPB (multi-point background) and even "shared" bgds can be useful for such matrices. I believe Karsten Goeman and Julien Allaz have published these methods and also have examples of these alternative off-peak methods posted elsewhere on the forum.
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