Accuracy and Precision in Using MAN Background Corrections

[Probeman]

When we consider traditional off-peak measurement we obtain a variance from the on-peak measurement and a variance from the off-peak measurement. When these measured on-peak and hi/lo off-peak intensities are subtracted from each other, the errors add in quadrature as described in the presentation posted here:

http://probesoftware.com/smf/index.php?topic=242.msg1531#msg1531

However, the MAN background method only measures the on-peak intensity and *not* the off-peak intensity. Instead the MAN background is determined by measuring the on-peak position only on a number of standard materials (pure metals, pure oxides or other relatively simple silicates and sulfides), that *do not* contain the element of interest and which cover the approximate range of average Z in the standards and unknowns.

In practice the background intensity is specified by the average atomic number of the material, which in turn is determined by the composition of the material. For determination of standards this is trivial since the standard composition is already known.  For unknown materials, the composition (and hence average Z), is determined by the matrix iteration and the background intensity is recalculated iteratively.

The important point being that for a given composition (e.g, SiO2), the MAN method always returns the same background intensity, unlike the off-peak measurement. In fact, since the MAN calibration curve is composed of multiple on-peak intensity measurements, each consisting of multiple standards, the precision of the background is over determined.

Therefore, if replicate measurements determines sensitivity, then the MAN background method provides essentially a constant background (for a given composition), and of course the method also automatically adjusts for changes in composition (as the average Z changes).

The main error associated with the MAN background is that of accuracy for concentrations below 100 to 200 PPM in silicates and oxides, slightly worse for higher Z materials). That is the reason I never considered using the MAN background method for trace elements... that is, until I realized I could apply the blank correction to deal with accuracy issues when measuring below the 200 PPM level.

Of course this only applies to specimen matrices with relatively simple compositions for which a suitable "blank" standard containing a zero (or known non-zero) concentration is available. But that includes pure metals, pure oxides, simple silicates and sulfides, etc., so that is a lot of materials.

Attached below are maps of the off-peak and MAN determined background intensities and their statistics and also the regression fits for the MAN calibration curves.

In addition here's a post showing how to compare off-peak and MAN methods on the same dataset and also a pdf comparing the off-peak, Nth point and MAN background methods on both homogeneous and heterogeneous materials.

http://probesoftware.com/smf/index.php?topic=4.msg189#msg189

Note that the x-ray maps below show the calculated backgrounds for each pixel. On the off-peak map, the calculated background is the linear interpolation of the hi and lo off-peak positions.

On the MAN map the calculated background is the regressed on-peak intensity of standards *not* containing the element of interest, corrected for continuum absorption (to obtain the generated continuum intensity inside the sample) and then based on the calculated composition and hence average atomic number, finally decorrecting the continuum intensity obtained from the regression for the unknown specimen matrix effects.

This results in a much more constant background which results in better precision (and for a given composition, the background production physics should be always the same, no?).

Think of it this way: if one re-measures the MAN regression, of course the fit coefficients will be slightly different, hence giving a different background intensity for the same average Z compared to the previous MAN calibration. This intensity difference between MAN regressions merely represents a systematic accuracy error, since each new MAN regression fit will repeatedly produce the same high precision intensity for a given composition and hence average Z for every new measurement resulting in improved precision when it is subtracted from the on-peak measurement.

[Probeman]

The MAN bgd intensities are recalculated in each iteration of the matrix correction.  Basically we have two iteration loops. One loop for the normal matrix correction (whatever that might be), and a second outer iteration loop for all the compositionally dependent corrections such as: MAN backgrounds, quantitative spectral interferences, area-peak factors, etc.

But although one can discuss the "variance" of the MAN regression (and it is calculated and printed out in PFE), I've thought about this and here's my take:  because variance is usually determined from replicate measurements and because every time we "measure" the MAN background we get almost the same intensity every time (that is for a given composition), that to me indicates that we have high precision but possibly not high accuracy (compared to actually measuring the off-peak intensities as is often done). 

Yes, if we re-measure the MAN calibration stds again will get a new regression, but again, the returned intensities vary only with average atomic number, and again the precision of the regression is very high (because it is the average of many std points regressed and even intensity drift corrected if more than one standard set is acquired).

On the other hand, for obtaining high accuracy we use the blank correction. Which by the way isn't even necessary for x-ray mapping in most cases, because the variance of the on-peak data will be larger than the blank correction itself. For point analyses, sufficient precision is obtainable in 10 or 20 seconds of on-peak counting, hence, the need for a blank correction when trying to determine trace element concentrations below 100 to 200 PPM in oxides and silicates.

[Karsten Goemann]

John, I've been thinking about this a little bit.

Your example comparison with the Ti in SiO2 mapping is nice empirical evidence that precision is better for MAN.

And you're right, once a set of MAN fit curves is established these will always return the same background intensity value for a given MAN. I'm not a statistician, but one could even argue that the MAN regression "variance" affects in fact accuracy and not precision, as it is more a measure of the scatter of the data points (so the fit might not be very reliable). But it might still be a valid measure of the error of the MAN background value, so could this variance propagated through to the background intensity? Just interested how large those uncertainties in the background intensities would be. Would that be as simple as using the calculated MAN regression variance (say 5% relative) for the background intensity?

The calculated MAN for an unknown would obviously also depend on its (mostly major element) composition which has a precision, so that should propagate to the calculated MAN and therefore the calculated background intensity. This is clearly irrelevant for trace analysis in simple matrices, where you can assume for example 99.99 wt% SiO2 and therefore fixed MAN, but not necessarily for more complex compositions, where multiple major/minor elements are measured with varying counting statistics. Still I'd assume that contribution to the overall precision to be smaller than a conventional off-peak measurement (as it is based on on-peak measurements with better counting statistics), but it should be possible to calculate that.

As you already said, there's still the issue that the calculated background value might be systematically wrong for a variety of other reasons (bad standards, wrong reference compositions, interferences, not enough standards, outliers in standard measurements, instrument drift since MAN curve acquisition...). As far as I can see these should also only affect the accuracy, not the precision. Many of them will show up as scatter in data points and with that in the MAN regression variance.

As you suggest a blank correction would remove many systematic errors. So this might also be a way of dealing with things like instrument drift, as no-one really seems to have long-term experience how stable MAN curves are over time, even though they seem quite stable. But the precision of the blank measurement should be propagated to the actual unknown measurements. Is this something you're doing? On the other hand, when using a blank correction, the MAN regression variance should definitely become irrelevant, shouldn't it?

[jared.wesley.singer]

Admittedly, we use multi-element reference materials most often, therefore MAN regressions should trend systematically high due to the collective effect of direct and higher-order interferences.  Rather than fit to on-peak intensities, I would fancy using carefully-selected, off-peak measurements to interpolate the on-peak MAN background.  Or to be Xtreme, could on-peak, off-peak, multi-point, wavelength scans, and any type of background be aggregated for complete characterization of the MAN background?

Karsten asked:

On the other hand, when using a blank correction, the MAN regression variance should definitely become irrelevant, shouldn't it?

MAN regression variance would be minimized for a collection of closely matrix-matched blanks.  Or that is to say a perfect matrix-matched blank correction requires no additional background treatment.  However, pseudo-blanks (on a different matrix) creates the MAN regression variance.

Sincerely,

Jared

[Probeman]

Admittedly, we use multi-element reference materials most often, therefore MAN regressions should trend systematically high due to the collective effect of direct and higher-order interferences. 

Hi Jared,
This is exactly why one should have a few pure oxides or even pure metals available for the MAN fit. We typically use MgO, Al2O3, SiO2, TiO2 and MnO and/or NiO.

Note that when an interference is present (and/or an unexpected contamination in the MAN std), the intensity for that standard will plot above the MAN regression line as seen here:



As for unexpected contamination in the std used for the MAN fit, it also looks similar as seen here where several of Paul Carpenter's in house standards contain some unexpected traces of Mn:



In these cases it is not actually necessary for the analyst to know whether the outlier is due to a contamination or an interference, but it really doesn't matter for most purposes (though if it really is a contamination that you found, at least you learned something about your standards you didn't know before!). Therefore simply unselect the offending std intensities using a <ctrl> click and PFE will update the fit.

Rather than fit to on-peak intensities, I would fancy using carefully-selected, off-peak measurements to interpolate the on-peak MAN background.

I'm sorry if this sounds a little harsh, but not using the on-peak intensities defeats the entire point of the MAN background method. Yes, one could interpolate from off-peak measurements, but then one is doing exactly what we are trying to avoid- an interpolation!

Using the on-peak intensities for materials that do *not* contain the element of interest (and/or interferences and/or contamination) allows us to *directly* measure the continuum. For example, what if the continuum is curved? Using the on-peak intensities eliminates the issue entirely.

Or to be Xtreme, could on-peak, off-peak, multi-point, wavelength scans, and any type of background be aggregated for complete characterization of the MAN background?

Well that certainly is "Xtreme", so I'll leave this task to the "next generation".   

Karsten asked:

On the other hand, when using a blank correction, the MAN regression variance should definitely become irrelevant, shouldn't it?

MAN regression variance would be minimized for a collection of closely matrix-matched blanks.  Or that is to say a perfect matrix-matched blank correction requires no additional background treatment.  However, pseudo-blanks (on a different matrix) creates the MAN regression variance.

I agree. Which is why I would only use a single blank standard for trace element work that is "matrix matched". E.g., pure elements, pure oxides and simple silicates (e.g., ZrSiO4).

But keep in mind that for most oxides and silicates, the MAN method accuracy *without* the blank correction is around 100 to 200 PPM. That is to say, within the counting statistics variance for most situations of major and minor elements.

Here's another way to think about this: with off-peak measurements one has to acquire three good intensities for every analysis point. But with the MAN method, you only need one good intensity measurement for every analysis point! Which includes MAN standards of course! That's 1/3 less chance of stumbling across a spectral interference at your spectrometer positions- comes to about 1/2 the acquisition time also. Not to mention better precision as described above.

Now it's true that one has to measure a few more standards for the MAN regression, but that only needs to be done once during a run because the continuum intensities (being what they are- that is, relatively flat), are very stable and reproducible and we see almost no drift in the MAN background intensities over days, weeks and depending on the instrument, even longer.

So when I fobbed your suggestion off (I hope I wasn't too snarky!) about using off-peak measurements for MAN calibrations, it wasn't so much that the work would be daunting- because it would be a lot of work, but I honestly can't see any advantages.

By the way, if you're interested in comparing the two background methods- along with Nth point backgrounds, see this:

http://probesoftware.com/smf/index.php?topic=4.msg189#msg189

[Probeman]

I've recently had some utterly illuminating discussions with Jared Singer (at RPI) regarding the above questions concerning accuracy and precision for MAN backgrounds and wanted to give a quick highlight of a few of the ideas we discussed. I'm at M&M at the moment so I will cover this in more detail after I get back to UofO.

One question of a few of my colleagues is "shouldn't you be including the precision of the MAN regression in the background calculation"?  And the answer that Jared and I have both come to is, yes and no... 

Here is a short response: consider a normal off-peak measurement where the interpolated off-peak intensity is subtracted from the on-peak intensity.  When this net intensity is then converted to a concentration, do you include in the concentration calculation any consideration of the precision of the measurement?  Of course not!  You simply convert the net intensity to concentration through the matrix correction physics method(s).

Now, should you include the precision of the off-peak measurement in your estimation of the measurement precision or sensitivity?  Of course you should! 

At a zero concentration, the variance of the off-peak measurement will be equal to the variance of the off-peak measurement. That is to say, just as important and therefore, you should (must) include the variance of both terms in the sensitivity calculation. See attachment below showing how they add in quadrature.

It is exactly the same for MAN background calculations!

When we calculate the net intensity, by subtracting the background intensity derived from the MAN regression curve from the on-peak measurement, we then simply convert that net intensity to a concentration using the matrix correction physics just as we did for the off-peak net intensity.

So let us be completely clear on this question: the concentrations calculated from the MAN background corrected net intensities include everything that should included. No different from off-peak intensity corrected net intensities.

Should we then include the statistics of the MAN regression curve in our calculation of the sensitivity of our measurement?  Yes, of course we should!  But here is where it gets a little complicated...

The off-peak variance is calculated simply from the off-peak intensity by taking the square root of the off-peak intensity (raw counts). However, we can't do that for the MAN sensitivity calculation because that calculation does *not* behave according to Poisson statistics!

Consider:

The MAN background intensity is based on the calculated average atomic number (Z-bar) of our material, which in turn is calculated from the complete composition of the material which is of course, dominated by the concentrations of the major elements in our material. And these major element concentrations have much, much better statistics than the off-peak photons we are measuring for our traditional off-peak measurement!

And this is part of the reason why we get so much better sensitivity for trace elements using the MAN method.  There is more to discuss but I will leave it here for the moment.

Edit by John: here is a good thought experiment for these questions: ask yourself how precisely we would be able to calculate the average Z of a material, if we could only base that calculation on a measurement of the off-peak continuum intensity?

[Probeman]

I've recently implemented new sensitivity expressions for the MAN background method using Jared Singer's sensitivity expressions (in press soon). In addition I've added code to handle the related situation of Nth point backgrounds.

These two background methods are somewhat related because with Nth point backgrounds the off-peak background is measured *once* and then re-utilized for subsequent measurements. This is statistically similar to the MAN background method where one uses only a *single* MAN standard for the MAN calibration curve.  In both these Nth point and MAN cases the background intensities are unchanging and there a constant subtraction to obtain the net intensity.

The advantage of the Nth point measurement is that it is a direct measurement of the background (on either side of the emission line), so as long as there are no off-peak interferences or other continuum artifacts, the accuracy should be reasonable. The disadvantage is that the Nth point method cannot handle heterogeneous compositions because it is constant (though of course it can be remeasured- see the "Nth point monitor element" feature in PFE under Acquisition Options for automatic handling of this issue).

On the other hand the MAN method (as long as one utilizes more than a single standard for the MAN calibration curve!), will automatically adjust the background intensity for changes in composition (z-bar).

Here is the same zircon data calculated for detection limits to demonstrate the difference in sensitivity for the three methods (off-peak, Nth point and MAN). First normal off-peak measurements:

ELEM:       Th      Hf       U       P       Y
BGDS:      LIN     EXP     LIN     EXP     LIN
TIME:   640.00  640.00  640.00  640.00  640.00
BEAM:   100.54  100.54  100.54  100.54  100.54

ELEM:       Th      Hf       U       P       Y   SUM 
    41    .000    .001   -.007    .000   -.001  99.994
    42   -.006    .000   -.005    .000    .000  99.989
    43    .004   -.005    .004   -.001    .000 100.002
    44    .001    .003    .009    .000   -.002 100.011
    45    .001    .001    .000    .000    .002 100.004

AVER:     .000    .000    .000    .000    .000 100.000
SDEV:     .003    .003    .007    .000    .001    .009
SERR:     .002    .001    .003    .000    .001
%RSD:     ----    ----    ----    ----    ----
STDS:       16      19      15    1016    1016

STKF:    .6826   .6120   .8775   .1524   .4418
STCT:    53.02  177.68  210.23  165.04   38.86

UNKF:    .0000   .0000   .0000   .0000   .0000
UNCT:      .00     .00     .00     .00     .00
UNBG:      .23    1.72     .59     .50     .12

ZCOR:   1.4540  1.2062  1.3919  1.3052  1.3133
KRAW:    .0000   .0000   .0000   .0000   .0000
PKBG:     1.00    1.00    1.00    1.00    1.00
BLNK#:       3       3       3       3       3
BLNKL: .000000 .000000 .000000 .000000 .000000
BLNKV: .002554 .007915 .019915 -.00383 -.00673

Detection limit at 99 % Confidence in Elemental Weight Percent (Single Line):

ELEM:       Th      Hf       U       P       Y
    41    .011    .006    .005    .001    .006
    42    .011    .006    .005    .001    .006
    43    .011    .006    .005    .001    .006
    44    .011    .006    .005    .001    .006
    45    .011    .006    .005    .001    .006

AVER:     .011    .006    .005    .001    .006
SDEV:     .000    .000    .000    .000    .000
SERR:     .000    .000    .000    .000    .000


Now the same data but calculated (artificially using only the off-peak measurement from the first point) using the Nth point method:

ELEM:       Th      Hf       U       P       Y
BGDS:      LIN     EXP     LIN     EXP     LIN
TIME:   640.00  640.00  640.00  640.00  640.00
BEAM:   100.54  100.54  100.54  100.54  100.54

ELEM:       Th      Hf       U       P       Y   SUM 
    41    .001    .002   -.002    .000    .002 100.003
    42   -.003   -.002    .003    .000    .002  99.999
    43    .002   -.001   -.001    .000    .000 100.000
    44   -.002    .000    .001    .000   -.004  99.996
    45    .001    .000   -.001    .000    .000 100.001

AVER:     .000    .000    .000    .000    .000 100.000
SDEV:     .002    .001    .002    .000    .002    .003
SERR:     .001    .001    .001    .000    .001
%RSD:     ----    ----    ----    ----    ----
STDS:       16      19      15    1016    1016

STKF:    .6826   .6120   .8775   .1524   .4418
STCT:    53.02  177.69  210.34  165.15   38.85

UNKF:    .0000   .0000   .0000   .0000   .0000
UNCT:      .00     .00     .00     .00     .00
UNBG:      .23    1.72     .60     .50     .13

ZCOR:   1.4540  1.2062  1.3919  1.3052  1.3133
KRAW:    .0000   .0000   .0000   .0000   .0000
PKBG:     1.00    1.00    1.00    1.00    1.00
BLNK#:       3       3       3       3       3
BLNKL: .000000 .000000 .000000 .000000 .000000
BLNKV: .002298 .007174 .014261 -.00378 -.00978

Detection limit at 99 % Confidence in Elemental Weight Percent (Single Line):

ELEM:       Th      Hf       U       P       Y
    41    .007    .004    .004    .001    .004
    42    .007    .004    .004    .001    .004
    43    .007    .004    .004    .001    .004
    44    .007    .004    .004    .001    .004
    45    .007    .004    .004    .001    .004

AVER:     .007    .004    .004    .001    .004
SDEV:     .000    .000    .000    .000    .000
SERR:     .000    .000    .000    .000    .000


Finally the same data again, but calculated using the MAN background method:

ELEM:       Th      Hf       U       P       Y
BGDS:      MAN     MAN     MAN     MAN     MAN
TIME:   640.00  640.00  640.00  640.00  640.00
BEAM:   100.54  100.54  100.54  100.54  100.54

ELEM:       Th      Hf       U       P       Y   SUM 
    41    .000    .002   -.002    .000    .002 100.002
    42   -.003   -.002    .002    .000    .002  99.998
    43    .002   -.001   -.002    .000    .000  99.999
    44   -.002    .000    .001    .000   -.004  99.995
    45    .001    .000   -.001    .000    .000 100.000

AVER:    -.001    .000    .000    .000    .000  99.999
SDEV:     .002    .001    .002    .000    .002    .003
SERR:     .001    .001    .001    .000    .001
%RSD:  -406.91    ---- -455.52-1696.42-2213.37
STDS:       16      19      15    1016    1016

STKF:    .6826   .6120   .8775   .1524   .4418
STCT:    53.02  177.68  210.23  165.04   38.86

UNKF:    .0000   .0000   .0000   .0000   .0000
UNCT:      .00     .00     .00     .00     .00
UNBG:      .25    1.71     .65     .28     .12

ZCOR:   1.4540  1.2062  1.3919  1.3052  1.3133
KRAW:    .0000   .0000   .0000   .0000   .0000
PKBG:     1.00    1.00    1.00    1.00    1.00
BLNK#:       3       3       3       3       3
BLNKL: .000000 .000000 .000000 .000000 .000000
BLNKV: -.03836 .011354 -.01593 .021674 .005046

Detection limit at 99 % Confidence in Elemental Weight Percent (Single Line):

ELEM:       Th      Hf       U       P       Y
    41    .007    .004    .004    .001    .004
    42    .007    .004    .004    .001    .004
    43    .007    .004    .004    .001    .004
    44    .007    .004    .004    .001    .004
    45    .007    .004    .004    .001    .004

AVER:     .007    .004    .004    .001    .004
SDEV:     .000    .000    .000    .000    .000
SERR:     .000    .000    .000    .000    .000


Note that the Nth point and MAN methods produce slightly different background intensities (see the row labeled UNBG:), but similar detection limits. This is because the variance on the Nth point background intensities is zero (a constant), and the average Z of the MAN method is almost zero, when the sample matrix is specified as ZrSiO4 by specified composition or by difference. When the major elements are measured rather than specified, the MAN background intensity variance is slightly larger but still smaller than compared to a direct measurement of the continuum.  Why?  Because the specimen average Z variance is dominated by the major element counting statistics, rather than continuum intensity statistics...

[Probeman]

The following graphs are from a recent abstract and makes a clear point about the advantages of MAN background methods for trace elements for points, but especially for x-ray mapping.

[Probeman]

The following graphs are from a recent abstract and makes a clear point about the advantages of MAN background methods for trace elements for points, but especially for x-ray mapping.

Here is a link to the full paper as a pdf, published this month in American Mineralogist, describing the precision improvements in detail:

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

[Probeman]

I'm at AGU this week with a presentation on using the MAN (mean atomic number) background correction (and the blank correction) for improving precision of trace element analyses. In thinking through the talk a number of points came to mind and I thought I would share them here:

1. The MAN background correction was originally invented because some early EPMA instruments had fixed monochromaters for some elements (necessity is the mother of invention!). For example, our ARL SEMQ instrument at UC Berkeley in the 1980s had four (normal) tunable spectrometers and also 4 fixed spectrometers permanently tuned to Si, Fe, Ca and Al. These fixed spectrometers required a method to correct for background because they could not be de-tuned off-peak! On the other hand, we could measure 8 elements in 10 seconds!  (so much for technological progress!)

By utilizing Kramers Law, where it is observed that the continuum intensity is a function of the specimen average atomic number (Z-bar), and constructing a calibration curve by measuring the on-peak intensities in standards that *do not* contain the element of interest, and a physics model for the difference in absorption of the continuum in both the MAN calibration standards and the unknown, one can accurately measure major and minor elements, down to around 100 to 200 PPM in any material.

The advantages of the MAN method are several, for example saving time by not measuring off-peak intensities or moving to and from off-peak positions. Also off-peak interferences become moot, because one does not measure any off-peaks! 

2. Originally we assumed that the MAN method was limited to major and minor elements due to continuum artifacts which appeared to limit the accuracy of the method to 100-200 PPM or so, but a few years ago after implementing the so called "blank correction" for improving accuracy for trace elements using traditional off-peak methods seen here:

http://pages.uoregon.edu/epmalab/pdfs/3631Donovan.pdf

I realized this same blank correction method could also be utilized to improve the accuracy of trace elements using the MAN background method. Hence the topic of my recent Amer. Min. paper here:

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

and the topic of my talk this week at AGU.

3. And in the case of trace elements (as demonstrated in the paper), the MAN correction has an additional advantage over traditional off-peak methods (where the continuum is measured directly): that is, the sensitivity of the MAN method is significantly better than the off-peak method. This is because the variances of the on-peak and off-peak intensities add in quadrature and therefore the precision of the measurement is worse when the off-peak background correction is performed to obtain the net intensities. Yes, the MAN background correction still contains the variance of the on-peak measurement, but the MAN background intensity is much more precise than the off-peak method for a couple of reasons.

4. First, because the MAN background correction is obtained form multiple measurements on multiple standards, the resulting regression is more precise than a normal off-peak measurement. Second, the MAN background intensity obtained from the MAN regression is determined by the *average Z* of the standards (which are fixed because their compositions are already known) and for the unknowns, the average Z is either determined by the measured matrix elements- which results in a very high precision because the matrix average Z is constrained by major element counting statistics not continuum statistics! Or because in the case of simple matrices such as SiO2, TiO2, ZrSiO4, FeS2, etc., etc., the matrix may simply be *specified", for example ZrSiO4 by difference from 100%. In which case the variation in the specimen average Z approaches zero, since the variation in the trace elements has little or no effect on the composition, and hence, average Z. It's almost as though your unknown average Z is as well constrained as the average Z of the standards, because the matrix is now highly reproducible (that is to say: known).

To be continued...
john

[Probeman]

5. Now originally, when I first began presenting these trace element measurements using the MAN correction, several colleagues took me aside to say that I was missing something. And what they said was: it is all well and good to use the MAN background correction for trace elements, but that I must include the precision of the MAN regression in the sensitivity calculation for detection limits.

But here is the interesting thing: that would be completely true only *if* we were to re-measure the MAN calibration curve for every point or pixel, but in fact we don't. Generally we measure the MAN calibration curve maybe once every probe session, and maybe even less often than that, as the continuum intensities for a given emission line for a given spectrometer/crystal are extremely stable (unlike on-peak intensities!), and therefore the uncertainty in the MAN regression curve is basically an accuracy issue, not a precision issue. Which can be corrected using the blank correction!

If you need more convincing on this point, please check the MAN trace paper where we compared calculated sentivities with and without the MAN regression precision, with the actual observed variance in the background intensities, and the results are clear that we should not be including the MAN regression precision in the sensitivity for detection limits.

Is this making more sense?  I hope so, because I certainly agree all this is rather unintuitive, as both reviewers of the MAN trace paper mentioned their reviews, even as they were convinced (I wonder who you are?).

6. The advantage of the MAN correction (over say the Nth point method) is that as the composition of the unknown changes, the calculation of average Z changes, and therefore the regressed MAN background intensity adapts automatically. So you never re-measure the background, but your background correction is always accurate.

7. Now in the case of trace element measurements, we have to deal with the fact that the accuracy of the MAN method becomes equal to the concentration below 100-200 PPM, due to various continuum artifacts, drift, etc. But by utilizing a standard for the blank correction, which has a known zero concentration, or even a known *non-zero* concentration of the element of interest, we convert that offset (measured under similar conditions as the unknown), from a concentration to a virtual intensity, which is then matrix corrected for the actual unknown composition (which is essentially no correction at all if the standard for the blank correction is a close matrix match to the unknown composition). But this means that the standard used for the blank correction doesn't really need to be a close matrix match to the unknown! 

8. Now I typically tell people, yes, use the MAN and blank correction together for trace element measurements in simple matrices where one has a close matrix match to the unknown, e.g., synthetic SiO2, ZrSiO4, etc., but use the traditional off-peak (or even better use the multi-point background method), for complex materials such as traces in amphiboles, feldspars or monazite. But, if we consider the fact that because the blank intensity offset is automatically corrected for the difference in matrix correction between the blank standard and the unknown, this might not even be necessary to have a close matrix match.

9. Do I have any evidence for the above claim?  Not a lot and we should perform some careful measurements using the MAN and blank correction on some (standard) complex materials to see how well it performs.  But I do have this:

http://pages.uoregon.edu/epmalab/reports/Withers%20hydrous%20glass.pdf

This was an attempt to measure water in glasses by measuring oxygen directly (as first described by B. Nash), then calculating the amount of oxygen from cation stoichiometry, and subtracting them, resulting in an excess (or a deficit) of oxygen, which can then be converted into water or hydroxyl. 

10. Now in the above example of measuring oxygen in hydrous glasses, even after I used the best MACs, corrected for peaks shape, and dealt with the intensity changes over time (TDI), my oxygen accuracy wasn't quite as good as I would have liked.  So then I thought: wait, I have the blank correction! And remember, the element in the standard used for the blank correction doesn't have to be zero, it can be non-zero as well. And because the blank offset is matrix corrected from the blank standard to the unklnown, I really don't need an exact matrix match.

So I ran the NIST mineral glasses as a blank standard for oxygen (that is I measured it as an unknown under the same conditions as my hydrous glasses), but from photometry of the NIST glasses, I know the ferric/ferrous ratio and hence the total oxygen, I can "blank" correct the oxygen measurement in my unknown hydrous glasses. I guess probably should not be calling this a "blank" correction, since the oxygen in the NIST glass is around 44 wt. %!

11. Now, I'm not claiming that one should try to measure water in glasses by direct measurement of oxygen- it is a very difficult measurement to make, but it does demonstrate that the standard used for the blank correction might not need to be a close matrix match to the unknown, even in the case of oxygen which of course has a very large matrix correction!

Just some ideas floating around in my head this afternoon...
john

[Probeman]

Just a weird thought for the day I'd like to share...

Many of you are familiar with the blank correction which relies on measuring a material (as an unknown) with a zero concentration of an element of interest, to determine our accuracy for that trace element:

https://probesoftware.com/smf/index.php?topic=928.0

https://probesoftware.com/smf/index.php?topic=29.0

The idea being that we can determine the accuracy of a zero concentration better than a non-zero concentration. That is, a non-zero concentration is subject to several sources of error, primarily the accuracy of the background correction.  However, a zero concentration, that is, well below our detection limit, is simply a zero concentration.  A zero concentration measurement in essence, defines our zero background.

And as I have stated on a few occasions, it is a rare event in science when once can be assured that our measurement accuracy is as good as our measurement sensitivity (usually our accuracy is considerably worse than our precision!).  So we should all thanks the science gods that when we make a zero concentration measurement (in a suitably matrix matched blank), we can actually obtain accuracy that is equal to our measurement precision. That is a rare and beautiful thing. And using the blank correction described above, we can apply that zero cocentration accuracy to our unknown samples.

So how does all this blank stuff apply to the MAN correction? Which is after all, the subject of this topic! 

Well it occurs to me that in a way, the MAN background correction curve is a sort of multi-standard blank correction! Because you see, we are also measuring our MAN background in materials that contain a zero concentration of the element of interest!

Now of course since we want to apply this MAN background to a range of compositions, we need to measure these zero concentration intensities in various materials that cover a range of z-bar. And because those materials are of varying composition, we need to apply an absorption correction to deal with the matrix differences (we don't want to apply a Z correction!).

In a way, this is very similar to how we handle a not exactly matrix matched blank sample or a blank sample with a non-zero concentration of the element of interest. That is we calculate the expected intensity of that element using a matrix correction. The details of that are explained in the following paper:

https://pubs.geoscienceworld.org/msa/ammin/article-abstract/96/2-3/274/45333/Improved-electron-probe-microanalysis-of-trace

Pretty weird if you think about it...

[Ben Buse]

I've probably asked before but I can't remember the answer

Does reported detection limit & sensivity for MAN use the equations in this paper https://pubs.geoscienceworld.org/msa/ammin/article-abstract/101/8/1839/264218/A-new-EPMA-method-for-fast-trace-element-analysis?redirectedFrom=fulltext

ie better than peak and background

For reported statistics in PFE and CalcImage

[Probeman]

I've probably asked before but I can't remember the answer

Does reported detection limit & sensivity for MAN use the equations in this paper https://pubs.geoscienceworld.org/msa/ammin/article-abstract/101/8/1839/264218/A-new-EPMA-method-for-fast-trace-element-analysis?redirectedFrom=fulltext

ie better than peak and background

For reported statistics in PFE and CalcImage

The short answer is no, but it's complicated and I would be open to looking into this further. There's actually a flag set in the code to not use Singer's regression fit statistics.  I think the reason was that his expression didn't work as well as a modified expression I came up with subsequent to publication.

Here's the specific line in the code:

Code: [Select]

' Now calculate the MAN bgd conc variance for this data point using Singer's full MAN variance expression
UseDonovanModificationFlag = True
If Not UseDonovanModificationFlag Then
conc1variance! = bgdcoeff!(2) * Sqr(zsumsq!) + (analysis.zbar! * sigma_slope!) + (1# * sigma_intercept!)

' Now calculate the MAN bgd conc variance for this data point using Donovans modification (w/o regression statistics)
Else
conc1variance! = bgdcoeff!(2) * Sqr(zsumsq!)
End If

The full code for the full function is here:

Code: [Select]

Function ConvertDetectionLimits3(datarow As Integer, chan As Integer, analysis As TypeAnalysis, sample() As TypeSample) As Single
' Calculate raw background variance for a single element using Jared Singer MAN expressions (assume linear fit situation)

ierror = False
On Error GoTo ConvertDetectionLimits3Error

Dim UseDonovanModificationFlag As Boolean
Dim n As Integer, i As Integer, j As Integer, ip As Integer, npts As Integer
Dim stdnum As Integer, spts As Integer

Dim stdbgdtime As Single, stdbgdbeam As Single, tbgddevraw As Single

Dim conc1variance As Single, conc2variance As Single, concvariance As Single
Dim peakvariance As Single, peakvariancecps As Single

Dim xprime As Single, yprime As Single
Dim xsumsq As Single, ysumsq As Single
Dim xsumsq_data As Single, zsumsq As Single

Dim sigma_slope As Single, sigma_intercept As Single
Dim sigma_intercept_x As Single, sigma_intercept_y As Single

Dim xdata() As Single
Dim ydata() As Single

Dim bgdcoeff(1 To MAXCOEFF%) As Single

' Default is zero deviation
ConvertDetectionLimits3! = 0#

' This statement assumes gaussian statistics and does *not* actually apply to MAN backgrounds
tbgddevraw! = Sqr(bgdcount!)                         ' in case there are insufficient regression points to utilize Singer MAN expressions
tbgddevraw! = tbgddevraw! * 0.66                     ' assume MAN statistics are 1/3 better than off-peak statistics in case there are insufficient regression points

' Therefore, until the new equations from Jared Singer are implemented, assume off-peak statistics for MAN sensitivity
If Not UseSingerMANExpressionsFlag Then
ConvertDetectionLimits3! = tbgddevraw!
bgd_onlydevcps! = tbgddevraw! / bgdtime!
Call DataCorrectDataBeamDrift(bgd_onlydevcps!, bgdbeam!)
If ierror Then Exit Function
Exit Function
End If

' Determine average count time and beam current for all MAN standards for this channel
spts% = 0
stdbgdtime! = 0#
stdbgdbeam! = 0#
For j% = 1 To MAXMAN%
If sample(1).MANStdAssigns(j%, chan%) > 0 Then
spts% = spts% + 1
stdbgdtime! = stdbgdtime! + analysis.MANAssignsCountTimes!(j%, chan%)
stdbgdbeam! = stdbgdbeam! + analysis.MANAssignsBeamCurrents!(j%, chan%)
End If
Next j%

' Calculate averages
If spts% < 1 Then Exit Function
stdbgdtime! = stdbgdtime! / spts%
stdbgdbeam! = stdbgdbeam! / spts%
If DebugMode Then Call IOWriteLog("ConvertDetectionLimits3: Chan: " & Format$(chan%) & ", avg time: " & Format$(stdbgdtime!) & ", avg beam: " & Format$(stdbgdbeam!))

' Calculate regression fit variance for linear MAN fit (polynomial regression statistics are too difficult says Jared Singer)
npts% = 0
For j% = 1 To MAXMAN%
If sample(1).MANStdAssigns(j%, chan%) > 0 Then

' Obtain average atomic number for this standard
ip% = IPOS2(NumberofStandards%, sample(1).MANStdAssigns%(j%, chan%), StandardNumbers%())
If ip% > 0 Then
npts% = npts% + 1
ReDim Preserve xdata(1 To npts%) As Single
ReDim Preserve ydata(1 To npts%) As Single

xdata!(npts%) = analysis.StdZbars!(ip%)
ydata!(npts%) = analysis.MANAssignsCounts!(j%, chan%)           ' normalized cps/nominal beam units

' Now convert MAN intensities to concentrations (1.0 = 100%)
If CorrectionFlag% = 0 Then
ydata!(npts%) = analysis.StdAssignsKfactors!(chan%) * ydata!(npts%) / analysis.StdAssignsCounts!(chan%) * analysis.UnkZAFCors!(4, chan%)
ElseIf CorrectionFlag% > 0 And CorrectionFlag% < 5 Then
ydata!(npts%) = ydata!(npts%) / analysis.StdAssignsCounts!(chan%) * analysis.UnkBetas!(chan%)
ElseIf CorrectionFlag% = MAXCORRECTION% Then
End If

End If

End If
Next j%

' Check for sufficient number of fit points for regression statistics (need at least three points for statistical calculations below!)
If npts% < 3 Then
ConvertDetectionLimits3! = tbgddevraw!                                           ' just use simple calculation above
Exit Function
End If

' Now re-fit the MAN intensities in raw intensities
Call LeastSquares(Int(1), npts%, xdata!(), ydata!(), bgdcoeff!())                ' use linear fit statistics
If ierror Then
ConvertDetectionLimits3! = tbgddevraw!                                           ' just use simple calculation above
Exit Function
End If

' Now sum the differences
xsumsq! = 0#
ysumsq! = 0#
xsumsq_data! = 0#

' Calculate the sum of differences squared
For n% = 1 To npts%
xprime! = (ydata!(n%) + bgdcoeff!(1)) / bgdcoeff!(2)                             ' assume linear fit (easier!)
yprime! = bgdcoeff!(1) + bgdcoeff!(2) * xdata!(n%)                               ' assume linear fit (easier!)

xsumsq! = xsumsq! + (xdata!(n%) - xprime!) ^ 2
ysumsq! = ysumsq! + (ydata!(n%) - yprime!) ^ 2
xsumsq_data! = xsumsq_data! + xdata!(n%) ^ 2
Next n%

' Now calculate the regression uncertainty for the slope (m)
sigma_slope! = 1# / (npts% - 2) * ysumsq!
sigma_slope! = sigma_slope! / xsumsq!
sigma_slope! = Sqr(sigma_slope!)

' Now calculate the regression uncertainty for the intercept (b)
sigma_intercept_x! = Sqr(xsumsq_data! / (npts% * xsumsq!))
sigma_intercept_y! = Sqr(ysumsq! / (npts% - 2#))
sigma_intercept! = sigma_intercept_x! * sigma_intercept_y!

' Calculate the concentration variances for unknown elements (calculate peakdevconc!())
Call ConvertDetectionLimits4(datarow%, analysis, sample())
If ierror Then
ConvertDetectionLimits3! = tbgddevraw!                                           ' just use simple calculation above
Exit Function
End If

' Calculate the sum of the atomic number * concentrations squared
zsumsq! = 0#
For i% = 1 To sample(1).LastElm%
zsumsq! = zsumsq! + (analysis.AtomicNumbers!(i%) * peakdevconc!(i%)) ^ 2
Next i%

' Now calculate the MAN bgd conc variance for this data point using Singer's full MAN variance expression
UseDonovanModificationFlag = True
'UseDonovanModificationFlag = False
If Not UseDonovanModificationFlag Then
conc1variance! = bgdcoeff!(2) * Sqr(zsumsq!) + (analysis.zbar! * sigma_slope!) + (1# * sigma_intercept!)

' Now calculate the MAN bgd conc variance for this data point using Donovans modification (w/o regression statistics)
Else
conc1variance! = bgdcoeff!(2) * Sqr(zsumsq!)
End If

' Convert bgd only concentration variance to cps variance (for output to debugmode log window in ConvertDetectionLimits5)
If CorrectionFlag% = 0 Then
bgd_onlydevcps! = analysis.StdAssignsCounts!(chan%) * conc1variance! / (analysis.StdAssignsKfactors!(chan%) * analysis.UnkZAFCors!(4, chan%))
ElseIf CorrectionFlag% > 0 And CorrectionFlag% < 5 Then
bgd_onlydevcps! = analysis.StdAssignsCounts!(chan%) * conc1variance! / (analysis.StdAssignsBetas!(chan%) * analysis.UnkBetas!(chan%))
ElseIf CorrectionFlag% = MAXCORRECTION% Then
End If

' Now calculate the raw intensity variance under the peak (bgdcount! is calculated in ConvertDetectionLimits2 module)
peakvariance! = Sqr(bgdcount!)

' Normalize peak variance intensity to cps for concentration conversion
peakvariancecps! = peakvariance! / bgdtime!
Call DataCorrectDataBeamDrift(peakvariancecps!, bgdbeam!)
If ierror Then Exit Function

' Convert peak (bgd) cps variance to concentration (1.0 = 100%)
If CorrectionFlag% = 0 Then
conc2variance! = analysis.StdAssignsKfactors!(chan%) * peakvariancecps! / analysis.StdAssignsCounts!(chan%) * analysis.UnkZAFCors!(4, chan%)
ElseIf CorrectionFlag% > 0 And CorrectionFlag% < 5 Then
conc2variance! = peakvariancecps! / analysis.StdAssignsCounts!(chan%) * analysis.UnkBetas!(chan%)
ElseIf CorrectionFlag% = MAXCORRECTION% Then
End If

' Now add the peak and bgd concentration variances in quadrature to obtain the net MAN concentration variance
concvariance! = Sqr(conc1variance! ^ 2 + conc2variance! ^ 2)

' Now convert the net concentration variance back to cps intensity variance
If CorrectionFlag% = 0 Then
bgddevcps! = analysis.StdAssignsCounts!(chan%) * concvariance! / (analysis.StdAssignsKfactors!(chan%) * analysis.UnkZAFCors!(4, chan%))
ElseIf CorrectionFlag% > 0 And CorrectionFlag% < 5 Then
bgddevcps! = analysis.StdAssignsCounts!(chan%) * concvariance! / (analysis.StdAssignsBetas!(chan%) * analysis.UnkBetas!(chan%))
ElseIf CorrectionFlag% = MAXCORRECTION% Then
End If

' Now convert cps intensity variance back to raw intensity variance (for consistency with off-peak variance calculation code in ConvertDetectionLimits2)
bgddevraw! = bgddevcps! * bgdtime!
Call DataCorrectDataBeamDrift2(bgddevraw!, bgdbeam!)
If ierror Then Exit Function

' Return the calculated net intensity variance in cps/nominal beam
ConvertDetectionLimits3! = bgddevraw!

Exit Function

' Errors
ConvertDetectionLimits3Error:
MsgBox Error$, vbOKOnly + vbCritical, "ConvertDetectionLimits3"
ierror = True
Exit Function

End Function

See also this post:

https://probesoftware.com/smf/index.php?topic=307.msg3698#msg3698

Anyway, I'd be pleased to investigate this further with you.

[Probeman]

I found this old slide that very simply describes the issue of calculating MAN sensitivity:



Where m is the slope...