Blank Assignments

[Joe Boesenberg]

John

I did the zero concentration test on Al2O3 on my Fo100 today. Using my OPX2525 standard for Al2O3, I come up with -0.0060 wt% Al2O3 (I am low 60ppm) on what should be zero. I assume the use of my background multiplier (slope) of 1.2 is a bit high and probably needs to be in the range of 1.1 to 1.15 to get to zero. Using the same 1.2 slope, but using corundum, I get -0.0075 wt% Al2O3 on Fo100, so either my opx is slightly off in its composition or my spectrometer is having a dead time issue. I suspect the latter is more likely.

Thanks Joe

[Probeman]

I did the zero concentration test on Al2O3 on my Fo100 today. Using my OPX2525 standard for Al2O3, I come up with -0.0060 wt% Al2O3 (I am low 60ppm) on what should be zero. I assume the use of my background multiplier (slope) of 1.2 is a bit high and probably needs to be in the range of 1.1 to 1.15 to get to zero. Using the same 1.2 slope, but using corundum, I get -0.0075 wt% Al2O3 on Fo100, so either my opx is slightly off in its composition or my spectrometer is having a dead time issue. I suspect the latter is more likely.

Hi Joe,
It's great that you are investigating this issue.  Please confirm that you are using Al2O3 as a primary standard for Al Ka and the Fo100 as a zero blank for Al in olivine (though we don't know exactly what the Al level in the Fo100 synthetic is, do we?).

Your problem is either your background slope (you'll have a much easier time using the polynomial or exponential background fit in PFE, because you won't have to guess at the slope), or your Al value is off in your opx standard. I would say either or both.

It's probably not the dead time, as dead time tends to be an insignificant correction at trace levels.  Yes, dead time  affects the measurement on your Al2O3 primary standard, but you can run the Al2O3 at a lower beam current than your unknown. Since your opx is only 4 wt%, any error in that value gets propagated to your unknown, so use Al2O3 as the primary Al standard for trace Al.

Here's post I made just now where I attempt to explain these considerations on standard selection that Anette von der Handt and I are working on:

https://probesoftware.com/smf/index.php?topic=610.msg11752#msg11752

[Ben Buse]

Hi

When using blank assignment, and exporting peak counts and background counts, from which if calculate manual error in excel get wrong error,, as the peak and background counts are before blank correction

Wondered how the blank correction is propergated through the error in PFE and whether the necessary data such as magnitude of blank correction could be exported to allow manual calculations in excel

Thanks

[Probeman]

Hi

When using blank assignment, and exporting peak counts and background counts, from which if calculate manual error in excel get wrong error,, as the peak and background counts are before blank correction

Wondered how the blank correction is propergated through the error in PFE and whether the necessary data such as magnitude of blank correction could be exported to allow manual calculations in excel

Thanks

It's a good question.

Since the blank correction only affects accuracy, I would output the error values without the blank correction as those error values should be correct as far as counting statistics goes.

Then utilize the blank corrected concentration values for the actual concentrations.

But now, thinking about it a bit more, the error statistics from the raw data are calculated without the blank correction (e.g., using the data button in the Analyze! window), so those should be unaffected by the blank correction.

[Ben Buse]

Hi John,

Here's an example - you'll see change in error given by PFE when blank corrected selected. Upper dataset blank turned off for Ti, turned on for Ti in lower dataset. For Al its on for both

What it is, is when you take the same absolute error and make it a relative error for a changed composition

[Probeman]

To confirm, your question is: why are the calculated analytical sensitivities slightly different when the blank correction is used or not?

[John Donovan]

Hi John,

Here's an example - you'll see change in error given by PFE when blank corrected selected. Upper dataset blank turned off for Ti, turned on for Ti in lower dataset. For Al its on for both

What it is, is when you take the same absolute error and make it a relative error for a changed composition

Aurelien and I looked into this and as you report there are small differences in the reported analytical sensitivity calculations (from Scott and Love, 1983) method when the blank correction is applied due to the way we calculate it (though this behavior has now been changed as described further below).  See the Probe for EPMA User Reference Manual for details on the Scott and Love 1983 calculation.

The reason for this previous behavior is that the Scott and Love (1983) calculation requires knowing the raw counts from the unknown peak and unknown background. Originally we calculated these raw counts from the peak and background counts after they had been corrected for dead time, beam drift and background (the interpolated off-peak or MPB or calculated MAN intensities).  This is mostly because one cannot use the raw high and low off-peak measurements because it's the interpolated or calculated background intensities that need to be utilized in the case of the MAN (and MPB to some extent), and these background intensity values are calculated during the quantification.

The problem with using these calculated background values is that they need to be de-normalized for dead time, beam drift and counting time (to obtain raw photon counts) in order to determine the standard deviations (SQRT).  But some time ago we began utilizing the original stored raw intensities for simple statistics such as the variance on the on peak and high/low off-peak intensities. Then skipping the de-normalization steps we previously utilized and re-normalizing them again for dead time, beam drift and counting time if these display normalizations were selected.

However, for statistical calculations such as the analytical sensitivities this approach will not work as we don't have the raw intensities stored for the calculated background intensities, as they are only calculated as needed and of course they are always in normalized intensity (not raw count) units.  The raw on-peak photon count intensities are of course available, just not the raw calculated background intensities, and that is why we continued to utilize the de-normalization, then take the square root, then the re-normalization method.

The problem with this method as you might already have realized is that the blank correction (and interference correction, etc) is applied during the quantification process, which is great if one wants to export k-ratios that are already corrected for everything, say for off-line thin film calculations.  But then there will be (very) small differences in the peak intensities from these corrections, and that is what Ben is seeing as quoted above. 

So, not a big deal, but I understand why Ben was wondering what was the cause of this.  Of course in my opinion, one should not even concern themselves with analytical sensitivity calculations for small values. That is because as the peak intensity approaches the background, the analytical sensitivity calculation gets very large, indicating of course that one's analytical sensitivity is worse than the background variance. In fact I believe one really should focus more on analytical sensitivity for higher concentrations, and be more concerned with the detection limits for low concentrations...

But as Aurelien and I were thinking about this issue, we also noticed that we were missing code in the analytical sensitivity calculation to de-normalize for dead time prior to taking the square root (it's the only place it was missing as we checked the other code!).  At low count rates this missing de-normalization has almost no effect but of course at high count rates it does.  But at high count rates the analytical sensitivity calculation is not sensitive to the background intensity, so that's why we never noticed this!

So we added the dead time de-normalization code and then immediately found a problem when de-normalizing small intensities for dead time using the logarithmic dead time correction. It's because the maximum value that one can handle when de-normalizing using the exponential math function is 10^308 in double precision, and small background intensities can generate values larger than this!

That's when Aurelien and I came up with the idea that for obtaining the raw background (interpolated/calculate) count intensity, we could simply apply the peak to background ratio values obtained from the quant calculation, to the raw on-peak intensity value and voila, we now have a raw background intensity and can take the square root directly without any de-normalization.  Nice!

Here are the detection limits and analytical sensitivities for some Ti in synthetic SiO2 (20 keV, 200 nA, 1920 sec on and 1920 sec off-peak), first without the blank correction:

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

ELEM:       Ti      Ti      Ti      Ti      Ti
   271  .00049  .00033  .00032  .00054  .00046
   272  .00048  .00033  .00032  .00054  .00046
   273  .00049  .00033  .00032  .00054  .00046
   274  .00049  .00033  .00032  .00054  .00046
   275  .00049  .00033  .00031  .00054  .00046

AVER:   .00049  .00033  .00032  .00054  .00046
SDEV:   .00000  .00000  .00000  .00000  .00000
SERR:   .00000  .00000  .00000  .00000  .00000

Percent Analytical Relative Error (One Sigma, Single Line):

ELEM:       Ti      Ti      Ti      Ti      Ti
   271   129.7    15.5     5.2    53.2   673.5
   272   501.4    15.4     5.6   136.4    25.6
   273   198.3    15.2     5.3    41.2   331.3
   274   192.8    12.7     5.4    51.1    47.4
   275    94.2    12.9     5.1    36.3    47.3

AVER:    223.3    14.3     5.3    63.6   225.0
SDEV:    161.5     1.4      .2    41.3   280.8
SERR:     72.2      .6      .1    18.5   125.6

And here with the blank correction:

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

ELEM:       Ti      Ti      Ti      Ti      Ti
   271  .00049  .00033  .00032  .00054  .00046
   272  .00048  .00033  .00032  .00054  .00046
   273  .00049  .00033  .00032  .00054  .00046
   274  .00049  .00033  .00032  .00054  .00046
   275  .00049  .00033  .00031  .00054  .00046

AVER:   .00049  .00033  .00032  .00054  .00046
SDEV:   .00000  .00000  .00000  .00000  .00000
SERR:   .00000  .00000  .00000  .00000  .00000

Percent Analytical Relative Error (One Sigma, Single Line):

ELEM:       Ti      Ti      Ti      Ti      Ti
   271   655.7    40.7   592.7   395.7    42.5
   272   238.3    40.6    67.1    70.8    72.3
   273   875.4    42.1   181.7   346.5    45.4
   274  1001.7    96.0   103.7   545.7   251.0
   275   226.5    81.3   978.9   163.5   249.1

AVER:    599.5    60.1   384.8   304.5   132.1
SDEV:    357.3    26.6   392.9   188.9   108.3
SERR:    159.8    11.9   175.7    84.5    48.5

Now the sharp-eyed among you will have noticed that the analytical sensitivities are still different (generally larger) with the blank correction applied. And why is that?  Well it's pretty much the same reason it was before.

With the previous de-normalize/re-normalize method, the background counts didn't change depending on the blank correction, but the peak counts did because the blank correction is applied to the (corrected) peak counts!

In the new code based on the raw peak counts and the calculated peak to background method,  the raw peak counts didn't change (because they are based on the measured count rate), but the background counts did change because the blank correction affects the calculated peak to background ratio.

Specifically, the peak to background ratio went from 0.998234 (for the first line of channel 1), to 0.999650 (closer to unity) when the blank correction is applied.

So after all that we are sort of where we were but the analytical sensitivity calculation is more accurate because now we are utilizing raw intensities for the Scott and Love calculation.  I still think for trace elements the detection limit is what one should be considering though...

I went ahead and posted the new analytical sensitivity code here for those interested:

https://probesoftware.com/smf/index.php?topic=1307.msg12149#msg12149

Oh, and one last thing: previously we always reported negative analytical sensitivities when the concentrations were negative (it happens when one is attempting to measure zero!). But someone (?) asked a while back why we did this, and now that we've thought about it a bit more, we now take the absolute value of the analytical sensitivity for reporting purposes. This also makes the average of the analytical sensitivities more sensible.  We can change this back if anyone has a reasonable objection.

[Ben Buse]

Hi John,

I don't entirely follow

But as I understand it there would be two components

1. counting stats error - as described by Scott & Love - which is the measurement before blank correction adjusted

2. systematic error - associated with the blank correction - which in part is the count stats on the sample used as blank correction standard - and in part indescribable - whether the blank correction standard is correct

[John Donovan]

The Scott and Love 1983 method for analytical sensitivity is essentially based on the peak to background ratios of the standard and unknown. If the peak to background ratio changes in the unknown because of the blank correction being applied (which it will for a trace element), the calculated analytical sensitivity changes (according to Scott and Love).

But I will say it again, for trace elements you should not be looking at the analytical sensitivity but rather the detection limit. Note that the detection limit for trace elements does not significantly change when the blank correction is applied as one would expect. 

Analytical sensitivity calculations, on the other hand, are really more appropriate for major and minor elements and used to discern whether two values are statistically significantly different from one another.  At trace levels all values are basically not statistically significantly different from each other.  The more appropriate question for trace elements is: are these trace levels statistically significant relative to the background level.

I tried to say this previously in the post above.

So, not a big deal, but I understand why Ben was wondering what was the cause of this.  Of course in my opinion, one should not even concern themselves with analytical sensitivity calculations for small values. That is because as the peak intensity approaches the background, the analytical sensitivity calculation gets very large, indicating of course that one's analytical sensitivity is worse than the background variance. In fact I believe one really should focus more on analytical sensitivity for higher concentrations, and be more concerned with the detection limits for low concentrations...