I have a question about the calculation by software (s) of detection limits in the case of elements determined in the presence of peak interferences. I have attached a rough diagram which should make my ramblings a bit more coherent. My current understanding is that detection limits are determined by statistics relating the No. of counts of the background (ie background count measurements under the peak as determined by measurement of off peaks and or slope determinations) , the number of counts obtained from the standard and a measurement of standard deviation of counts above background. In the case of a peak overlap as that shown in my diagram P(I) on a determined peak (P), the background of the measured peak is Background + overlap. Is this value used in the calculation of the detection limits and error when peak overlap correction is done automatically in software. By software I mean manufacturers and Probesoftware as I have not seen this mentioned in any manuals??
Quote from: Spratt NHM on April 15, 2014, 06:51:42 AM
Is this value used in the calculation of the detection limits and error when peak overlap correction is done automatically in software. By software I mean manufacturers and Probesoftware as I have not seen this mentioned in any manuals??
Hi John,
You are exactly correct I think. No one that I know of includes the precision of the interference correction intensity in the total analytical precision. Ideally one would include this estimate of precision in the analytical error calculation along with the P and B of the standard and the P and B of the unknown.
However, if we assume the interference is on the same order or less as the background correction (which it often is), the precision contribution is similar to what we already have. But it is a good point and I will have to look at adding that... 8)
In any event, in order to prevent the interference correction statistics from swamping the normal analytical statistics, I have added an option to the Probe for EPMA software (that you have) as seen here:
(https://smf.probesoftware.com/oldpics/i59.tinypic.com/des9k1.jpg)
This option ensures that if a standard intensity is needed for an interference correction, the software will automatically acquire that interference standard intensity using the same count time as the unknown sample.
I should also mention that aside from precision issues, the major issue for interference correction is accuracy. But because the interference correction in Probe for EPMA is fully matrix corrected, one can get excellent results in almost any situation, for example these results for Rb interfered by Si (and corrected) as seen here:
(https://smf.probesoftware.com/oldpics/i58.tinypic.com/iedonn.jpg)
The interference corrected results are all zero within precision. Without the quantitative interference correction, the Rb concentration would be around 0.3 to 0.4 percent. Important when trying to determine trace Rb in feldspars for example!
Note that K Ka(2) is also a potential source of interference for this particular problem. I can't remember exactly what the sine(theta) limit is for CAMECA spectrometers, but JEOL users have the option of using PETH to measure Rb La. Not only are the interferences largely circumvented, but the much greater peak/background more than compensates for the lower intensity.
Quote from: Brian Joy on April 17, 2014, 07:39:18 PM
Note that K Ka(2) is also a potential source of interference for this particular problem. I can't remember exactly what the sine(theta) limit is for CAMECA spectrometers, but JEOL users have the option of using PETH to measure Rb La. Not only are the interferences largely circumvented, but the much greater peak/background more than compensates for the lower intensity.
I checked and the Rb data above is from Rb La, but using LTAP. The problem with using PET for Rb La on the Cameca is that it is essentially at the upper spectro limit as seen here:
Table of Emission Line Spectrometer Positions
Ka Ka La La La La
Element LLIF LIF PET LPET TAP LTAP
Rb 23020.9 23020.9 83649.8 83649.8 28488.2 28488.2
So for this example, using a different crystal might help, it was just an example of interference correction statistics, which in this one case are a few hundred PPM variance. But I think John's original question was, given that an interference may be unavoidable or impractical to avoid, what effect does the interference correction have on one's detection limit statistics? Wait, yes, ok I just thought of an easy way to test this question...
Let's take one of the examples above, Rb in Ni2SiO4, and examine the counting statistics for Rb with the interference correction:
St 272 Set 3 Ni2SiO4 (synthetic), Results in Elemental Weight Percents
ELEM: Rb Si Ni O
TYPE: ANAL ANAL SPEC SPEC
BGDS: LIN LIN
TIME: 20.00 20.00
BEAM: 50.24 50.24
ELEM: Rb Si Ni O SUM
422 .005 13.293 56.047 30.547 99.892
423 .006 13.254 56.047 30.547 99.854
424 .017 13.366 56.047 30.547 99.977
425 .017 13.356 56.047 30.547 99.967
426 .015 13.280 56.047 30.547 99.889
AVER: .012 13.310 56.047 30.547 99.916
SDEV: .006 .049 .000 .000 .053
SERR: .003 .022 .000 .000
Above one can see that the standard deviation for Rb is 0.006 (60 PPM) with the interference correction. How about if we turn *off* the interference correction:
St 272 Set 3 Ni2SiO4 (synthetic), Results in Elemental Weight Percents
ELEM: Rb Si Ni O
TYPE: ANAL ANAL SPEC SPEC
BGDS: LIN LIN
TIME: 20.00 20.00
BEAM: 50.24 50.24
ELEM: Rb Si Ni O SUM
422 .335 13.273 56.047 30.547 100.203
423 .336 13.234 56.047 30.547 100.164
424 .349 13.346 56.047 30.547 100.289
425 .349 13.336 56.047 30.547 100.280
426 .345 13.261 56.047 30.547 100.200
AVER: .343 13.290 56.047 30.547 100.227
SDEV: .007 .049 .000 .000
Now, without the interference correction, the variance is now 0.007 or (70 PPM), slightly higher than with the interference correction! :o
I cannot explain this result, but let's try another example, Rb in Fe2SiO4:
St 263 Set 3 Fe2SiO4 (synthetic fayalite), Results in Elemental Weight Percents
ELEM: Rb Si Fe O
TYPE: ANAL ANAL SPEC SPEC
BGDS: LIN LIN
TIME: 20.00 20.00
BEAM: 50.24 50.24
ELEM: Rb Si Fe O SUM
417 .002 13.787 54.809 31.407 100.005
418 .019 13.622 54.809 31.407 99.857
419 .011 13.736 54.809 31.407 99.963
420 .013 13.750 54.809 31.407 99.979
421 .023 13.648 54.809 31.407 99.886
AVER: .014 13.709 54.809 31.407 99.938
SDEV: .008 .070 .000 .000 .063
OK, 0.008 variance or 80 PPM on the Rb *with* the interference correction and now, without the interference correction:
St 263 Set 3 Fe2SiO4 (synthetic fayalite), Results in Elemental Weight Percents
ELEM: Rb Si Fe O
TYPE: ANAL ANAL SPEC SPEC
BGDS: LIN LIN
TIME: 20.00 20.00
BEAM: 50.24 50.24
ELEM: Rb Si Fe O SUM
417 .345 13.770 54.809 31.407 100.330
418 .357 13.605 54.809 31.407 100.178
419 .352 13.719 54.809 31.407 100.287
420 .355 13.732 54.809 31.407 100.303
421 .362 13.631 54.809 31.407 100.208
AVER: .354 13.691 54.809 31.407 100.261
SDEV: .006 .070 .000 .000 .065
the variance is only 0.006 or 60 PPM without the interference correction, so I think that at least in these two cases we can see that the contribution of statistics from the interference correction is roughly similar to the statistics without the interference correction.
More importantly, as demonstrated above, Probe for EPMA gives the operator an easy way to test the effect of the interference correction on the counting statistics by simply toggling the interference correction on and off. Just to demonstrate, this toggling of the interference correction can be performed with a single mouse click as seen here:
(https://smf.probesoftware.com/oldpics/i60.tinypic.com/2zfk01g.jpg)
OK, I just thought of a way to answer John Spratt's question about including counting statistics for the interference correction in our detection limit calculations.
In the above examples I showed that, in one case the relative percent standard deviation (expressed as %VAR) decreased with the interference correction applied and another sample where the relative percent standard deviation increased with the interference correction applied.
So what we really need is a detection limit calculation which includes the standard deviation of the sample, and in fact we already do. It's the t-test for detection limit from Goldstein, et al. and shown here:
(https://smf.probesoftware.com/oldpics/i60.tinypic.com/qppeyu.jpg)
Since this expression is already implemented in Probe for EPMA as seen here:
(https://smf.probesoftware.com/oldpics/i61.tinypic.com/wcjz2e.jpg)
So all one has to do is check this box in the Calculation Options dialog, and the t-test detection limit will automatically include the change in variance due to the interference correction.
8)
Here is some sample output using this statistics output option, first without the aggregate intensity feature:
Detection Limit (t-test) in Elemental Weight Percent (Average of Sample):
ELEM: Ti Ti Ti Ti Ti
60ci .00008 .00004 .00019 .00014 .00009
80ci .00013 .00007 .00032 .00022 .00015
90ci .00018 .00009 .00044 .00031 .00021
95ci .00024 .00012 .00057 .00040 .00028
99ci .00039 .00020 .00095 .00066 .00046
and here *with* the aggregate intensity feature:
Detection Limit (t-test) in Elemental Weight Percent (Average of Sample):
ELEM: Ti Ti Ti Ti Ti
60ci .00008 --- --- --- ---
80ci .00012 --- --- --- ---
90ci .00017 --- --- --- ---
95ci .00022 --- --- --- ---
99ci .00037 --- --- --- ---
The "60ci" label refers to 60% confidence interval and the "99ci" refers to 99% confidence interval.