Quantitative Spectral Interference Corrections

John Donovan · November 22, 2024, 10:36:00 AM

But first, a bit of history... to better explain what Andrew saw and we subsequently found to be the issue.

In the mid 1990s we implemented the quantitative interference correction in Probe for EPMA using an iterative method. An iterative method is necessary when the correction in question is compositionally dependent, for example the MAN background correction depends on the average Z of the material to estimate the continuum production, and the average Z of the material is in turn dependent on the composition:

https://smf.probesoftware.com/index.php?topic=1378.0

Similarly the quantitative spectral interference correction is dependent on the concentration of the interfering element (not the intensity of the interfering element!):

https://epmalab.uoregon.edu/publ/Improved%20Interference%20(Micro.%20Anal,%201993).pdf

The same can be said for the Area-Peak Factor (APF) correction for peak shape/shift when using the "compound" APF feature:

https://smf.probesoftware.com/index.php?topic=536.0

and to some extent, also the volatile (TDI) correction:

https://smf.probesoftware.com/index.php?topic=11.0

although the TDI correction really only needs to be applied *prior* to the matrix correction for accuracy.

In any case, when the quantitative interference correction (and the other compositionally dependent corrections) was implemented in the mid 1990s, we utilized the existing iteration loop already used for the MAN background correction. At that time the MAN iteration loop was fixed to utilize a maximum of 10 iterations because one never needed more than 10 iterations to converge.

However, in the late 1990s Probeman started pushing the limits of the interference correction and found that in some of the most extreme pathological overlaps situations, e.g., Pb La and As Ka, we found that additional iterations were necessary to converge the iterations to accuracy. And the reason turns out to be because when calibrating As Ka and Pb La, it will be found that the intensity of the As overlap on the Pb Ma signal is actually *larger* than the Pb La signal, even though the concentration of the As in the GaAs standard is lower than the Pb in the Pb S standard. This is due to the fact that the As Ka emission is more efficient than the Pb La production, as seen here in the List Standard Intensities output in Probe for EPMA:

Drift array background intensities (cps/49.005nA) for standards:
ELMXRY: pb la as ka s ka
MOTCRY: 3 LIF 2 LIF 5 PET
INTEGR: 0 0 0
STDASS: 731 662 730
STDVIR: 0 0 0
224.5 124.6 42.2
226.1 124.3 42.5

Drift array standard intensities (cps/49.005nA) (background corrected):
ELMXRY: pb la as ka s ka
MOTCRY: 3 LIF 2 LIF 5 PET
STDASS: 731 662 730
STDVIR: 0 0 0
3550.2 4257.7 12340.3
3566.3 4266.5 12365.8

Drift array interference standard intensities (cps/49.005nA):

1st assigned interference elements
ELMXRY: pb la as ka s ka
INTFELM: as pb
INTFSTD: 662 731
4076.5 2736.3
4094.6 2763.6

Because of this "inverted" concentration to intensity ratio, the iteration becomes quite extended, as seen here:

Sorry about the quality of the above plot, it comes from the 1990s! The point is that this sort of pathological interference correction requires over 50 iterations! While a typical spectral interference only required 4 or 5 iterations. It's actually sort of amazing that this iteration even converges at all!

Anyway, it turns out that years later, in the late 2010s, we started working on the quantitative x-ray mapping method, which requires a full quantitative correction of every pixel, just as one would with an analytical point analysis:

https://smf.probesoftware.com/index.php?topic=1212.0

Some vendors attempt to quantify x-ray maps using a calibration curve, but there's a reason that we don't use calibration curves for our quantitative point analyses: it's not very quantitative!

Anyway, the downside of applying a full dead time, standard intensity drift, background, matrix and of course also interference and TDI (volatile) corrections, to every pixel is that it can be a bit time consuming to apply a complete quant correction to quantify hundreds of thousands of pixels.

The quant code in Probe for EPMA is pretty darn efficient, but still we tried modifying a few parameters to improve the iteration speed, and yup, you guessed it, we reduced the number of iterations for the MAN (and interference) corrections in the late 2010s because we found that we really didn't need so many iterations, forgetting about the rare cases of the extreme Pb la and As ka situation!

Anyway, this is all fixed in the latest version of Probe for EPMA (and CalcImage), so please update when you get a chance. And this doesn't seem to have affected the quantification speed in CalcImage for x-ray map quant.

Just for fun, I will post some examples of the Pb La and As Ka analyses in the next post.

John Donovan · November 25, 2024, 02:09:56 PM

Before I present an examples of these "pathological" spectral interferences, here is an early flow chart of the double iteration loop that is utilized for the interference (and MAN, TDI and APF) corrections:

Note that the inner iteration loop contains the matrix correction for the analyzed elements, along with any unanalyzed elements that need to be included in the matrix correction. That is, elements by stoichiometry, difference, and/or charge balance.

The outer loop contains the correction of spectral interferences (and also the MAN background, TDI (volatile) and Area Peak factor (APF) corrections).

This double iteration loop is the "secret sauce" in Probe for EPMA and CalcImage that allows for compositionally dependent corrections to be utilized in the matrix correction for best accuracy. Think of it this way: if you perform an interference or TDI correction to the composition, and the magnitude of the these corrections are greater than ~ 1%, you will want to re-calculate your matrix correction to reflect this modified composition. Here is a more detailed, but more complex flow chart of the same double iteration loop which we published in our 2019 quant mapping paper:

https://www.probesoftware.com/wp-content/uploads/2024/08/donovan_2021_amer_min_2021-7739.pdf

Performing these interference corrections *after* the matrix correction, will result in poor accuracy for your analyzed elements. Even an analyzed element such as Fe (Ka) can be significantly affected by these changes to the compositions as shown here:

https://smf.probesoftware.com/index.php?topic=92.105

John Donovan · November 27, 2024, 12:18:25 PM

OK, so back to actual interference corrections. In the case of a "self interfering" interferences such as As K a and Pb La, the changes in composition can be quite large. For example here is an analysis of a PbAs sulfide (Sartorite) WITHOUT the quantitative interference correction:


Un    7 Sartorite (rim high z )
TakeOff = 40.0  KiloVolt = 20.0  Beam Current = 50.0  Beam Size =    0
(Magnification (analytical) =   4000),        Beam Mode = Analog  Spot
(Magnification (default) =        0, Magnification (imaging) =    100)
Image Shift (X,Y):                                         .00,    .00
Number of Data Lines:   8             Number of 'Good' Data Lines:   6
First/Last Date-Time: 05/08/1998 05:37:49 PM to 05/08/1998 05:46:56 PM

Average Total Oxygen:         .000     Average Total Weight%:  172.947
Average Calculated Oxygen:    .000     Average Atomic Number:   60.812
Average Excess Oxygen:        .000     Average Atomic Weight:   93.989
Average ZAF Iteration:        4.00     Average Quant Iterate:     2.00

Un    7 Sartorite (rim high z ), Results in Elemental Weight Percents
 
ELEM:       Pb      As       S       O       H
TYPE:     ANAL    ANAL    ANAL    SPEC    SPEC
BGDS:      LIN     LIN     LIN
TIME:    30.00   30.00   30.00     ---     ---
BEAM:    50.02   50.02   50.02     ---     ---

ELEM:       Pb      As       S       O       H   SUM  
   991 106.124  41.202  24.532    .000    .000 171.859
   992 106.800  41.229  24.262    .000    .000 172.291
   994 108.183  41.744  24.609    .000    .000 174.537
   995 105.893  41.153  24.681    .000    .000 171.726
   996 106.981  41.826  25.485    .000    .000 174.291
   997 106.486  41.643  24.851    .000    .000 172.980

AVER:  106.744  41.466  24.737    .000    .000 172.947
SDEV:     .813    .304    .414    .000    .000   1.220
SERR:     .332    .124    .169    .000    .000
%RSD:      .76     .73    1.68     .00     .00
STDS:      731     662     730     ---     ---

STKF:    .8033   .4962   .4761     ---     ---
STCT:   3566.3  4266.5 12365.8     ---     ---

UNKF:    .9285   .4512   .2039     ---     ---
UNCT:   4121.9  3879.9  5296.9     ---     ---
UNBG:    167.1   161.4    57.2     ---     ---

ZCOR:   1.1497   .9190  1.2130     ---     ---
KRAW:   1.1558   .9094   .4283     ---     ---
PKBG:    25.67   25.05   93.78     ---     ---

OK, so we see the totals are around 175 wt%, so just a slight error!

Also note that the sulfur (which is not interfered with) averages ~24.7 wt% with this matrix (uncorrected for interferences). We'll see how this value changes when the interference correction is applied below.

Now let's turn on the interference correction of Pb by As and As by Pb:

Note that we utilized GaAs as the interference standard for Pb La (contains a known concentration of the interfering element As, but none of the interfered element Pb) and PbS as the interference standard for As Ka (again, contains a known concentration of the interfering element Pb, but none of the interfered element As).

Now, finally(!), here are the interference corrected results for the above mineral:

Un 7 Sartorite (rim high z )
TakeOff = 40.0 KiloVolt = 20.0 Beam Current = 50.0 Beam Size = 0
(Magnification (analytical) = 4000), Beam Mode = Analog Spot
(Magnification (default) = 0, Magnification (imaging) = 100)
Image Shift (X,Y): .00, .00
Number of Data Lines: 8 Number of 'Good' Data Lines: 6
First/Last Date-Time: 05/08/1998 05:37:49 PM to 05/08/1998 05:46:56 PM

Average Total Oxygen: .000 Average Total Weight%: 99.342
Average Calculated Oxygen: .000 Average Atomic Number: 50.041
Average Excess Oxygen: .000 Average Atomic Weight: 70.501
Average ZAF Iteration: 4.00 Average Quant Iterate: 58.00

Un 7 Sartorite (rim high z ), Results in Elemental Weight Percents

ELEM: Pb As S O H
TYPE: ANAL ANAL ANAL SPEC SPEC
BGDS: LIN LIN LIN
TIME: 30.00 30.00 30.00 --- ---
BEAM: 50.02 50.02 50.02 --- ---

ELEM: Pb As S O H SUM
991 43.299 30.282 25.168 .000 .000 98.749
992 45.643 29.386 24.768 .000 .000 99.796
994 46.395 29.681 25.111 .000 .000 101.188
995 42.864 30.405 25.339 .000 .000 98.608
996 41.166 31.912 26.299 .000 .000 99.377
997 40.860 31.810 25.667 .000 .000 98.337

AVER: 43.371 30.579 25.392 .000 .000 99.342
SDEV: 2.269 1.062 .533 .000 .000 1.050
SERR: .926 .434 .217 .000 .000
%RSD: 5.23 3.47 2.10 .00 .00
STDS: 731 662 730 --- ---

STKF: .8033 .4962 .4761 --- ---
STCT: 3566.3 4266.5 12365.8 --- ---

UNKF: .3500 .3100 .2039 --- ---
UNCT: 1554.0 2665.8 5296.9 --- ---
UNBG: 167.1 161.4 57.2 --- ---

ZCOR: 1.2394 .9862 1.2450 --- ---
KRAW: .4357 .6248 .4283 --- ---
PKBG: 10.30 17.53 93.78 --- ---
INT%: -62.31 -31.29 ---- --- ---

Just a slight improvement in the totals!

Also note that sulfur average value went from ~24.7 to ~25.4 wt%, which is roughly a 2.8% relative change in the sulfur concentrations. And remember, the sulfur itself was not affected by any interferences in this example, the change in the sulfur concentration is completely due to the change in the matrix correction due to the interference correction of Pb and As!

Just for laughs and giggles I've attached below, a rough transcription of the talk I gave back in 1998 (using 35 mm slides!) and the original 1993 interference iteration paper.

John Donovan · November 27, 2024, 06:02:13 PM

In summary, the important point of the last few posts in this topic, is that that when we modified the interference, MAN, TDI and APF iteration loop back in 2018 in an attempt to further speed up the x-ray mapping quantification by reducing the maximum iterations from 100 to 10, we accidentally caused the interference corrections to fail when more than 10 iterations are required, specifically in the case of "self interferences" such as As Ka and Pb La:

Average Total Oxygen:         .000     Average Total Weight%:   99.342
Average Calculated Oxygen:    .000     Average Atomic Number:   50.041
Average Excess Oxygen:        .000     Average Atomic Weight:   70.501
Average ZAF Iteration:        4.00     Average Quant Iterate:    58.00

I'm not sure if there any other "self interferences" as bad as As Ka and Pb la, but it doesn't seem to slow down the x-ray map quantification time for "normal" interferences in our testing...

Hey, would someone be willing to acquire an x-ray map of an As,Pb sulfide and try to quantify it?

Thank-you to Andrew Locock for noticing this issue and bringing it to our attention!

Update Probe for EPMA as usual using the Help menu to obtain this v. 13.9.4 update.

Probeman · April 05, 2026, 08:19:43 AM

Quote from: John Donovan on November 27, 2024, 06:02:13 PMIn summary, the important point of the last few posts in this topic, is that that when we modified the interference, MAN, TDI and APF iteration loop back in 2018 in an attempt to further speed up the x-ray mapping quantification by reducing the maximum iterations from 100 to 10, we accidentally caused the interference corrections to fail when more than 10 iterations are required, specifically in the case of "self interferences" such as As Ka and Pb La:
Average Total Oxygen:         .000     Average Total Weight%:   99.342
Average Calculated Oxygen:    .000     Average Atomic Number:   50.041
Average Excess Oxygen:        .000     Average Atomic Weight:   70.501
Average ZAF Iteration:        4.00     Average Quant Iterate:    58.00
I'm not sure if there any other "self interferences" as bad as As Ka and Pb la, but it doesn't seem to slow down the x-ray map quantification time for "normal" interferences in our testing...

Hey, would someone be willing to acquire an x-ray map of an As,Pb sulfide and try to quantify it?

Thank-you to Andrew Locock for noticing this issue and bringing it to our attention!

Update Probe for EPMA as usual using the Help menu to obtain this v. 13.9.4 update.

Andrew Locock did perform some As Ka and Pb La analyses recently and we found that even an iteration limit of 100 iterations isn't enough to handle these situations, so we recently increased the iteration max limit to 300! And it helped but not really enough...

Maybe it's the complexity of this run and non-ideal the background positions because I noticed that Andrew had a few elements with significantly negative net intensities and it's clear that the interference correction and the background correction do interact strongly and I did turn off the flags to zero out negative net intensities as these setting can make things worse in such situations.

This was a complicated run, here is just a partial listing of the spectral interferences:

Also, I note that although he corrected the As - Pb interferences, he didn't correct for the Pb Ma on S interference, which admittedly is difficult because one would require a standard containing Pb but no S.

Anyway, here are the results analyzing InAs using GaAs as the primary standard, WITHOUT an interference correction:

Pretty bad for sure. Now WITH the quant interference corrections:

Much better (at least the Pb analyses are within a standard deviation of zero!), but still not good enough for Andrew. So now he's running things again but this time using the As Kb and Pb Lb lines and counting a little longer, though I've personally had good luck just using the Pb Ma line and As Ka...

Probeman · April 08, 2026, 01:42:44 PM

It's interesting that Andrew Locock is seeing such instability in the As on Pb La measurements, so I went back to some runs I did back in 2015 where I measured Pb La and Pb Ma on GaAs. Here is GaAs using Pb La where there is a large interference of As Ka on Pb La uncorrected for spectral interferences:

St  662 Set   2 GaAs (synthetic), Results in Elemental Weight Percents
 
ELEM:        S      Pb      As      Ga
TYPE:     ANAL    ANAL    ANAL    SPEC
BGDS:      LIN     EXP     EXP
TIME:    80.00   80.00   80.00     ---
BEAM:    29.88   29.88   29.88     ---

ELEM:        S      Pb      As      Ga   SUM  
   327    .007 108.837  45.330  48.200 202.374
   328    .006 108.460  45.149  48.200 201.815
   329    .017 108.720  45.306  48.200 202.244

AVER:     .010 108.672  45.262  48.200 202.144
SDEV:     .006    .193    .098    .000    .292
SERR:     .004    .111    .057    .000
%RSD:    62.70     .18     .22     .00

PUBL:     n.a.    n.a.  51.800  48.200 100.000
%VAR:      ---     ---(-12.62)     ---
DIFF:      ---     --- (-6.54)     ---
STDS:      730     731     662     ---

It's pretty impressive that because the As Ka line is so much stronger than Pb La that we get more spurious Pb La counts from As than we get actual As Ka counts. Over 3 times more in fact!

On-Peak (off-peak corrected) or EDS (bgd corrected) or MAN On-Peak X-ray Counts (cps/1nA) (and Faraday/Absorbed Currents):
ELEM:     s ka   pb la   as ka   BEAM1   BEAM2
BGD:       OFF     OFF     OFF
SPEC:        1       3       5
CRYST:     PET    LLIF     LIF
ORDER:       1       1       1
  327G     .03  356.32   92.17  29.884  29.884
  328G     .02  355.04   91.79  29.887  29.885
  329G     .07  355.91   92.11  29.884  29.885

AVER:      .04  355.75   92.02  29.885  29.885
SDEV:      .03     .66     .21    .002    .001
1SIG:      .01     .38     .20
SIGR:     2.18    1.71    1.04
SERR:      .01     .38     .12
%RSD:    62.70     .18     .22
DEAD:    3.800   3.500   2.970
DTC%:       .0     3.8      .8

So it's kind of amazing that the interference correction can even attempt this. Here now is the same analysis but with the quantitative interference correction in Probe for EPMA:

St  662 Set   2 GaAs (synthetic), Results in Elemental Weight Percents
 
ELEM:        S      Pb      As      Ga
TYPE:     ANAL    ANAL    ANAL    SPEC
BGDS:      LIN     EXP     EXP
TIME:    80.00   80.00   80.00     ---
BEAM:    29.88   29.88   29.88     ---

ELEM:        S      Pb      As      Ga   SUM  
   327    .009    .002  51.880  48.200 100.092
   328    .008    .206  51.589  48.200 100.003
   329    .023   -.067  51.859  48.200 100.016

AVER:     .013    .047  51.776  48.200 100.037
SDEV:     .008    .142    .162    .000    .048
SERR:     .005    .082    .094    .000
%RSD:    62.75  299.67     .31     .00

PUBL:     n.a.    n.a.  51.800  48.200 100.000
%VAR:      ---     ---  (-.05)     ---
DIFF:      ---     ---  (-.02)     ---
STDS:      730     731     662     ---

Which gives an As concentration of 0.047 wt% +/- 0.142, so yeah a bit more variance than we'd like to see, but in my mind, pretty incredible that it works at all!

Now the GaAs again but this time measured using the Pb Ma line where there is no interference from As Ka:

St  662 Set   1 GaAs (synthetic), Results in Elemental Weight Percents
 
ELEM:       As       S      Pb      Bi      Si      Ga
TYPE:     ANAL    ANAL    ANAL    ANAL    SPEC    SPEC
BGDS:      EXP     LIN     LIN     LIN
TIME:    80.00   80.00   80.00   80.00     ---     ---
BEAM:    29.90   29.90   29.90   29.90     ---     ---

ELEM:       As       S      Pb      Bi      Si      Ga   SUM  
   212  51.804    .011   -.051    .101    .000  48.200 100.065
   213  51.885    .018   -.004    .027    .000  48.200 100.127
   214  51.747    .020   -.016    .122    .000  48.200 100.073

AVER:   51.812    .017   -.024    .083    .000  48.200 100.088
SDEV:     .069    .005    .025    .049    .000    .000    .034
SERR:     .040    .003    .014    .029    .000    .000
%RSD:      .13   29.33 -105.60   59.42     .00     .00

PUBL:   51.800    n.a.    n.a.    n.a.    n.a.  48.200 100.000
%VAR:    (.02)     ---     ---     ---     ---     ---
DIFF:    (.01)     ---     ---     ---     ---     ---
STDS:      662     730     731     583     ---     ---

Zero within one standard deviation though perhaps the backgrounds could be adjusted better. Andrew Ducharme and I will try again once the probe is available...

anenburg · April 10, 2026, 12:14:46 AM

Quote from: John Donovan on November 27, 2024, 06:02:13 PMHey, would someone be willing to acquire an x-ray map of an As,Pb sulfide and try to quantify it?

Here's pyrite with some As zoning in it:

As K line mapped on LIF.
Same thing, Pb EDS map:

The galena shows up very well in the As map. As counts on galena are actually much higher, I truncated the max values so the As zoning in pyrite is actually visible.

John Donovan · April 10, 2026, 07:43:19 AM

Quote from: anenburg on April 10, 2026, 12:14:46 AM
Quote from: John Donovan on November 27, 2024, 06:02:13 PMHey, would someone be willing to acquire an x-ray map of an As,Pb sulfide and try to quantify it?
Here's pyrite with some As zoning in it:

As K line mapped on LIF.
Same thing, Pb EDS map:

The galena shows up very well in the As map. As counts on galena are actually much higher, I truncated the max values so the As zoning in pyrite is actually visible.

I do not see any scale for concentrations in your maps.

Is this a map from a Probe for EPMA/CalcImage project? Would it be possible to share the MDB, GRD and CIP files with me so I can look into it more?

News:

Quantitative Spectral Interference Corrections