OK, I am going to start again this morning because I think I now understand the main reason why BJ and SG have been having so much trouble appreciating these new dead time expressions (aside from nomenclature issues!).

Though SG seems to appreciate most of what we have been trying to accomplish when he states:

...albeit it have potential to work satisfactory for EPMA with some restrictions. That is not bad, and for sure it is much better than keeping using classical simple form of correction.

I will work through a detailed example in a bit, but I'll start with a short explanation "in a nutshell" as they say:

Whatever we call these effects (pulse pile up, dead time, photon coincidence) we have a traditional expression which does not properly handle photon detection at high count rates. Let's call it dead time, because everybody calls the traditional expression the dead time correction expression. And all of us agree, there are many underlying causes both in the detector and in the pulse processing electronics.

**I maintain that at least some of these effects are attributable to more than one photon being coincident with another photon, and additionally that the traditional expression does not handle these multiple photon events properly.** And as I will demonstrate in a moment, we have some data that seems to support this hypothesis. There will be of course other effects that should be looked into and corrected for,

** but this effort has never claimed to be a "universal" correction for photon counting**, though I wish luck to SG in his efforts towards that holy grail.

Perhaps we need to go back to the beginning and ask: do you agree that we should (ideally) obtain the same k-ratio over a range of count rates (low to high beam currents)? Please answer this question before we proceed with any further discussion.

You know already my answer from other post about matrix correction vs matrix matched standards. And to repeat that answer it is **Absolutely Certainly Yes**!

So, yes our k-ratios should remain constant as a function of beam current/count rate given two materials with a different concentration of an element, for a specified emission line, beam energy and takeoff angle. And yes, we know that this k-ratio is also affected by a number of calibration issues. Dead time being one of these, and of course also spectrometer alignment, effective takeoff angle and whatever else we want to consider.

**But the interesting thing about the dead time correction itself, is that the correction becomes negligible at very low count rates! Regardless of whether these "dead time" effects are photon coincidence or pulse pile up or whatever they might be.**So some of you may recall in the initial FIGMAS round robin that you received an email from Will Nachlas asking everyone to perform their consensus k-ratio measurements at a very low beam current. And it was because of this very reason that we could not be sure, even at moderate beam currents, that people's k-ratios would be accurate because of these dead time or pulse pile up (or whatever you want to call them) effects.

So Will suggested that those in the FIGMAS round robin measure our k-ratios at a very low beam current/count rate and that these will be the most accurate k-ratios, which should then be reported. This is exactly the thought that John Fournelle and I had when we come up with the constant k-ratio method:

**That these k-ratios should remain constant as a function of higher beam currents if the instrument (and software) are properly calibrated.**Again aside from spectrometer alignment/effective takeoff angle issues, which can be identified from measuring these consensus k-ratios on more than one spectrometer!

Now I need to quote SG again, as this exchange got me thinking (a dangerous thing, I know!):

As I said, call it differently - for example "factor". Dead time constants are constants, constants are constants and does not change - that is why they are called "constants" in the first place. You can't calibrate a constant because if its value can be tweaked or influenced by time or setup then it is not a constant in a first place but a factor or variable.

And I responded:

Clearly it's a constant in the equation, but equally clearly it depends on how the constant is calibrated. If one assumes that there are zero multiple coincident photons, then one will obtain one constant, but if one does not assume there are zero multiple coincident photons, then one will obtain a different constant. At sufficiently high count rates of course.

I think the issue is that SG is trying to separate out all these different effects in the dead time correction and treat them all separately. And we wish him luck with his efforts.

**But we never claimed that our method is a universal method for dead time correction, merely that it is better than the traditional (or as he calls it the classical) expression.** **Roughly speaking, the new expressions allow us to utilize beam currents roughly 10x greater than previously and yet we can still maintain quantitative accuracy. **

It is also a fact that if one calibrates their dead time constant using the traditional expression, then one is going to obtain one dead time constant value, but if one utilizes a higher precision dead time expression that handles multiple photon coincidence, then they will obtain a (somewhat) different dead time constant. This was pointed out some time ago when Anette first reported her constant k-ratio measurements:

https://probesoftware.com/smf/index.php?topic=1466.msg10988#msg10988And this difference can be seen in the values of the dead time constants calibrated by the JEOL engineer vs. the dead time calibrations using the new higher precision dead time expressions that Anette utilized:

`Ti Ka dead times, JEOL iHP200F, UBC, von der Handt, 07/01/2022`

Sp1 Sp2 Sp3 Sp4 Sp5

PETJ LIFL PETL TAPL LIFL

1.26 1.26 1.27 1.1 1.25 (usec) optimized using constant k-ratio method (six term expression)

1.52 1.36 1.32 1.69 1.36 (usec) JEOL engineer using traditonal methodThe point being that one must reduce the dead time constant using these new (multiple coincidence) expressions or the intensity data will be over corrected! This will become clearer as we look at some data. So let's walk through constant k-ratio method in the next post.