simultaneous arrival of two or more X-ray photons at the EDS detector

[DirkMueller]

Hi all,

during an undergraduate class a student asked me what happens if two X-ray photons from different atoms enter the EDS detector at exactly the same time. Will their energy be summed up and finally give a wrong result by possibly simulating the existence of another element?

I would say yes, but:
a)   The simultaneous arrival of two or more photons at exactly the same time is quite rare, and
b)   It’s even rarer that their combined energies will exactly meet the energy of another elements X-ray line.

Correct?

Thanks
Dirk

[Probeman]

Hi all,

during an undergraduate class a student asked me what happens if two X-ray phonons from different atoms enter the EDS detector at exactly the same time. Will their energy be summed up and finally give a wrong result by possibly simulating the existence of another element?

I would say yes, but:
a)   The simultaneous arrival of two or more phonons at exactly the same time is quite rare, and
b)   It’s even rarer that their combined energies will exactly meet the energy of another elements X-ray line.

Correct?

Thanks
Dirk

Hi Dirk,
The answer is yes and the degree to which it occurs depends on the detector pulse processing time and the photon count rate. A classic example are so called sum peaks. Obviously these sum events occur much more frequently with photons from strong emission lines.

Fun fact: you may even notice a few photons with energies greater than the electron beam energy (Duane Hunt Limit). These are rare events formed when two continuum (moderate energy) photons enter the detector at the same time and are summed together. 

Search for "EDS detector dead time pulse rejection sum peaks".

Here's a good reference:

Scanning Electron Microscopy and X-Ray Microanalysis, Third Edition by J. Goldstein, D.E. Newbury, D.C. Joy, C. E. Lyman, P. Echlin, E. Lifshin, L. C. Sawyer, and J.R. Michael. Plenum Press. 2003.

[Nicholas Ritchie]

Yes, except it isn't really that rare.  A people push there EDS detectors harder and harder, they are becoming more of an issue.  It isn't uncommon at all to see a sum peak mistaken for a minor or trace element. Some vendors have attempted to address the problem by calculating the inverse transform that answers the question "what is the true spectrum that would produce the measured spectrum given the pulse-pair rejection performance characteristics of the detector?"  Sometimes the algorithms work really nicely.

[sem-geologist]

First we should precise up what is exact same time. As mentioned previously absolutely and exactly correctly, the exact "exact" same time would be extremely rare to achieve... However we do not posses such a hardware to measure events with such "exact" time resolution and we register events with pretty huge time windows/frames. Will we get spectral pile-up or not depends a lot from the hardware: counters (EDS SiLi or SDD or gas proportional counter) response to ionisation (or Townsend's electron chain or what ever it is called in given solid or gas counters) ( that is raise and fall times of discharge/voltage drop in the counter through temporary bridged anode and cathode), used decoupling capacitor between counter (which affects how much we can saturate counter with intensive beam and not completely drain the capacitor, and how fast it resets) and charge-preamplifier. Additionally to that further in pulse-processing chain there can be shaping electronics and delayers, amplifiers and pulse-hold analog circuits to hold the max registered amplitude of pulse for synchronous (and unfortunately often multiplexed - single ADC for few signals) with used clock analog-digital conversion, so that MCA could be done (which is in digital domain and pile ups does not happen there). One of main widespread misunderstanding is that deadtime has anything to do (or causes) with pile-ups - it has nothing to do with that! They can look as related as they respond to the increase in density (in time space) of pulses, where the probability of pile-up do increase too.

Pile-ups in 99.9% of cases are caused with too slow preamplifier+pulse shaper. Old preamplifiers (from 80'es still unfortunately stuffed into some recently built EDS and WDS) outputs pulses with pulse length of ~1µs, or down to 500ns (that is enormous timespan which makes possibility to register two (and more) x-ray photons as single event much more probable), so the probability to get a pile-up (per single pulse basis) with 10kcps input rate is about 10/1000, but with 200kcps that is 2/10. Actually math of this process is much more complicated than this, as probabilities of tripple, qoudruple, quantiple and more pile-ups affects the probability. Thus I agree, that probably some simple algorithms can cope with simple-pileups, but I don't think (and had not seen) that even modern EDS systems are capable to cope with n-tiple (n>2) pileups appearing with counting rate approaching 1Mcps. As far I could find, in example Amptek's newest generation preamplifier would be able to cope with 8 million pulses a second. That is only a single order of magnitude improvement compared to technology from three decades before. That is understandable, as it is not possible to shorten the sample time much further without sacrificing the precision and accuracy of measurement. To conclude, the pulse-pile-ups are non-linear process with exponential-like growth responding to increased count rate.

Dead time - it depends (EDS counting circuit vs WDS counting circuit). WDS gas proportional counter has no dead time. Dead time in WDS is generated at analog-digital domain crossing (and queuing) explicitly. On EDS it is more complicated, as preamplifier circuit has its dead time, and analog-digital converting circuit has another. Anyway deadtime is completely linear to counting rate in both cases.

Which leads me to say that this

Search for "EDS detector dead time pulse rejection sum peaks".

is completely irrelevant to this problem as pulse-pileups and deadtime is two separate independent from each other processes, while both dependant on counting rate, but their response to that is different.

I want to emphasize to N.Ritchie, that actually that is not only not rare, but happens in significant amounts during most of everyday EDS or WDS analysis. Actually WDS is more badly affected as pile-ups are completely not dealt with at all or their existance ignored completely, and correction is tied explicitly to dead-time. Which does not work at all with very high count rates (>50kcps). But even with moderate count rates (lets say major elements at typical probe current of EPMA of 10 or 20nA), the pile-ups will be about 0.5-1.5 % of counts, which is hidden normally with over-engineered deadtime correction procedures and most of operators are not even aware that there are these pile-ups at all (unless would be such adventurous as me hanging the oscilloscope to raw signal outputted from preamplifier).

[Probeman]

Here's an interesting real world example of these effects for EDS and WDS:

https://probesoftware.com/smf/index.php?topic=540.0

[DirkMueller]

Dear all,
thank you for this discussion! Good point to think about what "at exactly the same time" means in terms of X-ray phonon detection by electronics.
Best
Dirk

[Probeman]

Dear all,
thank you for this discussion! Good point to think about what "at exactly the same time" means in terms of X-ray phonon detection by electronics.
Best
Dirk

You are welcome, though please note that we are discussing photons, not *phonons*.  Phonons are lattice vibrations (a form of heat). Photons are x-rays.

Edit by Donovan: I edited all the other previous mentions of phonons to photons...

[John Donovan]

I rediscovered this topic from early this year and I have to wonder if this is what got Probeman and his colleagues thinking about multiple photon coincidence in the dead time correction of WDS detectors?

However, I did ask this question of Pat Camus, who works at Edax and previously at Thermo, while we were at M&M this month, and his answer is that because the coincidence circuit of EDS system turns off the WDS detector and automatically extends the live time of the detector, this is automatically handled so long as the photons do not arrive at *exactly* the same time.  If they do arrive at exactly the same time, they are counted as a single photon with the sum of the energies and show up as a sum peak.

Some EDS systems, will calculate (based on the count rate) and try to anticipate to what extent these sum peaks will appear, and will attempt to correct for these sum events in software, but from what I have seen it doesn't always seem to work perfectly.

Back to WDS. However, since we perform the WDS deadtime correction in software that is an entirely different matter. That is, we now think the classical (single term) dead time correction only calculates the probability of a single photon being coincident with another single photon.  Of course since photons are generated entirely at random there is a non zero chance that multiple WDS photons could also be coincident, as Dirk asks in his opening post.

See here for a more detailed description of these ideas:

https://probesoftware.com/smf/index.php?topic=1466.msg11033#msg11033

The good news is that Aurelien Moy's new logarithmic dead time expression can actually handle any number of coincident photons. This of course is now implemented in Probe for EPMA and allows for us to analyze major elements at high count rates with amazing accuracy:

https://probesoftware.com/smf/index.php?topic=829.msg11045#msg11045

The only parameters that matter are the count rate and the dead time interval of the detector.

[sem-geologist]

Back to WDS. However, since we perform the WDS deadtime correction in software that is an entirely different matter. That is, we now think the classical (single term) dead time correction only calculates the probability of a single photon being coincident with another single photon.  Of course since photons are generated entirely at random there is a non zero chance that multiple WDS photons could also be coincident, as Dirk asks in his opening post.

You miss the point, it is very similar problem as the EDS, also it is similarly divided between hardware and software. The final EDS dead time estimation is by software; Hardware (both EDS and WDS) intentionally induces the deterministic deadtime in extendable (EDS) or not-extendable (WDS) fashion. EDS is extendable as it is energy based method and accuracy of measured pulse amplitude is of most importance. WDS is not-extendable because... well historically seeing that gas proportional counters has much higher P/B ratio the electronic system uses much shorter pulse shapping times (250ns) where coexistent at those times Si(Li) EDS would use (25µs shaping or similar in that order). So at that time WDS was anyway beating EDS absolutely in throughput. Also PHA was seen of secondary importance, as it is diffration crystal which does the majority of work of extracting the part of spectrum. Thus WDS has simplified not-extendable dead-time injecting electronics if compared with EDS. In case of EDS there are some additional hardware tricks to make dead time assessment easier (i.e. pulser method - that 0keV peak on some vendor EDS is not only for scale calibration, but mostly for measuring the deadtime), and on WDS we don't have these. In both cases applied dead time on the signal is deterministic (there is exception with EDS as there is some additional dynamic deadtime introduced by reset of charge sensitive preamplifier) - the only problem is then pulses are "exact" piling up - it complicates the assessment, thus introduce the "missing" counts from expected.

so let me jump to modern comparison.

The SDDs are fast because they have a much better signal P/B ratio, which made it the much smaller shaping times (like 25ns and even less  ) practical, while manufactorers of WDS had not updated its counting design practically from 80es (there is only replacement of some counting component chips with equivalent modern counter parts). That is how EDS can cope with 8Mcps (at least on the paper: newest AMPTEK SDD systems) input count rates with "extendable" deadtime and practically with no PHA (energy) shifting, while our WDS counting can't cope with not-extendable deadtime and experience severe PHA shifting already at 150kcps. Software can do some corrections, but it is a bit uphill battle.