Needing more than a spark test?

[graham-xrf]

Looking at it from a theoretical standpoint, the Laplace Transform of A*f(t) = A*F(s). By extension if we use a linear filter we know the output is proportional to the amplitude of the input. That won't be a surprise to anyone who has spent any time at all in the vicinity of this thread.

I don't think it is a stretch to assume that the pulse height coming out of a TIA or charge amplifier being tickled by an x-ray generated event also is proportional to the total energy of the pulse, so I'm pretty confident that the amplitude of a stretched-out version of the pulse will be as well. The pulse height of our low-pass filtered signal won't be anywhere near the height of an unfiltered pulse, but that's something that can easily be addressed with some post-filter amplification.

This relationship is something I am also convinced about, even though I thought it was strictly only true of square-wave pulses, and triangular ones comprised of two triangles put together. I like it because it saves a forty bucks ADC.
Area = 1/2 base x height. If we make the base longer, the height gets less. That's OK, because we can either start with more than we need, or give it some gain after, or a bit of both.

As it happens, I already bought the ADC, so I decided to push it to to deliver to it's limit. Pulses from my TIA design can also be stretched with a filter afterward, if one decides to exploit the built-in audio channels in the computer end.

One thought I had about pulse stretching, was the need to block new incoming pulses while the filter is doing it's job. For this to work, we either trigger a window to keep the pulse exclusive, until it's over, or reject pulses that have too much content. This situation is also there, even without pulse stretching, but the shorter capture time leaves more for others to be captured, hopefully increasing the count. OR .. we just wait a bit longer for more count.

 

[graham-xrf]

I had to edit post #734 !
I keep getting this bit wrong. We do not reduce the number of electrons by any percentage of absorption probability.
We might, in the end, only get some percentage after circuit losses in the photodiode, but it's not that one.

When (say) a 59.5keV photon delivers 18,0390 electrons, we get to use all of them!
The 3% refers to the probability of it happening in the first place.
3% is not an efficiency over how many are subsequently lost to become heat. It's an absorption probability!
My apologies about that.

 

[homebrewed]

This relationship is something I am also convinced about, even though I thought it was strictly only true of square-wave pulses, and triangular ones comprised of two triangles put together. I like it because it saves a forty bucks ADC.
Area = 1/2 base x height. If we make the base longer, the height gets less. That's OK, because we can either start with more than we need, or give it some gain after, or a bit of both.

As it happens, I already bought the ADC, so I decided to push it to to deliver to it's limit. Pulses from my TIA design can also be stretched with a filter afterward, if one decides to exploit the built-in audio channels in the computer end.

One thought I had about pulse stretching, was the need to block new incoming pulses while the filter is doing it's job. For this to work, we either trigger a window to keep the pulse exclusive, until it's over, or reject pulses that have too much content. This situation is also there, even without pulse stretching, but the shorter capture time leaves more for others to be captured, hopefully increasing the count. OR .. we just wait a bit longer for more count.

Since square waves, triangle waves etc. can be represented by sums of sine waves they all should be subject to the same linearity relationship, i.e., L(f1(t) +f2(t)....) =L(f1(t) + L(f2(t) .... where L() represents the Laplace transform. Of course, the higher-frequency components will suffer greater attenuation through the LP filters.

The Theremino folks have stated that their approach does assume a relatively low count rate so the chances of pulse overlap are relatively low. I haven't looked at how they do it, but they also claim to use software discrimination to reject poorly-formed pulses. "Poorly formed" could be due to pulse overlap or noise pulses that mess up the peak-voltage determination.

I don't think your ADC has to be a writeoff, so to speak. You get more bits of resolution compared to a Teensy's ADC.

I've finished turning my "focus ring" out of aluminum. My initial sanity check was to see how it was fitting around my detector and for a moment I freaked out, because the corners of the package were covered by the ring. However, it turns out that the package is significantly larger than 10 x 10mm, and I used the actual diode dimensions to calculate the focus ring's ID.

The next thing I need to make is a mandrel to form the lead shield ring. I'll just use a leftover piece of Delrin rod for that. My plan is to cut the ends of the lead strip at about a 45 degree angle so they will overlap, rather than a butt joint that might allow x-rays to slip through.

 

[graham-xrf]

Re: Pulse information after filter distortion
It's easy to see amplititude will have say in the area under the waveform. The reason I am wary is that the constant cannot reasonably be the same for any arbitrary waveform, even those made of a sum of sines and cosines. Fortunately, the pulse we get has good approximations that apply.

eg. The area under (say) half a sinewave is the duration x 1/√2 * peak_amplitude, or 0.707*Vpeak.
For a square wave, the average is half the peak.
For other waveforms, there are other crest factors, unless you have a true-rms multimeter.
In the case of our pulses, they all have pretty much the same shape, so therefore the same constant.

Thus we probably need not care that much about the pulse shape, because at calibration time, the pulse(s) amplitudes that repeatedly happen when shown a known metal, can simply be stored as being representative of it.

Do we only get one at a time?
This is where I get to sheer ignorance about what happens. Suppose we have (say) some Tin Sn50 . There are 4 energies of photons it might release.
1. Do these photons arrive somewhat separated in time?
2. Do they ever all hit the photodiode together?
3. Might they have gone off each in in their own separate directions?
4. Would we be waiting for photons of the various energies to arrive one at a time, with the other three going their own way?

I am guessing we only get one of them at any time, and we just have to keep waiting to build up a sufficient count of all of them.

 

[whitmore]

The delay line amplifier is a tricky item, but the modules that do it are available on eBay (and
in genuine four-or-five decade old technology) in the form of modules to fit
a NIM power crate. There's a good overview of the workings in the ORTEC model 460 manual

 

[WobblyHand]

Do we only get one at a time?
This is where I get to sheer ignorance about what happens. Suppose we have (say) some Tin Sn50 . There are 4 energies of photons it might release.
1. Do these photons arrive somewhat separated in time?
2. Do they ever all hit the photodiode together?
3. Might they have gone off each in in their own separate directions?
4. Would we be waiting for photons of the various energies to arrive one at a time, with the other three going their own way?

The decay itself is random. So thinking there's any kind of sense or order to the released photons is folly. So to answer these questions, I'd hazard a guess of:
1. Don't have to be separated. Can be coincident (in the time frames we are concerned about). Not likely, but could happen
2. This can happen - see random
3. Yes, it's possible - random direction scatter
4. Possible, not likely. Eventually the other energy photons from a different decay should show up, due to random direction scatter

There will be a pile up of pulses occasionally. It is unavoidable. So one needs to somehow recognize this and discard that pulse, or figure out a way to decompose or deconvolve the pulse into it's sub-pulses. The deconvolution isn't easy. By far it is easier to discard the piled up pulse and wait a longer time for more counts to accumulate. If I were to bet, malformed pulse dropping is done in successful x-rf devices.

 

[homebrewed]

Do we only get one at a time?
This is where I get to sheer ignorance about what happens. Suppose we have (say) some Tin Sn50 . There are 4 energies of photons it might release.
1. Do these photons arrive somewhat separated in time?
2. Do they ever all hit the photodiode together?
3. Might they have gone off each in in their own separate directions?
4. Would we be waiting for photons of the various energies to arrive one at a time, with the other three going their own way?

I am guessing we only get one of them at any time, and we just have to keep waiting to build up a sufficient count of all of them.

All x-ray lines whose energy is less than the incident gamma ray will be excited, but I don't think that one atom will emit all the lines at once. Certainly, the sum total of emitted photon energies can't be greater than the incident photon energy. So the various XRF photons aren't correlated in time or direction of emission.

But, statistically speaking, on occasion photons can arrive close enough in time to produce pulse overlap, regardless of how fast the detector and electronics are. Therefore, some form of pulse culling is needed to get the best-possible energy resolution.

 

[graham-xrf]

All x-ray lines whose energy is less than the incident gamma ray will be excited, but I don't think that one atom will emit all the lines at once. Certainly, the sum total of emitted photon energies can't be greater than the incident photon energy. So the various XRF photons aren't correlated in time or direction of emission.

But, statistically speaking, on occasion photons can arrive close enough in time to produce pulse overlap, regardless of how fast the detector and electronics are. Therefore, some form of pulse culling is needed to get the best-possible energy resolution.

I was just getting paranoid about making basic mistakes - like the one about percentages.

When the incoming photon happens to energize an atom, (I think) it is capable of giving it's energy to raise the level of more than one of the electrons shells, provided it is energetic enough.

The alternative is that if the energetic photon gives over any energy to any electron, it's ability to anything with the excess is gone. So the remainder cannot do anything other than jangle the atom to a higher temperature. It gets wasted!

Basic questions by the ignorant, they may be, but they arrive in my head anyway!

 

[homebrewed]

According to the Wikipedia entry for X-ray fluorescence, the mechanism is as follows: The incident photon excites an inner-shell electron and as a result it is ejected from the atom. An outer-shell electron drops down into the lower orbital and emits another x-ray due to the energy change. This secondary photon's energy is characteristic of the atom, and of which shell it came from.

If one electron is ejected from the atom, only one electron is needed to refill the vacancy and just one photon will be emitted as a result. So far I haven't found any discussion regarding the possibility of a gamma ray ejecting more than one electron from a single atom. That doesn't mean it can't happen -- unless there's some quantum-mechanical reason for it. I note that photons, just like electrons, have momentum (p = E/c): but can one photon "share" its momentum among multiple electrons? Momentum has to be conserved......and it's a vector.....and what about the possibility of multiple electron-hopping events as the electron "hole" moves from orbital to orbital? Now my head is starting to hurt

But in a practical sense I don't think it is an issue. There's no reason to believe that if multiple photons can come from a single atom that they all are emitted in the same direction, so "pileup" due to that is quite unlikely, if it's even possible.

 

[WobblyHand]

Pileup can occur simply if charge packets due to any cause are received within the bandwidth of the detector circuit. We don't need to know their source, or from which original x-ray it came from. If two or more charge packets are received too close in time, then a malformed pulse will result. If we can recognize it's malformed, it can be rejected, accepted or further processed. In the case of a near coincident big and little pulse, it may be hard to separate them, or even recognize there were two pulses. Just a real world condition that need to be handled in a graceful, predictable fashion.