Problems calibrating between 1500-2600 keV

[ColoRad-o]

Hello all!

I have been taking spectra of low-level NORM samples. For the last couple of years I've been calibrating using a set of photopeaks from Th232 and U238 (with a little U235) samples. This is often satisfactory, but right now I'm trying to get fairly precise results (10-day long sample counts and background counts) using GADRAS-DRF (which analyzes full spectra, including Compton scattering and X rays) and a lack of reliable reference photopeaks in the range from about 1500-2600 keV is making life difficult. I'm using a 2"x2" NaI:Tl + PMT (at bias voltage 700V), basically what is now the GSB-2020-NAI kit from Steven, usually in about 2.3cm equivalent of Pb shielding.

As always, there is detector drift and for each new spectrum I carefully map my calibration data (AU/StdDev/peak count/keV) onto what I see in AU in my new spectrum, guided by the standard deviation and gross count for each photopeak. This has generally been fine. I've attached a 2-page PDF with the spectrum and fit (not really bad at all with GADRAS analysis), and on page 2 the calibration curve and attempts to correct for the errors in the calibration curve. As you can see the region 1500-2500 keV is problematic, because a relatively small range of AU in the PRA spectrum corresponds to a sizable range in keV. Luckily the GADRAS analysis doesn't depend very sensitively on the high-energy region.

Has anyone here experimented with piece-wise calibration? This would break up the entire spectrum into regions where I trust the calibration and others where it's shaky. Does anyone have experience with doing this. Most importantly: can anyone recommend a particular not too expensive source with at least two photopeaks between 1500 and 2600 keV?

Thanks!
DMW

[Sesselmann]

Has anyone here experimented with piece-wise calibration?

What exactly do you mean by "piece-wise", in PRA you have the option to "interpolate" which is essentially piece wise, meaning you draw a linear calibration between each peak. Say for example you have a peak at 1460 and one at 1588 then interpolate will linearly calbrate that region.

Alternatively a second order polynomial will correct for most non linear spectra. Sound card spectrometers can exhibit a bit of non linearity if the volume/voltage is set too high, reducing voltage usually improves it.

Both ImpulseQt and Becqmoni have simple second order polynomial calibration.

Not sure about using 4th and 6th order calibration as I don't understand how the detector or the electronics can throw a curved ball in that way. Simple exponential error is easy to understand if there is some resistance that limits current flow somewhere in the circuit, but multiple kinks and bends would require a gremlin.

Steven

[ColoRad-o]

Steven, by piecewise I meant permitting the functional form used for interpolation to change RADICALLY depend on the energy range, and keeping careful track of what this does to the spectrum.

Sound card spectrometers can exhibit a bit of non linearity if the volume/voltage is set too high, reducing voltage usually improves it.

I watch the audio input fairly carefully to make sure the vast majority of pulses are not clipped. I long ago learned not to boost the input audio signal using Windows--it produced strange artifacts at the high energy end. I picked 700 V bias since that was what the system recommended, but also because it was very close to the bias RANGE over which the count rate was most stable--essentially fixed over a plateau of bias voltage values.

Linear interpolation is great at low energies. The 4th order polynomial LOOKED good over the range 0-2600 keV, but the peak locations are off by roughly 19 keV over the whole range. I could lower this to 16 keV by acknowledging the overall shape of these deviations. But peak location errors are fairly big over the 1500-2500 range. This range could be split off, the gain changed (raised?) to push this range down into the region where the detector response is LINEAR in the AU corresponding to 1500-2500 keV, and somehow stitched together with the original spectrum.

In the past I've tried splines for interpolation, but generally low-order polynomials are the most systematically reliable, in my experience. I have also used PRA interpolation multiple different ways, but have yet to find a way to predict photopeaks to within, say, 10 keV reliably across the entire range 0-2600. Other well-calibrated detectors with solid state PMTs and different scintillators have managed errors of 6 keV (within +/- 1 standard deviation), and they also see errors well-described by low-order polynomials. So the ultimate extent ability to predict photopeak locations appears to depend (not surprisingly) on the electronics and the linearity of the detector response with gamma energy. I attach the GAGG/SiPM data.

Thanks for the response, Steven!

[Sesselmann]

Thanks, that's an interesting chart.., I might try to replicate this at my end when I have a few minutes to spare. We also make a very nice temperature compenstated GAGG detector. I have one in stock at the moment with around 5.5% resolution.

https://www.gammaspectacular.com/blue/g ... -nano-gagg

My experience is that the larger detectors 2" and above tend to exhibit better linearity and reducing voltage also helps.

Using higher order polynomials will obviosly help, just like furier series if you add enough polinomial orders you can fit any pattern, but knowing every point on the spectrum kind of defeats the purpose of gamma spectroscopy and risks overfitting.

We start with the hypothesis that pulse height is proportional to energy and prove that it is so by fitting the data to our hypothesis, you get my point.

Steven

[ColoRad-o]

Steven--Thanks for following up!

It's funny how one can get stuck in old habits. I ran lots of careful tests 5 years ago deciding on the mix of bias and audio gain, without thinking much about ease of calibration. Since 700V was the recommended bias, I stuck to that for a long while and only later noted the strong non-linearity of the calibration curve. Now I'm re-visiting that choice.
My old measurements for the Cs137 line are attached, and another graphic showing the impact on count rate and pulse width. I hope these are useful to someone getting started--these are from February 2020. Is it fair to say that the best combination for a LINEAR calibration curve is relatively low bias (say, 600 V) together with a value of gain boost selected to bring the 2614 keV Tl208 line to about 100 au in PRA? (I quote PRA because I'm familiar with it.)

[Sesselmann]

The effect of count rate also has to be measured. My friend and collaborator Max (Madmax) has introduced me to active voltage dividers, rather than just resistors and capacitors, these have transistors between dynodes and accordingly will allow more current to flow when the count rate goes crazy. This is a problem we don't really experience with a sound card spectrometer because we are in any case limited to around 2000 cps, however with our digital spectrometers you can push a NaI detector to 200,000 cps. if you have a hot enough source and then an active divider becomes critical.

[ColoRad-o]

For those following this thread, I 'm including calibration curves (keV vs. AU) for my usual situation (bias voltage 700, no boost gain in PRA) when I drop the bias to 600 V but increase the boost gain to 4. I was hoping to have a linear dependence for a broader range of AU. This APPEARS to be true, but in fact the curve at 600V is LESS well behaved than at 700V.

[Sesselmann]

Be aware that boost gain is purely a software gain, it just doubles the numbers, so any inaccuracy will double and double again.
The proper way to boost gain is via the voltage and or amplifier. It's unusual that you should require that much gain, the GS-2020-NAI should have enough gain at 580 - 600 volts.
Which version of the GS-PRO do you have?

[ColoRad-o]

Steven--thanks for the remarks about boost being strictly a software effect and having the potential for producing artifacts. Digging back into 5-year old data I took (I have a GS2020 kit with a GS-USB-PRO box) it is clear that my early work had not focused on calibration curves, and that there is a severe tradeoff between linearity of this curve and count rate. UNTIL I became quite familiar with the 'structure' of the Th232 spectrum, calibration seemed a secondary issue.

The first graphic shows how exceptionally linear the new calibration curve (wiith a 12x boost, before I knew the boost could have bad effects) at 500V bias. The second graphic

Plateaux.png (106.75 KiB) Viewed 9719 times

shows that at 500V the count rate is VERY MUCH lower than at my customary 700 V. For example, with all other parameters held fixed, the count rate was 15.35 cps at 500 V, but 592 at 700V. (The was probably before I had a firm grasp of using the 'shape medthod' in PRA, however.)

The curves at right are the interpolated derivative of the curves at left: peaking at the step, dropping to near zero over the plateau.) Thus an OPTIMUM bias setting does not exist. This is clear in the third graphic.


[I remember being suspicious of the used Ludlum M44-3 I'd bought, but my later work showed me it was tuned for the low-energy range.]

Any suggestions for NOT losing count rate at low bias voltages? I have never monkeyed with non-bias settings of the GS-USB-PRO.

Thanks again.

[Sesselmann]

David,

I love the way you are going deep on this subject 👍

The tricky part is figuring out "exactly" where the non linearity is happening.

Your count rate experiments clearly show a nice count rate plateau, so at least we somewhat understand how the photocathode behaves.

The Sodium Iodide Crystal
NaI(Tl) has an intrinsically non-proportional light yield, strongest at low energies especially at the iodine K-edge (~33 keV); at higher γ energies it’s closer to linear but still deviates by a few percent.

Crystal vs PMT Size
The photon emission across the face of a crystal might not be 100% uniform due to internal reflection, which means that if the PMT does not fully cover the face of the crystal some non linearity might be seen. I have never experimented with this, but I know for a fact that resolution is better with an over sized PMT than under-sized. This effect is probably due to electrons taking a shorter path to the first dynode (just guessing).

PMT and Divider
Larger PMTs generally hold pulse-height linearity better than smaller tubes because their last dynodes/anode run lower current density (less space-charge distortion). A standard “uniform” divider (equal resistors) is fine at moderate rates, but pushing bleeder resistors very high (e.g., up to 10 MΩ for low power) cuts the bleeder current so much that rising anode/dynode currents sag the stage voltages—causing nonlinearity at higher count rates. Two fixes are common: (1) tapered dividers that allocate more voltage to the last stages to stiffen them under load, and (2) active dividers (transistor/FET assisted) that hold dynode voltages nearly constant even when pulses are large or frequent. Also keep the anode load modest (tens–hundreds of Ω up to ~1 kΩ) so the signal current doesn’t drop voltage across it and compress big pulses. As a rule of thumb, keep average anode current well below the bleeder current (often ≤ 10–30%) to stay in the linear regime, older style NIM-era low-value chains (e.g., ~300 kΩ per section) did this with brute force current; today, tapered and active bases achieve similar linearity without requiring a mains powered HV supply.

Preamplifier and shaping
For sound-card spectrometry (µs-scale NaI(Tl) pulses) the preamp rarely sets linearity if we avoid slew limiting and clipping. A simple, low-noise, unity-gain-stable op-amp with adequate GBW and headroom, followed by gentle anti-alias filtering and proper impedance matching to the audio CODEC, is usually best, over-shaping in hardware just adds dispersion that can't be un-done. My view, “less is more” clean gain, modest filtering, and good headroom beats elaborate analog shaping for PRA/Impulse.

I did quite a bit of linearity measuring in the past, I need to search my drive to see if I can find it...


Steven