FWHM question

[Zagros]

hello,
I have a question about the procedure for calculating probe's FWHM.
I know the teorical calculation of FWHM and I suppose that softwares like Theremino and Atomspectra apply this method.
The problem is that increasing the system voltage the FWHM decreases.
So the question is : wich voltage is the correct?
I use theremino MCA hardware and homemade NaI(tl) probes (same behaviour with 3 different probes)
The probe I used for test in attach is a NaI(tl) 25x25 coupled to Hamamatsu R6094 and 10M-10M.....10M partitor.

Look at the attached images.
The setup is the same for both but voltage is different :
For 137Cs: @700v I obtain FWHM of 6% and Increasing in 50v steps the FWHM decreases down to a irreal 2,7% @800v. Same results with theremino software.
Is this due to hardware limitations?
Or I miss a step to determine the probe's correct working voltage?
thanks

http://www.mediafire.com/view/a4adaoa9g ... 5_700v.jpg
http://www.mediafire.com/view/m5pfbecez ... 5_800v.jpg

[Sesselmann]

Zagros,

The FWHM is limited by the type and quality of your detector. As you are using a NaI(Tl) detector the best resolution possible is around 6.5% and you would be very lucky if you have such a good crystal.

Theremino carries out some fancy software processing called convolution which artificially increases resolution, but it does little more than making a good peak look better like cosmetics. The problem is not knowing what it does to the less obvious peaks, maybe one will end up seeing something which isn't really there. I can't comment on Atomspectra as I don't use it.

I recommend going back to PRA to check the real resolution of your detector, and it will be accurate to within 0.5%.

PRA also calculates the Gaussian peak, which is a very good peak finder if you have calibrated correctly.

In the end software is a personal choice and you need to select the software that best suits your experiment.

The detector is definitely the weakest link in the chain.

Steven

[luuk]

Hello Zagros,

First, you have to remember that your resolution can only be calculated correctly is the linearity is correct.
Therefore first thing to do is calibrate your system or at least check if it is linear, if not you cannot get have a realistic resolution calculation.

Second you have to keep in mind that some detectors e.g tubes but also voltage dividers are depending on the used high voltage can get an none linear behaviour, mostly when you turn up the high voltage linearity will get worse.

If you compare your two spectra it is clearly to see that the 800 Volt spectra is completely none linear, therefore you will get a none realistic resolution.
If you want to calibrate your detector remember that NaI(Tl) is none linear below 100KeV.
If you have e.g. Cs-137 and Co-60 sources than the linearity is easily checked the 1332 Kev peak of Co-60 is “almost” double the Cs-137 662KeV so you can see instantly without calculating if the linearity is good or at least acceptable or completely wrong.

Luuk

[MaxGaspa]

I'd like to quote the statements from Steven.

1) The Theremino Software has several cosmetic capabilities creating nice spectrum but without any scientific sense. Supercorrelation (convolution with non-sense response function), resolution compensation, energy trimmers...and more. I'm usually turning off all those option using Theremino Software just as a recording software (I'll be moving to PRA shortly till I have time to write my own software) and then I export the raw data. So the first thing to do is to avoid any "cosmetic feature".

2) The FWHM estimation made by the Theremino is always optimistic. Even with all the cosmetic feature turned off. In any case any FWHM less than 6.5% should be considered with big criticism (There are some amateur spectrum in Internet with an unbelievable 4% at Cs137) . 6% seems false to me as well. Moreover 2.7% is against the Physics of the sensor. The FWHM has 3 different contribution

[processing LaTex...]FWHM(\%) = \sqrt{ a + \frac{b}{E} + \frac{c}{E^2}}


The first constant term is the contribution of the photomultiplier, the second term is the statistical spread of the number of created carriers in the PMT, the third term is the contribution of the noise and is usually the smallest contribution. So neglecting the third term we have a simple relationship to be used for verification of the measured FWHM. Measuring it at different energies it should decrease with the reciprocal of the square root of the energy. If it doesn't there is something wrong in the measurements.

3) I usually get the raw data with Theremino ad I wrote an external program to analyse the data. I apply a quadratic calibration of the channel-energy relation to the whole spectrum. The calibration is obtained using 5-7 peaks distributed (more or less evenly) in the range of interest to get less than 0.5 % error for energies greater than 100 keV. Then to evaluate the FWHM I select a ROI around the peak and then I'm fitting the data to a symmetric Gaussian shape + linear background (in future asymmetric Gaussian will be implemented). I systematically get 7.1% +/- 0.1% of FWHM at Cs137 gamma peak (Fano Factor = 1), that is a good, and true, value for an amateur system. Using a linear calibration instead of quadratic my system still have 7.1% of FWHM at Cs137 because the non linear term is small.

Please not that Theremino is getting 6.7% using the same raw data.
Changing the voltage, +/- 100V , the FWHM value doesn't change too much (less than 0.2%). I'm also using a tapered divider with 2R between the cathode and the first dynode, that may help a little to decrease the statistical noise.

I don't know the Atomspectra software, but if it is providing the same value of the Theremino estimation I'd like to think it is an optimistic value as well.

So in summary,

1) Disable all the option in Theremino and export the raw data
2) Apply a quadratic correction to the energy-channel relation. The magnitude of the quadratic term is a measure of your non-linearity. "more" or "less" linear are useless terms, you should have a quantitative measure of the linearity.
3) Fit the peak with a Gaussian shape

it's a more reliable way to estimate the FWHM. I can assure you that you never get FWHM of 6% or less!!!! Now you can change the voltage and measure the FWHM again.

Attached the spectrum, calibration, fitting of Cs137 and FWHM at different energies (fitting with a simple model the decreasing is following a reciprocal of the square root of the energy within few %) using a Scionix 2" crystal , Hamamatsu R6231 at 850 volt.

[Zagros]

Hello Zagros,

First, you have to remember that your resolution can only be calculated correctly is the linearity is correct.
Therefore first thing to do is calibrate your system or at least check if it is linear, if not you cannot get have a realistic resolution calculation.

Second you have to keep in mind that some detectors e.g tubes but also voltage dividers are depending on the used high voltage can get an none linear behaviour, mostly when you turn up the high voltage linearity will get worse.

If you compare your two spectra it is clearly to see that the 800 Volt spectra is completely none linear, therefore you will get a none realistic resolution.
If you want to calibrate your detector remember that NaI(Tl) is none linear below 100KeV.
If you have e.g. Cs-137 and Co-60 sources than the linearity is easily checked the 1332 Kev peak of Co-60 is “almost” double the Cs-137 662KeV so you can see instantly without calculating if the linearity is good or at least acceptable or completely wrong.

Luuk

Hello Luuk,
Thank you.
I deliberately exaggerated the spectrum at 800v to see how much irrealistic became the Fwhm.
I'll follow Your advice. I know that linearity depends from voltage but also from divider and crystal. I'll try to calibrate with two points-energy.

[Sesselmann]

Hi Guys,

For demonstration purposes only I attach a spectrum recorded with PRA from an electronic pulse generator, through a GS-1100-PRO and my Mac desktop built in sound card, and we get a staggering 0.4% resolution. The pulse generator is tuned to produce a pulse of similar height and width as Cs-137.

It should therefore be obvious to all, that the detector is the weakest link in the chain. With our hardware being capable of 0.4% resolution we get into the realm of HPGE detectors before we even have to worry about it.

Steven

test pulse.png

[MaxGaspa]

Steven wrote

>For demonstration purposes only I attach

Very interesting. Are you using an arbitrary waveform generator? In this case may I have the used shape of the pulse, in any format you like. I'd like to repeat this testing, in addition to other testing I'm planning to do, with my just arrived GS-1100-PRO. I can certainly create that shape acquiring the pulse but I'd like to repeat the test with the same pulses you used.

Bye

Max

[Sesselmann]

Max,

My pulse generator is a simple $5 square wave generator I bought on eBay, it has a trimmer pot for the pulse width and period on the board, I added a volume control and an RC filter to shape the pulse and a high voltage coupling with a BNC so I can connect it the the GS-1100. A 9V battery runs it forever.

You can download an audio sample of the file here: https://www.dropbox.com/s/jadw5vyl2nqo5 ... n.wav?dl=0

On the images below we can see how effective the PRA pulse shape filtering works.

This first image shows the wav file imported with pulse filter set to 10, and with this setting no pulses were dropped.

tolerance-threshold-10.png

Next we use the advanced filter to change the threshold to 5, and this causes 7% of the pulses to be dropped, but improves the resolution.
Note: Changing the threshold using the advanced filter post recording gives exactly the same result as changing it in Data acquisition and analysis before recording, with the advantage of being able to change it.

tolerance-theshold-5.png

As we keep tightening up the threshold, we gain resolution at the expense of losing some counts.

Tolerance-Threshold-2.5.png

The reason we often see a left shoulder on our peak is due to the low sample rate of sound card spectrometry, which causes the sharp peak of the pulse to sometimes fall between sample points. When this happens, the pulse height is always under-sampled never over sampled, hence left shoulder.

Tolerance-Threshold-1.png

As we keep tightening up the tolerance, we are effectively removing the under sampled pulses, leaving us with the better ones that have been sampled correctly and match the shape of the mean.

Tolerance-threshold-0.5.png

So we use a tight tolerance to identify our peaks, but when we are trying to quantify the amount of a given isotope, we should always consider the count loss and add this back in.



Steven