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3. Definition of calibration parameters

To analyse spectral data with Gamman, a calibration file (MCF file) is required for the gamma spectrometer used to record the data. A calibration file is generated during calibration of the system, where the system is placed into the Stonehenge setup, a semi-infinite cube of brick of density 2.32 kg/l. For each calibrated system a calibration report will be provided. This page shows a definition of some of the calibration parameters used in the calibration file and the calibration report.

3.1 Energy resolution

The resolution of the spectrum describes the width of the photo peaks. The resolution is calculated as the full width at half maximum (FWHM) for a 137Cs photo peak at 662 keV. The resolution depends on the configuration and electronics, but it is largely determined by the intrinsic properties of the scintillation crystal.

During the calibration, the resolution has been determined over the complete spectrum. The FWHM depends on the energy of the photo peak, and is presented in this report for 662 keV.

3.2 Overall scaling factor

A Monte Carlo model has been created to describe the spectrometer to be calibrated. The Monte Carlo model is used to generate the histograms which describe the response of the system to the calibration set-up. Aside from the crystal itself, materials and dimensions of all other system parts may have an effect on the response of the system and need to be included into the model as well. The Monte Carlo model never perfectly describes the system and even systems from the same series may differ slightly. As a result, there is often a slight difference between the measured spectrum and the generated spectrum, which can be corrected for by applying a scaling factor. The scaling factor is typically close to 100%.

3.3 Energy spectrum

An energy spectrum consists of 300 channels with 10 keV per channel. An energy  spectrum describes a range from 0 to 3000 keV.

3.4 Standard spectrum

The standard spectrum describes the response of the calibrated system for 1 unit of activity. Normally, the unit is provided in Bq/kg of a radionuclide in the geometry for which the system has been calibrated. A standard spectrum is also an energy spectrum.

A calibration file (MCF file) contains a set standard spectra, one for each radio nuclide in the file.

3.5 a0, a1 and a2 parameters

The a0, a1 and a2 parameters are the coefficients of a 2nd order function translating the channel numbers of a measured spectrum  into energy.

  • a0 represents the channel offset present in the multichannel system;
  • a1 represents the (temperature dependent) linear scaling factor;
  • a2 represents an alinear correction to the channel-energy scaling.

In an ideal system, the factors a0 and a2 would be zero and a1 varies solely with the temperature of the system (c.f. Hendriks et al, 2001). In practice, most systems show some offset (a0 <> 0) and/or some alinearity (a2 <> 0).

The a0, a1 and a2 parameters are independent of the length of the measured spectrum and always transfer a 512 channel measured spectrum into a 300 channel energy spectrum.

Each channel in the measured spectrum describes an energy range in the energy spectrum, the lower bound of which can be calculated using:

Here Slower is the lower bound in the energy spectrum for channel i in the measured spectrum. f is a scaling parameter defined as 512 divided by the number of channels in the measured spectrum (for a measured spectrum with 256 channels, f would be 2). Note that the upper boundary of the energy range for channel i is equal to the lower boundary of the next channel:

Gamman and the GammaBase DLL use a highly optimized version of the equations above to convert the measured spectrum to an energy spectrum.

An example of a calibration report: SFS177.pdf

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