Evaluation Methods According to Filß
The measurement-based determination of the efficiency constants \(H^{'}\) can be carried out using a point source, a surface source, or a volume source. The video exemplifies the procedure for conducting the three methods.
The video shows the efficiency calibration of a segmented gamma scanner for measurements in collimated geometry according to Filß.
Important:
All calibrations demonstrated below must be performed for each measurement system and each collimator used.
Calibration with Point Source(s)
The efficiency calibration with one or more certified or calibrated point sources is the most commonly used method. The point source is positioned directly in front of the collimator along the extension of the detector axis. For good reproducibility, the use of a special source holder is recommended, which can be attached at the output of the collimator.
The point source positioned at the output of the collimator (logically) does not cover the entire opening area of the collimator through which radiation can enter the detector during a measurement. This is accounted for by an additional "area factor" in the efficiency constant: in the case of a cylindrical opening with radius rKoll through the cross-sectional area \( \pi \cdot r_{Kol}^2 \), for a rectangular collimator opening this area factor must be replaced by \( b_{Kol} \cdot h_{Kol} \) (b: width; h: height).
Thus, the efficiency constant \( H_{Pkt}^{'} \) (in the case of a cylindrical collimator) for a characteristic line (i.e., an energy) with the emission probability η of a calibration nuclide with activity \( A_{Pkt_0} \) from the measured count rate Z0 can be determined by the expression
\[ H_{Pkt}^{'} = \frac{1}{\pi \cdot r_{Kol}^2} \cdot \frac{A_{Pkt_0} \cdot \eta_0}{Z_0} \]
.
The unit of the efficiency constant \( H_{Pkt}^{'} \) is cm-2.
Calibration with Surface Source
Using a surface source for efficiency calibration bypasses the area correction problem associated with the efficiency calibration using a point source regarding the opening area at the end of the collimator. Furthermore, a surface source also accounts for slight variations in detector effectiveness across the opening area of the collimator.
The surface source must have a homogeneous activity distribution over the entire cross-sectional area. It is also advantageous to have a surface source that has (multiple) radionuclides with a variety of characteristic lines over a wide energy range. The collimator used defines a field of view that must be fully covered by the surface source. Therefore, the surface source is usually directly attached at the end of the collimator during calibration measurements.
Note:
Compliance with the requirements regarding homogeneous surface activity can also be verified in some measurement systems in a segmented gamma scan measurement (meander scan mode). For this purpose, a collimator with a very small opening angle is used.
Thus, the efficiency constant \( H_{Fl}^{'} \) for a characteristic line (i.e., an energy) with the emission probability η of a calibration nuclide of the surface source with surface activity \( a_{Fl_0} \) from the measured count rate Z0 can be determined by the expression
\[ H_{Fl}^{'} = \frac{a_{Fl_0} \cdot \eta_0}{Z_0} \]
.
The unit of the efficiency constant \( H_{Fl}^{'} \) is cm-2.
Calibration with Volume Source
For the calibration with a volume source, the detector cone, which depends on the used collimator, must lie entirely within the volume source, meaning no areas of the detector cone can "see past" the source.
The volume source must have a homogeneous distribution of the contained material (e.g., sand, cement, bubble wrap) and radionuclides. It must also be ensured that the fill height of the container is known, ideally up to the top.
Note:
Compliance with the requirements regarding fill height and homogeneity can be verified in a segmented gamma scan measurement (e.g., in the multiple disc scan mode).
Thus, the efficiency constant \( H_{V}^{'} \) for a characteristic line (i.e., an energy) with the emission probability η of a calibration nuclide of the volume source with specific activity \( a_{V_0} \) from the measured count rate Z0 can be determined by the expression
\[ H_{V}^{'} = \left[ 1 - \exp \left( - \mu \cdot d \right) \right] \cdot \frac{a_{V_0} \cdot \eta_0}{Z_0} \cdot \left( \frac{\mu}{\rho} \right) \]
.
The unit of the efficiency constant \( H_{V}^{'} \) is cm-2.
