1 Introduction
The electronic personal dosimeter (EPD), characterized by miniaturization, multi-functionality, wide measuring range, real-time measurement, and low power consumption, has been widely used in personal dose equivalent Hp(10) monitoring in nuclear power environments, nuclear reactors, nuclear medicine, and other workplaces in which humans are exposed to radiation [1-3]. Since the Si-PIN semiconductor detector has advantages in sensitivity, volume, power consumption, price, etc., it is one of the key components of the EPD system [4-6]. At the same time, the Si-PIN detector has difficulty forming the equilibrium condition of charged particles because the atomic coefficient of the detector is higher than that of the tissue material and the sensitive layer is thin. For these reasons, the photon energy response of a Si-PIN detector is not consistent in the energy range from 48 keV to 1.25 MeV, especially in the low-energy region (less than 100 keV), where the photon energy response to 137Cs is high.
Because the energy response of a Si-PIN detector is not consistent, using the traditional single-channel counting method seriously affects the measurement accuracy of the instrument, so it is necessary to solve this problem by other methods. The method of correcting the energy response of a Si-PIN detector is one of the core technologies of an EPD. EPDs based on a Si-PIN detector mainly include three kinds of methods for energy response correction, namely the compensation material method, the spectrometer–dosimeter method, and the channel ratio method (CRM).
The related parameters of an energy-compensated material can be calculated by numerical calculation or Monte Carlo simulation [7-10]. The core idea of this method is to design a kind of composite material that can achieve the purpose of off-setting the high response of the Si-PIN detector in the low-energy region [11-14]. The difficulty of this method resides in its inability to process bulk materials to meet performance requirements. At the same time, the measurement error of this method is correspondingly large, and the performance requirements of a Si-PIN detector are relatively high.
The spectrometer–dosimeter method measures the pulse-height spectra of the Si-PIN detector, and the linear relationship between the pulse amplitude and the absorbed energy at the Si-PIN detector is obtained by experiments [15, 16]. Because the influence of photons of different energies on the personal dose equivalent (Hp(10)) is different, the energy response correction of the Si-PIN detector can be realized by using the counts of each channel multiplied by weighting factors [17]. However, this method does not meet the basic requirements of the EPD because of its power consumption, size, cost, and other factors. Historically, some authors have put forward a simplified multi-channel spectrometric system by using a few comparators, and the energy response correction of the detector was done in the same way. This method can reduce the power consumption and the cost of the instrument, but it is difficult to adjust the threshold parameters, and the measurement accuracy is limited. Another method was called the dose conversion unit (DCU), which considered the pulse amplitude as well as the pulse number simultaneously. The DCU used a microprocessor to control a digital-to-analog converter (DAC), and the output of the DAC was fed into a single-channel analyzer (SCA) as low-level discriminator (LLD) values based on the dose conversion function. The final output of the DCU system was the count rates of pulses, which were directly proportional to the exposure dose rate in air [18, 19]. From the relevant literature [17-19], it was found that this method had some limitations in the measuring range; in addition, the system structure and the calculation methods were relatively complex.
The basic idea of the CRM is that there is a relationship between the channel ratio value and the beam energy. By changing the thickness of the additional filter material of the two channels, the beam energy can be identified using the CRM. By utilizing the conversion factor under the specific energy conditions, the personal dose equivalent parameters can be obtained. So far, the CRM has not been successfully applied in the EPD, but the method has potential application value in neutron-gamma resolution and beta measurements [20-22].
In summary, the CRM is more advantageous in terms of instrument structure than the spectrometer–dosimeter method, and its measurement accuracy is higher than the compensation material method. Therefore, in this paper we focus on the principle and method of using the CRM to correct the photon energy response of an EPD.
2 Mathematical relationship between channel ratio and beam energy
Figure 1 is a schematic of the two-channel ratio method. CM1 and CM2 are composite filter materials, the thicknesses are T1 (cm) and T2 (cm), the linear attenuation coefficients are μ1(E) (cm-1) and μ2 (E) (cm-1, and the sensitive area is S (cm2. D1 and D2 are the Si-PIN detectors, the thickness of the sensitive layer is T3 (cm), the linear attenuation coefficient is μ3 (E) (cm-1, and the sensitive area is S (cm2. Channel 1 (CH1) consists of a composite material CM1 and a Si-PIN detector D1; channel 2 (CH2) consists of a composite material CM2 and a Si-PIN detector D2.
The back end of each channel also includes a charge-sensitive amplifier, a main amplifier, and a discriminator circuit (shown in Fig. 2). The multichannel design method is based on the extension of the measuring range, and the correction principle of the small detector is the same as that of the large detector.
Assuming that the particle fluence at the detector position is DS (cm-2), the particle energy is E (keV), and the particle numbers interacting with the Si-PIN detector are DM1 and DM2. Assuming that particles interacting with the Si-PIN detector are recorded by the subsequent circuit, the following relationship exists:
When μ1(E) is equal to μ2(E), Eq. (1) is further simplified as follows:
The linear attenuation coefficient μ1(E) can be calculated using Eq. (2). If the corresponding relation between μ1(E) and E is successfully established in a table, the energy information of the radiation field is obtained using the look-up table (LUT) method. Meanwhile, the channel ratio value and the beam energy should have a one-to-one relationship in the measurement range. μ1(E) should satisfy the monotone function characteristic in the energy range from 48 keV to 1.25 MeV. When the physical form of the filter material is considered, the photon mass attenuation coefficient [μ1(E)/ρ] is often used to describe the reduction of the photon fluence, where ρ is the density of the composite filter material (g/cm3) [23, 24]. After utilizing the mass attenuation coefficient, the basic feature remains unchanged.
The calculation model under the monotone energy radiation field is now discussed. In the continuous spectrum of the radiation field (such as the X-ray diagnostic radiation source), Eq. (2) will be complex, and is transformed to
where ϕ(E1), ϕ(E2),..., ϕ(En) are the particle fluences (cm-2), E1, E2,..., En are the energy of the X-ray particles (keV), and n indicates the particles of different energy. Although DM1, DM2, and the thickness of the composite material are known, the value μ1(E) is difficult to obtain using Eq. (3).
Equations (1)-(3) are established on the premise that the detection system meets the narrow-beam geometry. Under broad-beam geometry (BBG) conditions, the influence of the scattered photons must be considered, and the μ1(E) value of the filter material is not accurately computed using the channel ratio value. Owing to the EPD having performance requirements for angle response and sensitivity, the detector unit is in the BBG condition, assuming that the scattered photons are recorded by the subsequent circuit under the BBG condition. When using the buildup factor to correct the scattered photons, Eq. (2) will be transformed into Eq. (4), and Eq. (3) will be even more complex:
where Δ1(E,T1,μ1(E)) and Δ2(E,T2,μ1(E))) are the buildup factors [ Δ2(E,T2,μ1(E)) / Δ1(E,T1,μ1(E))>1] for the scattered photons, which are related to the beam energy E, material properties μ1(E), and the thickness of the material. From Eq. (4), it is not possible to calculate μ1(E) directly under the BBG condition. Because Eq. (3) cannot be solved, μ1(E) under the continuous spectrum condition and the further derivation of Eq. (3) under the BBG condition is ignored.
In summary, using the channel ratio value to solve for μ1(E), and then using μ1(E) to solve for the beam energy E, the measurement error of E under the BBG condition will increase.
In practical application, through the narrow-spectrum series produced by an X-ray machine and a mono-energetic isotope radiation field, the relation between channel ratio value and beam energy can be obtained using the calibration method. The calibration method allows one to by-pass the process of the Eqs. (2)-(4) to solve for μ1(E) using the CRM, and the beam energy can be directly obtained using the LUT method.
3 Energy response correction using the channel ratio method
In practical application, it is essential to consider the consistency of aspects of the instrument, such as the filter material, the Si-PIN detector, and the circuit parameters. At the same time, the depletion layer of the Si-PIN detector and the surrounding material are not tissue equivalent. Calibration of the EPD under the standard radiation field can further simplify the mathematical calculation model. It is assumed that the counts per second (CPS) detected by CH1 and CH2 are CT1 and CT2, and the CPS is linear with the dose rate. Assuming the dose rate at the position of the detector is Ds (μSv/h), the following relationship exists:
The sensitivity coefficients a1 (E) [CPS/(μSv/h)] and a2 (E) [CPS/(μSv/h)] of the two-channel detectors are calibrated under the condition of energy E in the standard radiation field. In practical application, the sensitivity of the detector, the measuring range, and other technical parameters must also be considered. The composite material described in this paper is mainly composed of Al, Cu, and scintillation materials. A simplified model of Eq. (6) can be used to overcome the uncertain properties of materials such as size and density. There is no exact analytical formula for the function y in Eq. (6), which can be solved using the calibration method in a radiation protection standard laboratory.
Equation (6) can be used to calculate the energy information of the radiation field using the LUT method.
Assuming b1 (E) = 1/a1 (E) and b2 (E) = 1/a2 (E), the accurate measurement of the personal dose rate equivalent can be accomplished using
The conversion factors b1 (E) and b2 (E) can be calculated using the LUT method. After using Eq. (7) in the energy range between 48 keV and 1.25 MeV, the photon energy response of the EPD is corrected.
4 Characteristics of reference radiation field
A medium-energy reference radiation field is based on the narrow-spectrum series produced by an X-ray machine. A high-energy reference radiation field is based on 137Cs and 60Co isotope radiation sources. The test conditions are summarized in Table 1, and the relevant standard values were obtained in a 1-liter spherical ionization chamber (type 32002) at PTW Freiburg GmbH.
| Tube voltage(kV) | Tube current(mA) | Additional filtration | Half-value layer (HVL) for mm Cu | Distance (m) | Mean energy (keV) | Standard value (μSv/h) | ||||
|---|---|---|---|---|---|---|---|---|---|---|
| (mm) | ||||||||||
| Al | Cu | Pb | Sn | |||||||
| Narrow spectrum | 60 | 1.5 | 4.0 | 0.61 | / | / | 0.24 | 3.0 | 47.9 | 1549 |
| 80 | 2.3 | 4.0 | 1.95 | / | / | 0.58 | 3.0 | 65.0 | 1498 | |
| 100 | 4.3 | 4.0 | 4.70 | / | / | 1.10 | 3.0 | 83.1 | 1496 | |
| 120 | 3.6 | 4.0 | 4.17 | / | 1.03 | 1.68 | 3.0 | 100.0 | 1515 | |
| 150 | 0.6 | 4.0 | 0.65 | / | 2.11 | 2.33 | 3.0 | 117.7 | 1563 | |
| 200 | 1.1 | 4.0 | 1.98 | 1.14 | 1.47 | 3.95 | 3.0 | 164.0 | 1436 | |
| 250 | 0.8 | 4.0 | / | 1.98 | 2.95 | 5.15 | 3.0 | 207.5 | 1478 | |
| Isotope source | 137Cs | / | 1.0 | 661.6 | 1148 | |||||
| 60Co | / | 1.0 | 1250.0 | 7334 | ||||||
The narrow-spectrum series used in the research described in this paper mainly include N60, N80, N100, N120, N150, N200, and N250 [25, 26]. The energy spectrum is shown in Fig. 3 (normalized to the maximum counts).
It can be seen from Fig. 3 that the narrow-spectrum series have the characteristics of a continuous spectrum, but the attenuation law is similar to that of mono-energetic rays.
The testing setup in the standard laboratory is shown in Fig. 4. The prototype model of the EPD tested was Nt2000. The EPD was located in the front of the water phantom and the Si-PIN detector was coincident with the center of the radiation field.
5 RESULTS AND DISCUSSION
The counts per second (CPS) detected by the two-channel detectors are shown in Table 2. There were 10 measurements made in each energy condition, and the CPS values in Table 2 are the arithmetic means of the 10 measured values in each energy condition. It can be seen from the results presented in the table that the photon energy responses of the two-channel detectors are inconsistent in the energy range between 48 keV and 1.25 MeV.
| Mean energy (keV) | 47.9 | 65.0 | 83.1 | 100.0 | 117.7 | 164.0 | 207.5 | 661.6 | 1250.0 |
|---|---|---|---|---|---|---|---|---|---|
| Standard value (μSv/h) | 1549 | 1498 | 1496 | 1515 | 1563 | 1436 | 1478 | 1148 | 7334 |
| CT1 (CPS) | 2895 | 2703 | 2251 | 2153 | 2081 | 1849 | 1735 | 732 | 3305 |
| CT2 (CPS) | 809 | 1032 | 1001 | 1084 | 1187 | 1278 | 1355 | 680 | 3808 |
The EPD uses a single-channel detector (CH1) to obtain the counts-dose rate conversion factor b1 (E) [(μSv/h)/ CPS] (as shown in Fig. 5) under the different beam energy conditions in the standard laboratory. The standard deviation of the counts-dose rate conversion factors of all energy conditions are between 0.016 and 0.039, and the standard deviation at the kink point of 207.5 keV is 0.023. If the photon energy response of CH1 is not corrected, the difference response from low energy to high energy can be up to approximately 5 times. This situation will seriously affect the accurate measurement of the personal dose equivalent for radiation field staff.
The plot shown in Fig. 6 was calculated in accordance with Eq. (2). Because the filter material, detector, and back-end circuit parameters may be inconsistent, the calculation results in Fig. 6 did not consider the density and thickness of the composite material. The standard deviation of the natural logarithm of the CT1/CT2 of all energy conditions is between 0.022 and 0.046, and the standard deviation at the kink point of 207.5 keV is 0.024. Under the 137Cs and 60Co conditions, the CT1/CT2 values are 1.077 and 0.868, respectively. As a result, the natural logarithm of the CT1/CT2 is negative in the 60Co condition. The reason for the above phenomenon is that the influence of the scattered photons in matter is neglected in Eq. (2). Because the purpose of this article is to determine the relationship between the channel ratio value and the beam energy, as long as they have a one-to-one relationship, the above problems have no effect on practical application. It can be seen from the curve of Fig. 6 that the natural logarithm of the CT1/CT2 satisfies the monotone function characteristic in the energy range from 48 keV to 1.25 MeV, which further proves the feasibility of using the channel ratio value to identify the beam energy.
Figure 7 plots the discrete data points of the function y in Eq. (6). The standard deviation of the CT2/CT1 of all energy conditions is between 0.013 and 0.019, and the standard deviation at the kink point of 207.5 keV is 0.019. It can be seen from Fig. 7 that, although there is no linear or exponential relationship between the beam energy and the channel ratio value, there is a one-to-one relationship between them, which meets the requirement of Eq. (2). The relationship between the beam energy and the channel ratio value can be realized by polynomial fitting or by interpolation in the energy range between 48 keV and 1.25 MeV. Using the relation curve of Fig. 7, the beam energy can be directly identified by the channel ratio value.
Figure 8 shows the relationship between the channel ratio value (CT2/CT1) and the counts-dose rate conversion factor of CH1. Owing to the change tendencies of the detector’s conversion factor over the entire energy range being different, the conversion factors in the low- and high-energy regions can be fitted. It can be seen from Fig. 8 that the counts-dose rate conversion factor [b1 (E)] of CH1 can also be directly obtained from the channel ratio value (CT2/CT1).
It can be seen from Figs. 6, 7, and 8 that the standard deviation exhibits no obvious differences between the kink point and the other points under the experimental conditions.
Table 3 presents the measurement results after the energy response correction of the EPD. Ten measurements were made for each condition. The measured values in Table 3 are the arithmetic mean of the 10 values in each energy condition. The personal dose rate equivalent Hp(10) parameters can be calculated using the CRM, and the measurement accuracy compared to the traditional single channel method is significantly improved.
| Energy(keV) | 47.9 | 65.0 | 83.1 | 100.0 | 117.7 | 164.0 | 207.5 | 661.6 | 1250.0 |
|---|---|---|---|---|---|---|---|---|---|
| Standard value (μSv/h) | 1549 | 1498 | 1496 | 1515 | 1563 | 1436 | 1478 | 1148 | 7334 |
| Measured value (μSv/h) | 1510 | 1478 | 1486 | 1530 | 1503 | 1465 | 1501 | 1140 | 6850 |
| Relative error (%) | -2.52 | -1.34 | -0.67 | 0.99 | -3.84 | 2.02 | 1.56 | -0.70 | -6.60 |
| Relative response to 137Cs | 0.98 | 0.99 | 1.00 | 1.02 | 0.97 | 1.03 | 1.02 | 1.00 | 0.94 |
| Response difference to 137Cs (%) | -1.83 | -0.64 | 0.03 | 1.70 | -0.32 | 2.74 | 2.27 | 0.00 | -5.94 |
It can be seen from Fig. 9 that the photon energy response to 137Cs using the CRM is similar to a horizontal line. The standard deviation of the corrected energy response to 137Cs is between 0.016 and 0.040.The relative error of the personal dose rate equivalent is within ±6.6%. The difference of the energy response to 137Cs is within ±6.0%, which fulfills the ±30% requirement of GB/T 13161-2003 and JJG 1009-2006.
6 Conclusion
In this paper, we described the use of composite screen detection technology, multi-channel acquisition technology, and the CRM, by identifying the beam energy information, to achieve photon energy response correction for an EPD in the energy range from 48 keV to 1.25 MeV. At the same time, the principle and method of the photon energy response correction were derived, and the relevant features of the standard radiation field were described. The proposed method has the advantages of simple structure, easy implementation, low cost, low power consumption, and high measurement accuracy. The CRM was used to correct the photon energy response of the EPD, and the difference of the energy response to 137Cs was almost constant within ±6.0%, which fulfilled the energy response requirement of GB/T 13161-2003 and JJG 1009-2006. From the related test results, it was shown that the proposed method can realize the accurate measurement of the personal dose equivalent of radiation workers, and the method has practical application value in a personal dose monitoring system.
Although the channel ratio value and the beam energy have a one-to-one relationship, the relationship between them is not linear. The CRM is thus more suitable for personal dose equivalent measurement in mono-energetic conditions. When the EPD is used in a mixed radiation field, the measurement error of the personal dose equivalent will increase. In the future, it will be necessary to research the measurement method in a standard mixed radiation field.
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