Experimental setup

Typhoon FLA 7000 (FLA) was used to image the alpha tracks in the IP. The alpha tracks stored in the IP can be eliminated by the FLA Image Eraser in approximately 15 min. BAS – TR 2025 was used as the IP in this study. The FLA, FLA Image Eraser, and IP were all developed by the Fujifilm Company.

Standard ²⁴¹Am sources were utilized to irradiate the IP, and the 2π emissivity was calibrated by the China National Institute of Metrology. A standard source of Radon progeny was used for testing the CNN algorithm, which is a product of the Pylon Electronic Development Company.

Experimental manipulation of IP imaging

The operation of each imaging process was as follows: (1) The FLA image Eraser was used for more than 15 min to erase the residual information in the IP. (2) The IP was irradiated by standard ²⁴¹Am sources with an effective diameter (the area of emitting the particles) of 10 or 20 mm. The distance between the surface of the source and IP was set to 2 mm. (3) The exposure time of the IP was controlled by the opening and closing times of the shading box. (4) The imaging information of the alpha tracks was obtained using Typhoon FLA 7000, and the photos were saved in the computers.

The imaging operations of the IP are shown in Fig. 1a. All the operations were performed in a dark room at 25 ℃. The BAS-TR IP consists of a phosphor and base layer without a surface protective layer. The size of the IP imaging board was captured as 3 cm×3 cm (601×601 pixels; the size of each pixel was 50 μm) using Python. A captured image contains radiation information generated by a single radiation source. The blank area in the IP image was randomly selected as the background image of the IP for CNN training. The size of the background image was the same as that of the source-irradiated image. After each imaging, FLA was used to perform extinction processing on the IP.

Fig. 1Full-screen View

(Color online) (a) Imaging operations of IP; (b) schematic structure of CNN.

Determination of detection efficiency parameter

The background and irradiation areas must be considered when counting alpha tracks [26]. In this study, a 100 mm×60 mm (2000×1200 pixels) IP and several sources (φ40 mm×4 mm, an effective diameter of φ10 mm or φ20 mm) were built in Geant 4 to perform the Monte Carlo simulations. The energy E(z) at which particle deposition occurs at a depth z of phosphor can be obtained.

The detection parameter, A, can be calibrated using the simulated energy E(z), depth z, and PSL gauged in the experiment [5]: $\text{PSL}=\underset{0}{\overset{d}{{\displaystyle \int }}}A\times E\left(z\right)\times \frac{6·\left(l+d-z\right)}{2l+d}\text{d}z,$ (1) where l is the mean free path of the visible light scattering in the phosphor layer (60 µm) and d is the depth of phosphor [5]. $A=\frac{q\times P}{{\overline{E}}_F}$ (2)

Here, q is the total factor parameter of the filter attenuation, photosensor attenuation, back-end electronic counting system, and efficiency of the PSL Blu-ray collected by the photomultiplier tubes, P is the ignited efficiency, ${\overline{E}}_{\text{F}}$ is the average energy of creating an F center, and q, P, and ${\overline{E}}_{\text{F}}$ are the determined parameters for the specific IP and reader type [5].

However, the energy deposition in phosphor is discrete, and the continuous changes with the depth of the photosensitive layer cannot be calculated using Geant 4. Therefore, the PSL can be calculated as follows: $\text{PSL}={\displaystyle \sum _{i=1}^{n}A\times E}\left(z_i\right)\times \frac{6\cdot \left(l+d-z_i\right)}{2l+d},$ (3) where $E\left(z_i\right)$ is the energy deposition produced by the i-th particle at depth z of the phosphor layer of the IP and n is the total number of particles that generate the PSL values.

Acquisition of simulated images

Geant 4 was adopted in this study. The IP imaging simulation processes are as follows: (1) the geometric model of IP is built based on Fig. 1a, (2) the radioactive sources and their spatial locations are built, (3) particles are randomly created and the particle transport is tracked, (4) the energy deposition and number of particles in the phosphor of the IP are counted, (5) PSL values are calculated based on the detection efficiency parameter A, (6) PSL values are converted into grayscale values using Eq. 4, (7) grayscale values are converted into imaging data, and (8) many images are created by repeating steps 3–7 to provide the fundamental data for training the CNN. Notably, in addition to the irradiating alpha sources, the irradiating background is also considered in the processes of randomly creating particles in step 3. Therefore, the entire IP is irradiated by the alpha, beta, and gamma background. Meanwhile, the alpha ray of ²⁴¹Am decay irradiates the IP. The Geant4 simulation process chose the EMStandardOpt4 physics list as the default, which includes the physical process of not only the alpha, but also beta and gamma particles [27].

Numerous images can be simulated using the Geant 4 software to calibrate the detection efficiency. The PSL values can be transformed into grayscale values using Eq. (4), and then converted to images that are used to train the CNN [28, 29]: $G=\left(\frac{1}{L}\times {\text{log}}_{10}\left(\text{PSL}\times \frac{S}{4000}\times {\left(\frac{100}{R}\right)}^2\right)+\frac{1}{2}\right)\times CL,$ (4) where L is the probe dynamic response range of IP (5), G is the raw image grayscale value, S is the sensitivity of IP (1000), CL is related to the bits of photos (2¹⁶, CL = 2⁸ is for 8-bit image files), and R is the resolution of the reader (50 µm) [17].

Images and particles were simulated using the Monte Carlo method to ensure that the counting of the CNN was accurate. Therefore, the code was loaded into the Beijing Super Cloud Computing Center for running it.

CNN algorithm

An ideal track appears when an alpha particle enters the IP. Therefore, the alpha particle count when entering the IP was set as the output (output of the CNN was set to one). The irradiated and background image areas of the IP were set as the inputs (size of imaging is 3 cm×3 cm, 601×601 pixels), leading to the creation of a CNN appropriate for counting the alpha track in the IP (Fig. 1b).

The CNN algorithm built in this study combines feature extraction and image recognition, including the processes of ensemble learning, backpropagation, and the selection of optimized self-learning. The CNN consists of the following two modules: a convolutional network module and a fully connected layer. Convolutional and max-pooling layers were used in the convolutional network module to learn high-order representations of the features. In particular, the convolution network computes higher-order feature maps through a two-dimensional convolution operation and activation function.

Furthermore, the CNN performs a convolution operation on the background and source regions to extract the image feature information. After combining the image feature data generated by convolution in the feature-binding layer, the distributed feature representation was mapped to the sample marker space in the fully connected layer to reduce the influence of the feature locations on classification.

The training data should contain experimental alpha counts. The minimum count rate of the standard Am-241 sources is 1.65×10³ (2π·min)^–1, which will ideally create 137.5 alpha counts per five seconds; therefore, the lower limit was 137 alpha counts. The upper limit should be as large as possible, ensuring that the CNN can be used for counting the experimental images, and simultaneously demonstrating the CNN's linear performance. Thus, 10⁸, which is the maximum possible count, was set as the upper limit. Therefore, the range of goal (number of particles entering the IP) magnitudes utilized for training was broad (137–10⁸). Before utilizing the data for CNN training (Fig. 1b), the data were normalized and preprocessed using Eq. 5 to eliminate the impact caused by the differences in the magnitudes. Subsequently, the trained CNN was used to calculate the alpha track counts. $x=\frac{\lg \left(p\right)-\lg \left[\min \left(p\right)\right]}{\text{lg}［\max \left(p\right)]-\lg \left[\min \left(p\right)\right]}$ (5)

Here, x is the data processed and used to train the CNN, p indicates the goals, min(p) is the smallest value in matrix p (137), max(p) is the largest value in matrix p (10⁸).

We set the learning rate to 0.001, the mini batch size to 64, and updated the network parameters using the Adam optimizer. The traning process is shown in Fig. 2. The model reached convergence after only five epochs. The average computation time for one epoch (64 samples) was only 2.11 s on a single NVIDIA TITAN X GPU.

Fig. 2Full-screen View

Loss in the training process.

Detection efficiency parameter and threshold of PSL

The detection efficiency parameter of the IP adopted in this study was 0.0484 PSL/MeV (3.02×10¹¹ PSL/J) based on the relationship between the experimentally measured PSL value and the energy E_(Z) of the alpha particles deposited on the IP simulated by Geant 4 (Fig. 3a).

Fig. 3Full-screen View

(Color online) (a) Linear response of the IP to energy, (b) alpha energy spectrum on the IP, (c) PSL produced by the irradiation, (d) background PSL.

Chen Bo obtained a detection efficiency parameter of 7.71×10¹¹ PSL/J using an X-ray calibration of the BAS-MS (multipurpose) IP [5]. There are two main reasons for this difference, the first of which is the method of calibration being different. In this study, the calibration was directly conducted by the alpha source, while Chen Bo performed the calibration by an X-ray machine. They first calculated the IP detection efficiency of the X-rays. Subsequently, the energy spectrum of the X-ray machine (tube voltage: 80 kVp, Tungsten target, inherent filtration: Al 1.2 mm, anode angle:12.0^o) was calculated using Xcomp5r software. Simultaneously, the total energy deposition in the IP and corresponding air kerma (kerma is a measure of energy transferred from radiation to matter and is an acronym for kinetic energy released to matter) was calculated based on the energy spectrum of the X-ray machine and the detection efficiency was finally calculated. Second, the energy of the alpha particles is nearly entirely deposited on the IP compared to the X-rays, which has a strong penetration. Therefore, the detection efficiency parameter of BAS-TR IP was lower than that of BAS-MS IP. Moreover, the IP types were different. The BAS-MS IP has a surface protective layer (9 µm), whereas the BAS-TR IP used in this study has no protective layer. When the particles pass through the surface protection layer, there is a certain amount of energy deposition, reducing the deposition energy E(z), and the detection efficiency parameter of BAS-MS IP is higher than that of the BAS-TR IP. The energy spectrum of the particles entering the BAS-TR type IP is shown in Fig. 3b.

This study compares the results of the CNN counting method with those of the PSL method. However, the PSL method must set a threshold to reduce the influence of the background on the counting results. Figs. 3c and 3d present the PSL values of the source irradiation and background, respectively. Distinct spikes in the IP imaging following alpha irradiation indicate that alpha particles lose nearly all of their energy at specific locations in the IP. The PSL values caused by the alpha particle radiation were all higher than 0.3, while the background PSL values were all lower than 0.033. The previous studies conducted by Chen Bo et al. reported that the PSL of beta rays and background irradiation were all lower than 0.25 [5]. Therefore, 0.25 was set as the threshold to avoid the influence of the beta rays and background in this study.

Based on the IP imaging method and the detection efficiency parameters calibrated in the experiment, this study simulated the images of the alpha particles in the IP and obtained the track data through experiments (Fig. 4). The simulated alpha particle track sizes (50–300 µm) were smaller than the experimentally measured tracks (100–350 µm), mainly because Geant 4 only simulates the process of the energy deposition and not the process of the F center formation and electron migration in the photosensitive layer. In addition, the IP reading process also causes the measured alpha track to spread [5].

Fig. 4Full-screen View

Alpha tracks in the simulations and experiments.

Source and background images of 601×601 pixels simulated by Geant 4 (Fig. 4) were used as inputs to train the CNN.

Count of simulated IP images by CNN

The CNN is trained by the simulated images in Geant 4, and the number of particles entering the IP is set as the output. Therefore, the relationship between the CNN counting results and the number of particles entering the IP can maintain a good linearity when the number of alpha particles exceeds 10⁶; the correlation coefficient is 0.9994, as indicated in Fig. 5a. Whereas, when there are less than 2×10⁴ particles, the PSL values also exhibit a high linearity; the correlation coefficients without and with the correction overlap are 0.9833 and 0.9879, respectively. The linear relationship gradually diminishes when the number of particles exceeds 2×10⁴; as the number of particles increases, it is more difficult to maintain a linear relationship (the correlation coefficient with the correction overlap is 0.2992, Fig. 5b). Despite this correction, a linear trend is not guaranteed (correlation coefficient of 0.2970). Previous studies [6] demonstrated that the PSL method maintained a good linearity when the alpha particle count was less than 2×10⁵ and the BAS-MS IPs were used in imaging. Since the TR IP lacks a surface protective layer, the alpha track in the BAS-TR IP is bigger than in the BAS-MS, and the probability of an overlap in the BAS-TR is higher than in the BAS_MS. Therefore, the counting is apparently decreased owing to the overlapping effect [6]. The linearity of counting is worse owing to the overlapping effect when the number of incident alpha particles is greater than 2×10⁴ and the PSL method is adopted. In addition, the poor correction of the overlap effect in this study is mainly because the correction method adopted is proposed based on the MS IP [6].

Fig. 5Full-screen View

(a) CNN counts results for the simulation, (b) PSL count results for the simulation, (c) CNN count of the experimental results, (d) relative error in CNN count.

CNN counting the results of the experimental images

The trained CNN should be able to count the alpha tracks according to the experimental images screened from the IP, which can be applied to the actual alpha track count. In this study, the incident alpha tracks in the experiment were counted by screening the blank (set as the background) and irritated areas in the IP imaging. Based on the counting results (Fig. 5c) and relative errors (Fig. 5d), the following conclusions can be obtained: (1) the counting results of the CNN maintain a good linear relationship in counting beyond 5000 (correlation coefficient is 0.9983), (2) alpha track counting results beyond 5000 are unaffected by the overlapping effect, (3) for a low count of less than 5000, the linearity of the evaluation results is poor (correlation coefficient is 0.8213).

The fraction of particles entering the IP is 0.6576 ± 0.0741 of that of the sources emitted, which is near the ratio of the CNN count to the source emitted (0.6251 ± 0.0421). Therefore, considering the fraction of particles entering the IP, a lower count results in a larger relative error (Fig. 5d), which is calculated by Eq. 6. For example, the mean relative error for counting beyond 5000 is 0.089. $RE=\frac{Y-X}{X}\times 100\text{\%}$ (6)

Here, RE is the relative error, X is the number of particles emitted by the sources, and Y is the CNN count divided by 0.6251.

Generally, the CNN count is unaffected by the track overlap effect and has a wider linear range, which is significant for measuring the high concentration of the alpha environment.

Detection efficiency

The detection efficiency was used to evaluate the performance of the detector. The counting methods directly affect the results; therefore, the detection efficiency is affected by the counting methods. Eq. 7 was used to calculate the detection efficiency as follows: $\eta =\frac{N}{N_0},$ (7) where $\eta$ is the detection efficiency, $N_0$ is the number of particles emitted by the sources, and $N$ is the number of particles counted by the CNN or PSL method based on the IP.

Herein, the inhomogeneous ²⁴¹Am source (φ 10 mm) was used to irradiate the IP and had an emissivity of 3.6×10³/(2π·min). Figure 6a and 6b show the entity and imaging of the inhomogeneous ²⁴¹Am source, respectively.

Fig. 6Full-screen View

(Color online) (a) Entity and (b) imaging of the inhomogeneous ²⁴¹Am source (φ 10 mm).

The CNN counting result sufficiently maintains linearity, whereas that of the PSL method is not apparent for inhomogeneous sources (Fig. 7a). Additionally, CNN counting has a source detection efficiency of 0.6050 ± 0.0399, whereas the PSL method has a curve-shaped source detection efficiency with an overlapping correction (Eq. 8). The PSL method is less effective than CNN counting (Fig. 7b). ${\eta }_{\text{PSL}}=a+b_1{N}_{\text{s}}+b_2{N}_{\text{s}}^2$ (8)

Fig. 7Full-screen View

(Color online) (a) Count results and (b) source detection efficiency of the CNN and PSL; (c) fading characteristics and (d) fading characteristics and correction for different sources.

Here, $N_{\text{s}}$ is the number of particles emitted by the sources, ${\eta }_{\text{PSL}}$ is the detection efficiency of the PSL method for IP, a = 0.5124 ± 0.0517, b₁ = –1.724×10^–5 ± 0.394×10^–5, and b₂ = 1.987×10^–10 ± 0.691×10^–10.

The number of particles entering the IP was set as the output of the CNN, which should correspond to the CNN counting results. However, the number of particles entering the IP is greater than that of the CNN. This is because the simulated imaging, which is used in CNN training, is different from the experimental imaging (see the Detection Efficiency Parameters section). Although the tracks of the alpha particles are slightly different in size, the generation process of the simulated image reflects the deposition process of the alpha particles in the IP; therefore, it can still be counted by the CNN.

The detection efficiency of the CNN is higher than that of the PSL method, and is a constant, which indicates that the CNN can be used to count alpha tracks without considering the size and homogeneity. However, the PSL method has a stable curve of detection efficiency in the linear range of the PSL. This is because the biases and weights are corrected by the errors in the training process of the CNN (the error in the CNN is inevitable) [30], whereas the PSL method directly analyzes the grayscale value. Therefore, the accuracy of the PSL is higher than that of the CNN counting method.

Application of CNN method for radon progeny

The trained CNN was used to count the tracks of ²²²Rn and its progeny to evaluate the counting capability of the CNN. In this study, a Pylon RN-190 standard (standard radon progeny source) was used to calibrate the detection efficiency of IP. A high-activity ²²⁶Ra source was placed in RN-190. Therefore, the radon progeny deposits on the filter when the filter is sealed in the device. A high-activity filter source of radon progeny can be created after the end of the progeny collection. The alpha tracks emitted by the radon progeny were obtained by irradiating the IP through the filter. Based on this, the CNN and PSL were used to count the tracks. The detection efficiency can be calculated as follows: $E= \frac{N\left(t_2,t_3\right)\times 100\%}{Q\times R\left(t_1\right)\times M\left(t_2,t_3\right)\times A},$ (9) where $N\left(t_2,t_3\right)$ indicates counting from time t₂ to t₃, Q is the calibrated average value given for the RA-190 standard (DPM/cm²), $R\left(t_1\right)$ is the equilibrium factor ($R\left(t_1\right)=1-e^{-\lambda t_1}$), $\lambda$ is the decay constant of radon ($\lambda$ = 0.0001258 min^–1), $t_1$ is the filter sealed time in the RN-190, $M\left(t_2,t_3\right)$ is the accumulated factor, $t_2$ and $t_3$ are the measuring start and end times, respectively, and A is the effective surface area (cm²) of the filter exposed to the IP.

Table 1 lists the detection efficiencies of the CNN and PSL. Based on the results, the CNN can be used to measure the concentration of the radon progeny, although with a higher uncertainty compared to that of the PSL method. This is because the CNN is trained by ²⁴¹Am, which decays into 5.486 MeV alpha particles. The energy of alpha particles emitted by ²⁴¹Am differs from that of the radon progeny, which decays to 6 and 7.68 MeV alpha particles. This difference leads to the difference in the detection efficiency of alpha particles emitted by ²⁴¹Am and radon progeny in the PSL count, and results in a higher uncertainty in the CNN counting processes. However, a wider linear range and higher detection efficiency of CNN are more suitable for a high concentration or other information regarding radon and its progeny.

Fading effect

The number of alpha tracks required to complete the IP imaging decreases over time. The fading effect is a crucial influence on the IP that is used to evaluate the alpha tracks [16]. Alpha counting also decreases in the process of CNN counting, but its fading effect follows a certain rule.

The alpha track count of the CNN at moment t is recorded as $N_{\left(t\right)}$, and the initial state count is recorded as $N_{\left(0\right)}$. The fading curve of the alpha track in the IP was plotted (Fig. 7c) using the ratio of $N_{\left(t\right)}/N_{\left(0\right)}$ as the vertical axis and the elapsed time as the abscissa. Furthermore, the fading characteristics were fitted to a curve using Eq. 10. However, the curve is not suitable for a longer elapsed time. The relative uncertainty corrected using Eq. 10 within 132.7 min is 0.0282. $N_{\left(t\right)}=-3.064\times {10}^{-11}{N}_{\left(0\right)}\times t^{4.952}+N_{\left(0\right)}$ (10)

Herein, the IP was irradiated using sources A and B, which have effective diameters of 10 and 20 mm, respectively, and emissivity of 3.6×10³ (2π·min)^–1 and 1.6×10⁴ (2π·min) ^–1, respectively. Moreover, the counting of the CNN was corrected at different times (Fig. 7d). The calculation results of the CNN demonstrate that the maximum relative errors of sources A and B corrected by Eq. (10) are 0.038 and 0.053, respectively.

Based on the aforementioned results, the following conclusions can be drawn:

1. The fading effect slowly decreases in the early stage and rapidly decreases in the late stage. During the first 60 min of imaging, the fading effect is small and negligible, which is an advantage of using CNN for counting. Therefore, CNN counting should be adopted as soon as possible after the imaging is complete.

2. As time progresses, the count of the alpha tracks decreases and rate of decline increases. For example, the curve of the alpha fading characteristics rapidly decrease beyond 60 min. Therefore, the counting results should consider the fading effect. The CNN counting method can be used for counting with a fading effect; however, it is not applicable after 132.7 min.

3. The fading effect is not affected by the activity and shape of the source.

The fading characteristics are different for the CNN and PSL counting methods. Initially, the counting rapidly decreased for the PSL method; however, the decreasing trend was slow after approximately 200 min [16]. This is mainly because CNN conducts a feature analysis of the IP images, which depends on the grayscale value and is related to the spatial distribution of the grayscale values and their correlation with one another. Therefore, the grayscale value and its spatial distribution facilitate the counting of the alpha tracks by the CNN until 60 min. However, owing to the fading effect, the image features do not reflect the relationship between the image and count thereafter; thus, the count declines rapidly until it is difficult to detect.

Therefore, the PSL method is more feasible for the fading time beyond 132.7 min. For an alpha count within 60 min, the CNN count is less affected by the fading effect, which is better than the PSL count method, and CNN count can also be modified within 132.7 min.