Counting of alpha particle tracks on imaging plate based on a convolutional neural network

Counting of alpha particle tracks on imaging plate based on a convolutional neural network 1 first-author 2 1 https://orcid.org/0000-0003-4922-0453 1 3 3 1 https://orcid.org/0000-0001-8124-7459 1 corresp * shanjian0666@163.com. * shanjian0666@163.com. shanjian0666@163.com https://orcid.org/0000-0002-7117-4564 School of Nuclear Science and Technology, Hunan provincial key laboratory of radon, University of South China, Hengyang 421001, China School of Nuclear Science and Technology, Hunan provincial key laboratory of radon, University of South China, Hengyang 421001, China School of Computer Science, University of South China, Hengyang 421001, China School of Computer Science, University of South China, Hengyang 421001, China China Institute of Atomic Energy, Beijing 102413, China China Institute of Atomic Energy, Beijing 102413, China Imaging plates are widely used to detect alpha particles to track information, and the number of alpha particle tracks is affected by the overlapping and fading effects of the track information. In this study, an experiment and a simulation were used to calibrate the efficiency parameter of an imaging plate, which was used to calculate the grayscale. Images were created by using grayscale, which trained the convolutional neural network to count the alpha tracks. The results demonstrated that the trained convolutional neural network can evaluate the alpha track counts based on the source and background images with a wider linear range, which was unaffected by the overlapping effect. The alpha track counts were unaffected by the fading effect within 60 min, where the calibrated formula for the fading effect was analyzed for 132.7 min. The detection efficiency of the trained convolutional neural network for inhomogeneous 241 Am sources (2π emission) was 0.6050 ± 0.0399, whereas the efficiency curve of the photo-stimulated luminescence (PSL) method was lower than that of the trained convolutional neural network. Imaging plate Convolutional neural network Alpha tracks counting Introduction 1 An imaging plate (IP), a two-dimensional detector, was developed for medical X-ray diagnosis [ 1 1 ]. IPs have a good radiation response to alpha, beta, and gamma rays; therefore, they have been used as radiation detectors to measure ionizing radiation. An IP consists of a special phosphor layer, which can store radiation information based on the photo-stimulated luminescence (PSL) phenomenon. The PSL value is related to the deposition energy of radiation and is an arbitrary unit for the PSL phenomenon [ 1 1 ]. The radiation information stored in the IPs can be read and converted to photos by imaging devices (Typhoon FLA 7000) and a Control Software. However, the information should be counted or discriminated against using counting procedures. Therefore, counting procedures are crucial for reading the particle tracks. Alpha radioactive particles in the environment contribute to personal doses [ 2 2 ]. Therefore, it is essential to investigate the concentration of radionuclides of alpha decay to limit the personal dose [ 3 3 , 4 4 ]. IPs are also frequently used to measure information regarding the concentration, size distribution, and the unattached fraction of radionuclides, such as Pu and Rn, because they have a vast detection area. Moreover, they are convenient and reusable and can store alpha tracks [ 5 5 ]. Both the spot counting and PSL value methods are frequently used to count the alpha tracks stored in an IP [ 6 6 ]. The PSL values range from 0.2 to 0.6 when particle energies range between 10 keV and 100 MeV [ 7 7 ]. Thus, the threshold of the PSL for alpha radiation is set to 0.2 by counting, which is alterable for different detections, such as alpha particles with different energies or types of IP. [ 8 8 ]. However, the PSL value is unsuitable for low counts (lower than 1×10 3 ) of alpha [ 9 9 ]. The counting results using various algorithms have a good linear response to the incidence of alpha in selecting various sizes of the region of interest (ROI). The larger the ROI area, the higher the detection efficiency and lower effectiveness in discriminating the alpha from the beta tracks [ 6 6 ]. The detection efficiency is determined by several factors [ 10 10 , 11 11 ], such as the absorption dose of the phosphor layer in the irradiating procedure, the relationship between the generation efficiency of the F centers and the absorbed dose in the luminescent layer, intensity of the excitation laser, PSL efficiency of the F center, and escape efficiency of the F center from the inside to the surface. An image analysis software was developed to measure the concentrations of the Radon progeny based on the IPs, which can accurately measure the size distribution of the unattached Radon progeny and the concentrations [ 12 12 , 13 13 ]. Furthermore, an autoradiographic method was developed to detect Pu particles and naturally occurring radon decay products on filters, which can be used without requiring special skills and tedious procedures [ 14 14 ]. Two or more alpha tracks occur in a pixel, leading to the overlapping of tracks and a decrease in the count (overlapping effect), which also occurs in the detection process of CR-39 detector [ 15 15 ]. The overlapping effect is apparent in a count of more than 2×10 5 . However, the linear response can be improved by correction [ 9 9 ]. The electrons in the F center of the IP, combined with the holes owing to thermal motion and ignition, decrease the count (fading effect). The decreasing trend caused by the fading effect slows down over time [ 16 16 ]. Correction of the fading effect is crucial for quantitatively measuring radiation. The correction function varies for different measurement environments and counting algorithms [ 16 16 ]. Procedures for correcting the overlapping and fading effects must be developed to use IPs in measurements effectively. Based on the Monte Carlo method, the response function of high-energy aluminum ions in IPs can be simulated [ 17 17 ], in addition to the energy deposition of X-rays and alpha particles in IPs [ 18 18 ]. Using the Monte Carlo program can significantly reduce experimental costs. The convolutional neural network (CNN) is a popular algorithm developed through deep learning research and has gained extensive attention as an efficient recognition method. In 1960s, Hubel and Wiesel studied the neurons used for local sensitivity and the direction selection of the cerebral cortex of a cat and discovered that a unique network structure can effectively reduce the complexity of the feedback neural network; subsequently, proposing a CNN [ 19 19 ]. CNNs have become one of the popular research topics in various scientific fields, particularly pattern classification [ 20 20 - 23 23 20-23 ]. A CNN avoids the complicated pre-processing of images and can directly input the original images, thus facilitating its wide usage. Furthermore, it can obtain the relationship between the inputs and outputs based on the training of numerous samples. A CNN can also avoid the extraction and analysis of photo characteristics. Therefore, it is widely used to process imaging [ 24 24 ]. Based on these characteristics, the CNN algorithm can be used to count the alpha tracks on IPs. In this study, the Monte Carlo software (Geant 4, developed by the European Organization for Nuclear Research) and an experimental method are combined to solve the problems of the overlapping effect, fading effect, and limited linear range when IPs are used for counting the alpha tracks [ 25 25 ]. The detection efficiency parameter of the BAS-TR (for tritium detection) IP is analyzed through a simulation and experiment. Based on the detection efficiency parameter, the PSL value was calculated by the distribution of the energy deposition in the IP using the Geant 4 software. Subsequently, the PSL values were converted into grayscale values and filled as images. The aforementioned simulated image generation process is repeated to obtain a large amount of image data, and the CNN is trained such that it can calculate the alpha count according to the background and source irradiated images. Based on the trained CNN, the detection efficiency of 241 Am and the Radon progeny was studied. Moreover, the fading effect formula was analogized in this study. Materials and methods 1 Experimental setup 2 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 241 Am 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 2 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 241 Am 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 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. Determination of detection efficiency parameter 2 The background and irradiation areas must be considered when counting alpha tracks [ 26 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 5 ]: <math display="block" id="M1"><mrow><mtext>PSL</mtext><mo>=</mo><munderover><mstyle mathsize="140%" displaystyle="true"><mo>∫</mo></mstyle><mn>0</mn><mi>d</mi></munderover><mi>A</mi><mo>×</mo><mi>E</mi><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mo>×</mo><mfrac><mrow><mn>6</mn><mo>·</mo><mrow><mo>(</mo><mrow><mi>l</mi><mo>+</mo><mi>d</mi><mo>−</mo><mi>z</mi></mrow><mo>)</mo></mrow></mrow><mrow><mn>2</mn><mi>l</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mtext>d</mtext><mi>z</mi><mo>,</mo></mrow></math> 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 5 ]. <math display="block" id="M2"><mrow><mi>A</mi><mo>=</mo><mfrac><mrow><mi>q</mi><mo>×</mo><mi>P</mi></mrow><mrow><msub><mover accent="true"><mi>E</mi><mo>¯</mo></mover><mi>F</mi></msub></mrow></mfrac></mrow></math> 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, <math id="M3"><mrow><msub><mover accent="true"><mi>E</mi><mo>¯</mo></mover><mtext>F</mtext></msub></mrow></math> is the average energy of creating an F center, and q , P , and <math id="M4"><mrow><msub><mover accent="true"><mi>E</mi><mo>¯</mo></mover><mtext>F</mtext></msub></mrow></math> are the determined parameters for the specific IP and reader type [ 5 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: <math display="block" id="M5"><mrow><mtext>PSL</mtext><mo>=</mo><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mrow><mi>A</mi><mo>×</mo><mi>E</mi></mrow></mstyle><mrow><mo>(</mo><mrow><msub><mi>z</mi><mi>i</mi></msub></mrow><mo>)</mo></mrow><mo>×</mo><mfrac><mrow><mn>6</mn><mo>⋅</mo><mrow><mo>(</mo><mrow><mi>l</mi><mo>+</mo><mi>d</mi><mo>−</mo><msub><mi>z</mi><mi>i</mi></msub></mrow><mo>)</mo></mrow></mrow><mrow><mn>2</mn><mi>l</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>,</mo></mrow></math> where <math id="M6"><mrow><mi>E</mi><mrow><mo>(</mo><mrow><msub><mi>z</mi><mi>i</mi></msub></mrow><mo>)</mo></mrow></mrow></math> 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 2 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 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 241 Am 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 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 28 , 29 29 ]: <math display="block" id="M7"><mrow><mi>G</mi><mo>=</mo><mrow><mo>(</mo><mrow><mfrac><mn>1</mn><mi>L</mi></mfrac><mo>×</mo><msub><mrow><mtext>log</mtext></mrow><mrow><mn>10</mn></mrow></msub><mrow><mo>(</mo><mrow><mtext>PSL</mtext><mo>×</mo><mfrac><mi>S</mi><mrow><mn>4000</mn></mrow></mfrac><mo>×</mo><msup><mrow><mrow><mo>(</mo><mrow><mfrac><mrow><mn>100</mn></mrow><mi>R</mi></mfrac></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mo>)</mo></mrow><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow><mo>)</mo></mrow><mo>×</mo><mi>C</mi><mi>L</mi><mo>,</mo></mrow></math> 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 (2 16 , CL = 2 8 is for 8-bit image files), and R is the resolution of the reader (50 µm) [ 17 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 2 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 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 1.65×10 3 (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, 10 8 , 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 (137–10 8 ). Before utilizing the data for CNN training ( Fig. 1b 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. <math display="block" id="M8"><mrow><mi>x</mi><mo>=</mo><mfrac><mrow><mi>lg</mi><mrow><mo>(</mo><mstyle mathvariant="bold" mathsize="normal"><mi>p</mi></mstyle><mo>)</mo></mrow><mo>−</mo><mi>lg</mi><mrow><mo>[</mo><mrow><mi>min</mi><mrow><mo>(</mo><mstyle mathvariant="bold" mathsize="normal"><mi>p</mi></mstyle><mo>)</mo></mrow></mrow><mo>]</mo></mrow></mrow><mrow><mtext>lg</mtext><mi>［</mi><mi>max</mi><mrow><mo>(</mo><mstyle mathvariant="bold" mathsize="normal"><mi>p</mi></mstyle><mo>)</mo></mrow><mo stretchy="false">]</mo><mo>−</mo><mi>lg</mi><mrow><mo>[</mo><mrow><mi>min</mi><mrow><mo>(</mo><mstyle mathvariant="bold" mathsize="normal"><mi>p</mi></mstyle><mo>)</mo></mrow></mrow><mo>]</mo></mrow></mrow></mfrac></mrow></math> 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 (10 8 ). 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 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. Results and discussion 1 Detection efficiency parameter and threshold of PSL 2 The detection efficiency parameter of the IP adopted in this study was 0.0484 PSL/MeV (3.02×10 11 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. 3a ). Chen Bo obtained a detection efficiency parameter of 7.71×10 11 PSL/J using an X-ray calibration of the BAS-MS (multipurpose) IP [ 5 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 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 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 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 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 5 ]. Source and background images of 601×601 pixels simulated by Geant 4 ( Fig. 4 Fig. 4 ) were used as inputs to train the CNN. Count of simulated IP images by CNN 2 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 10 6 ; the correlation coefficient is 0.9994, as indicated in Fig. 5a Fig. 5a . Whereas, when there are less than 2×10 4 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 2×10 4 ; 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 Fig. 5b ). Despite this correction, a linear trend is not guaranteed (correlation coefficient of 0.2970). Previous studies [ 6 6 ] demonstrated that the PSL method maintained a good linearity when the alpha particle count was less than 2×10 5 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 6 ]. The linearity of counting is worse owing to the overlapping effect when the number of incident alpha particles is greater than 2×10 4 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 6 ]. CNN counting the results of the experimental images 2 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 Fig. 5c ) and relative errors ( Fig. 5d 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 Fig. 5d ), which is calculated by Eq. 6. For example, the mean relative error for counting beyond 5000 is 0.089. <math display="block" id="M9"><mrow><mi>R</mi><mi>E</mi><mo>=</mo><mfrac><mrow><mi>Y</mi><mo>−</mo><mi>X</mi></mrow><mi>X</mi></mfrac><mo>×</mo><mn>100</mn><mtext>%</mtext></mrow></math> 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 2 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: <math display="block" id="M10"><mrow><mi>η</mi><mo>=</mo><mfrac><mi>N</mi><mrow><msub><mi>N</mi><mn>0</mn></msub></mrow></mfrac><mo>,</mo></mrow></math> where <math id="M11"><mi>η</mi></math> is the detection efficiency, <math id="M12"><mrow><msub><mi>N</mi><mn>0</mn></msub></mrow></math> is the number of particles emitted by the sources, and <math id="M13"><mi>N</mi></math> is the number of particles counted by the CNN or PSL method based on the IP. Herein, the inhomogeneous 241 Am source (φ 10 mm) was used to irradiate the IP and had an emissivity of 3.6×10 3 /(2π·min). Figure 6a and 6b Figure 6a and 6b show the entity and imaging of the inhomogeneous 241 Am source, respectively. The CNN counting result sufficiently maintains linearity, whereas that of the PSL method is not apparent for inhomogeneous sources ( Fig. 7a 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 Fig. 7b ). <math display="block" id="M14"><mrow><msub><mi>η</mi><mrow><mtext>PSL</mtext></mrow></msub><mo>=</mo><mi>a</mi><mo>+</mo><msub><mi>b</mi><mn>1</mn></msub><msub><mi>N</mi><mtext>s</mtext></msub><mo>+</mo><msub><mi>b</mi><mn>2</mn></msub><msubsup><mi>N</mi><mtext>s</mtext><mn>2</mn></msubsup></mrow></math> Here, <math id="M15"><mrow><msub><mi>N</mi><mtext>s</mtext></msub></mrow></math> is the number of particles emitted by the sources, <math id="M16"><mrow><msub><mi>η</mi><mrow><mtext>PSL</mtext></mrow></msub></mrow></math> is the detection efficiency of the PSL method for IP, a = 0.5124 ± 0.0517, b 1 = –1.724×10 –5 ± 0.394×10 –5 , and b 2 = 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 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 2 The trained CNN was used to count the tracks of 222 Rn 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 226 Ra 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: <math display="block" id="M17"><mrow><mi>E</mi><mo>=</mo><mo> </mo><mfrac><mrow><mi>N</mi><mrow><mo>(</mo><mrow><msub><mi>t</mi><mn>2</mn></msub><mo>,</mo><msub><mi>t</mi><mn>3</mn></msub></mrow><mo>)</mo></mrow><mo>×</mo><mn>100</mn><mi>%</mi></mrow><mrow><mi>Q</mi><mo>×</mo><mi>R</mi><mrow><mo>(</mo><mrow><msub><mi>t</mi><mn>1</mn></msub></mrow><mo>)</mo></mrow><mo>×</mo><mi>M</mi><mrow><mo>(</mo><mrow><msub><mi>t</mi><mn>2</mn></msub><mo>,</mo><msub><mi>t</mi><mn>3</mn></msub></mrow><mo>)</mo></mrow><mo>×</mo><mi>A</mi></mrow></mfrac><mo>,</mo></mrow></math> where <math id="M18"><mrow><mi>N</mi><mrow><mo>(</mo><mrow><msub><mi>t</mi><mn>2</mn></msub><mo>,</mo><msub><mi>t</mi><mn>3</mn></msub></mrow><mo>)</mo></mrow></mrow></math> indicates counting from time t 2 to t 3 , Q is the calibrated average value given for the RA-190 standard (DPM/cm 2 ), <math id="M19"><mrow><mi>R</mi><mrow><mo>(</mo><mrow><msub><mi>t</mi><mn>1</mn></msub></mrow><mo>)</mo></mrow></mrow></math> is the equilibrium factor ( <math id="M20"><mrow><mi>R</mi><mrow><mo>(</mo><mrow><msub><mi>t</mi><mn>1</mn></msub></mrow><mo>)</mo></mrow><mo>=</mo><mn>1</mn><mo>−</mo><msup><mi>e</mi><mrow><mo>−</mo><mi>λ</mi><msub><mi>t</mi><mn>1</mn></msub></mrow></msup></mrow></math> ), <math id="M21"><mi>λ</mi></math> is the decay constant of radon ( <math id="M22"><mi>λ</mi></math> = 0.0001258 min –1 ), <math id="M23"><mrow><msub><mi>t</mi><mn>1</mn></msub></mrow></math> is the filter sealed time in the RN-190, <math id="M24"><mrow><mi>M</mi><mrow><mo>(</mo><mrow><msub><mi>t</mi><mn>2</mn></msub><mo>,</mo><msub><mi>t</mi><mn>3</mn></msub></mrow><mo>)</mo></mrow></mrow></math> is the accumulated factor, <math id="M25"><mrow><msub><mi>t</mi><mn>2</mn></msub></mrow></math> and <math id="M26"><mrow><msub><mi>t</mi><mn>3</mn></msub></mrow></math> are the measuring start and end times, respectively, and A is the effective surface area (cm 2 ) of the filter exposed to the IP. Table 1 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 241 Am, which decays into 5.486 MeV alpha particles. The energy of alpha particles emitted by 241 Am 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 241 Am 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. 1 1 Method 1 1 <math id="M27"><mrow><mrow><mo>(</mo><mrow><msub><mi>t</mi><mn>2</mn></msub><mo>,</mo><msub><mi>t</mi><mn>3</mn></msub></mrow><mo>)</mo></mrow></mrow></math>   1 1 <math id="M28"><mrow><mi>M</mi><mrow><mo>(</mo><mrow><msub><mi>t</mi><mn>2</mn></msub><mo>,</mo><msub><mi>t</mi><mn>3</mn></msub></mrow><mo>)</mo></mrow></mrow></math>   1 1 E 1 1 Mean ± SD 1 1 PSL 1 1 (1, 6) 1 1 7.383 1 1 0.23 1 1 0.227 ± 0.038 1 1   1 1 (8, 23) 1 1 14.889 1 1 0.25 1 1   1 1 (24, 39) 1 1 12.040 1 1 0.20 1 1 CNN 1 1 (1, 6) 1 1 7.383 1 1 0.298 1 1 0.330 ± 0.090 1 1   1 1 (8, 23) 1 1 14.889 1 1 0.355 1 1   1 1 (24, 39) 1 1 12.040 1 1 0.337 1 1   Fading effect 2 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 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 <math id="M29"><mrow><msub><mi>N</mi><mrow><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></msub></mrow></math> , and the initial state count is recorded as <math id="M30"><mrow><msub><mi>N</mi><mrow><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></mrow></msub></mrow></math> . The fading curve of the alpha track in the IP was plotted ( Fig. 7c Fig. 7c ) using the ratio of <math id="M31"><mrow><msub><mi>N</mi><mrow><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></msub><mo>/</mo><msub><mi>N</mi><mrow><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></mrow></msub></mrow></math> 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. <math display="block" id="M32"><mrow><msub><mi>N</mi><mrow><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></msub><mo>=</mo><mo>−</mo><mn>3.064</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>11</mn></mrow></msup><msub><mi>N</mi><mrow><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></mrow></msub><mo>×</mo><msup><mi>t</mi><mrow><mn>4.952</mn></mrow></msup><mo>+</mo><msub><mi>N</mi><mrow><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></mrow></msub></mrow></math> Herein, the IP was irradiated using sources A and B, which have effective diameters of 10 and 20 mm, respectively, and emissivity of 3.6×10 3 (2π·min) –1 and 1.6×10 4 (2π·min) –1 , respectively. Moreover, the counting of the CNN was corrected at different times ( Fig. 7d 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 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. Conclusion 1 The overlapping effect, fading effect, and limited linear range cause the decline in the alpha count and inaccuracy in the IP. Therefore, a CNN algorithm was developed to overcome these problems. The detection efficiency parameter of the BAS-TR IP was determined to be 3.021×10 11 PSL/J using the 241 Am standard source-irradiated IP process combined with the Geant 4 simulation of the alpha-irradiated IP. The detection parameter and energy deposition simulated by Geant 4 were used to calculate the grayscale. Subsequently, multiple grayscale images were used to train the CNN. Finally, the trained CNN was used to count the alpha tracks in the IP. Furthermore, the trained CNN was applied to the measurement of the 241 Am and radon progeny. The count results of the CNN were observed to be sufficiently linear on the simulated and experimental images, whose number of tracks exceeded 5000. Compared with the PSL method, the CNN algorithm had a wider linear range and was not affected by the overlapping effect. The detection efficiency of the CNN algorithm for the 241 Am source was 0.6050 ± 0.0399, and the efficiency of the PSL was indicated by a curve (Eq. 8). For the radon progeny, the detection efficiencies of CNN and PSL were 0.330 ± 0.090 and 0.227 ± 0.038, respectively. Therefore, the detection effectiveness of the CNN algorithm is higher than that of the PSL method; however, the uncertainty of the CNN is also higher. When CNN was used for counting, the fading effect of the IP was observed to have a negligible effect within 60 min of sampling, which differed from the fading characteristics of the PSL method. Within 132.7 min of sampling, the fading effect can be corrected using Eq. (10). The mean relative uncertainty of the corrected results was 0.0282. The CNN trained in this study had a wider linear counting range and higher detection efficiency. Furthermore, the CNN can be used to count alpha tracks without the size and homogeneity of the sources. Thus, CNN was introduced to count the alpha tracks, which overcame the limitations of conventional algorithms. However, the CNN built in this study was trained only by using the image data of the BAS-TR IP type. This indicates that the CNN algorithm trained in this study can only be used for counting alpha tracks in BAS-TR IPs. Moreover, the counting operation conducted by the CNN must be completed within 132.7 min after imaging. Otherwise, the fading effect cannot be calibrated using Eq. (10). Therefore, perhaps merging the photos of several IP types can train the CNN for directly counting without differentiating between IP types. 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Shan, et al. , iEnhancer-BERT: A novel transfer learning architecture based on DNA-Language model for identifying enhancers and their strength . In: D.S. Huang , K.H. Jo , J. Jing , P. Premaratne , V. Bevilacqua , A. Hussain , (eds) Intelligent Computing Theories and Application. ICIC 2022 . Lecture Notes in Computer Science , vol 13394 . Springer, Cham . 153 - 165 ( 2022 ) doi: 10.1007/978-3-031-13829-4_13 http://doi.org/10.1007/978-3-031-13829-4_13 . Intelligent Computing Theories and Application. ICIC 2022 All authors contributed to the study conception and design. The Geant 4 simulation and experiment was performed by Feng-Di Qin. Jian Shan provided the radioactive sources, funding and overall guidance. The CNN was performed by Han-Yu Luo. The IP and imaging principal was supported by Zheng-Zhong He and Zhong-Kai Fan. The experimental data collected by Ke-Jun Lu, Chuan-Gao Wang and Meng-Meng Wu. All authors read and approved the final manuscript. 10.1007/s41365-023-01190-7 This work was supported by the Hunan Provincial Innovation Foundation for Postgraduates (No. QL20210228), the National Natural Science Foundation of China (No. 12075112), and the National Natural Science Foundation of China (No. 12175102). 2022-10-25 2022-12-20 2022-12-22 2023-03-22 2023-04-20 © China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2023 This is a post-peer-review, pre-copyedit version of an article published in Nuclear Science and Techniques. The final authenticated version is available online at: http://dx.doi.org/10.1007/s41365-023-01190-7 http://dx.doi.org/10.1007/s41365-023-01190-7 . Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. 2023 The data that support the findings of this study are openly available in Science Data Bank at https://www.doi.org/10.57760/sciencedb.07479 and http://resolve.pid21.cn/31253.11.sciencedb.07479. Data availability Nuclear Science and Techniques 3 34