Image sorting of nuclear reactions recorded on CR-39 nuclear track detector using deep learning

Deep learning has been utilized to trace nuclear reactions in the CR-39 nuclear track detector. Etch pit images on front and back surfaces of the CR-39 detector were obtained sequentially by moving the objective lens of a microscope, and merged to one image.

Radiation Measurements 151 (2022) 106706 Contents lists available at ScienceDirect Radiation Measurements journal homepage: www.elsevier.com/locate/radmeas Image sorting of nuclear reactions recorded on CR-39 nuclear track detector using deep learning Ken Tashiro a, *, Kazuki Noto a, Quazi Muhammad Rashed Nizam b, Eric Benton c, Nakahiro Yasuda a a b c Research Institute of Nuclear Engineering, University of Fukui, Tsuruga, Fukui, Japan Department of Physics, University of Chittagong, Chittagong, Bangladesh Department of Physics, Oklahoma State University, Stillwater, OK, USA A R T I C L E I N F O A B S T R A C T Keywords: CR-39 nuclear track detector Deep learning Object detection Image merging Total charge changing cross-section Deep learning has been utilized to trace nuclear reactions in the CR-39 nuclear track detector Etch pit images on front and back surfaces of the CR-39 detector were obtained sequentially by moving the objective lens of a microscope, and merged to one image This image merging makes it possible to combine information on the displacement of the position of the etch pits produced by single particle traversals through a CR-39 layer in a single image, thereby making it easier to recognize corresponding nuclear fragmentation reactions Object detection based on deep learning has been applied to the merged image to identify nuclear fragmentation events for measurement of the total charge changing cross-section based on the number of incident particles (Nin) and the number of particles that passed through target without any nuclear reaction (Nout) We verified the accuracy (correct answer rate) of algorithms for extracting the two patterns of etch pit in merged images which corre­ sponds to Nin and Nout using the learning curves expressed as a function of the number of trainings Accuracy of Nin and Nout were found to be 97.3 ± 4.0% and 98.0 ± 4.0%, respectively These results show that the object detection algorithm based on the deep learning can be a strong tool for CR-39 etch pit analysis Introduction CR-39 solid-state nuclear track detector has been a powerful tool to measure the total charge changing cross-section (Golovchenko et al., 2001, 2002; Cecchini et al., 2008; Duan et al., 2021; Huo et al., 2019; Zheng et al., 2021) and fragment emission angles (Giacomelli et al., 2004; Sihver et al., 2013; Zhang et al., 2018), since it has high charge resolution (Ota et al., 2011) and has the potential to accurately measure fragment emission angles (Rashed-Nizam et al., 2020) In this experi­ mental application, CR-39 nuclear track detector is frequently used not only as a detector but also as a target (material to be verified the cross-sections) since etch pits appear along the ion track on both the front and back surfaces after chemical etching The front and back sur­ face images are independently captured by a microscope These images are analyzed to extract the position and size of the etch pits to trace charged particle’s trajectory in the target (Yasuda et al., 2005, 2009) By matching the positions of the etch pits obtained from independently obtained images on the front and back surfaces of the detector, it has been possible to identify particles that have passed through the target or have undergone a nuclear reaction within the target (Skvarˇc and Golovchenko, 2001; Ota et al., 2008) In order to identify a nuclear re­ action, it is necessary to establish a one-to-one correspondence between the etch pits on the detector’s front and the back surfaces The matching method requires accurate alignment of the etch pits on both surfaces, and the alignment accuracy is estimated to be 2–3 μm (Ota et al., 2008) The accuracy of this alignment puts a limit on the matching method Recently, we have developed a technology to takes images on the front and back surfaces of the CR-39 detector sequentially by moving the objective lens of a microscope without any treatment for alignment of images (Rashed-Nizam et al., 2020) By this technology, this alignment (matching) error is only due to the verticality of the Z-axis movement of the microscope; the accuracy is to be within pixel (0.24 μm in this case) As a feasibility study, we applied object detection based on deep learning which can simultaneously classify nuclear reaction images and detect object positions Object detection is a computer technology that determines whether * Corresponding author Research Institute of Nuclear Engineering, University of Fukui, 1-3-33 Kanawa, 914-0055, Tsuruga, Fukui, Japan E-mail address: tashiro0716@gmail.com (K Tashiro) https://doi.org/10.1016/j.radmeas.2022.106706 Received 10 September 2021; Received in revised form 15 January 2022; Accepted 19 January 2022 Available online 22 January 2022 1350-4487/© 2022 The Authors Published by Elsevier Ltd This is an open (http://creativecommons.org/licenses/by-nc-nd/4.0/) access article under the CC BY-NC-ND license K Tashiro et al Radiation Measurements 151 (2022) 106706 Fig Images of the front (a) and back (b) surface were merged into the merged image (c) by image subtraction, after adding 200 (gray level) to each pixel value of the back image In the merged image (c), white circles represent the etch pits on the front surface, black circles represent the etch pits on the back surface were cut into 50 mm × 50 mm squares and exposed to a 55 MeV/ nucleon 12C beam with a particle density of 2500 ions/cm2 at the Wakasa Wan Energy Research Center (WERC) (Hatori et al., 2001) After irradiation, the detector was etched in N NaOH solution at 70 ◦ C for 20 h After chemical etching, images of the front and back surfaces of the CR-39 detector were acquired using a FSP-1000 imaging microscope, manufactured by SEIKO Time Creation Inc The autofocus system of the microscope was used to capture images of the front and back surfaces After capturing an image on the front surface, the objective lens moves to a lower depth (Z-axis of microscope system) of the CR-39 detector, and the back surface image is captured for the same field of view (Rashed-Nizam et al., 2020) The images of both surfaces (2500 pixels × 1800 pixels) were obtained using a 20× magnification objective lens with a pixel size of 0.24 μm × 0.24 μm These images are represented by a value from black (0) to white (255) in a grayscale image with 256 gray levels objects of a given class (such as humans, cars, or buildings) are present in digital images and movies When there are the objects, it returns the spatial location and size of each object as a result (Liu et al., 2020) This technology has been researched based on human-designed features in the field of computer vision for the development of technologies such as face recognition (Viola and Jones., 2004) The advent of deep learning techniques, a method of automatically learning features from data, has improved object detection technology in various research fields (LeCun et al., 2015) Performance of object detection is improving annually by incorporating deep learning technology (Liu et al., 2020; Zou et al., 2019) Recent studies in the field of radiation measurement are also advancing research that applies deep learning technology, such as a new method of visualizing the ambient dose rate distribution using artificial neural networks from airborne radiation monitoring results (Sasaki et al., 2021) Methods have been developed to analyze radon time-series sampling data by machine learning and analyze its relationship with environmental factors (Janik et al., 2018; Hosoda et al., 2020) For de­ tectors that require image analysis such as the nuclear emulsion and the fluorescent nuclear track detector (FNTD), analysis methods based on image classification using deep learning have also been developed For nuclear emulsion, an efficient classifier was developed that sorts alpha-decay events from various vertex-like objects in an emulsion using a convolutional neural network (Yoshida et al., 2021) For FNTD, an image processing technique involving convolutional neural networks has been demonstrated for neutron dosimetry applications (Akselrod et al., 2020) In this study, we have developed a new methodology for tracing ion track penetration by merging images on both sides of a CR-39 detector without relying on pattern matching Instead, object detection based on deep learning is applied to the etch pit analysis 2.2 Image merging of front and back surfaces on CR-39 detector We have employed image merging which is a method of detecting moving objects by comparing the observed image with the background image As shown in Fig 1, front (a) and back (b) images of the CR-39 detector were acquired from the microscope By subtracting each pixel value of the front image from each pixel value of the back image added 200 (gray level), we created a merged image (c) In the merged image, white and black circles represent the etch pits on the front and back surfaces, respectively The displacement of black and white etch pits position indicates that the ions penetrated the CR-39 detector with a small angle Here, it is easy to discriminate the corre­ sponding etch pits formed on the front and back surfaces by the passage of an incident ion without treatment of pattern matching by the align­ ment between the front and back surfaces This method is able to pro­ duce incident angle information by the displacement with distance (thickness) between front and back surface as described elsewhere (Rashed-Nizam et al., 2020), and also to indicate the presence or absence of nuclear reactions in the single image Fig shows examples of etch pits in the merged image Track events are classified into three categories: (a) the projectile passed through CR- Materials and methods 2.1 Experimental We used CR-39 detector (HARZLAS TD-1) manufactured by Fukuvi Chemical Industry Co., Ltd Layers of CR-39 detector (0.45 mm thick) Fig Examples of etch pits in the merged image: (a) the projectile passed through the CR-39 detector without any reaction, producing two etch pits on both surfaces (white and black); (b) the projectile decays into several lighter fragments, and these fragments are not detected due to the detection threshold; (c) nuclear fragments are observed as three tracks indicated by white arrows K Tashiro et al Radiation Measurements 151 (2022) 106706 Fig The learning curves of the (a) W/B and (b) W object extraction algorithms, respectively The accuracies (in %) of these algorithms are shown as a function of the number of training datasets 39 detector without producing any nuclear reaction; (b) no etch pits are observed on the back surface - one of possible reactions is C→6p+6n, where protons and neutrons are out of detection due to the detection threshold (Yasuda et al., 2008; Kodaira et al., 2016); (c) three etch pits are observed on the back surface and assumed to be the results of a re­ action, e.g., C→3α, where these α-particles have sufficient energy loss to be detected Here, the total charge changing cross-section (σTCC ) expresses the probability that the projectile changes its charge due to the nuclear interaction between the projectile and the target σ TCC is dominated by the total cross section σT and is defined as (Golovchenko et al., 2002) σ TCC = σ T − σel − σ nr , pixels × 416 pixels), as shown in Fig 2(a), contain various patterns based on the differences of the position between the etch pits on both surfaces and the distance between their centers The W images contain white etch pits images as shown in Fig 2(b) Thus, the validation dataset and two training datasets were used separately to train the object detection algorithms for counting of Nout and Nin For object detection, we adopted YOLOv3 (Redmon and Farhadi, 2018), an object detection algorithm based on convolutional neural networks, and used Python 3.7.11 as a machine learning package with the machine learning framework “Darknet”, and Open CV 4.1.2 on the execution environment “Google Colaboratory” (Bisong, 2019) The ob­ ject detection algorithms were trained by inputting the training dataset (W/B) to extract the W/B objects from the validation dataset The in­ dividual algorithms were prepared according to the number of training datasets varied from N = 100 to 1200 We applied these algorithms to the validation dataset and counted the number of W/B objects detected by each algorithm Accuracy was defined as the ratio of the number of W/B objects detected by the algorithms and the number of W/B objects in the validation dataset (1227), by the following equation (3): (1) where σ el is the elastic cross-section and σ nr is the neutron removal crosssection Using measurable quantities, the σTCC also expresses as σ TCC = − M ρ NA X Nout ), ln( Nin (2) where, NA, ρ, X and M indicate Avogadro’s number, the density and the thickness of the target, and its atomic or molecular mass, respectively (Cecchini et al., 2008; Huo et al., 2019) Nin is the number of incident particles and Nout is the number of particles that have passed through target without undergoing any reaction The σ TCC can be expressed as the ratio of number of ions that passed through the detector without any nuclear reaction to the number of incident ions that enter the CR-39 detector, i.e., σTCC ∝ Nout/Nin In short, the number of the white etch pits (Nin) in Fig 2(b) and the number of black etch pits (Nout) as in Fig 2(a) essential in determining the total charge changing cross-section Accuracy [%] = The number of detected objects by algorithm × 100 The number of objects in validation dataset (3) In a similar manner to the verification of Nout, the accuracy of Nin was also verified by the algorithms using the training dataset (W) and the validation dataset Results and discussions 3.1 Object detection accuracy and error estimation of image sorting As an evaluation of the algorithm, we employed a learning curve which shows predictive accuracy on the test examples as a function of the number of training examples (Perlich, 2011) Fig 3(a) shows the learning curve for the W/B object extraction algorithm The accuracy (in %) is shown as a function of the number of training datasets The ac­ curacy increased as the number of training datasets increased, reaching a maximum of 98.0 ± 4.0% calculated from the number of detected W/B objects (1203) and W/B objects (1227) in the validation dataset after 1000 trainings Fig 3(b) shows the learning curve of the W object extraction algorithm The accuracy improved as the number of training datasets increased, reaching 97.3 ± 4.0% calculated from the number of detected W objects (1196) and W objects (1229) in the validation dataset in 1000 trainings Errors in the accuracy are statistical errors calculated from the ratio of the number of W/B (W) objects detected by the algorithms and the number of W/B (W) objects in the validation dataset The accuracies as shown in Fig (a) and (b) were saturated 2.3 Object detection for etch pit image To verify the quantities Nout and Nin from etch pits images, a vali­ dation dataset and two training datasets were created from the merged images The validation dataset consists of 256 merged images (2500 pixels × 1800 pixels) and includes the white and black etch pits (W/B objects), similar to Fig 2(a), which were visually counted to be 1227 in those 256 images This dataset also includes objects for Fig 2(b) type image and objects for Fig 2(c) type image The validation dataset then consists of 1229 white etch pit objects (1227 W/B and W objects) as described above The training datasets (W/B and W) were prepared from merged images other than the validation dataset Those two training datasets consisted of 1200 white and black etch pits images (W/B images) and white etch pits images (W images), respectively W/B images (416 K Tashiro et al Radiation Measurements 151 (2022) 106706 Fig Four types of undetected objects: (a) the W/B etch pits are close each other; (b) the distance between the two etch pits is greater than expected due to multiple Coulomb scattering; (c) multiple W/B objects are overlapping; and (d) the W/B object locate at the edge of the image with 97–98% The accuracies were also repeated rising and falling ac­ cording to increasing training dataset This phenomenon, often observed in deep learning, is called overfitting (overtraining) which is a funda­ mental problem in applying deep learning (Salman and Liu, 2019; Ying, 2019) It may indicate that the algorithm was optimized only for the training dataset and that this optimization did not generalize to the validation dataset Various approaches are proposed to reduce this effect such as changes of the neural network architecture in the algorithm and expansion of the training dataset which includes more highly-varied images (Ying, 2019) These approaches are expected to improve accu­ racy in the future The maximum, statistical W/B and W object detection accuracies were found to be 98.0 ± 4.0% and are to be 97.3 ± 4.0% at N = 1000, respectively Errors in accuracy are statistical errors individually calculated from the ratio of the number of W/B (W) objects detected by the algorithms and the constant number of 1227 W/B and 1229 W ob­ jects in the validation dataset As a result, the statistical errors in these figures vary between 3.5 and 4.0 These statistical errors can be improved by increasing the number of validation datasets with suitable numbers of trainings On the other hand, the systematic error is due to the fact that the results vary due to the creation of different learning algorithms depending on how the training dataset is selected Here, we evaluated how much the results would vary by randomly selecting from 1200 when extracting 1000 training datasets For each of the training datasets (W/B and W), the training dataset was extracted and applied to the validation dataset only after the algorithm was created This was repeated ten times to determine the accuracies and evaluate standard deviation of the systematic errors for both W/B and W dataset The systematic errors (1σ) were estimated to be 0.6% and 0.7% for W/B and W objects, respectively The degree of contribution of the systematic errors to the charge changing cross-section is expressed as follows: √̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ ΔNin(sys) ΔNout(sys) M Δσ TCC(sys) = (4) ) +( ), ( ρN A X Nin Nout Fig Examples of undetected W objects Etch pits due to α-particle from the environment (a), and dust or tiny scratches on the surface of CR-39 (b) indi­ cated by arrows are imaged near the etch pit center-to-center distance was 2.7 μm, while the radius of the white etch pit was 13.4 μm in this case (b) The distance between the two etch pits is greater than expected, as a result of multiple Coulomb scattering (Highland, 1975; Beringer et al., 2012) In this case, W/B object detec­ tion succeeded, but is recognized as chance coincidence of irrelevant etch pits since the calculated distance by the scattering was to be 38.3 μm and the center-to-center distance was 43.8 μm (c) Multiple W/B objects are overlapping This is an essential limitation of the CR-39 detection technique that should be improved by reduction of exposure density and/or by shortening the etching time to avoid overlapping etch pits (d) The W/B object is located at the edge of the image and also cannot be processed by pattern matching It is necessary to take mea­ sures to reduce the relative number of objects located at the image edges by increasing the validation image size The (c) and (d) cases require additional processing in order to be included in the cross-section measurement On the other hand, for W objects, undetected objects (2.7% of total W object) were classified into two types, as shown in Fig 5(a) and (b) Etch pits due to α-particles from the environment (a) and dust or tiny scratches on the surface of CR-39 (b) are imaged near the detection target (W object) Improvements such as shortening the exposure time to the environment and handling without damaging the surface can be considered As a further usage of deep learning, in addition to the al­ gorithm for extracting etch pits, it is possible to create an algorithm to distinguish the etch pit from noises The conventional pattern matching method requires the measure­ ment of etch pits from images obtained of both surfaces of the CR-39 detector and execution of the pattern matching algorithm within the measurement accuracy of 2–3 μm (Ota et al., 2008) In the new method, the alignment (matching) error is negligible as described in Section such that we need to consider the multiple Coulomb scattering The presence or absence of a nuclear reaction can also be determined with high accuracy by using an image in which the front and back are merged where ΔNin(sys) = 0.007 × Nin and ΔNout(sys) = 0.006 × Nout As a result, the systematic error of the charge changing cross-section can be calculated as the sum of squares of these errors, resulting in ±0.9% (1σ) It should be pointed out that these statistical and systematic errors can be affected by the etch pit density and etching conditions (size of the etch pit), and it is necessary to optimize the algorithm for each set of conditions 3.2 Classification of undetected objects for further improvements The characteristics of the etch pits that could not be detected were classified for further improvement of the accuracy Undetected objects (2% of total W/B object) were classified into four types as shown in Fig (a) The W/B etch pits are close to each other and might be recognized as W objects since the distance between the centers of the two etch pits is shorter than the radii of each individual etch pit The Radiation Measurements 151 (2022) 106706 K Tashiro et al and performing object detection of it As a result, the total charge changing cross-section can be determined by sorting the etch pits in the merged image In addition, it is possible to apply the precise 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