Principle

As a unique NDT technique, NR has a range of applications in the nuclear and aerospace industries. When passing through an object, neutrons interact with the atomic nucleus of the object, causing a change in the transmitted neutron beam intensity (I). The Lambert-Beer law describes I by using the composite neutron interaction probability of each independent material as follows [28]: $I=I_0\exp {\displaystyle \sum _i}\left(N_i{\sigma }_{i}t\right),$ (1) where I₀ is the incident beam intensity, Ni is the bulk density of the target nucleus for element i, σi is the total neutron scattering cross-section for element i, and t is the thickness of the sample in the beam direction.

Owing to the varied intensities of transmitted neutrons in inhomogeneous or faulty objects, information on the internal structure of an item may be retrieved using specific techniques to detect neutron rays penetrating the object.

Based on the different exposure methods, NR can be divided into direct neutron radiography (DNR) and indirect neutron radiography (INR), as shown in Fig. 1 [29]. In DNR, both the film (imaging plate) and the conversion screen are exposed to the neutron beam. Furthermore, the film (imaging plate) absorbs the prompt radiation created by the neutron irradiation of the conversion screen [30]. While the rapid imaging speed of this technology is an advantage, it is prone to interference from gamma rays in the neutron beam, as well as those produced by the sample and neutrons, because the film (imaging plate) is also gamma-sensitive. The conversion screen, which is unaffected by γ-rays, is first placed at the back of the sample. During the INR, the conversion screen absorbs neutrons from the neutron beam through the sample [31, 32]. In addition, each location on the conversion screen produces a radioactivity intensity that is directly proportional to the intensity of the neutrons that hit the screen. Consequently, the conversion screen develops a possibly radioactive latent image after the neutron beam penetrates the sample, which is then moved to the dark box and placed on a film (imaging plate) for re-exposure to create an image. This technique avoids γ-ray interference and is therefore suitable for imaging in strong γ-ray environments. This transfer technique is one of the few that can produce high-quality radiographic images of irradiated fuel; however, it is also time-consuming [23, 33]. Hence, conducting indirect neutron CT is more time-consuming because of the utilization of sample multiangle photography for the reconstruction of a 3D image. This approach is an offline imaging technology in which the acquisition and exposure of each projected image involve the replacement of the absorption foil, resulting in variations before and after imaging.

Fig. 1Full-screen View

Principle of indirect neutron radiography

Indirect neutron CT encounters the two aforementioned technical challenges. The differences between the images are resolved by setting up an identifier as a reference for subsequent image adjustments. In addition, time and neutron beams are saved by optimizing the conversion screen or improving the reconstruction algorithm.

Dummy nuclear fuel rod

2.2.1

Material and structure

Pressurized water reactors (PWRs) are the predominant reactor types employed in contemporary commercial nuclear power facilities [34]. A fuel rod in PWRs is a typical multi-component device that is designed to continuously produce and transfer fission energy from fuel pellets to the coolant and safely contain fission products simultaneously [6]. These reactors contain diverse nuclear fuel components with distinct features. A typical PWR nuclear fuel rod comprises several components, including a UO₂ core block, zirconium alloy cladding, end plugs, compression springs, and helium cavity [6]. The enrichment of ²³⁵U in the UO₂ core typically ranges from 3% to 5%.

This study focuses on utilizing NR technology to inspect nuclear fuel rods, specifically in PWR. As an illustrative example, we developed a substitution sample for a nuclear fuel rod from the Daya Bay Nuclear Power Station. Figure 2 depicts the structure of the nuclear fuel rod of the Daya Bay Nuclear Power Plant. Table 1 lists the main parameters of the Daya Bay nuclear fuel rods.

Table 1Full-screen View

Main parameters of the Daya Bay fuel rod

Parameter	Value
Total length of fuel rod (mm)	3867.1
Diameter of fuel rod (mm)	9.5
Thickness of cladding (mm)	0.57
Gap of fuel meat and cladding (mm)	0.084
Material of cladding	M5
Content of uranium (kg)	1.75
Type of material	Ceramic UO2
Enrichment of 235U	4.45%; 4.2%; 3.7%; 3.1%; 2.5%; 2.4%; 1.8%
Diameter of fuel meat (mm)	8.192
Height of active zone (mm)	3657.6
Height of fuel meat (mm)	13.46
Density of fuel meat (g/cm3)	10.60

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Fig. 2Full-screen View

Structure of the Daya Bay nuclear power plant fuel rod

2.2.2

Calculation and production

Nuclear fuels used in reactors primarily comprise fuel meat and cladding, with fuel meat containing nuclear materials that must be carefully controlled and managed because of the associated risks. However, using real nuclear materials for sample preparation in INR detection of nuclear fuel rods can be challenging because of sample management, transportation, and high production costs.

This paper proposes the development of substitute samples for nuclear fuel rods. These substitute samples were specifically designed for research purposes in the field of INR. We designed a simulated sample structure that exhibited a high level of consistency with real fuel rods. Additionally, we built composite materials that could effectively substitute for real fuel rods. By manipulating the proportions of the constituents in the simulated substance, it is possible to make the substance more closely match the density of the fuel core and the coefficient of neutron absorption for cold neutrons. Table 2 presents the cold neutron cross-section data for each element of the PWR nuclear fuel rod.

Table 2Full-screen View

Cold neutron cross-section data for each nuclide of the fuel rod

Nuclide	Cold neutron cross-section (barn)
235U	1614.9049
235U	15.3223
O	4.3851
Pb	8.3682
C	5.7369
H	55.2910
10B	8539.5310
10B	5.9337
Al	2.0754

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The cold neutron cross-sections of the remaining nuclides present in the core material have significantly smaller values than ²³⁵U and ¹⁰B. Consequently, their effects are ignored during the substitute material formation procedure. UO₂ is the core material with a density of approximately 10.60 g/cm³. As a result, lead with a density closer to this value was chosen as a substitute for the substrate of the composite, and boron carbide was used to simulate the macroscopic absorption cross-section of the core of cold neutrons with various ²³⁵U enrichments. The relationship between the boron carbide content and ²³⁵U enrichment in the core is deduced as follows: ${{\displaystyle \sum }}^{235}\text{U}={\sigma }_{{}^{235}\text{U}}\times {\rho }_{{\text{UO}}_2}\times \frac{238}{270}\times p_{{}^{235}\text{U}}\times \frac{N_{\text{A}}}{M_{{}^{235}\text{U}}},$ (2) ${{\displaystyle \sum }}^{10}\text{B}={\sigma }_{{}^{10}\text{B}}\times {\rho }_{{\text{B}}_{\text{4}}\text{C}}\times \frac{43.2}{55.2}\times p_{{}^{10}\text{B}}\times \frac{N_{\text{A}}}{M_{{}^{10}\text{B}}},$ (3) ${\rho }_{{\text{B}}_{\text{4}}\text{C}}=\frac{{\sigma }_{{}^{235}\text{U}}}{{\sigma }_{{}^{10}\text{B}}}\times {\rho }_{{\text{UO}}_{\text{2}}}\text{×}\frac{238\times 55.2}{270\times 43.2}\times \frac{p_{{}^{235}\text{U}}}{p_{{}^{10}\text{B}}}\times \frac{M_{{}^{10}\text{B}}}{M_{{}^{235}\text{U}}},$ (4) $\begin{array}{c}\begin{array}{c}{\rho }_{{\text{B}}_{\text{4}}\text{C}}=\frac{691.7\times 10.6\times 238\times 55.2\times 10\times p_{{}^{235}\text{U}}}{3843.3\times 270\times 43.2\times 0.198\times 235}\\ \approx 0.485p_{{}^{235}\text{U}}\end{array}\end{array},$ (5) where ∑_i is the macroscopic cross-section of i, ${\sigma }_i$ is the microscopic cross-section of i, ρ_i is the density of i, ρ_i is the abundance of i, N_A is the Avogadro constant, and Mi is the molar mass of i.

The composition ratios and density information of dummy nuclear fuel rods with different ²³⁵U enrichments, calculated using Eq. (5) are listed in Table 3. The corresponding composite materials can be used for PWR nuclear fuel rod processing.

Table 3Full-screen View

Composition ratios and density information of simulated composites with different enrichments of UO₂ cores

Abundance of uranium 235U	B4C	Pb	Composite density
4.45	0.022	11.242	10.700
4.2	0.020	11.248	10.704
3.7	0.018	11.259	10.712
3.1	0.015	11.272	10.722
2.5	0.012	11.285	10.732
2.4	0.012	11.287	10.733
1.8	0.009	11.300	10.743
0.72	0.003	11.324	10.761

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Figure 3 depicts the process flow of the PWR dummy fuel core preparation. The first step is to measure a specific amount of lead powder and boron carbide powder. Subsequently, a minimal coupling agent is added to the mixing tank while adhering to the prescribed material ratios for the diverse enrichment fuel cores. Afterward, the powders are mixed evenly in a mixer for more than 48 h. Finally, the mixture is loaded into a hot-press mold and compacted in a hot-press furnace to create dummy fuel cores.

Fig. 3Full-screen View

(Color online) Pressurized water reactor dummy fuel core fabrication process

Figure 4 depicts the different components of the PWR dummy nuclear fuel rod, including aluminum gaskets, end plugs, cores, springs, and cladding tubes made of aluminum alloy. Moreover, aluminum gaskets were placed between different cores to simulate various size gaps between the cores. In addition, end plugs were used to encapsulate fuel rods. The core consisted of six distinct compositions of blended materials, with the enrichments of substitute fuel cores varying from 1.8% to 4.45%. Some of the cores had small holes machined on two end faces with hole diameters of 2 mm, 1.5 mm, 1 mm, 0.8 mm, 0.5 mm, 0.4 mm, and 0.2 mm. The hole depths were 3 mm, which were used to simulate defects of different scales within the cores.

Fig. 4Full-screen View

Partial assemblies of the pressurized water reactor dummy nuclear fuel rod include aluminum gaskets (a), end plugs (b), core (c), springs (d), and cladding tubes (e). Small holes of different sizes are machined in two cross-sections of the partial core to simulate core defects (f)

Neutron beams

We installed an experimental setup for NR at the Institute of Nuclear Physics and Chemistry of the Chinese Academy of Engineering Physics using the China Mianyang Research Reactor (CMRR) [35-38]. In the CMRR, we reduced the energy of the thermal neutrons by interacting them with the deceleration material in the slowing chamber, resulting in the production of lower-energy cold neutrons [39]. The flight tube consisted of 11 sections of 1-m-long aluminum tubes with vacuum inside to reduce the attenuation of the neutron beam by air, particularly for low-energy beams. The neutron spectra were measured using time-of-flight techniques, as shown in Fig. 5 with a peak wavelength of 2.65 Å and a spectrally weighted average wavelength of 3.99 Å. The facility also includes an object-handling system, an imaging system, a beam stop, and a shielding wall, as shown in Fig. 6.

Fig. 5Full-screen View

Time-of-flight techniques measure the relative neutron spectra

Fig. 6Full-screen View

(Color online) Overview of the incoherent neutron computed tomography system

The aperture size D directly impacts the neutron beam divergence and the neutron beam intensity at the sample location. The collimation ratio of the neutron beam (L/D) directly affects spatial resolution. Increasing the L/D ratio improves the spatial resolution by decreasing the aperture diameter [40, 41]. However, this comes at the expense of lowering the neutron flux reaching the sample. The experimental setup used in this study had an L/D ratio of 275. The neutron flux measured at the detector for the aperture setting reported here was Φ₀=6×10⁶ cm^-2s^-1.

Conversion screen

The crucial issue in the INR experimental method is determining the exposure time of the conversion screen in the neutron beam and the exposure time of the conversion screen to the NIP to ensure the efficient use of the neutron beam and save time. In Eq. (6), we describe the relationship between the radioactivity of a conversion screen exposed to a neutron beam. The exposure time (t₁) [21, 42] is given by $A\left(t_1\right)=\delta N\Phi \left(1-e^{-\lambda t_1}\right),$ (6) where $\delta$ is the neutron absorption cross-section of the converter, N is the number of atoms in the converter material, $\Phi$ is the neutron flux irradiating the neutron converter, $\lambda$ is the decay constant, $\lambda =0.693/\tau$, and $\tau$ is the half-life of the converter material. After exposure to the neutron beam, the conversion screen was transferred to a darkroom and exposed to the NIP for time t₂. The radioactivity of the converter, $A\left(t_2\right)$, is given by [21, 42] $A\left(t_2\right)=\left(\delta N\Phi \left(1-e^{-\lambda t_1}\right)\right)e^{-\lambda t_2}=A\left(t_1\right)e^{-\lambda t_2}.$ (7) Figure 7 shows the variations in the activity of the neutron conversion screen exposed to the neutron beam and after exposure cessation, according to Eq. (6) and (7).

Fig. 7Full-screen View

Activity curves of the conversion screen after neutron beam exposure and following exposure cessation

The activity of the conversion screen reaches a saturation point as the duration of exposure to the neutron beam increases. Once the exposure stops, the conversion screen’s activity decays rapidly. Regardless of whether the conversion screen is exposed to the neutron beam or the film, when the exposure time reaches three half-lives of the conversion screen material, the activity is close to 90% of the saturation value. The conversion screen used for INR should have a high neutron cross-section and be capable of generating decay particles through nuclear reactions with neutrons, which can then lead to NIP exposure. Consequently, dysprosium and indium meet these requirements, and their activation products have half-lives of approximately 1–2 h, meeting the time requirements for second-exposure operations without resulting in excessive exposure. In INR, the conversion screen thickness primarily affects the detection efficiency and resolution of the imaging results. Hence, selecting an appropriate conversion screen thickness is imperative to achieve optimal imaging quality, with thicker screens being more efficient but with lower screen intrinsic resolution and less precision. Fig. 8 shows the substitution results, illustrating the detection efficiency of cold neutrons using indium and dysprosium neutron conversion screens of varying thicknesses. Hence, the dysprosium screen exhibited greater detection effectiveness for cold neutrons than the indium screen.

Fig. 8Full-screen View

Efficiency of conversion screens for indirect neutron radiography for detecting cold neutrons at various thicknesses

We developed 50 μm and 100 μm thick dysprosium neutron conversion screens and 100 μm and 150 μm thick indium neutron conversion screens by considering the detection efficiency of cold neutrons and the intrinsic resolution of the conversion screen. Figure 9 illustrates the screen design. We performed a resolution test on INR converter screens using cold neutron beams in conjunction with a NIP. We then exposed the resolution test piece (Siemens Star) and INR converter screen to the neutron beam for 1 h. Afterward, we exposed the INR converter screens for 2 h in a second exposure with the NIP. Figure 10 shows the test results. The 50 μm and 100 μm thick dysprosium neutron conversion screens could effectively resolve 75 μm and 200 μm slits, respectively, and the 100 μm and 150 μm thick indium neutron conversion screens could effectively resolve 75 μm slits.

Fig. 9Full-screen View

(a) 50 μm thick dysprosium screen, (b) 100 μm thick indium screen

Fig. 10Full-screen View

(a) and (b) Resolution test results of 50 μm and 100 μm thick dysprosium screens. (c) and (d) Resolution test results of 100 μm and 150 μm thick indium screens

Image location

The fundamental principles of the X-ray CT are illustrated in Fig. 11. The object under examination was placed between the X-ray source and detector, and X-rays were used to perform a scanning procedure while the object underwent rotational motion. After each scan, the object was rotated by a certain angle before the next scan was conducted. This process was repeated iteratively, resulting in multiple sets of data for a specific cross-section of the object (the choice of rotation angle and number of rotations depends on the desired detection resolution). Subsequently, this information was processed and computed to reconstruct a complete cross-sectional image. By combining these cross-sectional images, a comprehensive 3D representation of an object can be generated. Conventional X-ray CT scans are typically performed in real time, and the positions of the detector and X-ray source remain fixed throughout the scanning process. The rotation of the object under examination was achieved using a rotating platform, and it was crucial to maintain the stability of the object during rotation. A strict coordinate system was established among the X-ray source, sample, and detector to ensure that the pixel values of the projection data accurately represented the information in the sample’s voxels.

Fig. 11Full-screen View

Fundamental principles of X-ray CT

During the INR experiment, the conversion screen was transferred to a dark room for a second exposure because of the high radioactivity of the sample. Consequently, the first step in indirect neutron computed tomography (INCT) is the acquisition of a high-quality 2D projection image, the core operations of which are exposure of the conversion screen to the neutron beam stream and exposure of the conversion screen to the film or NIP. While this process avoids interference with powerful radioactive samples, it changes the relative positions of the neutron beam and detector, resulting in image differences. This problem poses significant challenges for the reconstruction of projection data for INCT. We selected the region of interest and rotated it using feature markers in the image and precise positioning algorithms to obtain a 2D projected image for reconstruction, as show in Fig. 12. The specific operational procedures involved selecting the marker in a certain angle image as the reference and the others as the map to be adjusted. The area slightly larger than the marker pixels was circled, and we calculated the marker center pixels (x₀, y₀) and (x₁, y₁). We also calculated the difference between the center value of the marker in the map that should be adjusted, with the standard map serving as $\left(\text{Δ}x\mathrm{,}\text{Δ}y\right)$. Then, we adjusted the nonstandard image according to $\left(\text{Δ}x\mathrm{,}\text{Δ}y\right)$ and repeated the process until all the maps to be adjusted were traversed.

Fig. 12Full-screen View

Recognition and precise positioning process of the image

Sparse projection data reconstruction algorithm

In INR, the acquisition of each projection image involves a second exposure with a single image data acquisition time of more than 1 h. Additionally, the conventional online radiographic CT detection generally requires more than 360 projection images. This indicates that the efficiency of INCT is too low. Consequently, developing sparse reconstruction algorithms based on fewer images is critical. The sparse reconstruction algorithms necessitate only a limited number of images for the reconstruction process, as opposed to a substantial quantity. This is beneficial for protecting the operators from radiation risks. Moreover, it is helpful in improving the quality and resolution of images, particularly in situations where data are limited. Shortening the imaging time and improving efficiency are additional advantages of reducing the amount of sampled data. Furthermore, it can aid in reducing the costs of data storage and transmission.

Therefore, we developed a reconstruction algorithm for neutron-sparse projection data to improve INCT efficiency. Moreover, we introduced projections onto convex sets (POCS) [43] using a total variance minimization (TVM) algorithm based on the compressed sensing theory. We improved the algorithm for the low-gray value part of the image because the original algorithm reconstruction was unclear. The reconstruction steps of the improved POCS and TVM (POCS–TVM) algorithm are as follows:

(1) We assign an initial value to the reconstructed image, set to $f_{\text{ART}}^0\left(k=1\right)=0$, where k is the number of iterations of the algorithm.

(2) The iterative algebraic reconstruction technique (ART) algorithm was reconstructed once.

(3) The non-negative constraint; that is, if any of the ART iterative reconstruction matrices have negative values, we take the absolute value of the smallest value in matrix f(min(f)). In addition to the absolute value, the value of each matrix element is given by $f_{\text{POCS}}\left(k\right)\left(i\mathrm{,}j\right)=f_{\text{ART}}\left(k\right)\left(i\mathrm{,}j\right)+f(\min (f))\mathrm{.}$ (8)

(4) We take $f_{\text{TVM}}^0\left(k\right)=f_{\text{pocs}}\left(k\right)$ as the initial value for the TVM operation.

(5) We also calculate the incremental factor given by $d\left(k\right)=\Vert f_{\text{ART}}^0\left(k\right)-f_{\text{pocs}}\left(k\right)\Vert \mathrm{.}$ (9)

(6) We compute the global variational gradient and the direction of the gradient as $G^{n-1}\left(k\right)={\frac{\partial {\Vert f\Vert }_{\text{TV}}}{\partial f_{i\mathrm{,}j}}|}_{f=f_{\text{TVM}}^{n-1}\left(k\right)}\mathrm{,}$ (10) ${\widehat{G}}^{n-1}\left(k\right)=\frac{G^{n-1}\left(k\right)}{\left|G^{n-1}\left(k\right)\right|}\mathrm{,}$ (11) where n denotes the number of iterations of the TVM process.

(7) We correct the image by iterating along the direction of the decreasing gradient of the total variance, that is $f_{\text{TVM}}^n\left(k\right)=f_{\text{TVM}}^{n-1}\left(k\right)-\alpha d\left(k\right){\widehat{G}}^{n-1}\left(k\right)\mathrm{,}$ (12) where $\alpha$ is an adjustment factor for controlling the search step size. An iterative calculation is performed until the number of iterations n reaches the set value N.

(8) To determine whether the algorithm satisfies the termination condition, the common termination condition is $\Vert f_{\text{POCS}}\left(k+1\right)-f_{\text{POCS}}\left(k\right)\Vert <\delta$ (δ is a small positive number, e.g., δ =10^-5). Alternatively, the total number of iterations k reaches the set value K; otherwise, the result of the current TVM iteration is used as the initial value of the next round of POCS iterations; that is, $f_{\text{ART}}^0\left(k+1\right)=f_{\text{TVM}}^N\left(k\right)\mathrm{.}$ (13)

Experimental procedure

The experimental setup comprised a neutron beam, film stand, imaging dark box, dummy nuclear fuel rod, gadolinium sheet, in-metal conversion screen, NIP, image-reading equipment of the NIP, and a screen clearer. Figure 13 shows the experimental setup. We used INCT, an offline imaging technique that necessitates the transfer of the conversion screen in each instance of image acquisition and exposure, thereby establishing a novel coordinate system. Therefore, we used a 5 mm ×5 mm ×1 mm gadolinium metal sheet (a strong neutron absorber) as a marker for post-image processing. The marker was independent of the sample stage and conversion screen, ensuring that it remained fixed in each image in the CT system. The sample was fixed on the INCT sample stage during the experiment to achieve a 360 rotation. We positioned the indium conversion screen within an imaging dark box on the film stands. This setup facilitated the transfer of the conversion screen, which was used for the second exposure, from the radiation environment after the first exposure to the neutron beam. After the second exposure, NIP scanning was completed using a phosphor screen laser scanner (scanning optical resolution 50 μm, scanning bias voltage 600 V) with a clearing time greater than 15  min. 3D reconstruction places a high demand on the quality of the projected images. INR requires two exposures, during which variations in parameters such as the exposure time, neutron injection rate, and sample position can introduce significant errors. Therefore, 2D projection image must be subjected to background deduction, noise reduction, and data normalization prior to 3D reconstruction. Then, we gathered 180 projected images across a 360 range for 3D reconstruction using this process.

Fig. 13Full-screen View

(Color online) Layout of the neutron imaging plate offline neutron radiography experiment