Preamble

Development and Optimization of a Virtual Model for Coordinated Efficiency Calibration and trajectory Length Estimation in TGS Emission Measurements Biao Hu, San-Gang Li, 1, 2, 3, Jing Zhang, Li Yang, Zhi-Xing Gu, and Yi Cheng 1 College of Nuclear Technology and Automation Engineering, Chengdu University of Technology, Dongsanlu, Erxiangiao, Chengdu 610059, China Applied Nuclear Technology in Geosciences Key Laboratory of Sichuan Province (Chengdu University of Technology) No. 1, East 3rd Road, Erxianqiao, Chengdu 610059, China The Engineering and Technical College of Chengdu University of Technology,Leshan 614000,China; In tomographic gamma scanning (TGS) emission measurements, conventional methods typically compute analysis reveals a spatial consistency between the efficiency calibration and trajectory length. Building on this physical correlation, this paper proposes a novel joint calculation model, that simultaneously resolves both efficiency calibration and trajectory length. To further improve emission image quality and nuclide activity inversion accuracy, the radiation sources within voxels are treated as uniformly distributed multi-point sources, constructing a joint calculation model under the multi-point source and detector framework. For model verification, three calculation methods under the single-point source emission mode (point-point model, average trajectory model, and the point source mode of this model) and three multi-point source emission modes (uniform 8- Maximization algorithm (MLEM) was used to reconstruct images of volume sources at three different locations with multi-point source modes performing better than single-point source modes; in multi-point source modes, the distribution of radiation source points within voxels is not better with more points, with the uniform 64-point mode showing the best comprehensive performance, and demonstrating significant improvements in both emission image quality and nuclide activity accuracy compared to traditional point-to-point and average trajectory models.

Keywords

tomographic gamma scanning (TGS), emission imaging, efficiency calibration, trajectory length

1 Introduction

Under global carbon-neutral targets, nuclear power has re- gained prominence as a low-carbon, dispatchable baseload source. The International Energy Agency (IEA) projects that installed nuclear capacity must roughly double by 2050, con- tributing approximately 10% to the total global electricity

generation [ 1 ]. Although nuclear energy contributes signifi- 7

cantly to carbon reduction and energy security, its expansion inevitably generates radioactive waste during the entire fuel cycle. The safe and effective management of such waste has

become a key focus for the international community [ 2 – 4 ]. 11

Therefore, accurately assessing the radioactivity level of nu- clear waste is an essential step in ensuring the sustainable development and safe management of nuclear energy [ In the field of radioactive waste characterization, Tomo-

graphic Gamma Scanning (TGS) has emerged as an advanced 16

nondestructive γ -ray assay technique for drum waste inspec- 17

tion (as shown in Fig. ). The detection principle of TGS is as follows: first, a transmission measurement is performed to obtain the three-dimensional (3D) spatial distribution of materials inside the drum. Then, emission measurements are

This work was supported in part by the General Program of the Na- tional Natural Science Foundation of China (Grant 12075039), the Le- shan Nuclear Technology Application Engineering Research Center (Grant C32KFKT2025001), and the AI Research Fund of Chengdu University of Technology (Grant 2025AI023).

San-Gang Li,Dongsanlu, Erxiangiao, Chengdu

conducted to determine the 3D activity distribution of radionu- clides. Finally, the radioactive level of the waste is evaluated based on the reconstructed activity distribution [ ]. In the overall TGS detection process, the emission measurement is the key factor that determines the accuracy of the activity assessment. Therefore, this study focuses on the emission measurement process in TGS, where the precise computation of the efficiency calibration matrix and trajectory length matrix

constitutes the core technical challenge. 30

Regarding efficiency calibration, most existing studies sim- plify the radioactive source as an ideal-point source to reduce computational complexity. Typical approaches include the spa- tially symmetric equivalent matrix element method [

polar coordinate partitioning method, and function-fitting tech- 35

niques [ 14 – 18 ]. However, the point-source assumption ne- 36

glects the actual spatial distribution of radioactivity within a voxel. Cheng Yu’s study [ ] demonstrated that, within the collimator’s field of view, a volume source contributes more

detectable γ -rays than a point source, leading to significant 40

discrepancies in efficiency calibration results. Thus, incorpo- rating the geometric distribution of the source into the effi- ciency calibration process is crucial for accurately evaluating its influence on the emission image quality [ For the trajectory length model, the Estep team at the Los Alamos National Laboratory (LANL) simplified the TGS phys- ical model into a “point-source and point-detector” configu- ration for the trajectory length calculation [ ]. This model greatly simplifies the computation and has since become the mainstream approach. However, by treating both the source and detector as point-like, the model neglects their actual geo-

metrical dimensions, introducing significant deviations in the 52

computed trajectory length and subsequently degrading the image reconstruction quality.

To correct the geometric simplifications, subsequent research introduced more refined geometric representa- source and detector” configuration was proposed, which con- siders the real dimensions of detector rather than treating it as a point. The China Institute of Atomic Energy first incorpo- rated the concept of the detector solid angle into the average trajectory length model [ ]. Subsequently, various equivalent trajectory length calculation methods were developed under this configuration, including: Monte Carlo methods (e.g., the

volume flux method developed by the Chengdu University of 65

Technology [ ], and the Monte Carlo–based equivalent tra- jectory length model established by our group for transmission measurements [ ]); Mean-value methods (e.g., Han Miao-

miao of Harbin Engineering University proposed a method 69

based on the mean value of line connections between the

point-source and finite points on the detector surface [ 22 ]); 71

Computer graphics clipping methods (e.g., Zhang Quanhu of the China Institute of Atomic Energy used the Cyrus–Beck

algorithm [ 19 ], and Yan Yucheng of Chengdu University of 74

Technology applied the Cohen–Sutherland algorithm [ However, most of these methods still assume the source to be a point-source without considering the actual spatial dis- tribution of radioactivity. Consequently, when the voxels are

relatively large, significant deviations in the equivalent trajec- 79

tory length remain. Although assuming a uniformly distributed 80

volume source can reduce bias, applying mean-value or clip- ping methods requires extensive computations of numerous sub-voxel points, making the process extremely cumbersome.

In contrast, Monte Carlo methods can directly simulate particle transport in 3D space via probabilistic sampling, making them more suitable for handling multi-point distributions within a voxel.

Moreover, in existing emission measurement studies based on the “point-source–detector” configuration, efficiency cali- bration and trajectory length are typically computed indepen- dently, resulting in low computational efficiency, especially when the voxel source is non-point-like. Therefore, integrating the efficiency calibration and trajectory length computation processes, while accurately reflecting the geometric distri- bution of the source, is crucial for improving the emission Carlo-based efficiency calibration is consistent with that for trajectory length calculation. Specifically, the range of particle paths contributing to the full-energy peak count is identical Monte Carlo toolkit provides direct access to these particle computation of efficiency calibration and trajectory length while properly accounting for the source geometry.

Based on the actual TGS emission measurement scenario, this study addresses the cumbersome independent calculation of efficiency calibration and trajectory length computation in traditional workflows. Using a virtual vacuum waste drum model that preserves only the geometric features, we pro- pose for the first time a joint computation model of efficiency

calibration and trajectory length under a “single-point-source– detector” configuration. Furthermore, to account for the source distribution characteristics, the radioactivity within each voxel

was uniformly distributed to the centers of its subregions, lead- 114

ing to an innovative “multi-point-source–detector” joint com- putation model, which more realistically represents the source distribution. This model aims to improve computational effi- ciency while effectively enhancing the reconstruction quality of the emission images.

2.1 Transmission Measurement

In emission measurement, the count rate of a specific gamma ray can be described by the following Equation (1).

Among them, self-absorption attenuation correction for effi- ciency calibration is required, as shown in Equation (2). The solution for the absorption attenuation of gamma rays by the medium are presented in Equations (3) and (4) [

j =1 F ij · S j (1) 128

D i =

In the equation, represents the count rate of gamma rays emitted by all voxels in the sample and detected at the -th mea- surement position; denotes the efficiency matrix element corrected for self-absorption attenuation, which is referred to as the attenuation-corrected efficiency matrix element; stands for the activity of the radioactive source in the voxel.

F ij = E ij · A ij (2) 136

In the equation, is the detection efficiency of the detector

at the i -th scanning measurement position for the radioactive 138

source in the -th voxel; represents the attenuation factor of gamma rays emitted from the -th voxel and detected by

the detector at the i -th scanning measurement position, where 141

the attenuation is caused by the medium.

k =1 T ijk · µ k

A ij = exp

In the equation, represents the linear attenuation thick- ness, which is the thickness of gamma rays emitted from the

j -th voxel and detected by the detector at the i -th scanning 146

measurement position being attenuated by the -th voxel along the trajectory before reaching the detector; denotes the lin- ear attenuation coefficient of the k-th voxel.

According to the MC theory, is expressed as Equation

T ijk = � N j l =1 ε il T ijkl � N j l =1 ε il . (4) 152

In the equation, denotes the detection efficiency at a point on the end-face of the detector when the detector is at position represents the trajectory length of gamma particles from voxel passing through voxel before reaching point on the detector’s end-face; is the total number of particles emitted from voxel 2.2 TGS Model for Joint Calculation of Effi- ciency Calibration and Equivalent Trajec- tory Length To invert the activity distribution inside the waste drum, it is necessary to pre-solve the efficiency calibration matrix corrected for absorption and attenuation, as shown in Equation

( 1 ). By combining Equations ( 2 ) and ( 3 ), this problem can be 165

transformed into solving the efficiency calibration matrix and trajectory length matrix . Most existing studies calculate these two matrices independently, resulting in cumbersome processes. Notably, when the Monte Carlo method is used to calculate the detector efficiency matrix elements,the range of particle paths contributing to the full-energy peak count is iden- tical to the computational range of trajectory length, and the

MC program Geant4 can conveniently obtain the ray trajectory 173

step lengths. Therefore, both the efficiency calibration matrix elements and trajectory length matrix elements in this study were calculated using the Monte Carlo method. The equivalent trajectory length is calculated using Equation ( ), which can be understood as the average trajectory length of all -rays from voxel that pass through voxel and are detected by the detector end-face at position . Based on this, a virtual vacuum

nuclear waste drum model retaining only geometric features 181

was constructed using Geant4, and a joint calculation model for efficiency calibration and trajectory length was proposed for the first time to simplify the solution process and simulta- neously obtain the efficiency calibration matrix and equivalent trajectory length matrix. This model includes three modules:

TGS system geometric modeling, particle source emission, and calculation of efficiency matrix and trajectory length matrix , providing a new approach for the synchronous solu- tion of efficiency calibration and equivalent trajectory length.

The model was constructed as follows: This model is based on a single HPGe detection system and performs geometric modeling of a standard 200L waste drum. The density of the entire drum was set to zero, and it could be axially divided into layers. Each layer was further subdivided into rectangular voxels, resulting in a total voxels. Each layer can be configured with 1 to

I ( 1 ≤ I ≤ V ) measurement positions, and the entire system 198

detection positions. The particle source adopts a single-point emission mode at the voxel center (as shown in Figure (a)), with particles

uniformly distributed at the center of each voxel through uni- 202

form sampling. It is worth noting that this design includes

a technical highlight: for the rotating working condition of 204

the waste drum, the system can real-time match the rotational attitude of the drum, drive the particle source position to dy- namically adjust synchronously with the spatial coordinates of the voxel, and maintain a precise alignment with the voxel center at all times. This design can effectively avoid particle distribution deviation caused by drum rotation, ensure that the

uniformity of particles in the detection area is not affected by 211

rotation during the entire detection process, and provide stable support for the accuracy of subsequent matrix calculations.

The specific process is as follows:

During each particle emission, uniform sampling was used 215

to select the particle-emitting voxel, and the center coordinates of this voxel were obtained using G4VPhysicalVolume as the

initial particle position. The affine transformation class in 218

Geant4, which can realize coordinate transformation through

rotation and translation matrices, is utilized. Before parti-

cle emission, the initial position coordinates can be affine- 221

transformed with the rotation matrix of the waste drum to obtain the rotated particle emission coordinates, as expressed in Equation (

P ′ = M · P + T (5) 225

In the equation, denotes the transformed coordinate vec- represents the rotation transformation matrix, is the coordinate vector before transformation, and stands for the translation transformation vector.

In this model, the solution process for the efficiency matrix and equivalent trajectory length matrix is as follows (Figure

1. When a single

photon is emitted, the G4Track is used to trace the transport process of each photon. When the photon has a ParentID of 0 and a Step of 0, the geometry it is located in the particle source voxel , and the trajectory length within this voxel is obtained.

2. The

photon transport status was continuously tracked. When the ParentID is 0, Step is greater than 0, and the photon is inside the waste drum, the geometric space where the particle resides is the photon trajectory voxel , and the trajectory length within this voxel can be obtained.

3. The

photon entering the detector geometry was mon- itored. When a photon enters the -th detector geome- try, the energy deposited in this step is acquired using the GetTotalEnergyDeposit() member function of the G4Step class. The energy deposition variables corre- sponding to the -th detector are statistically added up to the energy deposited each time.

4. At the end of each event, the trajectory length identifi-

cation is recorded, and it is checked whether the total

deposited energy e ij in detector i equals the initial en- 253

. If so, the photon was considered to be detected.

The track length through the -th voxel is retained, and the value of the detector count matrix element is incremented by one.

After completing the transport and reaction processes of all sampled photons, the full-energy peak detection efficiency matrix element is calculated by dividing the number of

photons with full energy deposition � N j l =1 ε il recorded by the 261

detector at position for the emission source voxel (where

D ij = � N j l =1 ε il ) by the total number of emitted photons N j in 263

voxel . Using Eq. , the equivalent trajectory length matrix element is obtained through a ratio. The numerator is the

total valid trajectory length, � N j l =1 ε il x ijkl , of γ photons from 266

voxel that pass through voxel and are effectively detected.

The denominator is the expected number of photons with full-

energy deposition, � N j l =1 ε il , recorded for the emission source 269

voxel 2.3 Joint Calculation Model of Efficiency Cali- bration and Equivalent Trajectory Length Under Multi-Point Source Emission Radioactive distribution of single-point source at the voxel center.

Radioactive distribution of 8-point sources within a voxel.

In traditional emission imaging, the calculation of efficiency calibration and trajectory length usually assumes that the ra- dioactive source is concentrated at the center of the voxel (as shown in Figure (a)). However, radioactive sources in actual waste drums are mostly distributed as volume sources, and it is too rough to perform relevant calculations based solely on the assumption of a point source at the voxel center.

To address this, this section optimizes the particle emission module based on the TGS model for the joint calculation of the efficiency calibration and equivalent trajectory length. The radioactive distribution is regarded as covering a wider area inside the voxel, and two new emission modes are introduced

accordingly: the uniform volume source emission mode within 286

the voxel and the uniform multi-point source emission mode 287

within the voxel. Compared with the traditional point-source emission mode, these two new modes only change the sam- pling rules for particle emission positions, whereas other key calculation links (including efficiency calibration calculation, trajectory length calculation, and the total number of sam- pled particles in each voxel) remain unchanged. Specifically, the calculation logic for efficiency calibration and trajectory length is still consistent with the “single-point source emis- sion at the voxel center” mode in Section 2.2, with a single

voxel as the basic calculation unit. The main difference lies in 297

the design of the uniform multi-point source emission mode 298

within the voxel: this mode further subdivides a single voxel into multiple sub-regions of equal volume, takes the center of each sub-region as the point-source emission position, and

assumes that radioactivity is uniformly distributed at these 302

center points. In essence, the two new emission modes only adjust the distribution of radioactive sources within the voxel, allowing more particles to reach the detector within the col- limator’s field of view, thus conforming better to the volume source distribution characteristics in actual scenarios. Figure (b) shows the specific radioactive distribution when a single voxel is divided into 8 equal-volume regions.

3 Experimental Setup and Evaluation

3.1 TGS Geometry and System Setup

To verify the processing effect of the proposed model on the emission images, the experimental setup was as follows:

As shown in Figure , each layer of the standard 200L waste drum was divided into voxels, with 5 horizontal scan-

ning positions configured. The experiment selected half of 317

the drum area ( Z = 8 ), and the waste drum rotates around 318

its axis at intervals of 15 degrees ( ), with a total of 24 rota- tions. Combined with the above parameters, a total of 768,000 matrix elements were formed. The detection equipment used an HPGe detector with a crystal specification of 6.41 cm in diameter and 7.55 cm in length[ 3.2 Sampling Position Settings for Radioactive Source Emission Modes The emission modes include two types: single-point and multi-point sources. In the particle source module of the multi- point source emission mode, when the emission source is

distributed as a volume source, uniform sampling within the 329

voxel is adopted; when the emission source is distributed as a

uniform limited point source, a general method for generating 331

three-dimensional source points based on power-of-8 division is used. This method can flexibly achieve regular divisions four distribution modes are configured as shown in Figure

voxel center point source, voxel uniform 8-point source, voxel 336

uniform 64-point source, and uniform volume source, which 337

correspond to the joint point-detector (JPD) model, joint 8- point-detector (J8PD) model, joint 64-point-detector (J64PD) model, and joint volume-detector (JVD) model, respectively. 3.3 Medium and Nuclide Positions Inside the To quantitatively evaluate the results of the emission mea- surements, this study sets 7 filling methods for the medium inside the drum and three volume source positions. The linear attenuation coefficient of the medium was calculated using the Monte Carlo method.

As shown in Figure (a), three volume source samples were positioned in different layers with different radii, all emitting

1.332 MeV gamma rays from

Co, with an activity of Bq/s each. As shown in Figure (b), each layer inside the waste drum was filled with three identical cubes at the same positions, among which 4 voxels are filled with water, 3 voxels with

nylon 11, and 1 voxel with aluminum. The remaining matrix 355

positions were filled with the following materials respectively: wood (0.443 g/cm ), polyethylene (0.94 g/cm ), nylon 11 (1.425 g/cm ), concrete (2.3 g/cm ), aluminum (2.699 g/cm calcium oxide (3.3 g/cm ), and aluminum oxide (3.97 g/cm The average densities of the resulting waste drums were 0.7402 , 1.0782 g/cm , 1.4080 g/cm , 2.0030 g/cm , 2.2743 , 2.6830 g/cm , and 3.1386 g/cm respectively. j,ref j,ref

NMSE =

Where: j,ref represent the particle counts detected by the detector from voxel and the preset particle number of voxel in Geant4, respectively.

3.4 Image Quality Evaluation Methods

To evaluate the quality of the activity inversion images of nuclear waste drums, a combined qualitative and quantitative assessment system was adopted. The qualitative assessment in- tuitively judges the overall performance of the images through visual inspection, while the quantitative assessment is carried out from two dimensions: image difference and activity accu- racy, specifically including the Normalized Mean Square Error (NMSE), the Neighbor Ratio (NR) index, and the relative error of radioactive activity. In the assessment of radioactive activity accuracy, the relative error was used to quantify the deviation between the reconstructed activity value and the preset activity value in the Geant4 program. This study uses two relative error indicators for evaluation: the direct radioactive relative error and the summed radioactive relative error. Among them, direct radioactivity (DR) refers to the radioactive activity di- rectly calculated by the image reconstruction algorithm for the source position, and summed radioactivity (SR) is the sum of the reconstructed activity values of the source position and its adjacent voxels.

The NMSE represents the difference between the recon- structed and original images; thus, a smaller NMSE value is

better. To assess the positioning accuracy of the radioactive 389

source, the NR was also used to evaluate the radioactive source position in the reconstructed image. NR is defined as the ratio of direct radioactive activity to the summed radioactive activ-

ity. A larger NR value indicates more accurate positioning and 393

better distinguishability of the source position in the image than the other methods. A comprehensive assessment using the NMSE and NR was conducted to fully evaluate the image reconstruction quality.

The NMSE is calculated using the following equation ( 4 Results and Discussion To intuitively evaluate the computational model proposed in this study, the MLEM algorithm was used for image recon- struction. Six emission modes were established for system-

Single point source at the voxel center

(b) Uniform 8-point source within a voxel

(c) Uniform 64-point source within a voxel

(d) Uniform volume source within a voxel

atic comparative analysis, including the efficiency calibration- trajectory length joint calculation model under the point-source emission mode (MLEM-JPD), three efficiency calibration- trajectory length joint calculation models under multi-point source emission modes, namely, the 8-point source (MLEM-

J8PD), 64-point source (MLEM-J64PD), and voxel-uniform 408

volume source modes (MLEM-JVD), and two comparative models: the point-point model (MLEM-PP) and the average trajectory length model.

As shown in Figs. , they respectively present the imaging results of each volume source under different average densi- ties of waste drums for the three emission modes: MLEM-PP, MLEM-JPD, and MLEM-J8PD. Since the material settings of each layer are consistent, the imaging of radioactive sources is hardly affected by different layers. Among them, MLEM- JPD is similar to MLEM-AT, and MLEM-J8PD is similar to MLEM-J64PD and MLEM-JVD; therefore, they are not displayed separately. It can be seen from Figs. that the emission measurement images under the multi-point source

emission mode have the best quality, and the positioning and 422

recognition of each volume source are superior to those of 423

MLEM-PP and MLEM-JPD. Specifically, MLEM-PP could no longer locate volume source B when the average density reached 2.0030 g/cm , whereas MLEM-JPD could barely lo- cate the source at volume source B when the average density was 2.6830 g/cm , with poor imaging quality.

The reconstructed activity values and overall imaging qual- ity follow the following rules: at lower average densities,

Volume source setup details Medium distribution details the influence of other high-density media around the volume source dominates; at higher average densities, the density of the matrix and the radial position of the radioactive source in the drum become the main influencing factors, which is consistent with the laws of emission measurements. Specifi- cally, under low average density conditions, volume source C

is most significantly affected, which is attributed to the fact 437

that the types of non-matrix media distributed around it are

significantly greater than those around other volume sources. 439

In this case, when there is a large density difference between the drum’s matrix density and other filling media, the image

noise in high-density voxel regions will increase significantly, 442

leading to a decline in image quality. Thus, the quality of the emission images is closely related to the medium distribution around the volume source and the average density inside the drum. (NR) of different models under varying medium densities.

As shown in Fig. (a), the MLEM-PP emission mode ex- hibits the worst overall NMSE performance, particularly in the high-density range. Moreover, single-point source emis- sion modes are generally inferior to multi-point source modes. (d) further indicate that MLEM-PP performs the

worst in terms of NR values, with the most significant dis- 454

crepancy observed at volume source B under high-density

and MLEM-JPD demonstrate minimal differences in image 457

quality, fundamentally because both models are built upon the point source-detector configuration assumption. However,

MLEM-JPD offers significant advantages in computational 460

workflow: for the large number of matrix elements in the experimental setup, this method enables simultaneous compu- tation of both the efficiency calibration matrix and trajectory length matrix, whereas MLEM-AT requires separate indepen-

NMSE of Different Models Under Different Densities Neighboring Ratio of Volume source A Neighboring Ratio of Volume source B Neighboring Ratio of Volume source C dent calculations for these two matrices. Additionally, the three models under multi-point source emission modes can accurately locate radioactive sources. Compared with MLEM- PP, at a density of 2.2743 g/cm , MLEM-JVD reduces NMSE by 47.3%, 47.2%, and 48%, respectively, while increasing NR at volume source B by 84.7%, 84.9%, and 87.6%, re- spectively. Compared with MLEM-AT, at a density of 2.6830 , MLEM-JVD reduces NMSE by 12%, 14%, and 14.9%, respectively, and increases NR at volume source B by 26.9%, 30%, and 35.8%, respectively. ties for the direct radioactivity (DR) and summed radioactivity (SR) of the three volume sources in the waste drum under the seven medium conditions across the six models. Except for some density points of volume source A, where DR is slightly better than SR, the overall reconstruction accuracy of SR for the three volume sources is generally superior to that of DR.

A comparison of the 3-point source methods reveals that the

activity reconstruction accuracy of MLEM-JPD is significantly 483

better than that of MLEM-PP, with the greatest difference oc- curring at the volume source B. At this point, the relative error difference in the Specific Reconstruction (SR) compared to MLEM-PP at the highest average density point is reduced by 53.1%. Compared to MLEM-AT, MLEM-JPD shows only

slight differences at high-density points, with overall minimal 489

discrepancy. Further analysis of Fig. and Fig. shows that MLEM- J64PD is the optimal emission mode, With little difference in NMSE and NR compared to MLEM-JVD, and both can accurately locate radioactive sources. MLEM-J64PD achieves the smallest overall activity reconstruction errors at volume sources A and C, with a maximum difference of only 1.35% from MLEM-JVD at volume source B. This indicates that more points do not necessarily yield better results under multi- point source emission modes. Compared with MLEM-AT, MLEM-J64PD achieves the optimal improvement in SR, with a relative error reduction of 7.42% at volume source C under an average density of 2.6830 g/cm

Direct Radioactivity of Volume source A Summed Radioactivity of Volume source A Direct Radioactivity of Volume source B Summed Radioactivity of Volume source B Direct Radioactivity of Volume source C Summed Radioactivity of Volume source C

5 Conclusion

Based on a virtual vacuum nuclear waste drum that retains only geometric features, this study establishes, for the first time, a joint calculation model of efficiency calibration and tra- jectory length based on a point-source-detector configuration.

Measurement data were acquired under seven medium-filled waste drum conditions, and the MLEM algorithm was used emission mode, MLEM-JPD exhibits better imaging quality and more accurate radionuclide activity quantification than MLEM-PP. This method shows little difference compared to MLEM-AT. However, corresponding to the large number of matrix elements in the experimental setup, it avoids the cumbersome process of separately calculating efficiency cali- bration and trajectory length.

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