Preamble

Development and Hybrid Imaging Performance Evaluation of a 4π-FoV Compton Camera Based on Spherical Detector System

Huai-Zhong Gao,¹,²,³,⁴,⁵ Li-Ye Liu,³,⁴,⁵ San-Qiang Xia,³,⁴,⁵ Chong-Yang Wang,³,⁴,⁵ Xiao-Long Wang,³,⁴,⁵ Heng-Guan Yi,³,⁴,⁵ Hua Li,³,⁴,⁵ Fa-Guo Chen,³,⁴,⁵ and Ming Zeng¹,²,†

¹Key Laboratory of Particle and Radiation Imaging (Tsinghua University), Ministry of Education, Beijing 100084, China
²Department of Engineering Physics, Tsinghua University, Beijing 100084, China
³China Institute for Radiation Protection, Shanxi, Taiyuan 030006, China
⁴Shanxi Provincial Key Laboratory for Radiation Safety and Protection, Shanxi, Taiyuan 030006, China
⁵CNNC Key Laboratory for Radiation Protection Technology, Shanxi, Taiyuan 030006, China

Gamma-ray imaging plays a crucial role in source-term monitoring and consequence management of nuclear power plants. These applications typically involve mapping complex spatial distributions consisting of various radioactive isotopes and covering large areas through free-moving measurements. This requires imaging equipment to achieve not only a 4π field-of-view (FoV), but also an isotropic response within the FoV across a wide energy range. To address these requirements, we designed and implemented a spherical detector system functioning as a Compton camera with an isotropic FoV and active coded aperture imaging capabilities.

This camera system adopts Cerium-doped Gd₃Al₂Ga₃O₁₂ (Ce:GAGG) scintillator detectors and a multichannel electronics system utilizing application-specific integrated circuit (ASIC) technology. Besides Compton imaging, we developed a modified hybrid gamma-ray imaging approach that combines Compton and active coded aperture imaging capabilities, which was not fully explored in previous research. Through systematic evaluations of Compton, coded aperture, and hybrid imaging, we verified that the modified hybrid imaging method can provide enhanced imaging resolution and sensitivity along with an extended energy range. By applying this modified hybrid imaging technique, the developed camera system achieves fine imaging performance, making it well-suited for application in free-moving 3-D radiation mapping.

Keywords: 4π FoV, Spherical detector configuration, Compton camera, Active coded aperture imaging, Hybrid gamma-ray imaging

INTRODUCTION

Gamma-ray imaging has been applied in various industries such as nuclear safety and security [1–4], nuclear medicine [5–8], and astrophysics [9–11]. Two commonly adopted imaging methods are coded aperture imaging [12, 13] and Compton imaging [14–17]. Coded aperture imaging utilizes photon attenuation through patterned coded masks, making it excel at low energies (<500 keV) [37]. However, its effectiveness diminishes at higher energies due to increased penetration of gamma-ray photons. On the other hand, Compton imaging is advantageous at higher energies (500 keV–a few MeV) due to the relatively higher cross-section of the Compton scattering process [37]. This makes Compton imaging suitable for scenarios like source-term monitoring [19, 20], decommissioning [4, 21], contamination remediation, and consequence management of nuclear power plants (NPPs) [22, 23], where typical radioactive nuclides emit gamma-rays with energies ranging from several hundred keV to several MeV [24–27].

Nevertheless, these scenarios often require precise localization of radioactive sources within vast areas and mapping of possibly intricate spatial distributions of radioactivity. These distributions may originate either from complex spatial arrangements of radioactive substances or from complex shielding structures [28–31]. The integration of contextual sensors and scene data fusion approaches provides a viable solution, leading to the development of gamma-ray imaging systems capable of mapping 3D radiation distributions in real time while moving through a scene [19, 23, 29]. The utilization of free-moving measurement approaches and the mapping of complex source distributions both imply that gamma-rays may enter the imager from various angles. Thus, conventional imaging systems with planar configurations encounter significant limitations in imaging performance for these scenarios [31]. Additionally, evidence indicates the presence of radioactive isotopes with characteristic gamma-ray energies below the effective energy range of Compton imaging (>250 keV) in scenarios like source-term monitoring during maintenance and consequence management in NPPs [32–34]. Therefore, apart from attaining an isotropic 4π field of view for complex radiation distribution mapping and free-moving measurements, achieving fine imaging performance across a broad energy range is crucial for future development of gamma cameras in these applications.

To enhance gamma-ray imaging performance in free-moving measurements or mapping of complex distributions, Hellfeld et al. developed an active coded mask imaging system based on spherical detector configuration [29, 31]. Although the detector configuration is optimized to achieve an isotropic 4π FoV, the resulting configuration is not unique. The system also adopted CdZnTe detectors, which may not be the most cost-effective choice compared with novel heavy scintillator materials such as Ce-doped Gd₃Al₂Ga₃O₁₂ (Ce:GAGG). Moreover, the Compton imaging capability of this system was not exploited, leaving the issue of effective imaging across a wide energy range unaddressed. To address these issues, Liang et al. conducted a simulation study on the coded aperture and Compton imaging performance of a more uniformly distributed spherical detector configuration with Ce:GAGG sensors [35]. The isotropic dual-mode imaging capability of such design was verified through Monte Carlo simulations, enabling gamma-ray imaging across a broad energy range. However, this design still faces challenges due to the limited angular resolution of Compton imaging, which can affect image quality when employed in free-moving 3D distribution mapping.

For gamma-ray imagers with dual-mode imaging capabilities like the aforementioned spherical configuration, a great portion of gamma-ray photons are captured via direct photoelectric absorption apart from Compton scattering in the energy range of approximately 300 keV to 1 MeV. Alongside multiple-interaction Compton events, the utilization of these single photon interaction events can provide additional information for image reconstruction to achieve hybrid gamma imaging [36]. This method can improve both the angular resolution and sensitivity of the gamma-ray imager while enabling imaging at energies below 250 keV. Previous studies have demonstrated the effectiveness of such hybrid imaging methods on Compton imagers equipped with passive [37] or active coded masks [18, 38, 39], suggesting they can achieve better angular resolution than single-mode imaging methods. Xu applied this method to a gamma camera with multi-layer planar configuration that possesses 4π FoV for both Compton and active coded aperture imaging [39]. The 4π hybrid imaging capability was validated through Monte Carlo simulation [39]. While this method can effectively enhance imaging performance of Compton imagers with multi-layer configuration while preserving the 4π FoV, it has not yet been tested on a detector configuration with isotropic 4π FoV. Furthermore, this method has some issues related to convergence in iterative image reconstruction, which will be discussed in Sec. II B. The imperative remains to develop a dedicated and theoretically sound hybrid imaging technique for dual-mode gamma cameras with isotropic 4π FoV.

In this paper, we present the development of a Compton camera based on the spherical detector configuration similar to the one proposed by Liang et al. [35]. A spherical detector array comprised of Ce:GAGG detector units and a custom multichannel signal processing system were developed, with the array structure optimized to enhance Compton imaging performance. Compton and active coded aperture imaging tests were performed on this camera to evaluate its dual-mode imaging performance. Finally, a modified hybrid gamma-ray imaging method that aligns more closely with the dual-mode hybrid imaging model was developed based on previous research and applied to the developed Compton camera. This method proves effective in enhancing the imaging performance of the camera. Using this hybrid imaging method, high-resolution and high-sensitivity gamma-ray imaging with isotropic 4π FoV across a wide energy range is achieved on the developed Compton camera.

II. MATERIALS AND METHODS

Imaging System Design

The imaging system reported in this paper consists of a detector system based on spherical configuration, a multichannel frontend electronics system based on application-specific integrated circuit (ASIC), and a backend electronics system that employs field-programmable gate array (FPGA). A schematic illustration of the system composition is given in Fig. 1 [FIGURE:1].

The detector system consists of 80 detector units arranged in a configuration similar to the design proposed by Liang et al. [35]. The positioning of each detector unit is derived using the same strategy as Liang et al., with minor adjustments in the orientation of each unit for convenience in the design of the mechanical supporting structure. Since the geometry of the system and the spatial resolution of the detector unit can significantly influence the angular uncertainty of Compton measurements [40], the configuration of the detector array was optimized to ensure good intrinsic Compton imaging resolution as well as acceptable imaging sensitivity. This optimization involved analyzing the influence of key structural parameters, including sphere radius $r_d$ and crystal size $l_c$, on the imaging performance of the Compton camera. Monte Carlo simulations of the detector system were performed using the Geant4 toolkit [41] to evaluate the angular resolution and Compton detection efficiency across various values of the structural parameters. With engineering constraints including weight and size limits taken into account, the optimal structural parameters were determined as $r_d = 10$ cm and $l_c = 12$ mm. This specific configuration is expected to achieve an angular resolution of $\sim14^\circ$ when measuring the 662 keV gamma-ray emitted from a $^{137}$Cs point source.

Based on the optimized configuration, the detector system was fabricated. Each detector unit comprises a $1.2 \times 1.2 \times 1.2$ mm³ Ce:GAGG crystal coupled to a 6 mm silicon photomultiplier (SiPM, ONSEMI MicroFJ-60035-TSV) mounted on a circuit board and an aluminum shell securing the crystal to the SiPM circuit board. The average energy resolution of the detector units is 7.96% at 662 keV, as depicted in Fig. 2 [FIGURE:2].

Additionally, a plastic mechanical frame was designed and implemented to precisely position and orient each of the 80 detector units according to the optimized configuration. The detector units are divided into 10 groups, and the SiPM high voltage (HV) input and signal output wiring of the 8 adjacent units in each group are connected to a designated signal transferring unit. These connections are then consolidated into a single cable that connects to the electronics system, effectively preventing any potential wiring congestion that could arise from numerous input and output channels. The developed spherical detector system is depicted in Fig. 3 FIGURE:3.

To handle the signals from the 80 detector units, a multichannel signal processing frontend electronics system was developed. The system is composed of 3 32-channel ASICs, with 80 channels for signal processing along with 16 redundant channels for backup. Each channel processes and digitizes the input signal independently to acquire both the amplitude and the generation time of the signal. Subsequently, the data is relayed to the backend electronics system based on FPGA. At the backend electronics, a global timestamp is added to the data in order to identify coincident events. The processed data is packaged for transmission to the onboard computer to check for temporal coincidence and perform Compton event reconstruction as well as image reconstruction. The developed electronics system is depicted in Fig. 3(b).

Imaging Methods

The primary imaging modality of the developed gamma camera is Compton imaging. Additionally, the feasibility of applying active coded aperture imaging on the adopted spherical configuration has been proved by Hellfeld et al. [31] and Liang et al. [35]. Therefore, the capability to perform active coded aperture imaging is also validated for the developed Compton camera. Moreover, a modified hybrid gamma imaging method was devised to further enhance the imaging performance of the camera. Based on methods from previous research, this method effectively combines the Compton and active coded aperture imaging modalities in order to achieve high-quality imaging across a wide energy range (300 keV–1 MeV).

Compton Imaging. Compton imaging has diverse applications in fields such as astrophysics, medical imaging, radiation protection, and nuclear security. It utilizes the Compton scattering process to capture direction information of gamma-ray photons, enabling image reconstruction through back-projection. When an incident photon of energy $E_0$ undergoes Compton scattering in a detector unit, it creates a Compton event by depositing an amount of energy $E_1$ in that unit, with the remaining energy fully collected by one or a few other detector units. With these energy depositions recorded by the detector units, the scatter angle $\theta$ of the incident photon can be determined using the well-known Compton scattering formula:

$$\cos(\theta) = 1 + \frac{m_ec^2}{E_0} - \frac{m_ec^2}{E_0 - E_1}$$

where $m_ec^2$ is the rest mass energy of an electron. The scattering angle indicates the angle between the directions of the incident and scattered photons. While the direction of the scattered photon can be determined from the relative displacement of the detector units that recorded the first and second interactions, the direction of the incident photon cannot be pinpointed with the obtained information alone. Instead, the possible directions of the incident photon are described by a conical surface, referred to as the Compton cone. After accumulating a sufficient number of Compton events, the corresponding Compton cones are back-projected onto the 4π spherical image space surrounding the camera. The intersecting point of these cones denotes the position of the radioactive source.

Since the difference in occurrence times between the interactions of a Compton event amounts to a few hundred picoseconds in the adopted configuration, establishing the order of these interactions via the time-of-flight method is not feasible. Thus, the order of interaction is determined using the methods proposed by Boggs et al. [42], with distinct methods for the determination of two-interaction and multiple-interaction sequences.

With the ordering of the interactions determined, Compton events can be used for image reconstruction. For the reported camera, the list mode-maximum likelihood expectation maximization (LM ML-EM) algorithm [15] is adopted:

$$\lambda_j^{(l+1)} = \lambda_j^{(l)} \cdot \frac{\sum_{i=1}^{N} t_{ij}^C (\Delta\theta_i)^{-1}}{\sum_{k=1}^{M} s_k^C \lambda_k^{(l)}}$$

with $\lambda_j^{(l)}$ denoting the estimated intensity of source pixel $j$ on the 4π spherical image space after iteration $l$, $j = {1, 2, ..., M}$, $s_j^C$ being the sensitivity matrix element which represents the probability that a photon emitted from source pixel $j$ is detected anywhere in the camera in the form of Compton events, $\Delta\theta_i$ being the angular measurement uncertainty of Compton event $i$, $i = {1, 2, ..., N}$, and $t_{ij}^C$ being the system matrix element that describes the probability of producing event $i$ (assuming that the first interaction is recorded by detector unit $p$) given a photon emitted from source pixel $j$. The system matrix element is derived with [14]:

$$t_{ij}^C = \frac{\varepsilon_{ij}^C}{|d_{pj}|^2} \cdot K(\beta|E_0) \cdot \sqrt{2\pi(\sigma_{ER}^2 + \sigma_{DB}^2 + \sigma_{SR}^2)} \cdot \exp\left(-\frac{(\theta - \beta)^2}{2(\sigma_{ER}^2 + \sigma_{DB}^2 + \sigma_{SR}^2)}\right)$$

where $\varepsilon_{ij}^C$ is the probability of a photon emitted from source pixel $j$ being detected by detector unit $p$ via Compton scattering, $|d_{pj}|$ is the distance between source pixel $j$ and detector unit $p$, $\beta$ is the corresponding scatter angle for a photon emitted from source pixel $j$ to generate event $i$, $K(\beta|E_0)$ is the Klein-Nishina formula describing the Compton scattering cross-section [43], while $\sigma_{ER}$, $\sigma_{DB}$, and $\sigma_{SR}$ are the angular measurement uncertainties caused by detector energy resolution, Doppler broadening of Ce:GAGG, and detector spatial resolution, respectively. These angular uncertainties are determined using the method reported in Wu et al. [14].

Coded Aperture Imaging. The coded aperture imaging technique relies on the mutual attenuation of photons among detector units to form effective patterned projections that are essential for image formation. These projections, determined by the system response of the configuration, are crucial for the image reconstruction process. To accurately determine the system response, Monte Carlo simulations of the developed camera were conducted using the Geant4 toolkit. A total of 5762 directional points on the 4π image space were selected following the same strategy reported by Liang et al. [35] to ensure fine precision in the derived system response. Near-field point sources with various energies were placed at each selected point at specified distances to record the count of each detector unit in the simulation. A depiction of the obtained system response is portrayed in Fig. 4 [FIGURE:4].

With the full system response generated, coded aperture image reconstruction can be performed. The ML-EM algorithm is also employed for coded aperture imaging:

$$\lambda_j^{(l+1)} = \lambda_j^{(l)} \cdot \frac{\sum_{p=1}^{P} \varepsilon_{pj}^A C_A^p}{\sum_{k=1}^{M} s_k^A \lambda_k^{(l)}}$$

where $P$ denotes the total number of detector units, $s_j^A = \sum_{p=1}^{P} \varepsilon_{pj}^A$ is the absorption sensitivity matrix element that denotes the probability that a photon emitted from source pixel $j$ is detected anywhere in the camera in the form of single-interaction events, $\varepsilon_{pj}^A$ is the system response matrix element derived from the simulation, and $C_A^p$ is the single-interaction full-energy event count of detector unit $p$.

Hybrid Imaging. To further enhance imaging performance and extract additional physical information by effectively combining Compton and coded aperture data, a hybrid gamma imaging method was developed. Lee et al. initially introduced an approach for imaging reconstruction of hybrid imaging data based on the ML-EM algorithm [37]:

$$\lambda_j^{(l+1)} = \lambda_j^{(l)} \cdot \frac{s_j^C \sum_{i=1}^{N} t_{ij}^C (\Delta\theta_i)^{-1} + s_j^A \sum_{p=1}^{P} \varepsilon_{pj}^A C_A^p}{\sum_{k=1}^{M} (s_k^C + s_k^A) \lambda_k^{(l)}}$$

This approach has been successfully applied to a dual-mode camera with a coded mask. However, its applicability to cameras that utilize active masks is limited. This is because the coded aperture image requires a greater number of iterations to converge compared to the Compton image in such camera setups [39, 44]. Thus, synchronized iteration between the two modalities may not be appropriate. Apart from the issue with convergence rate, the algorithm described in Eq. 5 essentially combines two images corrected based on Compton and coded aperture data, with the weighting factor determined by the detection efficiency of the corresponding modality:

$$\lambda_j^{(l+1)} = \lambda_j^{(l)} \cdot \frac{s_j^C \sum_{i=1}^{N} t_{ij}^C (\Delta\theta_i)^{-1} + s_j^A \sum_{p=1}^{P} \varepsilon_{pj}^A C_A^p}{\sum_{k=1}^{M} (s_k^C + s_k^A) \lambda_k^{(l)}}$$

In dual-mode cameras utilizing active masks, the detection efficiency of single-interaction events typically surpasses Compton efficiency significantly. This causes the image derived using Eq. 5 to closely resemble the image reconstructed solely with coded aperture data, failing to effectively combine data from both modalities. To address these issues, Xu introduced a hybrid imaging method for cameras equipped solely with active masks [39]. Instead of simultaneously incorporating data from both modalities in each iteration for image correction, this method involves correcting the image with coded aperture data multiple times within each iteration step. These additional iterations for image correction (referred to as "sub-iterations" from here on) aim to align the convergence rate of the two modalities. Apart from the sub-iterations, the algorithm substitutes the weighting factors of the corrected images with an adjustable parameter. The iterative process of the algorithm can be expressed as:

Algorithm 1: Iteration Process of Hybrid Imaging

for l ← 0 to L do
    λ_A,(0)_j ← λ^(l)_j
    Begin sub-iteration;
    for r ← 1 to n₁ do
        λ_A,(r)_j = λ_A,(r-1)_j · [∑_{p=1}^{P} ε_{pj}^A C_A^p] / [∑_{k=1}^{M} ε_{pk}^A λ_A,(r-1)_k]
    λ_C,(l)_j = λ^(l)_j · [∑_{i=1}^{N} t_{ij}^C (Δθ_i)^{-1}] / [∑_{k=1}^{M} s_k^C λ^(l)_k]
    λ^(l+1)_j = w · λ_C,(l)_j + (1 - w) · λ_A,(n₁)_j

The parameter $l$ represents the total iterations for the reconstruction, $n₁$ denotes the number of sub-iterations conducted in each iteration step, and $w$ denotes the adjustable weighting factor. Additionally, the initial value $\lambda^{(0)}$ can be set as either the image reconstructed using a simple back-projection algorithm or uniform across the image space. Although the feasibility of the aforementioned algorithm for dual-mode imaging systems with active masks was verified via Monte Carlo simulations [39], a substantial drawback of the algorithm is identified in the coded aperture sub-iterations. Despite taking the weighted average of the Compton and coded aperture images to compensate for discrepancies between the two modalities, the coded aperture sub-iterations adopted the same iteration formula as the single-modality case. This formula is derived from the single-modality measurement model for coded aperture imaging. It focuses solely on optimizing the logarithmic likelihood of the coded aperture measurements rather than the combined log-likelihood of both coded aperture and Compton measurements. The oversight of additional information brought by the Compton dataset during the sub-iterations leads to a divergence from the intended search direction derived from the dual-modality measurement model. This deviation accumulates with each sub-iteration and results in failure to optimize the dual-modality log-likelihood, which serves as the objective function for optimization. It may even lead to a decreasing value of the objective function during the sub-iterations. Consequently, the existing hybrid imaging method can perform poorly in some circumstances, exhibiting inferior results compared to coded aperture imaging on the developed camera, as can be seen from the results in Sec. III.

To address the issues with the existing hybrid imaging method, a modified algorithm was developed based on the existing framework. Aimed at achieving better applicability across a wide energy range (300 keV–1 MeV) and for various camera configurations, we focused on improving the compatibility of the coded aperture sub-iterations with the dual-modality measurement model. The imaging model can be expressed with the combined probability of acquiring two independent sets of measurements both subject to Poisson statistics. These measurements involve the full-energy event counts $X$ in each detector unit and list-mode Compton events $A$ with corresponding counts $z$, from a given source distribution $\lambda$:

$$P_{\text{Hybrid}}(X, A, z|\lambda) = P_{\text{Coded}}(X|\lambda) \cdot P_{\text{Compton}}(A, z|\lambda)$$

$$= \prod_{p=1}^{P} \prod_{j=1}^{M} \frac{e^{-t_{pj}^A \lambda_j} (t_{pj}^A \lambda_j)^{X_{pj}}}{X_{pj}!} \cdot \prod_{i=1}^{N} \frac{e^{-T \sum_{k=1}^{M} s_k^C \lambda_k} (T \sum_{k=1}^{M} s_k^C \lambda_k)^{z_i}}{z_i!} \cdot p(A_i)$$

where $X_{pj}$ denotes the number of photons emitted from source pixel $j$ that contribute to the counts in detector unit $p$ [45], $z_i$ denotes the contribution of photons emitted from source pixel $j$ to event $i$, $T$ is the measurement time, and $p(A_i)$ is a likelihood term derived when applying Bayes' rule and is irrelevant to the iteration formula [46]. From this model, the log-likelihood can be derived:

$$L(X, A, z|\lambda) = \ln(P_{\text{Hybrid}}(X, A, z|\lambda))$$

$$= \sum_{p=1}^{P} \sum_{j=1}^{M} X_{pj} \ln(t_{pj}^A \lambda_j) + \sum_{i=1}^{N} \sum_{j=1}^{M} z_{ij} \ln(t_{ij}^C \lambda_j) - \sum_{j=1}^{M} (s_j^A + s_j^C) \lambda_j + \text{constant}$$

Note that terms that remain constant during iterations are discarded. Then the E-step of the ML-EM algorithm is applied by replacing variables $X$ and $z$ with their expected values under the reconstructed source distribution at the current iteration $l$:

$$Q(\lambda|\lambda^{(l)}) = E(L(X, A, z|\lambda)|\lambda^{(l)})$$

$$= \sum_{p=1}^{P} \sum_{j=1}^{M} E(X_{pj}|\lambda^{(l)}) \ln(t_{pj}^A \lambda_j) + \sum_{i=1}^{N} \sum_{j=1}^{M} E(z_{ij}|\lambda^{(l)}) \ln(t_{ij}^C \lambda_j) - \sum_{j=1}^{M} (s_j^A + s_j^C) \lambda_j + \text{constant}$$

The iteration formula can then be derived by setting the gradient of the objective function $Q(\lambda|\lambda^{(l)})$ to 0, which leads to Eq. 5. Based on this hybrid imaging model, the iteration formula of the sub-iterations in Algorithm 1 can be modified accordingly. Given that only the coded aperture estimation of the source distribution is updated during sub-iterations while Compton estimates remain unchanged, the expected values of $z_{ij}$ utilized at the E-step should correspond to the estimated source distribution before applying sub-iterations, $\lambda_j^{(l)}$. With this modification, the objective function for the sub-iterations can be expressed as:

$$Q(\lambda|\lambda^{(l)}, \lambda_{A,(r-1)}) = \sum_{p=1}^{P} \sum_{j=1}^{M} E(X_{pj}|\lambda_{A,(r-1)}) \ln(t_{pj}^A \lambda_j) + \sum_{i=1}^{N} \sum_{j=1}^{M} E(z_{ij}|\lambda^{(l)}) \ln(t_{ij}^C \lambda_j) - \sum_{j=1}^{M} (s_j^A + s_j^C) \lambda_j$$

The modified iteration formula can then be derived by setting the gradient of Eq. 10 to 0:

$$\lambda_{A,(r)}j = \lambdaj \cdot \frac{\sum$$}^{P} \varepsilon_{pj}^A C_A^p + \sum_{i=1}^{N} t_{ij}^C (\Delta\theta_i)^{-1} \frac{\sum_{k=1}^{M} t_{ik}^C \lambda_k^{(l)}}{\sum_{k=1}^{M} s_k^C \lambda_k^{(l)}}}{\sum_{k=1}^{M} \varepsilon_{pk}^A \lambda_{A,(r-1)}_k + s_j^C

Finally, the modified hybrid image reconstruction algorithm is given by substituting the formula of the sub-iterations in Algorithm 1 with Eq. 11. It should be noted that the modified algorithm may not perform well in the initial stages of the reconstruction process (i.e., the first few iterations) since the Compton estimation of the source distribution may undergo rapid changes. This may cause the coded aperture estimates to be corrected to inaccurate values when applying Eq. 11. Thus, the original formula in Algorithm 1 is retained in the first iteration.

III. RESULTS

The dual-mode and hybrid imaging performance of the developed Compton camera was evaluated using various radioactive isotopes with gamma-ray energies ranging from 60 keV to 1.274 MeV. A list of radioactive sources used for performance evaluation is provided in Table 1 [TABLE:1]. Data was collected under two distinctive scenarios: one involving measurements with a single point-like radioactive source and the other combining data from two measurements of the same point-like radioactive source placed at different locations with a predetermined opening angle. The single point source data serves to validate the core functionality of the developed camera to perform Compton, active coded aperture, and hybrid imaging, as well as to assess the sensitivity of different imaging methods. The double point source data was adopted for systematic evaluation of the imaging resolution of the two single-modality imaging methods and for comparing image quality between the proposed modified hybrid imaging technique and existing methods.

A. Verification of Basic Imaging Functionality

The verification of basic functionality for the developed camera was conducted with single point sources listed in Table 1 to ensure that Compton, active coded aperture, and hybrid imaging can be properly performed. To verify the validity of the modified hybrid imaging method, simulations were also performed for the corresponding isotopes, with some of the reconstructed images showcased in Fig. 5 [FIGURE:5] as an example.

Data collection was carried out for all isotopes with the camera to perform image reconstruction with different imaging methods. The resulting reconstructed images are depicted in Fig. 5. All Compton data undergo 30 iterations for reconstruction, while the iterations (or total sub-iterations) required for coded aperture data vary across different isotopes as indicated in the figure captions. The full width at half maximum (FWHM) values of these images are listed in Table 2 as a rough estimate for the angular resolution of the camera with different imaging methods. These results suggest that the modified imaging method can achieve angular resolutions equivalent to or better than those of the single-modality imaging methods, indicating that the proposed method has great potential for enhancing the imaging performance of the camera, which will be further analyzed in Sec. III D.

B. Evaluation of Imaging Sensitivity

To evaluate the sensitivity of the developed camera in Compton and coded aperture imaging, an additional measurement was conducted by placing the $^{241}$Am and $^{137}$Cs sources specified in Table 1 approximately 7.5 meters away from the camera, with the angular position of the sources being $(0^\circ, 0^\circ)$, to acquire coded aperture and Compton data, respectively. The camera is capable of localizing the $^{241}$Am source through coded aperture imaging within 10 seconds of data collection, obtaining a total of 1596 full-energy events. However, a decrease in sensitivity is observed for the $^{137}$Cs source compared to low energies. A total of 30 seconds is required to localize the $^{137}$Cs source using 1729 collected full-energy events. Nonetheless, Compton imaging displays slightly better sensitivity at such energies, being capable of localizing the $^{137}$Cs source within 15 seconds. The resulting count rate for full-energy Compton events is 3.47 cps (52 events collected within 15 seconds), corresponding to a detection efficiency of 91.32 cps/(µSv/h) under the dose rate of 0.038 µSv/h established by the setup. Additionally, to compare the sensitivity of hybrid imaging with the two single-modality imaging methods, the same measurement with the $^{137}$Cs source was performed using hybrid and modified hybrid imaging. Both hybrid imaging methods are capable of localizing the $^{137}$Cs source within 10 seconds, indicating that hybrid imaging can effectively improve the sensitivity of the developed camera. The aforementioned results regarding the time required to localize sources with different methods are summarized in Table 3 [TABLE:3].

The enhanced sensitivity of the hybrid imaging method can be attributed to its excellent capability of extracting physical information. Although the coded aperture and Compton imaging data collected within a very short period both contain numerous artifacts, these artifacts typically do not coincide spatially between the two modalities. In addition, the hotspot can be reconstructed at the position of the source in both images despite the presence of high-intensity artifacts. Through the weighted summation employed in the hybrid image reconstruction process, the intensity of source pixels in the vicinity of the radioactive source is amplified while artifacts are suppressed.

C. Evaluation of Intrinsic Angular Resolution

To systematically evaluate the angular resolution of Compton and active coded aperture imaging with the developed camera, the Rayleigh criterion [47] was employed. This evaluation was performed on data collected using two identical point sources with multiple isotopes. The results of coded aperture imaging are illustrated in Fig. 6 FIGURE:6 and 6(b) for $^{241}$Am and $^{137}$Cs sources. These results reveal that while the two $^{241}$Am sources can be distinguished at an opening angle of $5^\circ$, differentiation between the two $^{137}$Cs sources is only achievable when the opening angle reaches $10^\circ$. These findings indicate that the angular resolution of the developed camera in coded aperture imaging can reach $5^\circ$ at a few tens of keV but degrades at higher energies. On the other hand, the results of Compton imaging for $^{137}$Cs and $^{22}$Na sources shown in Fig. 6(c) and 6(d) suggest an angular resolution slightly better than $15^\circ$ at energies of 662 keV and 1274 keV.

D. Evaluation of Hybrid Imaging Performance

To evaluate the effectiveness of the modified hybrid imaging method, imaging data obtained with two identical point sources were reconstructed using both hybrid and single-modality imaging methods. The hybrid imaging method previously proposed by Xu [39] was also utilized for comparison. For each set of data, the iterations required for image reconstruction were consistent across different imaging methods, with the iterations for coded aperture imaging matching the total sub-iterations for hybrid imaging.

To compare results from different imaging methods, a reference source distribution was generated by applying 2-D blurring to the true source distribution to simulate data acquired with high-resolution cameras such as conventional coded aperture cameras [48], using a Gaussian filter with a standard deviation of $2^\circ$. Subsequently, image quality was evaluated with the normalized root mean squared error (NRMSE) between the reconstructed images and the reference source distributions [49]:

$$\text{NRMSE}(\lambda_r|\lambda_T) = \sqrt{\frac{1}{M} \sum_{j=1}^{M} (\lambda_{r,j} - \lambda_{T,j})^2}$$

The imaging results are depicted in Fig. 7 [FIGURE:7], with corresponding NRMSE values detailed in Table 4 [TABLE:4]. Through comparison, it is evident that the hybrid imaging method outperforms both single-modality imaging methods and the previously proposed hybrid imaging technique in terms of image quality. This advantage enables the extraction of additional physical information regarding the spatial distribution of radioactive sources, thereby leading to enhanced gamma-ray imaging capabilities.

IV. CONCLUSION

In situations such as source-term monitoring and consequence management in NPPs, an isotropic 4π FoV for free-moving measurement of complex source distributions and compatibility across a wide energy range is typically required for gamma-ray imaging devices. In this article, we presented the development and performance evaluation of a Compton camera based on a spherical detector array. The camera consists of 80 GAGG detector units, with the configuration optimized for Compton imaging, along with a multichannel electronics system based on ASIC. To achieve effective imaging across a wide energy range, the active coded aperture imaging capabilities of the developed camera were also tested. The imaging evaluation of the camera reveals good performance for both modalities, achieving angular resolutions of $15^\circ$ for Compton imaging at 662 keV and up to $5^\circ$ for coded aperture imaging at 60 keV. The camera is capable of localizing a 765.9 µCi $^{137}$Cs source placed 7.5 meters away (corresponding to a dose rate of 0.038 µSv/h) within 15 seconds through Compton imaging. For coded aperture imaging, localization of the $^{137}$Cs source requires 30 seconds, whereas localization of a 478.5 µCi $^{241}$Am source at the same distance can be accomplished in 10 seconds.

Additionally, a modified hybrid imaging method that combines Compton and coded aperture data was devised based on existing methods and applied to the camera to further enhance imaging performance. Through measurements involving various radioactive isotopes, it has been verified that the modified hybrid imaging method exhibits better imaging quality and improved sensitivity compared with Compton, coded aperture, and previously proposed hybrid imaging methods. With the modified hybrid imaging method applied, the developed camera can achieve high sensitivity and fine resolution for gamma-ray imaging across a wide energy range (30 keV–2 MeV) with isotropic 4π FoV.

With the excellent imaging performance achieved using the developed Compton camera in conjunction with the modified hybrid imaging method, free-moving 3-D mapping of radioactive sources across broad energy ranges is made feasible. This process involves integrating the camera with a simultaneous localization and mapping (SLAM) system to obtain 3-D scene data and then employing the scene data fusion approach through 3-D image reconstruction methods based on the acquired data. Currently, we have conducted preliminary tests on a prototype of such a system by combining the Compton imaging capability of the developed camera with a SLAM system, which yielded promising results. Further testing and enhancements of the system are in progress, with subsequent progress and results to be detailed in upcoming reports.