The world’s first deep underground repository for spent nuclear fuel will soon start operations in Eurajoki, Finland. Disposal tunnels have been excavated 430 meters below the ground surface in bedrock, and the spent nuclear fuel will be placed in deposition holes in copper canisters. After the fuel is disposed of, it will be practically unreachable [1]. For safeguarding nuclear material, all fuel items need to be reliably verified prior to disposal in the geological repository. Fuel assembly integrity is investigated to make sure all nuclear material stays in peaceful use.

Passive Gamma Emission Tomography (PGET) is a non-destructive assay method that allows for accurate 2D slice images of the fuel assembly to be reconstructed. Fuel assembly types we have studied are rectangular or hexagonal objects, about 4 meters long and about 15 cm in diameter, consisting of a bunch of 63-126 individual fuel rods in a fixed geometric arrangement. Spent nuclear fuel emits gamma-rays at a very high rate and with specific energies, providing a method to verify the presence of fuel rods in the assemblies. Gamma emission data is collected with the torus-shaped PGET device which has two highly collimated CdZnTe gamma detector banks that rotate a full 360 degree around the fuel assembly, which is placed in the central hole of the device. Gamma-rays are significantly attenuated in the fuel material, and thus the attenuation map of the object is reconstructed simultaneously with the activity map. The mathematical approach to this unique inverse problem is described in another presentation in this minisymposium, while the context of the method and the measurements are presented in more detail in this contribution [2,3].

During 2017-2022, over 100 spent nuclear fuel assemblies have been measured at the Finnish nuclear power plants with the PGET method [3,4]. The imaged fuel has had a range of characteristics and 10 different geometrical types. The measurement campaigns have concentrated on refining the measurement parameters for improving detection of possible empty rod positions. Data acquisition gamma energy windows have been fine-tuned, different sets of angles out of the full 360 angle data have been used in the reconstructions and different methods for quantitatively investigating the image quality have been developed. Even the use of less abundant but higher-energy and higher-penetrating gamma-rays were investigated to improve the detection of missing rods in the central parts of the fuel.

The PGET method has shown to detect individual missing rods with high confidence and has even demonstrated the ability to reproduce intra-rod activity differences. We have also shown that the method is able to distinguish activity differences in the axial direction of the fuel, which we show with a set of axial measurements conducted over a fuel assembly with partial-length fuel rods.

A variety of results from the measurement campaigns will be presented, illustrating the usability of the method for safeguards purposes in the Finnish context.

[1] www.posiva.fi

[2] R. Backholm, T. A. Bubba, C. Bélanger-Champagne, T. Helin, P. Dendooven, S. Siltanen. Simultaneous reconstruction of emission and attenuation in passive gamma emission tomography of spent nuclear fuel, Inv. Probl. Imag. 14: 317-337, 2020.

[3] P. Dendooven, T.A. Bubba. Gamma ray emission imaging in the medical and nuclear safeguards fields, Lecture Notes in Physics 1005: 245-295, 2022.

[4] R. Virta, R. Backholm, T. A. Bubba, T. Helin, M. Moring, S.Siltanen, P. Dendooven, T. Honkamaa. Fuel rod classification from Passive Gamma Emission Tomography (PGET) of spent nuclear fuel assemblies, ESARDA Bulletin 61: 10-21, 2020.

[5] R. Virta, T. A. Bubba, M. Moring, S. Siltanen, T. Honkamaa, P. Dendooven. Improved Passive Gamma Emission Tomography image quality in the central region of spent nuclear fuel, Scientific Reports 12: 12473, 2022.

In this work, we study a Compton Imager, made of an array of scintillation crystals. This imaging system differs from a more classical Compton camera since the sensor array acts simultaneously as a set of scatterers and absorbers. From the recorded data, the objective is to localize the positions of point-like sources responsible for the emission of the measured radiation. The inverse problem is formulated within a Bayesian framework, and a Markov chain Monte Carlo method is investigated to infer the source locations.

A Passive Gamma Emission Tomography (PGET) device is part of the IAEA-approved tools for safeguards inspections of spent nuclear fuel assemblies. In Finland, PGET has been selected to be part of the nuclear safeguards procedures at the geological repository for spent nuclear fuel (SNF), ONKALO [1]. In recent years, we have developed the PGET method for this purpose. This contribution will focus on the data analysis and image reconstruction methods. It will show how the methods chosen are dictated and influenced by the requirements and the physics of the application, as well as the characteristics of the tomographic device that is being used. The characteristics and performance of the reconstruction algorithm will be illustrated with examples from PGET measurements at the SNF storage pools at the Finnish nuclear power plants. The design and operation of the PGET device and the most important results will be discussed in a separate contribution to this minisymposium.

A safeguards inspection aims to verify that all nuclear material is present as declared, to assure that none has been diverted for non-declared use, most specifically the development of nuclear weapons. Because of this requirement, a PGET measurement should not assume any prior information on the object under tomographic investigation. An SNF assembly consists essentially of rods of highly radioactive uranium dioxide, highly attenuating for gamma rays, immersed in non-radioactive water with much lower gamma ray attenuation. Good images thus require some form of attenuation correction. It is in practice very challenging to independently measure an attenuation map of SNF, e.g. by transmission tomography. Also, given the binary nature of the object (fuel rods and water), a good attenuation map needs knowledge of the geometry of the SNF. We have dealt with this conflict between the need of a good attenuation map and the requirement not to use prior information by developing an image reconstruction algorithm that reconstructs a gamma ray emission and attenuation image simultaneously, mathematically treating both in the same way.

The image reconstruction involves 2 steps. The first step is a filtered back-projection (FBP) which uses no prior information at all. Experimentally we observe that the quality of the FBP image is good enough to deduce the SNF assembly geometry. The second step, which produces the final image, is an iterative image reconstruction algorithm which uses the knowledge of the assembly geometry as a regularization term, thus favouring images that resemble the SNF assembly type identified from the FBP image in step 1. The reconstruction problem is formulated as a constrained minimization problem with a least squares data mismatch term (i.e. it implicitly assumes a Gaussian distribution for the noise) and several regularization terms. Next to the geometry regularization term, there are 2 terms related to corrections for the variation of the sensitivity amongst the detectors. Physics knowledge is used to establish upper and lower bounds on the image of attenuation coefficients. The attenuation image is constrained to values between the attenuation coefficient of the relevant gamma ray energy in water (lower bound) and uranium dioxide (upper bound). Most often, imaging is focused on the 662 keV gamma rays emitted by 137Cs, the dominant gamma ray emitter in SNF. The PGET image reconstruction method and its practical implementation will be discussed in some detail. Full details are given in [2-4].

Since 2017, over 100 different SNF assemblies have been measured at the Finnish nuclear power plants. Some representative examples from this vast data set will be used to highlight the performance of the image reconstruction method, especially in identifying missing fuel rods [3,5].

Points for improvement that have been identified over the past few years will be discussed. These are e.g. careful selection of the set of viewing angles, careful selection of the gamma ray energy windows and combining sinograms from different gamma ray energy windows. Improving imaging of the centre of spent fuel assemblies is a major development goal.

[1] www.posiva.fi

[2] P. Dendooven, T. A. Bubba. Gamma ray emission imaging in the medical and nuclear safeguards fields, Lecture Notes in Physics 1005: 245-295, 2022.

[3] R. Virta, R. Backholm, T. A. Bubba, T. Helin, M. Moring, S. Siltanen, P. Dendooven, T. Honkamaa. Fuel rod classification from Passive Gamma Emission Tomography (PGET) of spent nuclear fuel assemblies, ESARDA Bulletin 61: 10-21, 2020.

[4] R. Backholm, T. A. Bubba, C. Bélanger-Champagne, T. Helin, P. Dendooven, S. Siltanen. Simultaneous reconstruction of emission and attenuation in passive gamma emission tomography of spent nuclear fuel, Inv. Probl. Imag. 14: 317-337, 2020.

[5] R. Virta, T. A. Bubba, M. Moring, S. Siltanen, T. Honkamaa, P. Dendooven. Improved Passive Gamma Emission Tomography image quality in the central region of spent nuclear fuel, Scientific Reports 12: 12473, 2022.

This talk addresses the overdetermined problem of inverting the n-dimensional cone (or Compton) transform that integrates a function over conical surfaces in $\mathbb{R}^n$. The study of the cone transform originates from Compton camera imaging, a nuclear imaging method for the passive detection of gamma-ray sources. We present a new identity relating the n-dimensional cone and Radon transforms through spherical convolutions with arbitrary weight functions. This relationship leads to various inversion formulas in n-dimensions under a mild assumption on the geometry of detectors. We present two such formulas along with the results of their numerical implementation using synthetic phantoms.