Computed tomography with fast-neutron sources

Lawrence Livermore National Laboratory (LLNL) is near-completion of a quasi-monoenergetic neutron source for fast-neutron imaging and computed tomography (CT). The source is expected to produce 10-MeV neutrons with an on-axis flux of ~10 11 per second per steradian through a collimated aperture with a ~7-degree opening angle. The application for this source is imaging and CT of low-Z materials heavily shielded by high-Z materials. Fast-neutron imaging and CT is a non-destructive technique for very thick objects. We have radiographed a variety of objects using various sources of fast neutrons. We will discuss our CT reconstruction methods and results from these measurements. We will also discuss our results as they relate to our expectations of the near-complete neutron source at LLNL.


Background
Neutron imaging was first demonstrated by Hartmut Kallmann and Ernst Kuhn ca.1935 (c.f.[1]), shortly after the discovery of the neutron by Chadwick in 1932 [2].Neutron radiography and x-ray radiography have mutually grown as technical analogs of each other.As such, both neutron and x-ray techniques may use similar tools such as CT reconstruction methods.However, there are fundamental differences that require slightly different techniques.X-rays and gamma-rays (i.e.high-energy x-rays) interact with the electrons of an atom as well as the nucleus of an atom (if the energies are large enough) due to the electromagnetic properties of the photon.In general, this implies that photons interact (i.e.scatter) more readily with higher-Z materials.Neutrons, however, have no measurable net electric charge and can only interact with the nucleus of the atom via strong-nuclear interactions.The reduced interaction field allows the neutrons to penetrate further than photons, providing additional complementary depth to the probes of x-ray radiography.
A simple approach for CT reconstruction of fast neutrons is to treat the neutrons as hardened x-rays.This approach has an advantage of using existing x-ray CT tools.The Constrained Conjugate Gradient (CCG) method for CT reconstruction (c.f.[3,4]) is one of many techniques that has been used for neutron imaging at LLNL. Figure 1 shows the comparison of neutron-based CT using backprojection (BP) and CCG of a test object of uranium and plastic.However, it is expected that since the nuclear interactions of fast-neautrons are different than x-rays and even their slower neutron siblings (i.e.thermal, epithermal), the scatter field will be very different; which may indicate the need for a different approach to CT reconstruction or at minimum new scatter correction algorithms.The scatter fields for fast neutrons depend on double-differential nuclear cross-sections that differ from isotope to isotope and have no trends similar to x-ray crosssections such as Compton scattering (e.g.E-and Z-dependence, c.f. [5]).Compton scattering, the dominant scattering in x-ray radiography, is sometimes grouped with multiple scattering and subsequently treated as flat or smooth.For example, if an object is homogeneous, the convolution of angular distributions is a convolution of itself, multiple times over the energy range of downscattered photons.For non-homogeous objects, the convolutions become complex and realistically have to be dealt with on a case-by-case basis, e.g.model-based.Summing over the constituents of a voxel to estimate the scattering behaior for a generalized ensemble (i.e.independent particle model) has many limitations from theory (e.g.[6]) to practice (e.g.[7]).X-ray

Introduction
There are many industrial applications that could benefit from fast-neutron radiography and CT.For example, steam flow and collection points in thick furnaces or engines, fuel combustion in heavy combustion engines, corrosion in bridge anchors and building foundations, etc… The common denominator for many of these examples, is low-Z imaging behind high-Z shielding.Take for example, the cross-sections for uranium-238 (the dominant isotope in in natural-or depeleteduranium) with Z=92 and hydrogen with Z=1, see Fig. 2, data taken from [12].Clearly, the lowest cross-section value for the displayed energy range in Fig. 2 is in the range of 10-to 14-MeV.This represents the energy range for which neutrons are most transparent in uranium.Notice that below 2 MeV, the cross-sections for hydrogen and uranium are sufficiently close, such that the attenuation length is dependent on number density alone, which may not be useful in certain situations.For energies above 15 MeV, the cross-sections for hydrogen become very small, which defeats the purpose of imaging hydrogen behind uranium.So, if our application is to measure hydrogenous materials in uranium shielding, the range of 10-to 14-MeV would be optimal.Additionally, we know that the total cross-sections for nitrogen-14 and oxygen-16 (the constituents of air) begin increasing above 10-MeV.To decrease backgrounds from these channels, it is useful to keep the neutron energies between 8-and 10-MeV.Altogether, this motivates building a neutron source that is 10-MeV.Moreover, the neutron source should be mono-energetic, to reduce backgrounds and maintain the best transmission.[12] for 238 U (blue) and 1 H (orange). Figure 3: Total neutron cross-section from ENDF [12] for 14 N (blue) and 16 O (red).

Measurements
Using the nuclear data, we embarked on a campaign to test the feasibility of fast-neutron imaging with quasimonoenergetic neutrons, see [13][14][15][16][17][18].Our measurements were performed at the Ohio University Accelerator Laboratory using the d+D reaction in a 3-atm-a, 8-cm D2 gas cell, with a 5-µm tungsten window.The deuteron energy was set at 7.5 MeV and the neutrons were measure with time-of-flight techniques using scintillator detectors.The source, transmitted, and scattrered neutrons were focused on a 4-cm thick BC400 scintillator.The scintillation photons were reflected from a turning mirror and collected with a f/1.2 lens-coupled, 1k x 1k CCD Princeton Instruments camera.A beam dump was situated behind the imaging system that extended about 20 meters.The distance from the source to the object was about 2 meters and the distance from the object to the image plane was also about 2 meters.The magnification was about 2. The pixel size at the image plane was 0.25 mm.The measured (edge) resolution was 0.75 mm.Exposure times were generally 20 minutes per frame (angle).
For our approach, our measurement choice was to look at plastic materials within various Z shells with a variety of image quality indicators (IQIs) and test objects, see figures 4-6.For the object in Fig. 5, the densities of the three plastic blocks 1.90, 1.87, and 1.84 g/cm 3 , in descending order.

Figure 6: Plastic rod insert (upper) and tungsten sleeve (middle). The plastic fits into the hollow core of the tungsten (lower). Units are given in inches. Maximum areal
density is 190 g/cm 2 .
Our reconstruction tool is an application called Constrained Conjugate Gradient [3].This code is typically used for xray CT but has been used for the fast-neutron CT to assess its effectiveness.The CCG code uses a least-squares approach for its cost function.The iterative procedure can be chosen in the sinogram domain or in the image domain.The optimization method is a descent approach for a set of conjugate directions, i.e. conjugate gradient (CG).Basically, the iteration of the object vector is: 10th Conference on Industrial Computed Tomography, Wels, Austria (iCT 2020), www.ict-conference.com/2020where   is the step length and:  # = −  +     is the step direction;   ≡ (  )  is the transpose of the gradient of : ℝ  ⟶ ℝ;  ∈ ℝ  .The quantity,   , is the CG update parameter.For the analysis in this paper, the Polak-Ribéire parameter [18] was used,
The constraints for the CCG code reduce the number of degrees-of-freedom, which improves accuracy.The constraints range from upper-and lower-bound scalar values, as well as vector values.Lagrange penalties are assigned to each constraint and updated during the calculations.Our CCG code does not offer scatter corrections of any kind, especially those used for other reconstruction codes, e.g.[8][9][10][11]22].We felt that for the first foray into the reconstruction algorithms, simplest is best.Applying photon scatter corrections to neutron events is disingenuous and self-deceptive, even if the results appear accurate.

Discussion
The results for the CCG reconstruction of the data collected for the objects in figures 5-7 are shown in figures 8-10.Lineouts are also shown in Figs.8-10 to highlight some of the observed features.The reconstruction domain for the reconstructions shown in Figs.8-10 is the sinogram domain.Rerunning of the reconstruction in the image domain will be done to determine if the solutions are domain dependent, however, they were not accomplished by the time of this publication due to time constraints.The fuzziness of the reconstructions in Figs.8-10 may be from scattering of fast-neutrons and could also be from large reaction volumes in the scintillator (recall our scintillator is 4 cm thick).One of our objectives for these measurements was to determine material differences and density differences through profile differences.First, the object shown in figure 5 contains three plastic blocks of similar size and shape but different desnsities, 1.90, 1.87, and 1.84 g/cm 3 , in descending order.Our CCG reconstruction projection of that object is shown in Fig. 10.The breaks between the plastic blocks is somewhat apparent around channels 130 and 260.However, the intensity profiles are not conclusive.Second, the object shown in figure 4 has three major material types, Pb, Al, and polyethylene (PE).The results of the reconstructed projection in Fig. 11 indicates some subtle differences between the different materials, most notably the Pb.The lineout profile shown in Fig. 11 (right) shows all three materials side-by-side on the left-most hump.The Al, on the left shoulder, is clearly lower than the PE on the right shoulder.These differences are a function of the neutron cross-sections and areal density of the materials.Given the successes of the measurements above, we have embarked on building a brighter and more compact imaging system.The accelerator will impinge 7.0-MeV deuterons into a windowless gas target at an average power of 2100 watts.Deuterium gas will be cycled through the windowless gas target [23] at a repetition rate of 3600 rpm and provide a pressure of 3-5-atm-a at the interaction position at the time of beam injection.The duty cycle of the gas pumping system provides the downtime necessary to prevent gas flow upstream into the accelerator sections.The source is expected to produce 10-MeV neutrons with an on-axis flux of ~10 11 per second per steradian through a collimated aperture with a ~7-degree opening angle.The final result will be a beam that is 20x times brighter than the OUAL source, reducing the above CT times of 20 minutes per exposure to a minute per exposure.Our camera system is a f/1.0 lens-coupled CCD (4k x 4k).Our system will also have a 13 C solid target for broadband exposures and a Varian flat-panel CCD for applications not requiring sub-mm resolution.

Conclusions
Lawrence Livermore National Laboratory (LLNL) is near-completion of a quasi-monoenergetic neutron source for fast-neutron imaging and CT and should be ready for CT in December 2020.Our measurements with a university source, provides a promising outlook for this technology.We have an extensive campaign to study the scatter from various materials to determine the correct prescription for scatter in reconstruction algorithms.Part of this effort will be to study the microscopic cross-sections for isotopes of interest.We plan to study reaction channels for scintillators to understand the effects of transmitted and scattered neutrons.

Figure 1 :
Figure 1: Comparison of CT Reconstruction of neutron radiographs of a test object (left) using backprojection (middle) and CCG (right)

Figure 5 :
Figure 5: Test object of an alloyed uranium shell with various density plastic cylinder blocks.A beryllium sleeve is located in the center.Photograph shown in Fig. 1.

Figure 7 :
Figure 7: (Above) Reconstructed projection of IQI featured in Fig. 4, using CCG.(Lower) Lineout of the CCG reconstruction along solid line shown above.

Figure 10 :
Figure 10: (Left) Reconstructed projection of object in Fig. 5 using CCG.(Right) Lineout profile of projection along solid line shown.

Figure 11 :
Figure 11: (Left) Reconstructed projection of object in Fig. 4 using CCG.(Right) Lineout profile of projection along solid line shown.