Computed tomography with fast-neutron sources · Neutron imaging was first demonstrated by Hartmut...

10th Conference on Industrial Computed Tomography, Wels, Austria (iCT 2020), www.ict-conference.com/2020

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Computed tomography with fast-neutron sources

Micah S. Johnson1*, Scott G. Anderson1, Darren Bleuel1, Joseph A. Caggiano1, Peter J. Fitsos1, David Gibson1, Jeff Gronberg1,

James M. Hall1, Roark Marsh1, Andrew Ratkiewicz1, Brian Rusnak1

1Lawrence Livermore National Laboratory, 7000 East Ave., Livermore CA 94550, USA; *[email protected]

Abstract

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

~1011 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.

Keywords: neutrons, fast neutrons, neutron CT

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.

Figure 1: Comparison of CT Reconstruction of neutron radiographs of a test object (left)

using backprojection (middle) and CCG (right)

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 cross-

sections 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 down-

scattered 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

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sources are typically bremsstrahlung which is, by definition, broadband and wash out enhanced scattering effects. Fast neutrons are not expected to play by any of these rules because of their primary interaction medium, the nucleus and all of its shells.

CT reconstruction is based an attenuated line-of-sight signal from a source to a detector. Scatter fields violate this

principle and corrupt the overall image. Methods to mitigate the scatter from x-ray CT includes software and hardware methods.

Hardware tools that are commonly used are grids or collimators. Software techniques for x-ray scatter reduction include

theoretical or empirical models (c.f. [8], [9]), kernel-based methods (c.f. [10]), Monte-Carlo (MC) techniques (c.f. [10]), and

machine-learning applications (c.f. [11]). Hardware approaches, such as collimators, are challenging for fast-neutrons, because

all materials moderate, reflect, and scatter the fast neutrons to one-degree or another. Software techniques are going to be limited

to MC and machine-learning applications for fast-neutrons, because of the complexities using models and kernels for fast

neutrons. This implies that high-performance computing is going to be the baseline analytical tool for fast-neutron imaging.

Iterative methods for CT reconstruction are necessary for noise reduction, artifact corrections, and general image quality

improvement. This is based on the assumption that the collected signals are low, or the source is weak, resulting in low signals.

Low signals have a large amount of statistical fluctuations, which interferes with the analytical reconstruction methods. Applications that require the penetration of fast neutrons, will most likely suffer from large statistical fluctuations. Parallel beam

and fan beam reconstruction tools that are designed to reduce computation infrastructure by only looking at subsets of data, may

not be applicable to fast-neutron CT because of the unique scatter. Cone beam reconstruction has its own challenges. Most

notably, neutron sources are generally not point sources and collimation is not as effective as its x-ray counterpart.

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 depeleted-

uranium) 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.

Figure 2: Total neutron cross-section from ENDF [12] for

238U (blue) and 1H (orange). Figure 3: Total neutron cross-section from ENDF [12] for 14N

(blue) and 16O (red).

Measurements

Using the nuclear data, we embarked on a campaign to test the feasibility of fast-neutron imaging with

quasimonoenergetic neutrons, see [13-18]. 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


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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/cm3, in descending order.

Figure 4: IQI of Al-Pb-Plastic. Maximum areal density of 107

g/cm2.

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 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/cm2.

Our reconstruction tool is an application called Constrained Conjugate Gradient [3]. This code is typically used for x-

ray 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:

𝒙𝒌#𝟏 = 𝒙𝒌 + 𝜶𝒌𝒅𝒌,


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where 𝜶𝒌 is the step length and: 𝒅𝒌#𝟏 = −𝒈𝒌 + 𝜷𝒌𝒅𝒌 is the step direction; 𝒈𝒌 ≡ 𝛁𝐟(𝒙𝒌)𝑻 is the transpose of the gradient of

𝒇:ℝ𝒏 ⟶ℝ;𝒙 ∈ ℝ𝒏. The quantity, 𝜷𝒌, is the CG update parameter. For the analysis in this paper, the Polak-Ribéire

parameter [18] was used,

𝜷𝒌 = 𝒈𝒌9𝟏𝑻 𝒚𝒌‖𝒈𝒌‖𝟐 ,

with the modification: 𝜷𝒌 = 𝐦𝐚𝐱 A𝒈𝒌9𝟏𝑻 𝒚𝒌‖𝒈𝒌‖𝟐 , 𝟎D, as suggested in [20]. In our approach for this effort the step length, 𝜶𝒌, was

determined by a line search using Goldstein conditions, c.f. [21].

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. [8-11, 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).

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 8: (Above) Reconstructed projection

of IQI featured in Fig. 5, using CCG. (Lower) Lineout of CCG reconstruction

along solid line shown above.

Figure 9: (Above) Reconstructed slice of

IQI featured in Fig. 6, using CCG. (Lower) Lineout of CCG reconstruction along

dashed line shown above.

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/cm3, in descending order. Our CCG reconstruction projection of that object is shown in Fig.


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10. The breaks between the plastic blocks is somewhat apparent around channels 130 and 260. However, the intensity profiles

are not conclusive.

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

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.

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

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 ~1011 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 13C 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.

*This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344


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**Special thanks to Jessie Jackson for assistance with CCG reconstruction.

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