ELSEVIER Physica B 241-243 (1998) 1197-1203

On neutron tomography

W. Treimer a'b'*, U. Feye-Treimer a, C. Herz ig a

a Technische Fachhochschule Berlin, Fachbereich Mathematik/Physik, 13353 Berlin, Germany b Hahn-Meitner-lnstitut Berlin, NI, 14109 Berlin, Germany

Abstract

Two- and three-dimensional reconstructions of objects from projections were performed with one- and two-dimen- sional detectors. For three-dimensional reconstruction conventional X-ray films with gadolinium converters as two- dimensional detectors have been used with a spatial resolution of the reconstruction better than 200 lam. For two- dimensional reconstruction small angle scattering and refraction can be used as signals for high resolution tomographic investigations of matter. These interactions can only be detected with a double crystal diffractometer, where the analyzer crystal acts as one-dimensional detector. Inhomogeneities less than 20 lam can be imaged two-dimensionally. ~ 1998 Elsevier Science B.V. All rights reserved.

Keywords: Neutron tomography; Small angle contrast; Refraction contrast; Film imaging

1. Introduction

Non-destructive investigation of matter depends on the structures in matter that shall be imaged. Atomic defects demand radiation with wave lengths of the same order as the inter-atomic dis- tances and special scatter methods. At the length scale of cracks or flaws in stressed materials imaging was performed up to now rather with radiographic or tomographic methods than with scattering. In conventional computerized neutron tomography only absorption is used as the imaging

*Correspondence address. Technische Fachhochschule Berlin, Fachbereich Mathematik/Physik, Luxemburger Stral~e 10, 13353 Berlin, Germany. Fax: + 49 30 4504 2011; e-mail: treimer@hmi.de.

signal [1]. In the framework of this paper it will be demonstrated that absorption is not the only sig- nal which can be used for tomography. The range that can be covered by scattering processes is large: structure sizes from 0.0001 to 50 lam can in prin- ciple be detected. This is understood, if one con- siders all possible interactions a neutron (neutron wave) experiences or causes if it passes through matter. They are

(a) absorption, (b) scattering (all kinds of scattering), (c) excitation, (d) depolarization, and (e) change of the phase of the neutron wave. Usually these signals are registered by means of

neutron detectors, CCD cameras or image plates. In the first part of this paper it is shown that with

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1198 W. Treimer et al. / Physica B 241 243 (1998) 1197-1203

simple X-ray films together with Gd converter foils three dimensional structures also can be imaged from projections (radiographs). The first results were quite promising because this technique can be improved. In the second part it will be shown that especially in the case of small structures refraction and small angle scattering contribute much more to image contrast than absorption and that they can be distinguished from each other. The effect of refraction and small angle scattering is analyzed and demonstrated how that can be used to image structures which are not detected by conventional computerized tomography.

2. Theoretical background

The problem of reconstruction of a two-dimen- sional function from its projection was already sol- ved in the early part of this century by Radon [2]. The reconstruction itself is based on the procedure of filtered backprojection (FBP) [3,4], which as- sumes, that a slice of an object is scanned from 0 to 180 ° (360°). A two dimensional image of this slice then can be reconstructed from these projections. The quality of the reconstruction depends strongly on the number of projections and that no other effects contribute to image contrast than absorp- tion. Using the formalism of FBP means that re- fraction or scattering processes must be avoided. Nevertheless, in the case of small angle scattering or refraction as imaging signals, one can demonstrate that FBP indeed can be used for image reconstruc- tion if and only if only one of the effects contribute to image contrast. That means, that either refrac- tion or small angle scattering may occur.

The absorption of a ray through a two-dimen- sional function p(x, y) is described by a line integral (sometimes called ray integral), the total set of line integrals covering the field is called a projection. A beam (neutrons, X-rays .. . . ) is attenuated by the well known law

where/t(x, y) is the linear attenuation coefficient at (x, y) and ds is an element of length along the path

of the ray through the sample, /l(x,y) is to be reconstructed from line integrals, given in Eq. (1). The line integrals covering the whole field are meas- ured over the angular range of 180 '~ either by rotat- ing a source and a detector around the sample or by rotating the sample. To use FBP it is important to scan the whole angle range from 0 ~ to 180". In special experimental cases of strongly reduced range of scanning angle (e.g. scanning from 0' till 903 FBP cannot reconstruct satisfactory pictures. In that case a modified iterative technique close to ART [5,6] (ART = algebraic reconstruction tech- nique) delivers much better reconstructions. In the case of neutron tomography, the sample was ro- tated from 0" to 180' and the transmitted neutrons were detected either one dimensionally (detector) or two dimensionally (film) (see below).

3. Experiments

3.1. The.film-method

A neutron beam from the BER II reactor (Hahn-Meitner-Institut) was reflected by a perfect Ge-crystal to the experimental set up as shown in Fig. 1. The sample was mounted on a goniometer which delivered the 180 ° rotation. As two-dimen- sional detector X-ray films (commercial dental X- ray film) with Gd converter foils were used, which had the spatial standard resolution ("resolving power") of app. < 300 dpi (85 jam x 85 jam). Any image detected with a converter foil has an inherent lower limit of resolution of ~ 1000 dpi due to its thickness of ,-~ 25 jam. The incident divergence of the neutron beam limited the resolution of the set up to be ~ (100 jam x 200 jam), which was deter- mined by measuring the vertical and horizontal modulation transfer function (MTF). The neutron tomography was performed in such a way, that for each orientation of the sample the X-ray film registered a two-dimensional transmission pattern, a so-called "neutron radiography". Considering this transmission image as a matrix, then each line at the film determines one slice of the object which had to be reconstructed. Depending on the size of the object with respect to the cross section of the

W. Treimer et al. / Physica B 241-243 (1998) 1197 1203 1199

Fig. 1, Experimental set up for neutron tomography.

neutron beam several projections could be made with one film. After each irradiation the sample was rotated about a certain angle and the film was translated perpendicular to the neutron beam into the next irradiation position. 40 Projections were made for one neutron tomography, each one lasted one hour. The images then were digitized and the

slices reconstructed by means of the FBP and a modified ART-method. Then the reconstructed slices were put together to form a three-dimen- sional image. One of the first test objects was a ball bearing. Fig. 2 shows the result.

To isolate different materials in the sample, ab- sorption-isosurfaces have been defined and imaged and other parts of the reconstruction were omitted. The balls in the bearing in Fig. 2 are surrounded inhomogeneously with fat-like material, which ap- parently influences the imaging of the balls. The interesting image is number (3) of the ball bearing. One clearly can see e.g. the snapping cage of the ball bearing and that it contains an additional structure (5) (glass fibres based reinforced poly- amide).

The advantages of this method of tomography are the good spatial resolution ( < 100~tm× 200 ~tm) and that no complicated and expensive instruments or devices must be used. The disadvan- tage is the restriction to 256 gray levels for all intensity levels of the transmitted beam. The film method, however, can be improved, if a more in- tense neutron beam, a better incident beam col- limating and some more mathematics for picture restoring can be used. With these improvements, a spatial resolution better than 50 ~tm x 50 ~tm is possible.

Fig. 2. Neutron computerized tomography of a ball bearing: (1) the whole object, (2) the ball bearing without upper sealing ring, (3) the snapping cage, (4) the steel cage with balls, (5) glass fibres strengthening structure within the snapping cage of image (3).

1200 HI. Treimer et al. / Physica B 241-243 (1998) 1197-1203

3.2. High resolution neutron tomography

Beside absorption there are two additional fun- damental interactions which can be used for to- mographic investigations of matter: Small angle scattering (SAS) and refraction. The impulse to investigate these interactions in the connection with computerized tomography was the challenge to detect and image structures embedded in homo- geneous matrices, which do not contribute to ab- sorption contrast. Both interactions cause small angular deviations of the order of some sec of arc of the traversing beam, that cannot be detected by conventional set ups for tomography. To "see" these deviations in a tomography one has to use a special diffractometer (a so-called double crystal diffractometer, DCD) that registers them as "ab- sorption-like" contrast. The kind of interaction (SAS, refraction) depends on the beam preparation, i.e. on the monochromacy of the neutrons (of neu- tron wavelength, strictly spoken) and on the trans- verse momentum of the incident neutron wave with respect to the size of the interacting surface. The simplest way to determine the monochromacy is to measure the wave length spread A2/2. The lateral coherence length was measured by Frauenhofer single-slit diffraction after [7] and found to be ~< 50 ~m for this set up, which agreed well with

theory. To measure the effect of refraction or small angle

scattering, these effects must be separated from absorption contrast. Refraction and small angle scattering cause different angular deviations of the beam: a shift in the case of refraction, a broadening of the reflection peak in the case of small angle scattering. This was measured with the double crys- tal diffractometer (DCD) at the BER II (Fig. 3).

A DCD consists of two perfect crystals (e.g. Si monochromator and Si analyzer) that reflect neu- trons if and only if the crystalline planes are parallel to each other within a few sec of arc ("Darwin width"). If a sample is placed between mono- chromator and analyzer any inhomogeneity in the sample gives rise to small angle scattering or refraction of the neutron beam. The size of this inhomogeneity determines whether small angle scattering or refraction occurs. If the effective size of the inhomogeneity (i.e. the lateral width of the

Si (Mo) ons

Sample

Si (An)

Fig. 3. Layout of the double crystal diffractometer (DCD); the sample can be translated (80mm) and rotated (360°), wave length: 0.522 nm, FWHM: 6.53(5)sec of arc, angle resolution of the analyzer crystal: 0.2 sec of arc.

inhomogeneity with respect to the width of the lateral coherence length) is smaller than the width of the coherent wavefront of the neutron wave packet, small angle scattering will happen, refrac- tion otherwise. This differentiation was demon- strated by tomographing 14 pm glass fibres held between glass plates (Fig. 4) and then a glass capil- lary with an outer diameter of 1.14 mm and an inner one of 0.81 mm (Fig. 5).

In the case of small angle scattering (Fig. 4) a broadening of the F W H M of the rocking curve is observed, in the case of refraction by the wall of a capillary, the central peak is shifted by an amount which can be calculated from simple optic formulas (and found to be in excellent agreement with the experiment) (Fig. 5). The change of the shape and the decrease of intensity of the rocking curve is explained by the finite size of the incident beam that causes a variation of the glancing angle at the cylinder surface.

To demonstrate the contrast variation of neu- tron tomography due to small angle scattering and refraction, an Al-rod with diameter of 20 mm and an hole (diameter 1.5 mm) had been tomographed with the DCD. As mentioned above, the parallel arrangement of the monochromator and analyzer of the DCD produces a strong angle dependence of the neutron beam between these crystals. If the beam is deviated by the sample (due to small angle scattering or refraction) by some sec of arc the intensity decreases very rapidly (the F W H M of the analyzer is approximately 6.5 s of arC). Therefore at

W. Treimer et al. I Physica B 241-243 (1998) 1197-1203 1201

Rocking curves with and without fibres; slit = 0.8mm

8O

7O

..~ 40 • without fibres

30

20

-50 -40 -30 -20 -10 0 10 20 30 40 50

sec of arc

Fig. 4. Rocking curves of the analyzer crystal of the DCD; in the case of small angle scattering by a bundle of 14 ~tm glass fibres a broadening of the FWHM is observed.

Rocking curves with and without capillary; slit : 0.12 mm

I! ,.,./" ",, / \ 7 7 " , ,

~ E m p t y

- D Right Edge

- -s- -Lef t Edge

• . 4 ,Center

-4.00 -3,00 -2.00 -1.00 0.00 1.00 2.00 3.00 4.00

steps (1 s tep : 9 sec of arc*)

Fig. 5. Rocking curves of the analyzer crystal of the DCD; due to refraction at the cylinder wall of the glass capillary. Refraction in different directions occurs, depending on the curvature the neutron wave "sees" and the peak is shifted.

the edge of the hole refraction occurs and intensity decreases, though less material attenuates the beam. Fig. 6 shows a very different result as pre-

dicted by absorption contrast. Note the behavior of the transmitted beam. Despite increasing path length of the neutron beam towards the center of

1202 W. Treimer et al. / Physica B 241 243 (1998) 1197 1203

AI cylinder, transmitted intensity, diameter: 1.5 mm; slit width: 0.3 mm

100

80

60

M e-

c 4o

2 0 L ;

, i ~ i i i i , 0 i i I i i i i i I i i i

31.0 36.0 41.0 46.0 51.0 56.0

Translation [mrn]

Fig. 6. One projection of an AI cylinder (0 20 mm) with an empty hole (O 1.5 mm). Note the strong decrease of intensity due to refraction at the edges of the hole.

the cylinder, intensity increases because refraction decreases. Close to the edges of the hole again refraction dominates and intensity decreases. If the neutron beam traverses perpendicular the hole, no refraction changes the beam direction, only absorption (and small angle scattering) occurs. Neutron tomography with the DCD (Fig. 7) therefore clearly indicates not only the center of the hole (black, less absorption) but also its edges (white, "strong absorption"). Note the white edge of the cylinder, which also simulates strong absorption. In both cases the beam was refracted.

To image structures by refraction and small angle contrast a bundle of 14 pm glass fibres were put into the hole (Fig. 8). Again one observes re- fraction contrast at the edges of the hole, if it is empty (Fig. 8a), but if the beam traverses through the center of the hole it hits the fibre bundle and causes small angle scattering. Therefore intensity is scattered off the main beam direction and simulates strong absorption (white center in Fig. 8b).

Fig. 7. Neutron tomography of an AI cylinder as in Fig. 6. Due to the rotationally symmetric object only one projection was used for reconstruction.

W. Treimer et al. / Physica B 241-243 (1998) 1197 1203 1203

4. Summary

Neutron tomography performs well with X-ray films together with Gd-converter foils and can pro- duce spatial resolution better than 1001am× 200 ~tm. This can be improved by collimating the incident neutron beam and using e.g. a graphite monochromator instead of a nearly perfect Ge- crystal. To image single structures larger than 50 tam refraction contrast seems to be a convenient tool, to link the gap between 50 lam and the ram- region. Isolated structures smaller than 50 ~tm down to 0.5 ~tm can be best tomographed by small angle scattering using a double crystal diffrac- tometer. These signals are applicable for non-de- structive testing of nearly perfect materials and they are extremely sensitive to small inhomogeneities in homogenous matrices.

Acknowledgements

This work was supported by the BMBF, project no. 1703296.

Fig. 8. (a) AI rod (O 20 mm) with empty hole (cp. Fig. 7), O 1.5 mm, only the central part is shown. (b) AI rod of (a) with a bundle of 14 I.tm glass fibres. Note the decrease of intensity at the center of the hole due to small angle scattering at the glass fibres.

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