“4D” dynamic tomography system

Abstract

A tomography scanner includes at least one first emission source (GX1), one first matrix detector (D1), and a computer (C) arranged to produce an initial tomography of an object (E) based on radiographs arising from the first matrix detector, taken from various angles. The tomography scanner further includes a second emission source (GX2) and a second matrix detector (D2) arranged so that, when the object is subjected to a loading that is known at a given instant in time, the computer determines the changes in the object subjected to said loading based only on the information from the first radiograph of the object under loading arising from the first matrix detector, from the second radiograph of the object under loading arising from the second matrix detector and the initial tomograph, the first radiograph and the second radiograph being taken simultaneously at the same given instant in time.

Claims

1. A tomography scanner comprising: at least one first emission source (GX1), one first matrix detector (D1), and a computer (C) that produces an initial tomography of an object (E) on the basis of radiographs arising from the first matrix detector, which are taken from various angles, a second emission source (GX2), and a second matrix detector (D2), wherein, when the object is subjected to a loading whose descriptive framework is known at a given instant in time, the computer determines changes in the object subjected to said loading based only on the information: from a first radiograph of the object under loading arising from the first matrix detector, from a second radiograph of the object under loading arising from the second matrix detector, and from the initial tomograph, the first radiograph and the second radiograph being taken simultaneously at the same given instant in time.

2. The tomography scanner as claimed in claim 1, wherein the tomography scanner records a temporal succession of pairs of the first and second radiographs so as to reconstruct the change in the object shape over time.

3. The tomography scanner as claimed in claim 1, wherein as the object is a porous medium, the loading is a two-phase flow of a second fluid through said porous medium comprising a first fluid.

4. The tomography scanner as claimed in claim 1, wherein the loading is a mechanical loading, the object being deformed under the loading.

5. The tomography scanner as claimed in claim 1, wherein the first and second emission sources are X-ray sources.

6. The tomography scanner as claimed in claim 2, wherein as the object is a porous medium, the loading is a two-phase flow of a second fluid through said porous medium comprising a first fluid.

7. The tomography scanner as claimed in claim 2, wherein the loading is a mechanical loading, the object being deformed under the loading.

8. The tomography scanner as claimed in claim 2, wherein the first and second emission sources are X-ray sources.

9. The tomography scanner as claimed in claim 4, wherein the computer implements an algorithm of P-DVC (or projection-based digital volume correlation) type, a displacement field of the object under loading being determined on the basis of the minimization of functions dependent on the first and second radiographs of the object under loading, and the initial full tomography carried out in the reference state.

10. The tomography scanner as claimed in claim 7, wherein the computer implements an algorithm of P-DVC (or projection-based digital volume correlation) type, a displacement field of the object under loading being determined on the basis of the minimization of functions dependent on the first and second radiographs of the object under loading, and the initial full tomography carried out in the reference state.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The invention will be better understood and other advantages will become apparent on reading the following description, which is given by way of non-limiting example, and from the appended figures in which:

(2) FIG. 1, mentioned above, shows the overview of a tomography scanner according to the prior art;

(3) FIG. 2, mentioned above, shows the general principle of a transformation between two states which is analyzed using 3D images of these different states;

(4) FIGS. 3, 4 and 5 schematically represent three successive states of a cross section through a porous medium during an immiscible two-phase flow;

(5) FIG. 6 shows the difference in structure of the porous medium between two instants in time, those of FIGS. 3 and 4, of the flow of the fluid;

(6) FIG. 7, mentioned above, shows the general principle of a transformation between two states which is analyzed using 3D images of these different states in the particular case of a mechanical deformation analyzed via DVC;

(7) FIG. 8 shows the overview of a tomography scanner according to the invention;

(8) FIG. 9 shows the principle of DVC modified according to the invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

(9) By way of non-limiting example, a tomography scanner according to the invention is shown in FIG. 8. It principally comprises: two X-ray generators, denoted by GX1 and GX2, whose power is matched to the size and the absorption of the sample E to be analyzed. These generators have substantially the same technical features; two matrix detectors, D1 and D2, each detector being associated with one of the two X-ray generators. The two detectors are positioned in two different planes. Generally, the two planes are mutually perpendicular. These two detectors have substantially the same technical features. Their definition, in terms of rows and columns, is generally a few thousand pixels. By way of example, the technology employed is based on CMOS (complementary metal oxide semiconductor) detectors with a cesium scintillator. a set of motorized plates PM for translational and rotational movements bearing the sample E. This set comprises, in particular, a rotating plate allowing the sample E to be turned at an angle over 360 degrees with a high level of precision. The plate is positioned so as not to screen the detectors from the generators. The sample is located at substantially identical distances from the two detectors and the two generators; means for controlling the two generators and the various plates, not shown in FIG. 8; means for acquiring and processing the various data and for reconstructing the sample in three dimensions on the basis of the various radiographs. These means are represented by a computer C in FIG. 8.

(10) As stated above, the tomography scanner according to the invention finds a large number of applications: it may be used to characterize two-phase flows in porous media. The technique employed is a variant of the reconstruction adapted to parsimonious and binary fields; it may be used to measure the movement of a sample of a material subjected to a known loading. The technique employed is a variant of the technique referred to as projection-based digital volume correlation, mentioned above.

(11) In the first case, an exemplary binary reconstruction algorithm is presented in the article entitled Efficient Binary Tomographic Reconstruction by S. Roux, H. Leclerc and F. Hild, J. Math Imaging Vis. (2014) 49:335-351.

(12) In the second case, the technique takes inspiration from the principles described in the article entitled Projection savings in CT-based Digital Volume Correlation by H. Leclerc, S. Roux and F. Hild, published in Experimental Mechanics (DOI 10.1007/s11340-014-9871-5). The fundamental difference between the device described in this article and the tomography scanner according to the invention is that the described device comprises only one X-ray generator and only one detector. Thus, in order to produce two radiographs from two different angles, it is necessary to rotate the sample with the constraints that this involves, the main one being the impossibility to track the change in the sample in real time without disruptions.

(13) As above, the measurement comprises two steps. Its principle is shown in FIG. 9.

(14) In a first step, a first tomograph of the sample E that it is desired to analyze is produced conventionally. Denoting the tomographic images of the sample by s.sub.1(r,), a first three-dimensional reconstruction function .sub.1 is calculated whose value, as above, is:
.sub.1(x)=R[s.sub.i(r,)]

(15) This tomograph is produced by the two sets operating simultaneously. The two series of images obtained are brought into correspondence, allowing the two frames of reference of the detectors to be associated.

(16) In a second step, the desired loading S is applied to the sample E. The loading S is symbolically represented by a black chevron arrow in FIG. 9. Just two simultaneous radiographs of the sample E under loading are then produced, the first taken by the first set comprising the first generator GX1 and the first detector D1, the second taken by the second set comprising the second generator GX2 and the second detector D2. By construction, these two radiographs are taken from two different angles without requiring the sample to be rotated. These two images are denoted by s.sub.2(r,).

(17) It is known, by virtue of the preceding, that the data arising from the two radiographs are potentially sufficient for calculating the parameters p of the transformation T. Thus, in the particular case of the deformation of a material, the amplitudes {a} of the displacement field are calculated:

(18) $U\left(X\right)=\underset{i}{.Math.}{a}_i{}_i\left(X\right)$
over the basis of fields .sub.i(x) according to the P-DVC algorithm or equivalent. Conventionally, the fields .sub.i are finite element shape functions. The amplitudes a.sub.i are determined by means of minimizing the following function, close to equation (2), using the same notation as above:

(19) $\left\{a\right\}={\mathrm{argmin}}_{\left\{b\right\}}\underset{}{.Math.}{\left(s_2\left(r,\right)-P_{}\left[f_1\left(X-b_i{}_i\left(X\right)\right)\right]\right)}^2\mathrm{dr}$
where P.sub. corresponds to the projection of the three-dimensional reconstruction .sub.1 corrected for movement over the planes of the detectors. In the context of the invention, the calculations are carried out on the basis of the information arising solely from the two images s.sub.2(r,).

(20) According to one possible embodiment of the displacement field calculation according to the P-DVC algorithm, the estimation is carried out via successive iterations n. On each iteration, an artificially deformed reference image is constructed: {tilde over ()}.sub.i(X). The relationship is:
{tilde over ()}.sub.1(X)=.sub.1(Xa.sub.i.sup.n.sub.i(X))

(21) Between two iterations, the simple relationship is:
a.sub.i.sup.n+1=a.sub.i.sup.n+da.sub.i.sup.n+1

(22) The correction terms da.sub.i.sup.n+1 are obtained on the basis of the linearization of the differences in the projected images. The following is defined:
g.sub.i.sup.n(r,)=P.sub.[{tilde over ()}.sub.1.sup.n.Math..sub.i(X)]

(23) The calculation of the correction terms da.sub.i.sup.n+1 is obtained by solving the following linear system:

(24) $M_{\mathrm{ij}}^n{\mathrm{da}}_{\mathrm{ij}}^{n+1}={dB}_i^n$$\mathrm{where}{M}_{\mathrm{ij}}^n=\underset{}{.Math.}{g}_i^n\left(r,\right)g_j^n\left(r,\right)\mathrm{dr}$$\mathrm{and}{\mathrm{dB}}_i^n=\underset{}{.Math.}\left(s_2\left(r,\right)-P_{}\left[{\tilde{f}}_1^n\left(X\right)\right]\right).Math.g_j^n\left(r,\right)\mathrm{dr}$

(25) The process of iterations is halted as soon as the correction terms fall below a predetermined threshold. In practice, convergence is obtained after about ten iterations.

(26) Thus, the number of radiographs required to determine the displacement field is very substantially decreased. Moreover, by recording a temporal succession of pairs of first and second radiographs, it is possible to reconstruct the change in the displacement field of the object over time, whence the terminology 4D or dynamic tomography.

(27) The main advantage of the tomography scanner according to the invention is to allow dynamic tracking of the change in a sample subjected to a given loading. By way of first example, it may be used to track the dynamic change in the front between two immiscible fluids in a dynamic flow under the effect of an applied pressure. By way of second example, the time dependence of the kinematics of a sample subjected to a mechanical loading may also be analyzed.

(28) A tomography scanner according to the invention, with two sets of sources/detectors, necessarily costs more than a tomography scanner comprising a single assembly. However, the increase in cost is quite limited inasmuch as numerous elements of the tomographic system may be mutualized, such as the radiation protection screens, the motorized plates, the anti-vibration devices or else the air-conditioning systems.