COLLIMATOR FOR X-RAY DIFFRACTION SPECTROSCOPY, ASSOCIATED DEVICE AND ITS USE
20170125133 ยท 2017-05-04
Assignee
Inventors
Cpc classification
G01N23/20091
PHYSICS
International classification
G01N23/20
PHYSICS
Abstract
The invention relates to the field of the analysis of objects by x-ray diffraction spectroscopy. One subject of the invention is a device for analysing an object by x-ray diffraction spectroscopy, comprising a collimator the shape of which allows various portions of an object to be analysed simultaneously. To do this, the collimator includes channels inclined with respect to an axis, called the central axis of the collimator, in such a way that various channels address various elementary volumes distributed through the object. Another subject of the invention is a method allowing an object to be analysed using such a device. The object may for example be a biological tissue that it is desired to characterize non-invasively and non-destructively.
Claims
1. A Device for analysing an object, comprising: a radiation source configured to produce ionizing electromagnetic radiation, the radiation propagating towards a holder, the holder being able to hold the object; a first collimator, placed between the radiation source and the holder, the first collimator having an aperture configured to form a collimated beam propagating along a propagation axis towards the holder; a detector, comprising pixels, each pixel being able to detect ionizing electromagnetic radiation and to form therefrom an energy spectrum; a second collimator, placed between the holder and the detector, the second collimator being configured to selectively direct radiation emitted by the object, which is held by the holder, towards said detector, depending on a scattering angle of the radiation emitted by the object; wherein the second collimator extends, between a first end and a second end, around a central axis, the second collimator including a plurality of channels, each channel being bounded by lateral walls, the second collimator being such that: each channel has a median axis, the median axis extending, in the centre of the channel, between said lateral walls bounding the channel; the median axis of each channel makes an acute angle, called the collimating angle of the channel, with the central axis of the second collimator; each channel being associated to a point, called the focal point, formed by an intersection between the median axis of the channel and the central axis of the second collimator; the second collimator including at least two channels, the collimating angles of which are different, the focal points respectively associated with these channels being different and spaced apart from each other along the central axis of the second collimator; such that each channel transmits to the detector a radiation emitted by an elementary volume of the object, which is placed on the holder, extending around a focal point defined by the second collimator, in a preset angular range.
2. The Device according to claim 1, wherein the second collimator comprises a plurality of channels having the same collimating angle, the channels extending around the central axis of the second collimator, the focal points of the channels being coincident.
3. The Device according to claim 1, wherein at least one channel has a cross section in a plane perpendicular to the central axis, the cross section forming all or some of a ring around the central axis of the second collimator.
4. The Device according to claim 3, wherein at least one ring is circular or polygonal.
5. The Device according to claim 1, wherein at least two focal points are spaced apart, along the central axis of the second collimator, by a distance larger than 2 cm.
6. The Device according to claim 1, wherein each lateral wall bounding a channel of the second collimator is produced from a material the atomic number of which is higher than 26.
7. The Device according to claim 1, wherein each channel of the second collimator is bounded by a lateral wall called the proximal wall and a lateral wall called the distal wall, the proximal wall being closer to the central axis than the distal wall, and wherein each of these walls extends, between the first end of the channel and the second end of the channel, in such a way as to form a frustoconical area defined: by an apex, located on the central axis; and, at said second end, by a generatrice describing all or some of a ring.
8. The Device according to claim 1, wherein the second collimator includes what is called a base wall extending around the central axis and describing a cylinder or conical frustum, of thickness larger than 5 mm.
9. The Device according to claim 1, wherein the second collimator is placed such that its central axis is coaxial with the propagation axis of the collimated incident beam.
10. The Device according to claim 1, wherein the detector extends in a plane perpendicular to the central axis of the second collimator.
11. The Device according to claim 1, wherein the detector is connected to a microprocessor able to subdivide each pixel of the detector into virtual pixels, and wherein a plurality of pixels or virtual pixels are placed in the extension of a given channel.
12. A Method for characterizing an object using a device according to claim 1, comprising the following steps: a) placing the object on the holder of the device and irradiating the object using the irradiation source, so as to form a collimated incident beam propagating towards the object along a propagation axis, the object being placed such that a plurality of focal points, which are defined by the second collimator, are placed in said object; b) using each pixel of the detector, detecting radiation scattered by the object following its radiation by said collimated incident beam and forming a spectrum representative of the energy distribution of said detected radiation; c) defining a plurality of groups of pixels, each group of pixels receiving radiation scattered by a given volume element of the object, the volume element being located on the propagation axis, two different groups of pixels receiving radiation scattered by two different volume elements; d) for each group of pixels defined in the preceding step, combining the spectrum acquired by each pixel, so as to establish a spectrum, called the combined spectrum, associated with said group of pixels; and e) using the combined spectra respectively associated with various groups of pixels, determining a nature of the material constituting a plurality of volume elements of the object.
13. The Method according to claim 12, wherein the central axis of the second collimator is coincident with the propagation axis of the collimated beam; and the detector extends perpendicularly to the axis of the second collimator, each group of pixels including pixels located at the same distance, called the radial distance from said central axis of the second collimator.
14. The Method according to claim 12, wherein the direction of the collimated incident beam is defined on the basis of knowledge considered to be gained by prior inspection of the object.
15. The Method according to claim 14, wherein said prior inspection is carried out by x-ray radiography, or x-ray tomography, or echography, or magnetic resonance imaging.
Description
FIGURES
[0037]
[0038]
[0039]
[0040]
[0041]
[0042]
DESCRIPTION OF PARTICULAR EMBODIMENTS
[0043]
[0044] The analysing device 1 includes a second collimator 40, which is interposed between the object 10 and the detector 20. This collimator extends around an axis, called the central axis 45. It is able to selectively direct, towards the detector, scattered radiation 14.sub.1, 14.sub.2, 14.sub.3, 14.sub.4 transmitted by the object 10 depending on an angle .sub.1, .sub.2, .sub.3, .sub.4 of propagation of this radiation with respect to the central axis 45. The term selectively means that the radiation transmitted towards the detector depends on the angle at which it is propagating and on the portion of the object from which it was emitted. This second collimator, designated by the term collimator in the rest of the text, is a key element of the invention and will be described more precisely below.
[0045] The analysing device 1 is placed in a reference frame with which an orthogonal coordinate system X, Y, Z such as shown in
[0046] The expression ionizing electromagnetic radiation designates electromagnetic radiation consisting of photons of energy higher than 1 keV, and preferably lower than 5 MeV. The energy range of the ionizing radiation may be comprised between 1 keV and 2 MeV, but it most often extends between 1 keV and 150 keV or 300 keV. The ionizing radiation may be x-ray or -ray radiation. Preferably, the source of ionizing radiation is polyenergetic, the incident radiation being emitted in an energy range generally extending over several tens or even several hundreds of keV. It is especially a an X-ray emitting tube.
[0047] The radiation detector is a detector comprising pixels 20.sub.i,j that are arranged in a plane called the detection plane P.sub.20. The indices i, j designate the coordinates of each pixel in the detection plane. The pixels may form a linear array but in general they form a two-dimensional regular matrix array. In the examples described in this patent application, the detection plane is an XY plane perpendicular to the central axis 45 of the collimator, the latter axis being coincident with the propagation axis 12z of the collimated incident beam 12c. This is a preferred configuration.
[0048] The radiation source 11 is an X-ray tube equipped with a tungsten anode that is subjected to a voltage, generally comprised between 40 and 150 kV, which may be varied in order to modify the energy range of the incident radiation 12. The detector 20 comprises 40 pixels along the X-axis by 40 pixels along the Y-axis, namely 1600 pixels, each pixel having an area of 2.52.5 mm.sup.2, its thickness being 5 mm. Each pixel is made from a semiconductor material, for example CdTe or CdZnTe, or any other material able to produce spectroscopic measurements, preferably at room temperature. It could also be a scintillator material, providing it has a sufficient energy resolution. The detector is resolved in energy, and each pixel allows spectra to be obtained in energy channels of about 1 keV. The radiation source 11 may include a metal screen, for example made of copper, so as to block the propagation, towards the pre-collimator 30, of radiation the energy of which is lower than a threshold, for example 20 keV. When this screen is made of copper, its thickness is for example equal to 0.2 mm.
[0049] The first collimator 30, or pre-collimator, includes a block of dense material 31 so as to absorb almost all the radiation 12 emitted by the radiation source 11. It contains a small aperture 32, extending along an axis, called the propagation axis 12z, allowing a narrow collimated beam 12c to pass. By small aperture, what is meant is an aperture the diameter of which or the largest diagonal of which is smaller than 2 cm, or even than 1 cm. In this example, the aperture is a cylinder of 1 mm diameter.
[0050] The object 10 may be a living biological tissue, for example a portion of the body of an animal or of a human being. The device is then a medical imaging device. The portion of the body may in particular be an organ in which, following a first examination, for example an X-ray or scan, the presence of an anomaly, in particular a cancerous tumour, is suspected. This first examination also allows an approximate location of the anomaly in the tissue to be determined. The device 1 may then be implemented during a second indication, in order to characterize the nature of the tissues making up the organ in the location of said anomaly and in its vicinity. The organ is especially an organ located on the periphery of the body, so as to allow an easy analysis without being affected by attenuation due to bones or other organs. It may in particular be a breast, a testicle, or an organ of the abdominal cavity. In other applications, the object may also be an industrial part or a piece of luggage, the device 1 then being used for non-destructive inspection purposes.
[0051] Each pixel 20.sub.i,j of the radiation detector 20 includes: [0052] a detector material, able to interact with the photons of the radiation 14.sub.1, 14.sub.2 . . . 14.sub.n . . . 14.sub.N transmitted by the object 10, through the second collimator 40, this material being a scintillator material or, preferably, a semiconductor material compatible with use at room temperature, such as CdTe or CdZnTe; [0053] an electronic circuit, able to generate a signal the amplitude A of which depends on, and is preferably proportional to, an energy E deposited by each photon interacting with the detector material; and [0054] a spectroscopy circuit, able to establish an energy spectrum, denoted S.sub.i,j, from the signals detected during a period of time called the period of acquisition.
[0055] Thus, when the pixels are regularly arranged in a matrix array, each pixel is able to produce a spectrum S.sub.i,j from the radiation 14 transmitted by the object according to this matrix array.
[0056] The expression energy spectrum corresponds to a histogram of the amplitude A of the signals detected during a period of acquisition of the spectrum. A relationship between the amplitude A of a signal and the energy E of the radiation may be obtained using an energy calibration function g such that E=g(A), according to principles known to those skilled in the art. An energy spectrum S.sub.i,j may therefore take the form of a vector, each term of which S.sub.i,j(E) represents an amount of radiation detected by the pixel 20.sub.i,j in an energy range EE/2, where E is the spectral width of an energy discretization step of the spectrum.
[0057] The device also comprises a computing unit, or processor 22, for example a microprocessor, able to process each spectrum S.sub.i,j measured by the pixels 20.sub.i,j of the detector 20. In particular, the processor is a microprocessor connected to a programmable memory 23 in which is stored a sequence of instructions for performing the spectra-processing and computing operations described in this description. These instructions may be saved on a storage medium, which is readable by the processor, such as a hard disk, CD-ROM or another type of memory. The processor may be connected to a display unit 24, for example a screen.
[0058] The collimator 40 includes channels 42, the channels extending around the central axis 45 and converging towards the latter. More precisely, each channel 42.sub.n is able to transmit transmitted radiation 14.sub.n at a scattering angle .sub.n belonging to a preset angular range .sub.n, the radiation being transmitted by the object 10 towards the detector 20.
[0059]
[0060] In the rest of the text, n is a natural integer higher than or equal to 1 and lower than or equal to N, N being a strictly positive integer. n designates any channel 42.sub.n of the collimator whereas N designates the number of channels of the second collimator. The same goes for the lateral walls 41.sub.n, which are defined below, or the first ends 46.sub.n or 47.sub.n, the index n referring to the channel 42.sub.n.
[0061] Each channel 42.sub.n is bounded by at least two lateral walls 41.sub.n-1, 41.sub.n, the wall 41.sub.n-1, which is called the proximal wall, being closer to the central axis 45 than the wall 41.sub.n, which is called the distal wall. Thus, the channels 42.sub.1, 42.sub.2, 42.sub.3 and 42.sub.4 are respectively bounded by the lateral walls 41.sub.0 and 41.sub.1, 41.sub.1 and 41.sub.2, 41.sub.2 and 41.sub.3, 41.sub.3 and 41.sub.4. These lateral walls are produced from a material that is dense enough to significantly attenuate electromagnetic radiation in the emission energy range in which the radiation source 11 emits the incident radiation 12. Metal materials are preferred, and in particular materials the atomic number of which is higher than or equal to that of iron (26), and preferably higher than or equal to that of lead (82). Collimators made of lead or of an alloy mainly containing tungsten are conventionally used for this type of application. The thickness of these walls is generally smaller than 1 cm, or even 0.5 cm. It may vary between the first end and the second end of the collimator 40. Each channel extending between the various walls is filled with a material that does not attenuate much, air for example.
[0062] In the example shown, the lateral walls 41.sub.1, 41.sub.2, 41.sub.3, 41.sub.4 have a substantially frustoconical shape and extend around the central axis 45 of the collimator. The frustoconical shape of each lateral wall 41.sub.n may be defined by an apex, located on the central axis 45, and by an annular generatrice extending, at the second end 47.sub.n of a channel 42.sub.n bounded by said lateral wall, around the central axis of the collimator. Thus in a transverse plane P.sub.40 extending perpendicularly to the central axis 45, the cross section of each channel describes a portion of a ring the centre of which is located on this central axis. The term ring designates a circular or polygonal ring.
[0063] In this example, the collimator includes a central wall, called the base wall, 41.sub.0 which is solid and the outside radius of which bounds the channel 42.sub.1. This base wall extends between the central axis of the collimator and the channel that is closest to this central axis. This base wall is cylindrical or frustoconical. It extends around the central axis 45, so as to prevent transmission of radiation transmitted by the object in an incident direction parallel to the axis of propagation 12.sub.z. According to one variant, whatever the embodiment, the collimator may include a hollow base wall 41.sub.0. In this case, the base wall extends around the central axis 45, defining a cylinder or a cone, and bounds a cavity the median axis of which is the central axis 45 of the collimator. This allows a measurement, by the detector 20, of a spectrum of the radiation propagating along the central axis 45 after transmission by the object 10. When the central axis of the collimator is coincident with the propagation axis 12z of the incident collimated beam 12c, this allows a measurement, by the detector 20, of the spectrum of radiation transmitted by the object and not deviated by the latter. This allows the attenuation of the collimated radiation 12c which is caused by the object to be estimated.
[0064] Each lateral wall extends between an outside radius and/or an inside radius. These radii, at the first end 46 of the collimator, vary between a few millimetres for the wall the closest to the central axis 45 to a few centimetres, for example 1 or 2 cm for the lateral wall furthest from the central axis 45. At the second end 47, these outside radii vary between a few millimetres for the closest wall to a few centimetres, for example 6 cm, for the furthest wall. The aperture of a channel 42.sub.n, i.e. the distance between the lateral walls bounding it, is for example smaller than 1 mm at the first end 46.sub.n, and is comprised between 1 mm and 1 cm at the second end 47.sub.n.
[0065] Each channel 42.sub.n extends, between its first end 46.sub.n and its second end 47.sub.n, around a median axis 44.sub.n.
[0066]
[0067] Each median axis 44.sub.n of a channel 42.sub.n intersects the central axis 45 of the collimator at a point P.sub.n called a focal point. A noteworthy aspect of this collimator is that the focal points P.sub.1, P.sub.2, P.sub.3, P.sub.4 associated with channels the respective collimating angles .sub.1, .sub.2, .sub.3, .sub.4 of which are different are spaced apart from one another. In other words, and this is a notable difference with respect to the prior art, the channels of the collimator 42.sub.n extend around median axes 44.sub.n intersecting the central axis 45 of the collimator in such a way that: [0068] the median axes 44.sub.n, 44.sub.n of two channels 42.sub.n, 42.sub.n having the same collimating angle .sub.n are secant, and intersect at a same point, called a focal point P.sub.n, at the collimating angle .sub.n, this point being located along the central axis 45 of the collimator; [0069] the median axes 44.sub.n, 44.sub.n of two channels 42.sub.n, 42.sub.n the collimating angles (.sub.n, .sub.n) of which are different, intersect the central axis at two different focal points P.sub.n, P.sub.n located along the central axis 45 of the collimator.
[0070] Each channel 42.sub.n is able to transmit radiation 14.sub.r, transmitted by the object 10 around a focal point P.sub.n, said radiation propagating in an angular range .sub.n extending around the collimating angle .sub.n of the channel. Apart from the collimating angle .sub.n, this angular range .sub.n depends on the diameter of the channel, or its diagonal, and the length of the channel 42.sub.n between its first end 46.sub.n and its second end 47.sub.n. The greater this length, the narrower the angular range .sub.n around the collimating angle .sub.n will be. The smaller the aperture of a channel, the narrower the angular range .sub.n around the collimating angle .sub.n will be. The aperture of a channel 42.sub.n designates the distance between the two proximal and distal lateral walls bounding it.
[0071] The fact that the focal points are spaced apart from one another allows various portions of the object 10 to be examined simultaneously. Specifically, as shown in
[0072]
[0073]
[0074] The first and second ends of the collimator respectively correspond, in this example, to the planes P.sub.40.1 and P.sub.40.2 between which the collimator 40 extends. They are separated by a height H, called the height of the collimator, generally comprised between 5 and 100 cm and preferably between 5 and 50 cm. The higher it is, the narrower the angular range .sub.n associated with each channel 42.sub.n, thereby improving the angular resolution, but the greater the cost, bulk and weight of the collimator.
[0075] The distance d.sub.1 between the object 10 and the collimator 40 may be adjusted: it may be zero, the collimator making contact with the object. It may also reach a few cm, while usually being less than 10 cm. The same goes for the distance d.sub.2 separating the collimator 40 from the detector 20. Generally, the collimator is placed such that a plurality of focal points, and preferably all the focal points, are included in the object 10. In this way, the detector 20 allows transmitted radiation 14.sub.n coming from various elementary volumes V.sub.n of the object, each elementary volume extending around a focal point P.sub.n, to be detected.
[0076] The detector 20 extends between two planes P.sub.20.1 and P.sub.20.2, which are preferably perpendicular to the central axis 45 of the collimator 40. Thus, in this example, the detector extends perpendicularly to the propagation axis 12.sub.z of the collimated incident beam 12.sub.c. The thickness s of the detector 20 corresponds to the distance between the two planes P.sub.20.1 and P.sub.20.2. It is generally comprised between 1 and 10 mm and, in this example, reaches 5 mm.
[0077] Each pixel 20.sub.i,j of the detector is located at a distance R, called the radial distance, from the central axis 45 of the collimator. When, as in this embodiment, the detector 20 extends perpendicularly to this central axis 45, it is possible to define a group of pixels 20.sub.R including all the pixels 20.sub.i,j that are equidistant from the central axis 45, and therefore from the axis 12z of the collimated beam 12c. A group of pixels 20.sub.R then corresponds to pixels 20.sub.i,j the radial distance R of which is identical. Because of the geometry of the collimator, each group of pixels 20.sub.R is associated with one volume element V.sub.R of the object, corresponding to the intersection between the solid angle .sub.i,j under which a pixel 20.sub.i,j of said group sees the object, with the collimated incident beam 12c. This volume element V.sub.R is defined depending on a distance z between the detector and said volume element, and a scattering angle .sub.n.
[0078]
[0079]
[0080]
[0081] The collimator 40 takes the form of an assembly of plates including apertures, each plate possibly having a thickness of 1 mm. The size of each aperture increases as it gets closer to the plane P.sub.40.2. Thus, the assembly of plates forms a collimator, each channel of which is formed by the apertures of the plates, which are adhesively bonded to one another. In each of these figures, with white dashed lines, each lateral wall 41.sub.1, 41.sub.2, 41.sub.3, 41.sub.4 has been shown. In this configuration, each lateral wall describes a square generatrice ring around the axis 45.
[0082]
[0083]
[0084]
[0085]
[0086] Calculations have allowed the angular range addressed by each channel 42.sub.n to be determined. The abscissa represents the distance z with respect to the detector, along the Z axis, the detector being located at z=0. The scattering angles are indicated according to the colour scale shown next to this figure. It may be seen that, except for the channel 42.sub.1 closest to the central axis 45 of the collimator, each channel 42.sub.n addresses an angular range .sub.n extending over about 1 for the channels furthest from the central axis, up to a few degrees for the closest channels. For example, the angular range associated with the channel 42.sub.2 is comprised between 6 and 10. The abscissa allows the spatial extension z.sub.n addressed by each channel 42.sub.n along the central axis 45 of the collimator to be measured, such a spatial extension having being defined with reference to
[0087] This figure also allows, for each pixel located at a radial distance R from the central axis 45, the scattering angle .sub.R addressed and the distance z, with respect to the detector, to be determined, thereby allowing the volume element V.sub.R of the object 10 seen by the pixel to be determined. The ordinate represents the radial distances R, the latter varying between a few mm (pixels closest to the central axis 45) and 50 mm, this corresponding to the half-width of the detector. For example, each pixel located at a radial distance R=20 mm from the axis of the collimator 45 detects scattered radiation transmitted by a volume element V.sub.R of the object 10 located, along the propagation axis 12.sub.z of the collimated beam 12.sub.c, in a distance range z.sub.R=20 comprised between 126 mm and 130 mm from the detector, this radiation being emitted at a scattering angle .sub.R comprised between 8 and 9.
[0088]
[0089]
[0090] A method allowing an object 10 to be analysed using the device 1 and a collimator such as described above will now be described.
[0091] Just as in
where: [0092] d is a distance characteristic of the atomic or molecular arrangement of a material making up the object. When the analysed material is a crystal, d corresponds to the interplanar spacing; [0093] E is the energy of the scattered radiation, expressed in keV; [0094] is the scattering angle with respect to the path of unscattered radiation; and [0095] h and c are Planck's constant and the speed of light, respectively.
[0096] It is common to express a quantity, referred to as the momentum transfer, represented by the letter x and expressed in nm.sup.1, such that:
[0097] To each pixel 20.sub.i,j, and a fortiori to each virtual pixel 20*.sub.k,l, of the detector 20 there corresponds a scattering angle corresponding to the most probable angle at which scattered radiation 14 will reach the pixel. The advantage of the sur-pixelation is that pixels of small size are obtained, thereby decreasing the angular range of the scattered radiation liable to reach them. Specifically, by decreasing the size of the pixels, the size of each solid angle .sub.ij under which a pixel sees the object is decreased. The sub-pixelation is therefore advantageous because it allows virtual pixels 20*.sub.k,l of small size to be obtained.
[0098] Since the detector 20 extends perpendicularly to the central axis 45 of the collimator 40, the locations of the pixels 20.sub.i,j or the virtual pixels 20*.sub.k,l associated with a given scattering angle have an annular arrangement. These pixels form a group of pixels 20.sub.R, each pixel of this group addressing a given volume element V.sub.R of the object 10. The pixels of a given group of pixels are located at the same radial distance R from the central axis 45 of the collimator. The association of a pixel with a volume element designates the fact that the scattered radiation received by this pixel will have mainly come from this volume element V.sub.R.
[0099] The method for analysing materials then comprises the following steps, which are described with reference to
[0105] With each volume element V.sub.R there may be associated a distance z with respect to the detector. Each volume element V.sub.R is located on the propagation axis 12z of the incident collimated beam 12c. To each volume element V.sub.R there corresponds a scattering angle .sub.R corresponding to the angle at which scattered radiation propagates between the volume element V.sub.R and each pixel of the group of pixels.
[0106] The method then allows the nature of the materials constituting the volume elements V.sub.R, lying at various distances z from the detector, to be deduced.
[0107] Step 160 may be implemented as follows: this step assumes a response matrix, denoted Rep, has been established, said matrix containing the spectra obtained by each pixel located at a radial distance R from the central axis of the collimator, when a material i is located at a distance z from the detector. Each term Rep(E, R, z, i) of this matrix represents a number of photons detected at the energy E by a pixel located at a radial distance R from the central axis of the collimator, when a material i is located at a distance z from the detector.
[0108] This response matrix comprises N.sub.EN.sub.R rows and N.sub.zN.sub.i columns, where N.sub.E, N.sub.R, N.sub.z and N.sub.i are respectively the number of energy channels of each spectrum, the number of radial distances R, the number of distances z and the number of materials i in question.
[0109] The various combined spectra S.sub.R.sup.E obtained for the N.sub.R radial distances R with respect to the central axis of the collimator, may be concatenated to form a vector S, called the overall spectrum, of N.sub.EN.sub.R size. Each term S (E, R) of the vector S represents a number of photons detected, at the energy E, by a pixel located at a radial distance R from the central axis of the collimator.
[0110] The method aims to determine a proportion f(z, i) of the material i at the distance z from the detector, i.e. to determine a vector f of the proportions, of (N.sub.zN.sub.i, 1) size, each term of which is a proportion f(z, i).
[0111] Thus, S=Rep*f, (3), where * designates matrix multiplication, each term S(E,R) of the vector S being such that:
S(E, R)=.sub.z,iRep(E, R, z, i).Math.f(z, i) (4)
[0112] The matrix Rep is determined in a calibrating step, carried out: [0113] either using experimental measurements, the object being replaced by known standard materials; [0114] or by simulation, using computational codes simulating the path of photons through the material; [0115] or by combining experimental measurements and simulations.
[0116] Such a calibrating step is a conventional procedure.
[0117] The vectors S, f and the matrix Rep are written out componentwise as follows:
where Emin, Rmin, zmin and imin respectively designate the minimum indices of E, R, z and i, and Emax, Rmax, zmax and imax respectively designate the maximum indices of E, R, z and i.
[0118] Having determined the response matrix Rep, and having obtained the overall spectrum S from the measurements, it is possible to obtain an estimation {hacek over (f)} of the vector of the compositions f using a reconstruction algorithm. Among commonly used iterative reconstruction algorithms, a MLEM algorithm (MLEM standing for maximum likelihood expectation maximization) may be used. According to such an algorithm, the value of each term of the vector {hacek over (f)}.sup.n may be obtained using the following expression:
the exponent q designating the rank of each iteration.
[0119] According to one embodiment, the method includes a step of changing variable, in which each spectrum S.sub.i,j.sup.E is converted using equation (2) into a spectrum S.sub.i,j.sup.X representing a distribution of the momentum transfer, the angle corresponding to the angle associated with the pixel 20.sub.i,j (or the virtual pixel 20*.sub.k,l where appropriate). Such a spectrum is not an energy spectrum, but indeed remains a spectrum representative of the energy distribution of said detected radiation.
[0120] The invention will possibly be used to provide data necessary to make a diagnosis. For example, it will possibly be implemented on suspect zones detected beforehand by an imaging method such as x-ray radiography, x-ray tomography, echography or MRI. This allows an in vivo characterization of tissues considered to be suspect to be obtained, and the need to use more invasive, and more traumatizing, techniques such as biopsies to be avoided. The fact that the location is considered to be known makes it possible to concentrate on the suspect zones and to limit the integrated dose received by the patient. Specifically, using such knowledge considered to be gained, the device may be used such that the axis of the collimated beam 12.sub.z passes through the suspect zone determined beforehand.
[0121] The invention will possibly also be implemented in other non-destructive material inspection applications: inspection of luggage, detection of illicit substances, inspection of the integrity of structures, etc.