Talbot effect based nearfield diffraction for spectral filtering

Abstract

The invention relates to a grating arrangement and a method for spectral filtering of an X-ray beam (B), the grating arrangement comprising: a dispersive element (10) comprising a prism configured to diffract the X-ray beam (B) into a first beam component (BC1) comprising a first direction (D1) and a second beam component comprising (BC2) a second direction (D2), tilted with respect to the first direction; a first grating (20) configured to generate a first diffraction pattern (DP1) of the first beam component (BC1) and a second diffraction pattern (DP2) of the second beam component (BC2), the second diffraction pattern (DP2) shifted with respect to the first diffraction patter (DP1); and a second grating (30) comprising at least one opening (31) which is aligned along a line (d) from a maximum (MA) to a minimum (MI) of intensity of the first diffraction pattern (DP1) or of the second diffraction pattern (DP2).

Claims

1. A grating arrangement for spectral filtering of an X-ray beam (B), comprising: a dispersive element comprising a prism configured to diffract the X-ray beam (B) into a first beam component (BC1) comprising a first direction (D1) and a second beam component (BC2) comprising a second direction (D2), tilted with respect to the first direction; a first grating configured to generate a first diffraction pattern (DP1) of the first beam component (BC1) and a second diffraction pattern (DP2) of the second beam component (BC2), the second diffraction pattern (DP2) shifted with respect to the first diffraction pattern (DP1); and a second grating comprising at least one opening which is aligned along a line (d) from a maximum (MA) to a minimum (MI) of intensity of the first diffraction pattern (DP1) or of the second diffraction pattern (DP2).

2. The grating arrangement according to claim 1, wherein the first direction (D1) and the second direction (D2) are tilted, spanning a tilt angle (+).

3. The grating arrangement according to claim 1, wherein the first grating is configured to shift the second diffraction pattern (DP2) with respect to the first diffraction pattern (DP1) along a direction corresponding to the direction of the line (d).

4. The grating arrangement according to claim 1, wherein at least one of the first beam component (BC1) and the second beam component (BC2) comprises quasi-monochromatic X-ray radiation.

5. The grating arrangement according to claim 1, wherein the first grating is configured to generate the first diffraction pattern (DP1) of the first beam component (BC1) and the second diffraction pattern (DP2) of the second beam component (BC2) as a near-field diffraction effect.

6. The grating arrangement according to claim 1, wherein the second diffraction pattern (DP2) is shifted with respect to the first diffraction pattern (DP1) by means of an energy-dependent lateral shift.

7. The grating arrangement according to claim 1, wherein at least one of the first grating and the second grating comprises a periodic structure.

8. The grating arrangement according to claim 1, wherein at least one of the first grating and the second grating is configured to be movable in such way that the at least one opening is moveable along the line (d) from the maximum (MA) to the minimum (MI) of intensity of the first diffraction pattern (DP1) or of the second diffraction pattern (DP2).

9. The grating arrangement according to claim 1, wherein the dispersive element and the first grating are integrated such as to constitute a dispersive grating.

10. The grating arrangement according to claim 1, wherein the dispersive element comprises a periodic structure of prisms, wherein each of said prisms is configured for diffracting the X-ray beam (B) into the first beam component (BC1) comprising the first direction (D1) and the second beam component (BC2) comprising the second direction (D2), and wherein said second direction is tilted with respect to the first direction.

11. The grating arrangement according to claim 1, wherein the first grating is a microlensing grating.

12. An X-ray system, with an X-ray source, which is adapted to generate a polychromatic spectrum of X-rays, a detector and at least one grating system according to claim 1.

13. The grating arrangement of claim 1, further comprising a processor and an actuator and configured for, via said processor, controlling said actuator to align said second grating so as to perform the aligning of said at least one opening along said line (d).

14. A method for spectral filtering of an X-ray beam (B), comprising the steps of: diffracting (S1) the X-ray beam (B) into a first beam component (BC1) comprising a first direction (D1) and a second beam component (BC2) comprising a second direction (D2) tilted with respect to the first direction (D1) by means of a dispersive element comprising a prism; generating (S2) a first diffraction pattern (DP1) of the first beam component (BC1) and a second diffraction pattern (DP2) of the second beam component (BC2) by means of a first grating, the second diffraction pattern (DP2) shifted with respect to the first diffraction pattern (DP1); and aligning (S3) a second grating with at least one opening in such way that the at least one opening is aligned along a line (d) from a maximum (MA) to a minimum (MI) of an intensity of the first diffraction pattern (DP1) or of the second diffraction pattern (DP2).

15. A non-transitory computer-readable medium, on which is stored a computer program for spectral filtering of X-ray beam, said computer program including instructions executable by a processor for carrying out a plurality of acts, from among said plurality there being the acts of; diffracting (S1) the X-ray beam (B) into a first beam component (BC1) comprising a first direction (D1) and a second beam component (BC2) comprising a second direction (D2) tilted with respect to the first direction (D1) by means of a dispersive elemant comprising a prism; generating (S2) a first diffraction pattern (DP1) of the first beam component (BC1) and a second diffraction pattern (DP2) of the second beam component (BC2) by means of a first grating, the second diffraction pattern (DP2) shifted with respect to the first diffraction pattern (DP1); and aligning (S3) a second grating with at least one opening in such way that the at least one opening is aligned along a line (d) from a maximum (MA) to a minimum (MI) of an intensity of the first diffraction pattern (DP1) or of the second diffraction pattern (DP2).

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) A more complete appreciation of the invention and the attendant advantages thereof will be more clearly understood by reference to the following schematic drawings, which are not to scale, wherein:

(2) FIG. 1 shows a schematic diagram of a grating arrangement for spectral filtering of an X-ray beam according to an exemplary embodiment of the invention;

(3) FIG. 2 shows a schematic diagram of a grating arrangement for spectral filtering of an X-ray beam according to an exemplary embodiment of the invention;

(4) FIG. 3 shows a schematic diagram of an X-ray system according to an exemplary embodiment of the invention;

(5) FIG. 4 shows a schematic diagram of a grating arrangement for spectral filtering of an X-ray beam according to an exemplary embodiment of the invention;

(6) FIG. 5 shows a set of spectra of the spectral filtered X-ray beam for explaining the invention;

(7) FIGS. 6A, 6B and 6C show schematic diagrams of grating arrangements according to exemplary embodiments of the invention wherein the dispersive element and the first grating are integrated into a dispersive grating;

(8) FIGS. 7A and 7B show schematic diagrams of grating arrangements according to exemplary embodiments of the invention wherein the first grating is a microlensing grating;

(9) FIG. 8 shows a schematic diagram of a grating arrangement for spectral filtering of an X-ray beam according to an exemplary embodiment of the invention; and

(10) FIG. 9 shows a flowchart diagram of a method for spectral filtering of an X-ray beam according to an exemplary embodiment of the invention.

DETAILED DESCRIPTION OF EMBODIMENTS

(11) The illustration in the drawings is schematically and not to scale. In different drawings, similar or identical elements are provided with the same reference numerals. Generally, identical parts, units, entities or steps are provided with the same reference symbols in the figures.

(12) Apparently, the described embodiments are only some embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making any creative effort shall fall within the protection scope of the present invention.

(13) The grating arrangement for spectral filtering of an X-ray beam may be arranged in the beam path of an X-ray tube of a tomography system or of any other medical X-ray imaging system.

(14) FIG. 1 shows a schematic diagram of a grating arrangement for spectral filtering of an X-ray beam according to an exemplary embodiment of the invention.

(15) The Talbot effect is a near-field diffraction effect. When a plane wave is incident upon a periodic diffraction grating, the image of the grating is repeated at regular distances away from the grating plane.

(16) A first grating 20 represents the periodic diffraction grating, in FIG. 1, two plane waves of the first beam component BC1 and the second beam component BC2 are visualized. The first beam component BC1 and the second beam component BC2 are tilted, spanning a tilt angle +.

(17) A spatial modulation of period of a plane wave, e.g. a plane wave hitting a grating, is reproduced after a certain distance behind the grating. The distance is called the Talbot-length L.sub.Talbot, and the repeated images are called self images or Talbot images. The intensity distribution at any point behind the grating is called diffraction pattern. In FIG. 1 two diffraction pattern DP1 and DP2 of a first order are shown. Furthermore, at half the Talbot length, a self-image also occurs, but phase-shifted by half a period (the physical meaning of this is that it is laterally shifted by half the width of the grating period). At smaller regular fractions of the Talbot length, sub-images can also be observed.

(18) If the grating is a pi-phase grating, then after odd multiples of L.sub.Talbot/16 an interference pattern is present, i.e. and intensity modulation with twice the spatial frequency of the grating. A so-called pi/2 phase grating may also be considered, but then the interesting interference pattern occurs at a different distance and a different spatial frequency.

(19) At the Talbot distance, a wavefront with just a phase modulation is present. In the fractional distances, the phase modulation has been transformed into an intensity modulation which is exploited. The first diffraction pattern DP1 and the second diffraction pattern DP2 each comprise maxima MA and minima MI of intensity. The second grating may be moveable along a line d from one maximum MA to one minimum MI of intensity of the first diffraction pattern DP1 or of the second diffraction pattern DP2.

(20) FIG. 2 shows a schematic diagram of a grating arrangement for spectral filtering of an X-ray beam according to an exemplary embodiment of the invention.

(21) FIG. 2 shows an illustration of the Talbot filtration effect for spectral filtering of an X-ray beam B. Two quasi-monochromatic components BC1 and BC2 of the X-ray beam B are singled out for illustration purposes. These two quasi-monochromatic components BC1 and BC2 are basically parallel to each other before they hit the dispersive element 10. The higher energy component BC1 is diffracted less than the low energy component BC2 by the dispersive element 10 and the interference fringes formed by means of the first grating 10 at the location of the second grating 30 are shifted with respect to one another.

(22) In the X-ray regime, the shift of the fringes of the first diffraction pattern DP1 and the second diffraction pattern DP2 from their reference position (no prism present) is inversely proportional to the square X-ray energy. The phase itself goes inversely with energy, the phase of the interference pattern with 1/E.sup.2. This effect can be used in conjunction with a certain analyzer grating to single out one component and block the other.

(23) According to one embodiment, a grating arrangement 100 for spectral filtering of an X-ray beam B comprises a dispersive element 10, a first grating 20, and a second grating 30.

(24) The dispersive element 10 is configured to diffract the X-ray beam B into a first beam component BC1 comprising a first direction D1 and a second beam component comprising BC2 a second direction D2, tilted with respect to the first direction.

(25) The first grating 20 is configured to generate a first diffraction pattern DP1 of the first beam component BC1 and a second diffraction pattern DP2 of the second beam component BC2, the second diffraction pattern DP2 shifted with respect to the first diffraction patter DP1; and

(26) The second grating 30 comprises at least one opening 31 which is aligned along a line d from a maximum MA to a minimum MI of intensity of the first diffraction pattern DP1 or of the second diffraction pattern DP2.

(27) Optionally, according to an embodiment, the first grating 20 and/or the second grating 30 is configured to be movable in such way that the at least one opening 31 is moveable along the line d from the maximum MA to the minimum MI of intensity of the first diffraction pattern DP1 or of the second diffraction pattern DP2.

(28) FIG. 3 shows a schematic diagram of an X-ray system according to an exemplary embodiment of the invention.

(29) The X-ray system may comprise an X-ray source 210, which is adapted to generate a polychromatic spectrum of X-rays, i.e. an X-ray beam B, a detector 220 and at least one grating arrangement 100.

(30) The grating arrangement 100 can be applied in a multitude of fields where the requirements of the filtration of X-ray spectra goes beyond what is traditionally achievable using the insertion of a certain material and using attenuation according to the linear attenuation coefficient of that material. Typical application might be medical imaging, as for instance, mammography, interventional imaging, X-ray computed tomography (X-ray CT), producing topographic images, non-destructive testing, X-ray microscopy, bio-medical imaging and many more.

(31) The grating arrangement 100 may filter the X-ray beam B into a filtered X-ray beam B1 comprising a modified spectrum.

(32) FIG. 4 shows a schematic diagram of a grating arrangement for spectral filtering of an X-ray beam according to an exemplary embodiment of the invention.

(33) FIG. 4 shows relative shifts of the interference patters of two quasi-monochromatic components corresponding to different energies in the X-ray wave field.

(34) In the lower part of FIG. 4, the second grating 30 is shown. The second grating 30 may comprise multiple openings 31 and bars 32. The bars 32 and the openings 31 of the second grating 30 may form and be arranged as a periodic structure.

(35) The high energy component corresponding to the second diffraction pattern DP2 is transmitted when the openings 31 of the second grating 30 are brought in alignment with the maxima MA of the intensity for the high energy component.

(36) Contrary, the low energy component corresponding to the first diffraction pattern DP1 is transmitted when the openings 31 of the second grating 30 are brought in alignment with the maxima of the intensity for the low energy component.

(37) In the upper part of FIG. 4, a lateral intensity distribution is shown. The Y-axis shows the intensity of the high and low energy component, the X-Axis denotes the place x. The two diffraction pattern DP1 and DP2 are visualized by two functions comprising a sinusoidal form.

(38) FIG. 5 shows a set of spectra of the spectral filtered X-ray beam for explaining the invention. The experimental realization of the spectral Talbot filtration effect is presented in FIG. 5. For this experiment a conventional X-ray tube spectrum with the tube voltage set to 38 kV was used.

(39) FIG. 5 shows a family of curves as a set of spectra, each spectrum of which is given by a spectrum recorded at a different position of the second grating 30. The spectra shown were measured with a high-purity germanium detectors (HPGe) and feature energy resolution better than 1 keV. The modulations in the spectrum are due to the described effect illustrated in the figure description corresponding to FIG. 4, i.e. that the various monochromatic components in the spectrum get more or less blocked by the second grating 30 depending on the relative position of the fringes to the absorbing grating structures. The black arrow indicates the effect of moving the second grating 30 along a line d from a maximum MA to a minimum MI of intensity of the first or the second diffraction pattern.

(40) The efficiency of the filtration to radiation of a given energy depends strongly on the visibility of the fringes at that energy. Hence, it is desirable to have as high a visibility as possible realized in the gratings interferometer.

(41) FIGS. 6A, 6B and 6C show schematic diagrams of grating arrangements according to exemplary embodiments of the invention wherein the dispersive element is mounted on top of the first grating 20.

(42) FIG. 6A shows a schematic diagram of a grating arrangement 100 wherein the dispersive element 10, along the direction of the X-ray beam B, is mounted on top of the first grating 20, such as to constitute a dispersive grating 40. The dispersive grating 40, which jointly incorporates the dispersive element 10 and the first grating 20, is configured for diffracting the X-ray beam B into the first beam component BC1 comprising the first direction D1 and the second beam component BC2 comprising the second direction D2, wherein the second direction is being tilted with respect to the first direction. The dispersive grating 40 is furthermore arranged for generating the first diffraction pattern (not shown) of the first beam component and the second diffraction pattern (not shown) of the second beam component, wherein the second diffraction pattern is being shifted with respect to the first diffraction pattern. In this specific example, dispersive element 10 is a triangular prism. Optionally, according to a specific embodiment, the grating arrangement 100 furthermore comprises a second grating 30.

(43) Similar to FIG. 6A, FIG. 6B shows a schematic diagram of a grating arrangement 100 wherein the dispersive element 10, along the direction of the X-ray beam B, is mounted on top of the first grating 20 such as to constitute a dispersive grating 40. However, in this specific example, dispersive element 10 comprises a periodic structure of prisms 50, wherein each of such prisms is configured for diffracting the X-ray beam B into the first beam component BC1 comprising a first direction D1 and the second beam component comprising BC2 the second direction D2, and wherein said second direction is tilted with respect to the first direction. In this specific example, the periodic structures of dispersive elements 10 and first grating 20 have periods Td and Tg, respectively, wherein period Td equals half of Period Tg. Please note the slopes of the prisms 50 not necessarily equal that of dispersive element 10 as comprised in the exemplary embodiment of the invention depicted in FIG. 6A. Alternatively, according to another exemplary embodiment of the invention, the periodic structure of prisms 50 may be mounted, along the direction of the X-ray beam B, at the bottom of the first grating 20 such as to constitute a dispersive grating 40. Optionally, according to another exemplary embodiment of the invention, the grating arrangement 100 furthermore comprises a second grating 30.

(44) Similar to FIG. 6B, FIG. 6C shows a schematic diagram of a grating arrangement 100 wherein the dispersive element 10, along the direction of the X-ray beam B, is mounted on top of the first grating 20 such as to constitute a dispersive grating 40, and wherein the dispersive element 10 comprises a periodic structure of prisms 50. However, in this specific example, the dispersive element 10 and the first grating 20 are integrated into the dispersive grating 40, wherein the prisms 50 (which are, for the purpose of explanation, identical to those of the specific example as displayed in FIG. 6B) are super-imposed on the periodic structure of the first grating 20. Consequently, contrary to the specific example as depicted in FIG. 6B, in this exemplary embodiment of the invention, no gaps are present between the prisms 50 and the minima of the periodic structure. Similar to the exemplary embodiment of the invention as displayed in FIG. 6B, period Td equals half of Period Tg. Optionally, according to a specific embodiment, the grating arrangement 100 furthermore comprises a second grating 30.

(45) FIGS. 7A and 7B show schematic diagrams of grating arrangements according to exemplary embodiments of the invention wherein the first grating is a microlensing grating.

(46) FIG. 7A shows a schematic diagram of a grating arrangement 100 comprising a dispersive element 10 and a first grating 20 being a micro lensing grating. In this specific example, the microlensing grating is constituted by a periodic structure of triangular prisms. Alternatively, according to another exemplary embodiment of the invention, the micro lensing grating may be constituted by semi-circular or parabolic prisms. In this specific example, the microlensing grating has a height equal to (2n+1)*pi/2, wherein n denotes the amount of fringes as comprised in the microlensing grating. In this specific embodiment the dispersive element 10 comprises a periodic structure of prisms 50. In this specific example, the periodic structure of the dispersive element 10 and the first grating 20 have periods Td and Tg, respectively, wherein period Td equals period Tg. Optionally, according to a specific embodiment of the invention, the dispersive element 10 may be mounted, along the direction of X-ray beam B, on top of the first grating 20 such as to constitute a dispersive grating. Alternatively, according to another exemplary embodiment of the invention, the dispersive element 10 may be mounted, along the direction of X-ray beam B, at the bottom of the first grating 20 such as to constitute a dispersive grating. Optionally, according to another specific embodiment of the invention, the grating arrangement 100 furthermore comprises a second grating 30. Owing to the first grating 20 being a microlensing grating, the duty cycle of the second grating 30 may be reduced compared to the exemplary embodiments of the invention as displayed in FIGS. 6A, 6B and 6C.

(47) Similar to FIG. 7A, FIG. 7B shows a schematic diagram of a grating arrangement 100 comprising a dispersive element 10 and a first grating 20 being a microlensing grating. However, in this specific example the prisms 50 (which are, for the purpose of explanation, identical to those of the specific example as displayed in FIG. 6B) are superimposed on the periodic structure of the microlensing grating. Consequently, contrary to the specific example as depicted in FIG. 7A, in this exemplary embodiment of the invention, no gaps are present between the prisms 50 and the microlensing grating. Hence, in this exemplary embodiment of the invention, the dispersive element 10 and the first grating 20 being a micro lensing grating are integrated into a dispersive grating 40. The micro lensing grating has a height equal to (2n+1)*pi/2, wherein n denotes the amount of fringes as comprised in the micro lensing grating. Similar to the exemplary embodiment of the invention as displayed in FIG. 7A, period Td equals period Tg.

(48) FIG. 8 shows a schematic diagram of a grating arrangement for spectral filtering of an X-ray beam according to an exemplary embodiment of the invention.

(49) The spatial separation between the various fringes, corresponding to different mono-chromatic components in the original wave-field, increases with the refractive index of the prism and with the prism angle. It is determined by the total phase-gradient imprinted onto the wave field by the prism.

(50) The duty cycle of both the first grating 20 and the second grating 30 can be tuned in such a way as to obtain interference fringes with higher visibility. In this way spectral separation or selection by splitting in the spatial domain is even more efficient when used together with appropriate second gratings 30 with a pitch adapted to the particular needs of the application. Much more complex masks can be designed so that pre-selected mono-chromatic components can be singled out arbitrarily. Shifting the second gratings 30 can easily also be used to quickly modify the spectrum with only a tiny lateral displacement, easily realized with, i.e. piezo-electric actuators.

(51) For very high gradients realized, e.g. by a very steep grating (close to 180 degree) or a very electron-dense material, the energy dispersion might be so large that energies will wrap, meaning that fringes corresponding to distinct energies will again align. This can lead to quasi-periodic oscillation of the transmittance of the filter as a function of energy (leading to comb-like spectra), a feature very difficult to obtain by other means for X-rays. These combs could be shifted in energy via a translation of the second grating 30.

(52) The comb structure can of course be easily removed by cascading two or more of the proposed filters with different prisms. To avoid the attenuation gradient cascading could also help by putting two identical systems behind one another with the only difference of flipping the prism in one case.

(53) The further elements and reference signs of FIG. 8 are already explained and described in the description corresponding to FIG. 4. Therefore, a repeated description of these elements and reference signs is omitted.

(54) FIG. 9 shows a flowchart diagram of a method for spectral filtering of an X-ray beam according to an exemplary embodiment of the invention.

(55) The method for spectral filtering of an X-ray beam B may comprise the following steps:

(56) As a first step of the method, diffracting S1 the X-ray beam B into a first beam component BC1 comprising a first direction D1 and a second beam component BC2 comprising a second direction D2 tilted with respect to the first direction D1 by means of a dispersive element 10 is performed.

(57) As a second step of the method, generating S2 a first diffraction pattern DP1 of the first beam component BC1 and a second diffraction pattern DP2 of the second beam component BC2 by means of a first grating 20 is conducted, the second diffraction pattern DP2 shifted with respect to the first diffraction pattern DP.

(58) As a third step of the method, aligning S3 a second grating 30 with at least one opening 31, in such a way that the at least one opening 31 is aligned along a line d from a maximum MA to a minimum MI of an intensity of the first diffraction pattern DP1 or of the second diffraction pattern DP2 is conducted.

(59) Optionally, according to an embodiment of the invention, in a further step of the method, moving S3 the first grating 20 and/or the second grating 30 with at least one opening 31 in such way is conducted, that the at least one opening 31 is moved moveable along a line d from a maximum MA to a minimum MI of an intensity of the first diffraction pattern DP1 or of the second diffraction pattern DP2.

(60) While the invention has been illustrated and described in detail in the drawings and foregoing description, such illustration and description are to be considered illustrative or exemplary and not restrictive; the invention is not limited to the disclosed embodiments. Other variations to the disclosed embodiments can be understood and effected by those skilled in the art and practicing the claimed invention, from a study of the drawings, the disclosure, and the appended claims.

(61) In the claims, the word comprising does not exclude other elements or steps, and the indefinite article a or an does not exclude a plurality. A single processor or controller or other unit may fulfill the functions of several items recited in the claims. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage. Any reference signs in the claims should not be construed as limiting the scope.

LIST OF REFERENCE SIGNS

(62) 10 dispersive element 20 first grating 30 second grating 40 dispersive grating 50 prism 31 opening 32 bar 100 grating arrangement 200 X-ray system 210 X-ray source 220 X-ray detector B X-ray beam B1 filtered X-ray beam BC1 first beam component BC2 second beam component + tilt angle d line D1 first direction D2 second direction DP1 first diffraction pattern DP1-1 diffraction pattern of higher order DP2 second diffraction pattern MA maximum MI minimum Td period of the dispersive element Tg period of the first grating