Plenoptic X-ray imager with diffraction crystals

Abstract

The invention relates to a plenoptic imaging system for acquiring an image of an object, this system comprising: - a source for generating an X-ray beam directed towards the object, - a main optical device for receiving and reflecting the beam from the object, - an array of lenses or holes, - a photodetector array, each receiving an X-ray beam from a lens or hole. According to the invention, the main optical device comprises at least one curved crystal. Figure for the abstract: Fig. 1

Description

Title of the invention: Plenoptic imager for X-rays with diffraction crystals Technical field

[0001] The present invention relates to a plenoptic imaging system for acquiring an image of an object. It finds a particularly interesting application in the field of biological imaging ranging from cells to small animals, but also in materials science.

[0002] The invention aims at an improvement of so-called plenoptic or “lightfield” cameras in English. State of the prior art

[0003] Generally speaking, plenoptic imaging consists of refocusing an image digitally from a single physical acquisition. This refocusing makes it possible to reconstruct a scene in three dimensions and if the object is transparent (which is the case when using X-rays) the volume can be reconstructed in three dimensions.

[0004] In the visible, the plenoptic camera is composed of a lens or a set of lenses, for example a microscope objective, followed by a matrix of lenses and then a pixelated detector. This set creates numerous sub-images of the same scene or of an object which, after digital processing, allows digital refocusing at the desired distance.

[0005] We know the document T. Georgiev and C. Intwala, “Light field camera design for integral view photography,” Adobe System, Inc, Tech. Rep., 2003. This document describes the principle of a plenoptic camera in the visible.

[0006] The present invention aims at the design of a plenoptic camera for use with X-rays. This makes it possible to visualize certain objects in transparency and thus to carry out 3D reconstructions.

[0007] We know the document E. Longo et AL., “Flexible Plenoptic X-ray Microscopy” Photonics, February 2022. This document describes the principle of an X-ray-based plenoptic camera. However, the lenses used do not allow 3D reconstructions to be carried out. X-ray lenses, such as Fresnel lenses (“Fresnel Zone plate” in English) or refractive lenses have two intrinsic problems: very low numerical aperture and very high chromatism.

[0008] The first problem concerns the lateral and longitudinal resolutions which vary in 1 / NA and 1 / NA2 respectively, with NA the numerical aperture of the optical system. Optics for hard X-rays (i.e. for photon energies above a few keV which is equivalent to wavelengths below 1 nm) have ac typically have numerical apertures of 10 4. So the lateral resolution is equivalent to about 10,000 times the wavelength (i.e. 100 nm at 1 keV), which is very poor compared to visible optics which easily achieve an NA of 1 and even slightly higher than 1 with submerged microscopes. It should be noted here that the most powerful commercial visible microscopes have spatial resolutions much lower than 100 nm. As it stands, there is no point in moving into X-rays, which are technically much more complex to manage than the visible.

[0009] The first problem is related to the aspect ratio between the lateral and longitudinal resolutions which varies in 1 / NA and then produces voxels having an anamorphosis of 10,000. This anamorphosis prevents a three-dimensional reconstruction. In such a case, performing plenoptics under X-rays is no longer of interest.

[0010] The second problem prevents the use of X-ray plenoptics with table sources which emit polychromatic radiation and therefore produce blurred images.

[0011] The present invention aims to provide a new X-ray plenoptic imaging system enabling the production of high-quality three-dimensional reconstructions.

[0012] Another object of the invention is a novel high-resolution plenoptic camera. Statement of the invention

[0013] At least one of the objectives is achieved with a plenoptic imaging system for acquiring an image of an object, this system comprising: - a source to generate an X-ray beam towards the object, - a main optical device to receive and reflect the beam coming from the object, - a matrix of lenses or holes, - an array of photodetectors, each receiving a beam of X-rays from a lens or hole.

[0014] According to the invention, the main optical device comprises at least one curved crystal.

[0015] By photodetector array is meant, for example, any detector capable of capturing in a spatially distinct manner the X-ray beams coming from the matrix of lenses or holes. Such a detector is, for example, a CCD sensor.

[0016] The present invention makes it possible to produce an X-ray camera capable of producing 3D views using the plenoptic technique. Indeed, the optical system for X-rays according to the invention proposes a main optical device with a numerical aperture greater than the systems of the prior art. Compared to X-ray systems using Fresnel lenses for example, the system according to the invention makes it possible to achieve a numerical aperture of the order of 0.3, which improves the lateral resolution by a factor of 3000 and the longitudinal resolution by a factor of 9 million. In addition, the anamorphosis of the voxels is only a factor of 3, which is easily compensated for numerically. These characteristics allow the production of true 3D reconstructions from a single acquisition.

[0017] The ratio between longitudinal resolution and lateral resolution varies as 1 / NA, with NA the numerical aperture.

[0018] Ideally, with the system according to the invention, one can ideally approach a numerical aperture equal to 1, in particular so as to have cubic voxels.

[0019] Preferably, the X-ray source and the curved crystal are determined so that the ratio 1 / NA is less than 10, therefore NA greater than 0.1

[0020] For example, one can define a useful surface (surface of the curved crystal capable of reflecting the incident X-ray beam) of the curved crystal sufficiently large to ensure a strong NA greater than 0.1.

[0021] The X-ray beam reflected by the curved crystal forms an image of the object beyond the image focal plane of the curved crystal; the matrix of lenses or holes being placed beyond this image focal plane.

[0022] According to one embodiment of the invention, the source, the curved crystal and the orientation of the curved crystal can be determined so that the X-ray beam is reflected according to the diffraction law known as Bragg's law:

[0023] 2d sm(0)=nX

[0024] where 0 is the diffraction angle, X the wavelength of the X-rays and "d" the reticular pitch, therefore the distance between two crystal planes of the curved crystal.

[0025] Compliance with this law ensures better reflectivity of the curved crystal.

[0026] According to a preferred embodiment, the source can be positioned on a first virtual circle, known as the Rowland circle, with radius R equal to half the radius of a second virtual circle in which a crystal plane of the curved crystal is inscribed.

[0027] The two virtual circles are concentric, the Rowland circle being adjacent to the central point of the curvature made on the curved crystal.

[0028] With such a circle, when the source is positioned on the circle, the image focal point of the curved crystal is also located on the same circle.

[0029] In addition to all of the above, the surface of the curved crystal can be polished according to a curvature identical to the curvature of a crystal plane of the curved crystal according to a geometry called Johann geometry.

[0030] In this case, the polishing carried out on the useful surface of the curved crystal makes it possible to obtain a surface said to be parallel to the crystallographic planes of the curved crystal. This realization makes it possible to improve the numerical aperture, but only on a part of the surface presented by the curved crystal.

[0031] According to one embodiment, the surface of the curved crystal can be polished according to a curvature identical to the curvature of the Rowland circle according to a geometry called Johansson geometry.

[0032] In this case, the polishing carried out on the useful surface of the curved crystal makes it possible to obtain a surface which crosses crystallographic planes of the curved crystal. Such an achievement makes it possible to ensure a good numerical aperture on almost the entire polished surface presented by the curved crystal.

[0033] In Johan's or Johansson's geometry, the source is ideally positioned on the Rowland circle but it is possible to consider positioning it inside or outside the circle.

[0034] According to one embodiment of the invention, the matrix of lenses or holes may be a one-dimensional matrix and each photodetector is a one-dimensional photodetector.

[0035] In such a case, one can envisage producing an image in one direction and producing a spectrum in the other direction.

[0036] Alternatively, the array of lenses or holes may be a two-dimensional array and each photodetector is a two-dimensional photodetector.

[0037] According to a preferred embodiment of the invention, the curved crystal may be of the toric type.

[0038] In the system according to the invention, the toroidal crystal has two advantages: a large effective diffraction surface, leading to a high numerical aperture and good collection of the beam flux, beneficial for the image quality.

[0039] According to one embodiment of the invention, the curved crystal may be of the cylindrical or spherical type.

[0040] According to one embodiment of the invention, the curved crystal may be a single crystal with a single radius of curvature.

[0041] According to a preferred embodiment, the curved crystal may be a single crystal with double perpendicular radii of curvature.

[0042] According to one embodiment of the invention, the main optical device may comprise two crystals, each having a single radius of curvature, the two radii of curvature being perpendicular.

[0043] When there is only one radius of curvature, focusing is done in one direction only. In such a case, two crystals placed at approximately 90° to each other can be used, thus ensuring focusing in both directions. An example of such an implementation is the so-called Kirkpatrick-Baez assembly. This solution makes it possible to significantly reduce the constraints of producing curved crystals.

[0044] One can work with a curved crystal in 2D, whatever the shape, or with two curved crystals in 1D and mounted together or with a curved crystal mounted alone.

[0045] According to an advantageous characteristic of the invention, the source can be a monochromatic source.

[0046] Any type of X-ray monochromator can be used, such as a crystal or diffraction grating monochromator.

[0047] Thus, with monochromatic radiation incident on the object, the reflectivity of the curved crystal can be very high, several tens of percent compared to a polychromatic source.

[0048]

[0049] According to a preferred embodiment, the monochromatic source may be a source point obtained from a polychromatic source illuminating a second curved crystal whose image focal plane constitutes said source point.

[0050] Such an arrangement makes it possible to use a second curved crystal to make the incident X-rays monochrome. This second curved crystal may have identical or possibly different parameters from the first curved crystal. This second curved crystal is placed between the source and the object. This solution ensures that the X-rays passing through the object are reflected with very good efficiency by the curved crystal, greatly limiting the absorbed dose.

[0051] This is a considerable advantage compared to current X-ray tomography which uses hundreds or thousands of views to form the three-dimensional image, producing a high dose on the person, animal or object as well as a long exposure time.

[0052] According to another aspect of the invention, there is provided a novel plenoptic camera comprising the system as described above and a processing unit for the digital reconstruction of images at different depths of field.

[0053] Description of the figures and embodiments.

[0054] Other advantages and particularities of the invention will appear on reading the detailed description of implementations and embodiments which are in no way limiting, and the following appended drawings:

[0055] [Fig-1]: [Fig.l] is a schematic view of the system according to the invention,

[0056] [Fig.2]: [Fig.2] is a schematic top view of the system according to the invention illustrating the path of X-rays according to Johann geometry,

[0057] [Fig.3]: [Fig.3] is a schematic view illustrating Johann's geometry,

[0058] [Fig.4]: [Fig.4] is a schematic top view of the system according to the invention illustrating the path of X-rays according to Johansson geometry,

[0059] [Fig.5]: [Fig.5] is a schematic view illustrating Johansson's geometry, and

[0060] [Fig.6]: [Fig.6] is a schematic view of a crystal-based monochromator curve in the system according to the invention.

[0061] The embodiments which will be described below are in no way limiting; In particular, it will be possible to implement variants of the invention comprising only a selection of features described below isolated from the other features described, if this selection of features is sufficient to confer a technical advantage or to differentiate the invention from the prior art. This selection includes at least one preferably functional feature without structural details, or with only part of the structural details if only this part is sufficient to confer a technical advantage or to differentiate the invention from the prior art.

[0062] In particular, all the variants and all the embodiments described are intended to be combined with each other in all combinations where there is nothing technically opposed to this.

[0063] Although the invention is not limited thereto, a plenoptic imager for X-rays based on a curved crystal having a toric surface will now be described.

[0064] In [Fig.l] we can see a source 1 capable of emitting a beam of X-rays towards an object 2 to be imaged. The X-ray beam is then reflected by a curved crystal 3 suitably designed and positioned in alignment with the source 1 and the object 2. The reflected X-ray beam then reaches a lens matrix and then a detector 5. This is a plenoptic system in which the main lens has been advantageously replaced by a curved crystal having a high numerical aperture.

[0065] The beam passing through each lens of the matrix 4 is collected on a part of the detector 5.

[0066] In [Fig.l], an intermediate image 6 is simply illustrated for information purposes. It represents the image of the object, this image being contained in the reflected X-ray beam.

[0067] A single acquisition thus makes it possible to obtain several spatially separated flows at the detector level. Digital processing then makes it possible to carry out three-dimensional reconstructions in a conventional manner.

[0068] The X-ray source is a source at, for example, 11 keV. The invention can be applied to any type of X-ray. In particular, we speak of X-rays as soon as the optical index of the material is less than 1. Typically, this corresponds to approximately 20-30 eV. For the upper part, we can consider that gamma rays start at around 1 MeV when a photon can create an electron-positron pair.

[0069] The curved crystal 3 has a surface 3A that has been polished and positioned to serve as the working surface, i.e., the surface that receives and reflects the X-ray beam. The curved crystal geometry can be divided into two main aspects: the curvature of the internal planes of the crystal lattice and the curvature of the working surface 3A. Both can affect the imaging quality of the crystal, such as aberration, image fluence and numerical aperture. Adjusting the curvature of the internal crystal lattice planes optimizes the focusing performance of the crystal. Polishing along a toric curve has been found to achieve excellent results.

[0070] Generally speaking, a crystal reflects X-rays by diffraction on the crystal planes which behave like a lattice. The diffraction law is the so-called Bragg law:

[0071] 2dsin(S)=n.\

[0072] where 0 is the diffraction angle, X the wavelength of the X-rays and "d" the reticular pitch, therefore the distance between two crystal planes of the curved crystal. Therefore, each wavelength corresponds to a diffraction angle. Outside this angle the crystal does not reflect X-rays of this wavelength.

[0073] In reality, the crystals are not perfect: the reticular planes are not all spaced the same distance apart, creating an angular broadening for which a crystal will reflect monochromatic radiation. This angular band is commonly called the oscillation curve or "rocking curve" in English, and obviously depends on each crystal. For example, for a germanium crystal cut along the (220) planes, the "rocking curve" has a width at mid-height of 0.00383°, or 6.5x105 rad. This is a very low numerical aperture.

[0074]

[0075] Due to Bragg diffraction, the curved crystal behaves like a curved mirror for X-rays.

[0076] The curved crystals according to the invention are advantageously concave curved.

[0077] A curved crystal has a "focus circle" in the horizontal plane tangent to its center point. The radius of this circle is equal to half the radius of curvature of the crystal (radius of curvature of the crystal planes). This circle is called the Rowland circle and was defined for a concave lattice in visible light. If a point source lies on the Rowland circle of a concave curved crystal, it will be focused at another point on this circle.

[0078] In [Fig. 1], the Rowland circle 7 is tangent to the center of the curved crystal 3. The source 1 is positioned on this circle. The object to be imaged is located between the source and the curved crystal, inside the Rowland circle 7. The intermediate image 6 is located outside the Rowland circle in the optical axis of the reflected X-ray beam.

[0079] According to the invention, by curving the crystal and placing the source on a circle equivalent to twice the radius of curvature of the crystal, the rays which arrive on the surface form an angle which remains within the oscillation curve ("rocking curve") for an area of ​​the crystal.

[0080] [Fig.2] is a very schematic geometric representation in top view of the system according to the invention.

[0081] We distinguish a source A illuminating an object C to be imaged. The source A can be real or a source point created by a real source remote and whose image is relayed to this point.

[0082] The X-ray beam from A passing through C reaches an area of ​​the curved crystal B. The reflected beam is directed towards a lens matrix E before reaching the detector F.

[0083] The angle between the lines Bi-B0-B2 and A-Bo satisfies the Bragg condition, Bo being the central bridge of the curved surface of the curved crystal.

[0084] Curved crystal B has a polished surface in accordance with the so-called Johann geometry, that is to say the polishing is parallel to a crystal plane inside the curved crystal.

[0085] A Rowland circle G is shown. This circle has a radius equal to half the radius of curvature of the polished surface of the curved crystal. With such a circle, the source point A placed on the circle has its focal point A' also placed on the same Rowland circle.

[0086] The crystal being curved in one dimension or two dimensions, an intermediate image D, one dimension or two dimensions, is formed by respecting the formula for conjugation of thin lenses: l / CBo+l / BoD=l / f with f=RMsin(0) / 2 for the meridional plane and f=Rs / 2sin(0) for the sagittal plane, RM being the radius in the meridional plane and Rs being the radius in the sagittal plane. If the crystal is curved only in one dimension, then only the formula for the meridional plane is used.

[0087] The distances DE and EF respect the formula for thin lenses: l / DE+l / EF=l / f where here f is the focal length of the lenses placed in the plane E. In the case where a matrix of holes is used, there are no conditions to be fulfilled here.

[0088] In [Fig.3] the principle of Johann geometry is illustrated. The rays from the surface of the crystal and the crystal plane P are the same, so only rays reaching an area near the center of the crystal satisfy the Bragg condition.

[0089] Even if the source divergence is large enough to illuminate the entire crystal, only the main ray arriving at the center of the crystal satisfies the Bragg condition and can be intensely reflected. Although the crystal has a certain tolerance on the angle of incidence depending on its rocking curve, the width of the rocking curve is very narrow, 0.0029° for a nearly perfect crystal and 0.029° for an imperfect crystal. Therefore, the effective diffraction area is very small and the reflection efficiency of the crystal is quite low.

[0090] This can be improved by polishing the crystal in the crystal planes P and not parallel to them. This is the Johansson geometry as used in [Fig.4].

[0091] In [Fig.4] is also a very schematic geometric representation in top view of the system according to the invention. The principle and the elements are identical to those of [Fig.2] except the curved crystal is different.

[0092] The X-ray beam from A passing through C reaches the entire surface of the curved crystal B. The reflected beam is directed towards the lens array E before reaching the detector F.

[0093] The curved crystal B has a polished surface in accordance with the so-called Johansson geometry, that is to say the polishing has a curve identical to the curvature of the Rowland circle G.

[0094] The crystal being curved in one dimension or two dimensions, an intermediate image D, one dimension or two dimensions, is formed by respecting the formula for conjugation of thin lenses: l / CB0+l / B0D=l / f with f=RMsin(0) / 2 for the meridional plane and f=Rs / 2sin(0) for the sagittal plane, RM being the radius in the meridional plane and Rs being the radius in the sagittal plane. If the crystal is curved only in one dimension, then only the formula for the meridional plane is used.

[0095] The distances DE and EF respect the formula for thin lenses: l / DE+l / EF=l / f where here f is the focal length of the lenses placed in the plane E. In the case where a matrix of holes is used, there are no conditions to be fulfilled here.

[0096] In [Fig.5] the principle of Johansson geometry is illustrated. The radius of the internal surface of the crystal is equal to half the radius of its crystal plane P. Due to the theorem of the inscribed angle of a circle, such a geometry allows the rays from the source to arrive on the entire surface of the crystal at the Bragg angle.

[0097] With the system according to the invention, the source can advantageously be positioned on the Rowland circle. In this case, the maximum numerical aperture NA can be determined by: max(height / 2; width / 2) / (source-crystal distance). In an exemplary embodiment with a useful surface of 2cm in height and 4cm in width and a source-crystal distance of 13 cm, the maximum numerical aperture would be 2 / 13=0.15.

[0098] In [Fig.6] is shown a geometry of a two-crystal plenoptic camera allowing to very significantly reduce the dose received per sample / animal / person. We find the elements of [Fig.2] with a crystal B polished according to the Johann geometry. But one or both crystals can be polished according to the Johann or Johansson geometry.

[0099] In [Fig.6], the source A is a point source formed from a real source A' offset. This real source A' is polychromatic and illuminates a second curved crystal B' so that the beam reflected by this second crystal is monochromatic. The focal point of the beam reflected by the second crystal B' is the point source A.

[0100] Concerning the field of application of the invention, X-ray plenoptic imaging potentially affects all the fields normally covered by X-ray tomography, ranging from medical to biology, to materials science, metallurgy, mechanics, plasma physics, agri-food, cultural heritage etc.

[0101] Of course, the invention is not limited to the examples which have just been described and numerous adjustments can be made to these examples without departing from the scope of the invention.

Claims

Claims

1. Plenoptic imaging system for acquiring an image of an object, this system comprising: - a source for generating an X-ray beam towards the object, - a main optical device comprising at least one curved crystal for receiving and reflecting the beam coming from the object, - a matrix of lenses or holes, - an array of photodetectors, each receiving an X-ray beam coming from a lens or a hole, characterized in that the source is a monochromatic source.

2. System according to claim 1, characterized in that the source, the curved crystal and the orientation of the curved crystal are determined so that the X-ray beam is reflected according to the diffraction law known as Bragg's law: 2d sindy)=nd. where 0 is the diffraction angle, X the wavelength of the X-rays and "d" the reticular pitch, therefore the distance between two crystal planes of the curved crystal.

3. System according to any one of the preceding claims, characterized in that the source is positioned on a first virtual circle, known as the Rowland circle, of radius R equal to half the radius of a second virtual circle in which a crystal plane of the curved crystal is inscribed.

4. System according to any one of the preceding claims, characterized in that the surface of the curved crystal is polished according to a curvature identical to the curvature of a crystal plane of the curved crystal according to a geometry called Johann geometry.

5. System according to any one of claims 1 to 3, characterized in that the surface of the curved crystal is polished according to a curvature identical to the curvature of the Rowland circle according to a geometry called Johansson geometry.

6. A system according to any preceding claim, characterized in that the array of lenses or holes is a one-dimensional array and each photodetector is a one-dimensional photodetector.

7. System according to any one of claims 1 to 5, characterized in that the matrix of lenses or holes is a two-di- mensions and each photodetector is a two-dimensional photodetector.

8. System according to any one of the preceding claims, characterized in that the curved crystal is of the toric type.

9. System according to any one of claims 1 to 7, characterized in that the curved crystal is of the cylindrical type.

10. System according to any one of claims 1 to 7, characterized in that the curved crystal is of the spherical type.

11. System according to any one of claims 1 to 7, characterized in that the curved crystal is a single crystal with a single radius of curvature.

12. System according to any one of claims 1 to 7, characterized in that the curved crystal is a single crystal with double perpendicular radii of curvature s.

13. System according to any one of claims 1 to 7, characterized in that the main optical device comprises two crystals, each having a single radius of curvature, the two radii of curvature being perpendicular.

14. System according to any one of the preceding claims, characterized in that the monochromatic source is a source point obtained from a polychromatic source illuminating another curved crystal whose image focal plane constitutes said source point.

15. A plenoptic camera comprising the system according to any one of the preceding claims and a processing unit for the digital reconstruction of images at different depths of field.

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