[0001] The present invention relates to a method and apparatus for X-ray shaft expansion
and/or compression and/or collimation and/or focusing and/or X-ray magnification.
Technological background
[0002] Modern radiography and computer tomography has reached sub-micrometer resolution
[
P.J. Withers, Materials Today 10, 12, 26-34, (2007)]. Besides various scanning methods, a parallel projection of a collimated beam or
a cone projection of a divergent beam are widely employed [
U. Bonse, F. Busch, Progress in Biophysics and Molecular Biology, 56, 1/2, 133-169,
1996]. Whilst different methods of obtaining real space image contrasts are employed,
it is always mandatory to have 2d X-ray detectors with best possible spatial resolution.
For state of the art X-ray detectors the resolution is limited to few tens of micrometers.
To improve the radiographic/tomographic resolution beyond the detector limit in parallel
projection various X-ray shaft magnification devices and methods are known.
[0003] One of the technics that improves the tomographic/radiographic resolution by a factor
of up to 100 in projection-based imaging uses Bragg magnifiers [
P.J. Withers, Materials Today 10, 12, 26-34, (2007);
SPIE Proceedings 2516, 1995]. In such systems a single Bragg-diffracted X-ray beam from an asymmetrically cut
crystal results in an increase of the beam cross-section in one dimension. A second
scattering from an asymmetrically cut crystal rotated by 90° stretches the beam in
another dimension.
[0004] In recent years X-ray free electron lasers (FELs) such as the one currently in operation
in Hamburg, Germany are used for research in many disciplines. For example, by using
X-ray FELs it is possible to determine the structure of molecules critical to biology,
to determine ultrafast energy transfers within molecules and the structure of nanocrystals.
[0005] US 5,259,013 A discloses a hard X-ray magnification apparatus and method with submicrometer spatial
resolution of images in more than one dimension. A monochromatic hard X-ray beam is
applied to a specimen and thereafter is directed to arrive at a small angle of incidence
at a flat, optically polished surface of a nearly perfect crystal, to be diffracted
at the surface thereof. The diffracted X-ray beam is directed at a small angle of
incidence to the surface of a second nearly perfect crystal, the receiving surface
being oriented orthogonal to the surface of the first nearly perfect crystal.
[0006] Prior art document
JP H06-235704 A relates to a method for monochromatizing and enlarging X-rays, for example synchrotron
radiation by using a single crystal.
[0007] The magnification factor of Bragg-magnifiers with asymmetric cut crystals in coplanar
Bragg-scattering is determined by the ratio of exit and incidence angles. Thus, in
coplanar Bragg scattering the magnification factor drops rapidly with the decrease
of X-ray beam energy [
M. Stamponini, Nuclear Instruments and Methods in Physics research A 551, 119-124,
(2005)]. Importantly, in coplanar Bragg-scattering it is not possible to control or stabilize
the magnification factor over a larger energy or wavelength range. To stabilize the
magnification factor over a larger energy range, a new asymmetric crystal with a different
miss cut angle is required for each new X-ray energy or wavelength of interest.
Disclosure of the invention: problem, solution, advantages
[0008] It is an object of the present invention to provide a method and an apparatus for
X-ray shaft expansion and/or compression and/or collimation and/or focusing and/or
X-ray magnification in a broad energy or wavelength range with a single Bragg-scattering
setup and without the requirement to exchange the scattering crystals for each new
X-ray energy or wavelength of interest.
[0009] The problem is solved by the provision of a method for X-ray shaft expansion and/or
compression and/or collimation and/or focusing and/or X-ray image magnification, wherein
a first shaft of X-ray radiation is scattered in a first scattering process at a first
plurality of parallel lattice planes of a first crystal to generate a scattered second
shaft of X-ray radiation, wherein the scattered second shaft of X-ray radiation is
scattered in a second scattering process at a second plurality of parallel lattice
planes of a second crystal to generate a scattered third shaft of X-ray radiation,
wherein the first scattering process and the second scattering process are non-coplanar
Bragg scattering processes.
[0010] The first shaft of X-ray radiation and/or the scattered second shaft of X-ray radiation
and/or the scattered third shaft of X-ray radiation can be collimated or directional
shafts of radiation with a finite divergence. Furthermore, in particular when the
first, second or third shaft of X-ray radiation is a collimated or directional shaft
of radiation with a small divergence, the first shaft of X-ray radiation, the second
shaft of X-ray radiation or the third shaft of X-ray radiation can be configured as
X-ray beams.
[0011] The first shaft of X-ray radiation and/or the scattered second shaft of X-ray radiation
and/or the scattered third shaft of X-ray radiation can have a respective first, second
or third beam axis.
[0012] Bragg scattering occurs, when radiation with a wavelength comparable to atomic spacings
is scattered in a specular fashion by atoms of a crystalline system and undergoes
constructive interference. For a crystalline solid, the waves are scattered from lattice
planes separated by an inter-planar distance d. Scattered waves interfere constructively
when the difference between the path lengths of waves scattered at different parallel
lattice planes is equal to an integer multiple of the wavelength. Thus, constructive
Bragg scattering occurs when the Bragg condition 2d sin(θ) = nλ is satisfied, where
d is the inter-planar distance, n is a positive integer, λ is the wavelength of the
incident waves and θ is the incidence angle with the scattering lattice planes.
[0013] The non-coplanar Bragg scattering processes are preferably asymmetric Bragg scattering
processes.
[0014] In asymmetric Bragg scattering the lattice planes of the crystals off of which the
respective shaft of X-ray radiation is scattered are not parallel to the incidence
surface of the scattering crystal, the incidence surface being the crystal surface
onto which the shaft of X-ray radiation impinges. Since for the Bragg scattering process
the incidence and exit angle with the scattering lattice planes are equal, the incidence
and exit angle of the radiation with the incidence surface of the crystal are not
equal, resulting in an expansion or compression of the shaft of X-ray radiation.
[0015] The first crystal has an incidence surface onto which the first shaft of X-ray radiation
impinges at an incidence angle. The scattered second shaft of X-ray radiation leaves
the incidence surface at an exit angle. A surface normal of the incidence surface
and the beam axis of the incident first shaft of X-ray radiation define an incidence
plane. Similarly, the surface normal of the incidence surface and the beam axis of
the scattered second shaft of X-ray radiation define a scattering plane.
[0016] In coplanar Bragg scattering the incidence plane coincides with scattering plane.
In contrast, in non-coplanar Bragg scattering the incidence plane does not coincide
with scattering plane, i.e. these planes are not parallel. In non-coplanar Bragg scattering
the surface normal of the incidence surface is not parallel to the normal vector of
the scattering lattice planes.
[0017] In asymmetric coplanar Bragg scattering processes the magnification factor drops
rapidly with a decrease of X-ray radiation energy or increase in wavelength, respectively.
The reason for this drop of the magnification factor is that because of the coplanarity
condition the incidence angle of the first shaft of X-ray radiation with the scattering
lattice plane cannot be chosen independently of the incidence angle of the first shaft
of X-ray radiation with the incidence surface of the crystal.
[0018] The present invention is based on the insight that in non-coplanar Bragg scattering
the angle between the first and/or second shaft of X-ray radiation and the scattering
lattice plane and the incidence angle of the first and/or second shaft of X-ray radiation
with the incidence surface of the first or second crystal can be adjusted at least
over a certain range mostly independently from each other.
[0019] For example, when the Bragg condition is satisfied for asymmetric Bragg scattering,
i.e. when the surface normal of the incidence surface is not parallel to the normal
vector of the scattering lattice planes, the incidence angle of the incident X-ray
radiation with the incidence surface can be adjusted by rotating the scattering crystal
about the normal vector of the scattering lattice planes, all the while satisfying
the Bragg condition.
[0020] The applicant has found that in non-coplanar Bragg scattering processes an additional
degree of freedom for the orientation of the scattering crystal can be exploited to
adjust the incidence and/or exit angles of the X-ray radiation with the incidence
surface and, thus, the magnification factor for X-ray radiation of a certain wavelength
can be fixed or stabilized over a certain large energy or wavelength range.
[0021] By employing two successive non-coplanar Bragg scattering processes, an X-ray image
can be magnified or compressed in two dimensions.
[0022] Preferably, in contrast to prior art the incidence surface of the first crystal and
the incidence surface of the second crystal are not restricted to be orthogonal to
each other.
[0023] The inventive method can also be used for monochromatization of X-ray radiation,
for polarisation experiments, for tomography, radiography or for tweaking of coherence
properties of radiation, in particular of X-ray radiation.
[0024] Due to the non-coplanar Bragg scattering processes the cross section of the first,
second or third shaft of X-ray radiation can be subjected to an isomorphic distortion.
For example if a cross section of the first shaft of X-ray radiation is rectangular,
the cross section of the scattered third shaft of X-ray radiation can have the shape
of a parallelogram. If the first shaft of X-ray radiation has a circular cross section,
the scattered third shaft of X-ray radiation can have an elliptical cross section.
[0025] Similarly, a magnified or compressed X-ray image can be isomorphically distorted.
[0026] Preferably, a sample is disposed in the first shaft of X-ray radiation or in the
scattered second shaft of X-ray radiation or in the scattered third shaft of X-ray
radiation for imaging, and/or the scattered third shaft of X-ray radiation is detected
with an X-ray detector.
[0027] Further preferably, the scattered third shaft of X-ray radiation detected with the
X-ray detector, in particular an X-ray image detected with the X-ray detector, is
corrected for the distortion using image processing methods.
[0028] Furthermore, the method can be used to determine lattice constants and/or unit cell
angles of the first crystal and/or the second crystal.
[0029] Still further, more than two non-coplanar Bragg scattering processes can be employed
in the method.
[0030] The first crystal and/or the second crystal can be a symmetric cut or an asymmetric
cut crystal and/or an elastically bent crystal.
[0031] In crystallography, lattice planes of a crystal are usually described using Miller
indices (hkl) with h, k, I being integer. A family of lattice planes is defined by
vector hb
1+kb
2+hb
3 where b
1, b
2 and b
3 are the basis vectors of the reciprocal crystal lattice.
[0032] In the context of the present invention a symmetric cut crystal is a crystal whose
incidence surface is parallel to a lattice plane defined by three integer Miller indices.
Accordingly, an asymmetric cut crystal is a crystal having an incidence surface not
parallel to such a lattice plane. In analogy to the Miller indices, the surfaces of
asymmetric cut crystals could be specified using a vector (mno) where the indices
m, n, o are real numbers excluding integers.
[0033] Furthermore, in a more restricted sense, a symmetric cut crystal can be understood
as a crystal having a surface parallel to an (hkl) lattice plane with h, k, I integer
and with a maximum difference between h, k and I of less than 3, preferably less than
2, more preferably less than 1. Thus, using this definition a symmetric cut crystal
can have an incidence surface parallel to, for example the (100) or (020) or (113)
lattice planes, etc.
[0034] While the method works with both asymmetric cut and symmetric cut crystals it is
preferred that the crystals are symmetric cut crystals.
[0035] An advantage of using symmetric cut crystals is that symmetric cut crystals possess
lower surface energy compared to crystals with asymmetric cut surfaces. Therefore,
even naturally grown crystals of many minerals in ores are found in the so called
"equilibrium crystal shape" that has faces that would correspond to a symmetrically
cut crystal. Symmetrically cut crystals, therefore, are closer to their equilibrium
shape and therefore are generally more stable.
[0036] For symmetric cut crystals smoothening processes other than polishing, such as UHV-based
ion sputtering and/or annealing and the like can be used to achieve atomic scale smoothness.
When working at angles of total X-ray reflection and below, which is covered by this
invention, the surface quality is relevant.
[0037] The symmetric cut crystal may be cut with tolerances of less than 2°, preferably
less than 1°, more preferably less than 0.5°.
[0038] An elastically bent crystal has a crystal surface, in particular an incidence surface
for the first shaft of X-ray radiation or the scattered second shaft of X-ray radiation,
which is not planar but has a curvature. By using an elastically bent crystal focusing
and/or defocusing characteristics of the method can be manipulated or improved and/or
strain fields due to crystal lattice imperfections can be compensated for. For providing
an elastically bent crystal a mechanical crystal bending mechanism may be employed
to introduce the desired crystal lattice elastic deformation fields.
[0039] Preferably a wavelength for the first shaft of X-ray radiation is chosen, and an
incidence angle for the first shaft of X-ray radiation with an incidence surface of
the first crystal and/or an incidence angle for the scattered second shaft of X-ray
radiation with an incidence surface of the second crystal is chosen, and/or an exit
angle for the scattered second shaft of X-ray radiation with the incidence surface
of the first crystal and/or an exit angle for the scattered third shaft of X-ray radiation
with the incidence surface of the second crystal is chosen, and/or a magnification
factor is chosen, and the first and/or the second crystal are positioned and/or oriented
so that the Bragg condition for the first non-coplanar Bragg scattering process and
the second non-coplanar Bragg scattering process are fulfilled for the chosen wavelength
and the chosen incidence angle and/or exit angle and/or magnification factor.
[0040] By employing double non-coplanar Bragg scattering processes the additional degree
of freedom available for orienting the first and/or the second crystal can beneficially
be used to set or fix incidence and/or exit angles and/or magnification factors over
a large range of wavelengths, i.e. energies, of the X-ray radiation. Thus, in contrast
to the prior art it is possible to choose a wavelength and/or energy of the first
shaft of X-ray radiation and, in addition, to choose an incidence angle or exit angle
or magnification factor comparatively independently from the wavelength or the energy
of the X-ray radiation. In other words, because of the additional degree of freedom
accessible in non-coplanar Bragg scattering the first and/or the second crystal can
be positioned and/or oriented so that the Bragg condition for the first non-coplanar
Bragg scattering and the second non-coplanar Bragg scattering process are fulfilled
for the chosen wavelength and incidence angle, exit angle or magnification factor.
[0041] Preferably the energy of the first X-ray radiation is between 1 keV and 500 keV,
more preferably between 4 keV and 100 keV, further preferably between 4 keV and 50
keV, still further preferably between 5 keV to 30 keV.
[0042] It is furthermore preferred, that the wavelength of the first shaft of X-ray radiation
is changed and that the first crystal and/or the second crystal are repositioned and/or
reoriented so that the Bragg condition for the first non-coplanar Bragg scattering
process and the second non-coplanar Bragg scattering process are fulfilled for the
changed wavelength and the chosen incidence angle and/or exit angle and/or magnification
factor, and that further preferably the first crystal and/or the second crystal are
not exchanged or substituted for the changed wavelength of the first shaft of X-ray
radiation.
[0043] Thus, during conducting the method the wavelength of the first shaft of X-ray radiation
can be changed in a comparatively broad range. Due to the additional degree of freedom
accessible in non-coplanar Bragg scattering the first and second crystal can be reoriented
such that the Bragg condition for the first non-coplanar Bragg scattering and the
second non-coplanar Bragg scattering processes are fulfilled while simultaneously
the exit angle, incidence angle or magnification factor are kept relatively constant.
[0044] Preferably the first crystal is oriented or reoriented by applying a first rotation
to the first crystal, which includes at least one of
- a rotation about an axis not parallel to a normal vector of the first plurality of
parallel lattice planes to fulfill the Bragg condition for the first shaft of X-ray
radiation and the first plurality of parallel lattice planes, and/or
- a rotation about a normal vector of the first plurality of parallel lattice planes
to adjust the incidence angle of the first shaft of X-ray radiation with the incidence
surface of the first crystal.
[0045] In case both rotations are conducted the rotations must not necessarily be conducted
sequentially, but can be conducted in a combined rotation. It is also possible that
more than two rotations of the first crystal are conducted.
[0046] Still further preferably, the second crystal is oriented or reoriented by applying
a second rotation to the second crystal, which includes at least one of
- a rotation about a beam axis of the scattered second shaft of X-ray radiation, and/or
- a rotation about an axis to adjust the incidence angle of the scattered second shaft
of X-ray radiation with the incidence surface of second crystal, and/or
- a rotation about a surface normal of the incidence surface of the second crystal until
Bragg condition is satisfied for the scattered second shaft of X-ray radiation and
the second plurality of parallel lattice planes.
[0047] The rotation about an axis to adjust the incidence angle of the scattered second
shaft of X-ray radiation with the incidence surface of the second crystal is preferably
about an axis normal to the beam axis of the scattered second shaft of X-ray radiation
and parallel to a plane tangent to the incidence surface at a point of incidence.
The rotations can be either sequential rotations or they can be conducted in one combined
rotation.
[0048] The rotations of the first and/or second crystal can be rotations about Euler angles
of the first and/or second crystal.
[0049] For rotating the first and/or the second crystal manipulation stages comprising rotator
elements can be used.
[0050] For determining the individual rotations or the combined rotations a dedicated algorithm,
formula or computer program can be used.
[0051] An advantage of rotating the second crystal about the beam axis of the scattered
second shaft of X-ray radiation is that skew and/or distortions of the shaft of X-ray
radiation or of a magnified or compressed image can be reduced.
[0052] Furthermore, by rotating the first crystal and/or the second crystal about at least
one angle, the shape of the cross section of the scattered second shaft of X-ray radiation
and/or of the third scattered shaft of X-ray radiation can be adjusted or modified.
[0053] It is furthermore preferred that the first and/or the second crystal are repositioned
by a translation in the X-, Y- or Z direction.
[0054] Still further, since the first and the second crystal can be rotated and/or oriented
and/or positioned and/or repositioned in the X-, Y- and/or Z direction it is possible
to use different crystal surfaces as incidence surfaces.
[0055] By positioning, orienting, repositioning or reorienting the first and/or the second
crystal the divergence of the shafts of X-ray radiation can be adjusted or modified.
[0056] For example, by expanding a shaft of X-ray radiation in one dimension the divergence
of the shaft of X-ray radiation in said dimension will be decreased and vice versa.
[0057] It may furthermore be preferred that the second crystal is translated in at least
one direction.
[0058] For translating the second crystal a translation stage, preferably an XYZ-translation
stage may be used.
[0059] A further solution to the problem is the provision of an apparatus for X-ray shaft
expansion and/or compression and/or collimation and/or focusing and/or X-ray image
magnification, in particular for conducting a method as described above, comprising
a first crystal mounted on a first manipulation stage and a second crystal mounted
on a second manipulation stage, wherein the first manipulation stage is configured
for rotating the first crystal about at least two angles, in particular about at least
two Euler angles, wherein the second manipulation stages is configured for rotating
the second crystal about at least three angles, in particular at least three Euler
angles.
[0060] It is particularly preferred, that the first manipulation stage and/or the second
manipulation stage are configured so that the first and second crystal can be oriented
such that the orientation of the incidence surfaces or the first and second crystal
is not restricted to an orthogonal orientation.
[0061] Preferably the first manipulation stage is configured for rotating the first crystal
about at least three angles, in particular Euler angles.
[0062] The first manipulation stage and/or the second manipulation stage may comprise rotator
elements for conducting the rotations about the at least two angles for the first
crystal and about the at least three angles for the second crystal. The manipulation
stages may be configured as hexapods or the like.
[0063] The rotations conductible by the first manipulation stage may be rotations about
Euler angles denoted with ω
1 and φ
1. The second manipulation stage may be configured to rotate the second crystal about
Euler angles ω
2 and φ
2 and χ
2.
[0064] Furthermore, it may be preferred that the first manipulation stage provides an additional
rotation axis about Euler angle.
[0065] The first and second manipulation stage may comprise additional rotator elements
for rotating the first and/or second crystal about more than three angles.
[0066] By allowing additional rotation axes for the first and/or the second manipulation
stage, a more convenient and precise orientation of the first crystal and the second
crystal can be achieved.
[0067] Preferably the first crystal and/or the second crystal are symmetric cut or asymmetric
cut crystals.
[0068] Still further preferably, an incidence surface of the first crystal is located in
a center of rotation of the first manipulation stage and/or an incidence surface of
the second crystal is located in a center or rotation of the second manipulation stage.
[0069] The incidence surface of the first and/or of the second crystal is the respective
surfaces of the crystal, onto which the first shaft of X-ray radiation and/or the
scattered second shaft of X-ray radiation are impinging.
[0070] In particular by using XYZ-translation stages the first and/or the second crystal
can be moved and positioned such that the respective shaft of incoming X-ray radiation
hits the respective incidence surface.
[0071] Still further preferably the apparatus comprises a base on which the first and second
manipulation stage are arranged. The base can be rotatable about an axis.
[0072] The axis about which the base is rotatable is preferably an axis in approximately
the direction of the first second or third shaft of X-ray radiation. By providing
an additional rotation of the base, the direction of the first shaft of X-ray radiation
and/or of the scattered third shaft of X-ray radiation can be adjusted to lie in a
desired laboratory plane.
[0073] Still further preferably the first manipulation stage and/or the second manipulation
stage comprises a translation stage, preferably an XYZ-translation stage.
[0074] It may be preferred that the apparatus comprises X-ray optics, in particular collimators
and/or X-ray mirrors, preferably Göbel mirrors, and/or Kirkpatrik-Baez optics or mirrors
and/or X-ray lenses, preferably compound refractive lenses.
[0075] It may be preferred to introduce a mechanical crystal bending mechanism for each
of the crystals to be able to introduce desired crystal lattice elastic deformation
fields for each of the crystal to improve focusing/defocusing characteristics of the
setup or to compensate for strain fields due to crystal lattice imperfections.
[0076] The X-ray optics are preferably positioned in the path of the first shaft of X-ray
radiation. Additionally or alternatively it is also possible to provide X-ray optics
in the scattered second shaft of X-ray radiation or the scattered third shaft of X-ray
radiation.
[0077] It is a particular advantage of the apparatus that the direction of the X-ray radiation
through the apparatus can be reversed.
[0078] Preferably, the apparatus comprises a sample stage, wherein the sample stage is further
preferably configured to rotate the sample about at least one angle.
[0079] By allowing for rotations of the sample about at least one angle, the apparatus is
particularly suited for use in three dimensional X-ray tomography.
Short description of the figures
[0080] The present invention is described with reference to the accompanying figures.
- Fig. 1
- shows a schematic of the basic concept of asymmetric Bragg scattering,
- Fig.
- 2a shows a configuration of non-coplanar Bragg scattering,
- Fig.
- 2bshows a configuration of asymmetric non-coplanar Bragg scattering using an elastically
bent crystal,
- Fig. 3
- shows a configuration for conducting the method for X-ray shaft expansion and/or compression
and/or collimation and/or focusing and/or X-ray image magnification,
- Fig. 4
- a first apparatus for X-ray shaft expansion and/or compression and/or collimation
and/or focusing and/or X-ray image magnification, and
- Fig. 5
- shows a second apparatus for X-ray shaft expansion and/or compression and/or collimation
and/or focusing and/or X-ray image magnification.
Detailed description of the figures
[0081] Fig. 1 shows the basic concept of asymmetric Bragg scattering. A first shaft of X-ray
radiation 200 is directed onto an incidence surface 201 of a crystal 202 at an incidence
angle θ
in with the incidence surface 201. The first shaft of X-ray radiation 200 satisfies
the Bragg condition with lattice planes 203 of crystal 202. Because lattice planes
203 are not parallel to the incidence surface 201 the scattered second shaft of X-ray
radiation 204 is scattered off of incidence surface 201 at an exit angle θ
out which is larger than incidence angle θ
in, resulting in an expansion of the X-ray radiation in one dimension. The asymmetric
Bragg scattering process shown in Fig. 1 is a coplanar Bragg scattering process, i.e.,
the incidence plane 205 of the incoming first shaft of X-ray radiation 200 defined
by the beam axis 205 of the first shaft of X-ray radiation 200 and the surface normal
207 of the incidence surface 201 coincides with the scattering plane 208 defined by
the beam axis 209 of the scattered second shaft of X-ray radiation 204 and the surface
normal 207. Incidence plane 205 and scattering plane 208 lie in the drawing plane
of Fig. 1. By rotating the crystal 202 about the normal vector 210 of the scattering
lattice planes 203 non-coplanar Bragg scattering occurs. At each point during rotation
of crystal 202 about normal vector 210 the incident first shaft of X-ray radiation
200 fulfills the Bragg condition with lattice planes 203, while the surface normal
207 rotates about normal vector 210.
[0082] A configuration for non-coplanar Bragg scattering is shown in Fig. 2a. In non-coplanar
Bragg scattering, the incidence plane 205 of the incoming first shaft of X-ray radiation
200 defined by the beam axis 206 of the first shaft of X-ray radiation 200 and the
surface normal 207 of the incidence surface 201 does not coincide with the scattering
plane 208 defined by the beam axis 209 of the scattered second shaft of X-ray radiation
204 and the surface normal 207.
[0083] Fig. 2b shows a further configuration for asymmetric non-coplanar Bragg scattering.
In the configuration of Fig. 2b crystal 202 is an elastically bent crystal, which
has an incidence surface 201 for the first shaft of X-ray radiation 200, which is
not planar but has a curvature. Because of the elastically bending of crystal 200
lattice planes 203 are subject to crystal lattice elastic deformation fields, which
result in a deformation of lattice planes 203. The elastically bent crystal 202 can
be used for Bragg scattering with a parallelized X-ray radiation as shown in Fig.
1 or, as shown in Fig. 2b, with divergent X-ray radiation. The divergent first shaft
of X-ray radiation 200 is directed onto curved incidence surface 201 of a crystal
202 at an incidence angle θ
in with the incidence surface 201. First shaft of X-ray radiation 200 satisfies the
Bragg condition with lattice planes 203 of crystal 202. Scattered second shaft of
X-ray radiation 204 is scattered off of incidence surface 201 at an exit angle θ
out. The incidence plane 205 of the incoming first shaft of X-ray radiation 200 defined
by the beam axis 206 of the first shaft of X-ray radiation 200 and the surface normal
207 of the incidence surface 201 does not coincide with the scattering plane 208 defined
by the beam axis 209 of the scattered second shaft of X-ray radiation 204 and the
surface normal 207. By using an elastically bent crystal 202 first shaft of X-ray
radiation 200 can be focused or defocused.
[0084] Fig. 3 discloses a configuration for conducting the method 100 of the present invention.
According to the method 100 a first shaft of X-ray radiation 10 is scattered in a
first non-coplanar Bragg scattering process at a first plurality of parallel lattice
planes 11 of a first crystal 12 to generate a scattered second shaft of X-ray radiation
13. The scattered second shaft X-ray radiation 13 is scattered in a second non-coplanar
Bragg scattering process at a second plurality of parallel lattice plane 14 of a second
crystal 15 to generate a scattered third shaft of X-ray radiation 16. In the first
non-coplanar Bragg scattering process at the first crystal 12 the first shaft of X-ray
radiation 10 is expanded in a first dimension to yield expanded second shaft of X-ray
radiation 13. In the subsequent second non-coplanar Bragg scattering process the second
shaft of X-ray radiation 13 is expanded in a second dimension to yield expanded third
shaft of X-ray radiation 16. The magnification factor is roughly 100 in both dimensions.
The first crystal 12 and/or the second crystal 15 can be unbent crystals such as crystal
202 of Figs. 1 and 2a, or the first crystal 12 and/or the second crystal 15 can be
mechanically bent crystals such as crystal 202 of Fig. 2b. It is also possible that
one of the crystals 12, 15 is an unbent crystal while the other crystal 12, 15 is
a mechanically bent crystal.
The incidence surface 17 of the first crystal 12 is defined by surface normal 18.
The scattering lattice planes 11 of first crystal 12 are defined by normal vector
19. When the energy or wavelength of the first shaft of X-ray radiation 10 is changed,
the Bragg condition 2d sin(θ) = nλ for the first shaft of X-ray radiation 10 and the
scattering lattice planes 11 is no longer fulfilled. Hence, the first crystal 12 has
to be reoriented by applying a first rotation to the first crystal 12. The first rotation
can include a rotation about an axis 20, which is not parallel to normal vector 19
of the first lattice planes 11. In the configuration shown in Fig. 3 axis 20 is perpendicular
to normal vector 19 and beam axis 21 of the first shaft of X-ray radiation 10. When
the Bragg condition is once again fulfilled, the first crystal 12 can be rotated about
the normal vector 19 to reorient the incidence surface 17 of the first crystal 12
with respect to the beam axis 21 of the first shaft of X-ray radiation 10 to adjust
the incidence angle θ
1,in of first shaft of X-ray radiation 10 with incidence surface 17 and/or the exit angle
θ
1,out of the scattered second shaft of X-ray radiation 13 with incidence surface 17 and/or
the magnification factor provided by the first non-coplanar Bragg scattering process.
Since the first rotation may change the direction of the scattered second shaft of
X-ray radiation 13 it might be necessary to move the second crystal 15 in X-, Y-,
or Z-direction until the scattered second shaft of X-ray radiation 13 impinges on
incidence surface 22 of the second crystal 15. A further reorientation of the second
crystal 15 might then be necessary. The second crystal 15 can be rotated about the
beam axis 23 of the scattered second shaft of X-ray radiation 13. With this rotation,
skew or distortions of the third shaft of X-ray radiation 16 can be eliminated or
manipulated. Furthermore a rotation about an axis 24, which is preferably perpendicular
to the beam axis 23 and the surface normal 25 of the incidence surface 22 of the second
crystal 15, is applied to adjust the incidence angle θ
2,in of second shaft of X-ray radiation 13 and/or the exit angle θ
2,out of the scattered third shaft of X-ray radiation 16 and/or the magnification factor
provided by the second non-coplanar Bragg scattering process. Still further, a rotation
about the surface normal 25 of the incidence surface 22 of the second crystal 15 is
applied until Bragg condition of the second shaft of X-ray radiation 13 with lattice
planes 14 is fulfilled. The rotations of the first crystal 12 and the second crystal
15 must not necessarily conducted sequentially, but can be conducted in a respective
single combined rotation. For calculating the rotations or the combined rotations
a dedicated formula, for example implemented with a software program executed on a
computer, may be used. It is important to notice, that in most configurations incidence
surface 17 of the first crystal 12 and incidence surface 22 of the second crystal
15 are not orthogonal to each other. Furthermore, second plurality of parallel lattice
planes 14 is defined by normal vector 26.
[0085] Fig. 4 shows an apparatus 150 for X-ray shaft expansion and/or compression and/or
collimation and/or focusing and/or X-ray image magnification. The apparatus comprises
a first manipulation stage 27 and a second manipulation stage 28. A first crystal
12 is mounted on the first manipulation stage 27 and a second crystal 15 is mounted
on the second manipulation stage 28. The first manipulation stage 27 comprises rotator
elements 29 for rotating the first crystal 12 about Euler angles ω
1 and φ
1. The second manipulation stage 28 comprises rotator elements 30 for rotating the
second crystal 15 about Euler angles ω
2, φ
2 and χ
2. In addition, the second manipulating stage 28 comprises an XYZ-translation stage
31 to move the second crystal 15 in the X-, Y- or Z-direction. The first manipulation
stage 27 and the second manipulation stage 28 are mounted on a base 32. A sample 33
is mounted on a sample stage 34, by which the sample 33 can be rotated about rotation
axis 35. For X-ray imaging of sample 33, sample 33 is positioned in the first shaft
of X-ray radiation 10. The first shaft of X-ray radiation 10 carrying an X-ray image
of sample 33 is scattered in a first scattering process at a first lattice plane 11
of first crystal 12 to generate a scattered second shaft of X-ray radiation 13 in
a non-coplanar Bragg scattering process. The scattered second shaft X-ray radiation
13 is scattered in a subsequent second scattering process at a second lattice plane
14 of a second crystal 15 to generate a scattered third shaft of X-ray radiation 16
in a second non-coplanar Bragg scattering process. The magnified X-ray image of sample
33 is detected with X-ray detector 36.
[0086] Fig. 5 shows a variation of the apparatus 150 of Fig. 4. Apparatus 150 of Fig. 5
additionally comprises a rotating mechanism 37 to rotate base 32 about an additional
angle χ
1.
List of reference numerals
[0087]
- 100
- Method
- 150
- Apparatus
- 10
- First shaft of X-ray radiation
- 11
- Lattice plane of first plurality
- 12
- First crystal
- 13
- Second shaft of X-ray radiation
- 14
- Lattice plane of second plurality
- 15
- Second crystal
- 16
- Third shaft of X-ray radiation
- 17
- Incidence surface of first crystal
- 18
- Surface normal of incidence surface of first crystal
- 19
- Normal vector of lattice planes of first plurality
- 20
- Axis
- 21
- Beam axis of first shaft of X-ray radiation
- 22
- Incidence surface of second crystal
- 23
- Beam axis of second shaft of X-ray radiation
- 24
- Axis
- 25
- Surface normal of incidence surface of second crystal
- 26
- Normal vector of lattice planes of second plurality
- 27
- First manipulation stage
- 28
- Second manipulation stage
- 29
- Rotator elements of first manipulation stage
- 30
- Rotator elements of second manipulation stage
- 31
- XYZ-translation stage
- 32
- Base
- 33
- Sample
- 34
- Sample stage
- 35
- Rotation axis
- 36
- X-ray detector
- 200
- First shaft of X-ray radiation
- 201
- Incidence surface
- 202
- Crystal
- 203
- Lattice plane
- 204
- Second shaft of X-ray radiation
- 205
- Incidence plane
- 206
- Beam axis
- 207
- Surface normal
- 208
- Scattering plane
- 209
- Beam axis
- 210
- Normal vector
1. Method (100) for X-ray shaft expansion and/or compression and/or collimation and/or
focusing and/or X-ray image magnification, wherein a first shaft of X-ray radiation
(10) is scattered in a first scattering process at a first plurality of parallel lattice
planes (11) of a first crystal (12) to generate a scattered second shaft of X-ray
radiation (13), wherein the scattered second shaft of X-ray radiation (13) is scattered
in a second scattering process at a second plurality of parallel lattice planes (14)
of a second crystal (15) to generate a scattered third shaft of X-ray radiation (16),
characterized in that the first scattering process and the second scattering process are non-coplanar Bragg-scattering
processes.
2. Method (100) according to claim 1, characterized in that a sample (33) is disposed in the first shaft of X-ray radiation (10) or the scattered
second shaft of X-ray radiation (13) or the scattered third shaft of X-ray radiation
(16) for imaging, and/or that the scattered third shaft of X-ray radiation (16) is
detected with an X-Ray detector (36).
3. Method (100) according to claim 1 or 2, characterized in that the first crystal (12) and/or the second crystal (15) is a symmetric cut or an asymmetric
cut crystal and/or an elastically bent crystal.
4. Method (100) according to any one of the preceding claims, characterized in that a wavelength for the first shaft of X-ray radiation (10) is chosen, and that an incidence
angle (θ1,in) for the first shaft of X-ray radiation (10) with an incidence surface (17) of the
first crystal (12) and/or an incidence angle (θ2,in) for the scattered second shaft of X-ray radiation (13) with an incidence surface
(22) of the second crystal (15) is chosen, and/or that an exit angle (θ1,out) for the scattered second shaft of X-ray radiation (13) with the incidence surface
(17) of the first crystal (12) and/or an exit angle (θ2,out) for the scattered third shaft of X-ray radiation (16) with the incidence surface
(22) of the second crystal (15) is chosen, and/or that a magnification factor is chosen,
and that the first crystal (12) and/or the second crystal (15) are positioned and/or
oriented so that the Bragg condition for the first non-coplanar Bragg scattering process
and the second non-coplanar Bragg scattering process are fulfilled for the chosen
wavelength and the chosen incidence angle (θ1,in, θ2,in) and/or exit angle (θ1,out, θ2,out) and/or magnification vector.
5. Method (100) according to any one of claim 4, characterized in that the wavelength of the first shaft of X-ray radiation (10) is changed and that the
first crystal (12) and/or the second crystal (15) are repositioned and/or reoriented
so that the Bragg condition for the first non-coplanar Bragg-scattering process and
the second non-coplanar Bragg-scattering process are fulfilled for the changed wavelength
and the chosen incidence angle (θ1,in, θ2,in) and/or exit angle (θ1,out, θ2,out) and/or magnification factor, and that preferably the first crystal (12) and/or the
second crystal (15) are not exchanged for the changed wavelength of the first shaft
of X-ray radiation (10).
6. Method (100) according to claim 4 or 5,
characterized in that the first crystal (12) is oriented or reoriented by applying a first rotation to
the first crystal (12), which includes at least one of
- a rotation about an axis (20) not parallel to a normal vector (19) of the first
plurality of parallel lattice planes (11) to fulfill the Bragg condition for the first
shaft of X-ray radiation (10) and the first plurality of parallel lattice planes (11),
and/or
- a rotation about a normal vector (19) of the first plurality of parallel lattice
planes (11) to adjust the incidence angle (θ1,in) of the first shaft of X-ray radiation (10) with the incidence surface (17) of the
first crystal (12).
7. Method (100) according to any one of claims 4 to 6
characterized in that the second crystal (15) is oriented or reoriented by applying a second rotation to
the second crystal (15), which includes at least one of
- a rotation about a beam axis (23) of the scattered second shaft of X-ray radiation
(13), and/or
- a rotation about an axis (24) to adjust the incidence angle (θ2,in) of the scattered second shaft of X-ray radiation (13) with the incidence surface
(22) of second crystal (15), said axis (24) being preferably normal to the beam axis
(23) of the scattered second shaft of X-ray radiation (13) and parallel to a plane
tangent to the incidence surface (22) at a point of incidence, and/or
- a rotation about a surface normal (25) of the incidence surface (22) of the second
crystal (15) until Bragg condition is satisfied for the scattered second shaft of
X-ray radiation (13) and the second plurality of parallel lattice planes (14).
8. Method (100) according to any one of claims 4 to 7, characterized in that the second crystal (15) is translated in at least one direction.
9. Apparatus (150) for X-ray shaft expansion and/or compression and/or collimation and/or
focusing and/or X-ray image magnification, in particular for conducting a method (100)
according to any one of claims 1 to 8, comprising a first crystal (12) mounted on
a first manipulation stage (27) and a second crystal (15) mounted on a second manipulation
stage (28), wherein the first manipulation stage (27) is configured for rotating the
first crystal (12) about at least two angles, in particular about at least two Euler
angles (ω1, φ1), characterized in that the second manipulation stage is configured for rotating the second crystal (15)
about at least three angles, in particular at least three Euler angles (ω2, φ2, χ2).
10. Apparatus (150) according to claim 9, characterized in that the first manipulation stage (27) is configured for rotating the first crystal (12)
about at least three angles, in particular Euler angles (ω1, φ1, χ1).
11. Apparatus (150) according to claim 9 or 10, characterized in that the first crystal (12) and/or the second crystal (15) are symmetric cut or asymmetric
cut crystals.
12. Apparatus (150) according to any one of claims 9 to 11, characterized in that an incidence surface (17) of the first crystal (12) is located in the center of rotation
of the first manipulation stage (27) and/or that an incidence surface (22) of the
second crystal (15) is located in the center of rotation of the second manipulation
stage (28).
13. Apparatus (150) according to any one of claims 9 to 12, characterized in that the apparatus comprises a base (32) on which the first manipulation stage (27) and
the second manipulation stage (28) are arranged, and that the base (32) is rotatable
about an axis.
14. Apparatus (150) according to any one of claims 9 to 13, characterized in that the first manipulation stage (27) and/or the second manipulation stage (28) comprises
a translation stage, preferably a XYZ-translation stage (31).
15. Apparatus (150) according to any one of claims 9 to 14, characterized in that the apparatus comprises X-ray optics, in particular collimators and/or X-ray mirrors,
preferably Göbel-Mirrors, and/or Kirkpatrik-Baez optics or mirrors and/or X-ray lenses,
preferably compound refractive lenses.
Amended claims in accordance with Rule 137(2) EPC.
1. Method (100) for X-ray beam expansion and/or compression and/or collimation and/or
focusing and/or X-ray image magnification, wherein a first beam of X-ray radiation
(10) is scattered in a first scattering process at a first plurality of parallel lattice
planes (11) of a first crystal (12) to generate a scattered second beam of X-ray radiation
(13), wherein the scattered second beam of X-ray radiation (13) is scattered in a
second scattering process at a second plurality of parallel lattice planes (14) of
a second crystal (15) to generate a scattered third beam of X-ray radiation (16),
wherein the first scattering process and the second scattering process are non-coplanar
Bragg-scattering processes, wherein in the first non-coplanar Bragg-scattering process
the incidence plane (205) of the first beam of X-ray radiation (10) does not coincide
with the scattering plane (207) of the scattered second beam of X-ray radiation (13)
and wherein in the second non-coplanar Bragg-scattering process the incidence plane
(205) of the second beam of X-ray radiation (10) does not coincide with the scattering
plane (207) of the third beam of X-ray radiation (13),
characterized in that
- a wavelength for the first beam of X-ray radiation (10) is chosen,
- and that an incidence angle (θ1,in) for the first beam of X-ray radiation (10) with an incidence surface (17) of the
first crystal (12) or that an exit angle (θ1,out) for the scattered second beam of X-ray radiation (13) with the incidence surface
(17) of the first crystal (12) is chosen,
- and that an incidence angle (θ2,in) for the scattered second beam of X-ray radiation (13) with an incidence surface
(22) of the second crystal (15) or an exit angle (θ2,out) for the scattered third beam of X-ray radiation (16) with the incidence surface
(22) of the second crystal (15) is chosen,
- and that a magnification factor is chosen,
and that the first crystal (12) and/or the second crystal (15) are positioned and/or
oriented so that the Bragg condition for the first non-coplanar Bragg scattering process
and the second non-coplanar Bragg scattering process are fulfilled for the chosen
wavelength and the chosen incidence angle (θ
1,in) or exit angle (θ
1,out) with the incidence surface (17) of the first crystal (12) and the chosen incidence
angle (θ
2,in) or exit angle (θ
2,out) with the incidence surface (22) of the second crystal (15) and the chosen magnification
factor.
2. Method (100) according to claim 1, characterized in that a sample (33) is disposed in the first beam of X-ray radiation (10) or the scattered
second beam of X-ray radiation (13) or the scattered third beam of X-ray radiation
(16) for imaging, and/or that the scattered third beam of X-ray radiation (16) is
detected with an X-Ray detector (36).
3. Method (100) according to claim 1 or 2, characterized in that the first crystal (12) and/or the second crystal (15) is a symmetric cut or an asymmetric
cut crystal and/or an elastically bent crystal.
4. Method (100) according to any one of the preceding claims, characterized in that the wavelength of the first beam of X-ray radiation (10) is changed and that the
first crystal (12) and/or the second crystal (15) are repositioned and/or reoriented
so that the Bragg condition for the first non-coplanar Bragg-scattering process and
the second non-coplanar Bragg-scattering process are fulfilled for the changed wavelength
and the chosen incidence angle (θ1,in, θ2,in) and/or exit angle (θ1,out, θ2,out) and/or magnification factor, and that preferably the first crystal (12) and/or the
second crystal (15) are not exchanged for the changed wavelength of the first beam
of X-ray radiation (10).
5. Method (100) according to any one of the preceding claims,
characterized in that the first crystal (12) is oriented or reoriented by applying a first rotation to
the first crystal (12), which includes at least one of
- a rotation about an axis (20) not parallel to a normal vector (19) of the first
plurality of parallel lattice planes (11) to fulfill the Bragg condition for the first
beam of X-ray radiation (10) and the first plurality of parallel lattice planes (11),
and/or
- a rotation about a normal vector (19) of the first plurality of parallel lattice
planes (11) to adjust the incidence angle (θ1,in) of the first beam of X-ray radiation (10) with the incidence surface (17) of the
first crystal (12).
6. Method (100) according to any one of the preceding claims,
characterized in that the second crystal (15) is oriented or reoriented by applying a second rotation to
the second crystal (15), which includes at least one of
- a rotation about a beam axis (23) of the scattered second beam of X-ray radiation
(13), and/or
- a rotation about an axis (24) to adjust the incidence angle (θ2,in) of the scattered second beam of X-ray radiation (13) with the incidence surface
(22) of second crystal (15), said axis (24) being preferably normal to the beam axis
(23) of the scattered second beam of X-ray radiation (13) and parallel to a plane
tangent to the incidence surface (22) at a point of incidence, and/or
- a rotation about a surface normal (25) of the incidence surface (22) of the second
crystal (15) until Bragg condition is satisfied for the scattered second beam of X-ray
radiation (13) and the second plurality of parallel lattice planes (14).
7. Method (100) according to any one of the preceding claims, characterized in that the second crystal (15) is translated in at least one direction.
8. Apparatus (150) for X-ray beam expansion and/or compression and/or collimation and/or
focusing and/or X-ray image magnification for conducting a method (100) according
to any one of claims 1 to 7, comprising a first crystal (12) mounted on a first manipulation
stage (27) and a second crystal (15) mounted on a second manipulation stage (28),
wherein the first manipulation stage (27) is configured for rotating the first crystal
(12) about at least two angles, in particular about at least two Euler angles (ω1, φ1), characterized in that the second manipulation stage is configured for rotating the second crystal (15)
about at least three angles, in particular at least three Euler angles (ω2, φ2, χ2).
9. Apparatus (150) according to claim 8, characterized in that the first manipulation stage (27) is configured for rotating the first crystal (12)
about at least three angles, in particular Euler angles (ω1, φ1, χ1).
10. Apparatus (150) according to claim 8 or 9, characterized in that the first crystal (12) and/or the second crystal (15) are symmetric cut or asymmetric
cut crystals.
11. Apparatus (150) according to any one of claims 8 to 10, characterized in that an incidence surface (17) of the first crystal (12) is located in the center of rotation
of the first manipulation stage (27) and/or that an incidence surface (22) of the
second crystal (15) is located in the center of rotation of the second manipulation
stage (28).
12. Apparatus (150) according to any one of claims 8 to 11, characterized in that the apparatus comprises a base (32) on which the first manipulation stage (27) and
the second manipulation stage (28) are arranged, and that the base (32) is rotatable
about an axis.
13. Apparatus (150) according to any one of claims 8 to 12, characterized in that the first manipulation stage (27) and/or the second manipulation stage (28) comprises
a translation stage, preferably a XYZ-translation stage (31).
14. Apparatus (150) according to any one of claims 8 to 13, characterized in that the apparatus comprises X-ray optics, in particular collimators and/or X-ray mirrors,
preferably Gobel-Mirrors, and/or Kirkpatrik-Baez optics or mirrors and/or X-ray lenses,
preferably compound refractive lenses.