| Comparison
of focusing optics for femtosecond X-ray diffraction
Bargheer, Zhavoronkov, Bruch, Legall, Stiehl, Wörner,
Elsässer
[BZB05]
X-ray optics for ultrafast x-ray
diffraction
|



|
X-ray optics can be
used to collimate the isotropic output into a beam or
to focus the x-rays on the target. We have tested different
kinds of optics with the result that each of them serve
a specific task best. Depending on the experiment, relevant
parameters are the total photon flux, the flux per unit
angle or the flux density in the focus.
a) A 100 µm thick Germanium crystal cut along
the (111) plane is bonded to a toroidally bent quartz
substrate. Here the (444) reflex is used and the curvature
of the crystal is chosen in such a way that the entire
surface area (12 x 40 mm2) is reflecting. The mirror
is made for 1:1 imaging with a working distance of 468
mm, and the deflection angle is given by the angle 2Q
= 70° of the Ge (444) reflex. The focus is rather
close to the source (200 mm) which imposes some geometric
constraints on the experimental design of the setup.
b) The second imaging device consists of two perpendicular
elliptical multilayer mirrors (MLM) reflecting at a
Bragg angle of approx. 3°, determined by the multilayer
periodicity. There are two possible optical paths to
focus in two dimensions by the Kirkpatrick-Baez scheme.
The reflectivity of the optic over the entire solid
angle W0 is very large (approx. 0.3 for a 15 µm
small source size), because the thickness of the multilayers
is graded along the ellipse. This makes the design of
the MLM very flexible, e.g., regarding the magnification
ratio. We have chosen a magnification M = 2 : 1 with
a source-focus distance of 300 mm. The multilayer periodicity
is designed to suppress Cu Kb radiation efficiently.
The white Bremsstrahlung background is strongly suppressed
with an average reflectivity of approximately 10-4.
c) Capillary x-ray optics are glass capillaries or poly-capillaries,
which guide x-rays by total reflection. The elliptical
capillary optic is made from a thin lead glass tube
which is pulled in such a way as to approximate the
shape of an ellipsoid. The resulting focusing is cylindrically
symmetric and occurs by total reflection of the x-rays
on the Helium/Glass interface. (The optic is filled
with He.) We selected a 150 mm long section of the ellipsoid
which images the x-rays with a magnification of M =
1 : 7. The small deflection angle is determined by the
angle of total reflection (0:3° for lead glass),
and the calculated average reflectivity of the capillary
is 0.8. The high energetic x-rays are somewhat suppressed,
as the angle of total reflection decreases with increasing
photon energy. The source to optic-housing distance
is 50 mm.
d) The principle of operation of typical poly-capillary
elements consisting of bundles of glass or quartz capillaries
is also based on the effect of total internal reflection
of radiation, however, here several reflections are
needed. This reduces the transmission through the optic
and leads to an increase of the x-ray pulse duration.
A more substantial broadening stems from the different
single capillary lengths within the array of 59000 capillaries.
The spectral response is similarly unselective as in
the single-capillary case, and the convergence angle
is very large (3.4°). |

The first row shows the cross section in the focal plane
of the optics. The 23 mu focus of optic a) is limited by the
pixel size of the CCD used for recording the images. The lower
panel shows cross sections of the x-ray beam in the far field.
|