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Figure 1: (a) Cylindrical refractive X-ray lens focusing in one dimension. (b) Crossed cylindrical X-ray lens focusing in two dimensions.
In every day life we are surrounded by refractive optics for visible light: Glasses, cameras, microscopes or our own eyes are just some examples. The refractive index for visible light is high enough (n around 1.5) to produce a sufficiently strong refraction at the interface between air and glass to allow for small focal lengths (in the range of a few centimeters). Focusing lenses for visible light are convex, i.e. bulging outward.
Hard X-rays are refracted in matter in the same way as visible light is. For hard X-rays, however, the refractive index in matter is smaller than 1 although only slightly, and absorption in matter is high. Therefore X-rays are hardly refracted but strongly absorbed in matter. Since the refractive index for X-rays in matter is smaller than 1, focusing optics have to have concave form, i. e., have to be curved inward, as opposed to a focusing glass lens for visible light.
The small refraction and strong absorption led to the wide spread belief, that refractive lenses for hard X-rays could not be fabricated.
Despite thereof, it has been shown in recent years that refraction can be used to focus X-rays [3-6]. A first type of X-ray lens consists of a linear array of tightly spaced holes in a lens material as shown in Figure 1(a). This type of lens is called a cylindrical lens. The material between the holes acts like a concave lens, focusing the X-ray beam. Note that such a lens only focuses in one direction. To achieve a focusing in two dimensions, crossed cylindrical holes can be drilled in the lens material to form a crossed cylindrical lens as shown in Figure 1(b).
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Figure 1: (a) Cylindrical refractive X-ray lens focusing in one dimension. (b) Crossed cylindrical X-ray lens focusing in two dimensions.
In the meantime, these lenses have been taken into use by other groups and are installed for beam conditioning in the front-ends of some beamlines at the ESRF in Grenoble.
Due to the circular shape of the holes, these lenses show strong spherical aberration and are not well suited for imaging purposes. Besides beam conditioning, however, they are useful for microanalysis experiments.
A second generation of refractive lenses with circular symmetry and parabolic shape is currently developed at the II. Physikalisches Institut the University of Technology in Aachen, Germany. They are tested at the European Synchrotron Radiation Facility in Grenoble, France.
The parabolic lenses are genuine imaging devices. All what can be done with glass lenses with visible light can be done with these lenses with hard X-rays. Due to their excellent imaging properties, the parabolic compound refractive lenses are well suited for imaging, in particular in an X-ray microscopy setup, and to produce a small focal spot for microanalysis experiments, such as microdiffraction and microfluorescence. Some of the applications are described below.
Figure 2: Single refractive lens for X-rays.
When a parabolic profile for the lens shape is used, there is virtually no spherical aberration.
Because the refraction of X-rays in matter is small, a large number of lenses is stacked behind each other to achieve an appropriate focal length. Such a lens is called compound refractive lens
Figure 3: Focusing compound refractive lens for hard X-rays.
To reduce absorption the lens material is preferably made of materials that contain chemical elements with small atomic number Z., such as beryllium (Be), boron (B), carbon (C) or aluminum (Al).
The thickness of the lens is also an important parameter that influences the absorption. It is important to make the lenses as thin as possible. A typical value for the thickness of the lens at the thinnest point is about 20 microns.
Imaging the X-ray source:
The X-ray source (undulator) at ID22 of the ESRF with elliptical profile (35 microns by 700 microns) is imaged through a compound refractive lens to obtain a small focal spot.
Figure 4: Imaging the X-ray source through a compound refractive lens in a strongly demagnifying setup.
The distance L1 from the source to the detector is typically between 40m and 70m. With a focal distance f in the range of one meter, the source can be demagnified by a factor 30 to 80, yielding an X-ray spot in the micrometer range.
Figure 5 depicts the image of the undulator source at ID22 of the ESRF (L1 = 63m, f = 1.26m, demagnification: 59).
Figure 5: Image of the X-ray undulator source at ID22 of the ESRF in Grenoble. The image was recorded with a high resolution X-ray camera. In (b) are shown cross sections through the spot along the major axis.
The small focal spot can be used for microanalysis experiments: Structure analysis or chemical composition of specimens from many fields, such as in medical sciences, in semiconductor physics, in environmental sciences, in material sciences.
X-ray microscope: An object illuminated by an X-ray source is imaged through the lens onto a position sensitive detector. For details see the microscopy page.
Figure 6: Setup for an X-ray microscope. The object is illuminated with X-rays from behind and imaged through the lens onto a position sensitive detector.
Figure 7: (a) X-ray micrograph of a gold mesh. Note that the finer horizontal gold grid supported by the coarser mesh in the lower part of the image is visible behind the thicker bars. (b) X-ray micrograph of a Fresnel zone plate, consisting of concentric rings of gold. The outermost gold ring has a width of 0.3 microns.
Imaging of opaque objects that do not tolerate sample preparation:
It is also possible to tomographically reconstruct opaque samples with (sub)-µm resolution. Due to the large depth of field of the microscope, tomographic reconstruction is necessary for thick samples.