IMAGING & DIFFRACTION

A common application for refractive lenses from RXOPTICS is x-ray imaging in transmission mode. Usually, illumination of the object from behind is achieved by a prefocusing lens (condenser) in order to adjust the beam size to the sample (see Figure 1 and the section on focusing). The image is formed by an objective lens with a small focal length which allows a large magnification L2 / L1. A large magnification relieves the requirements on the resolution of the x-ray detector.

Imaging
Fig. 1. Imaging

Figure 2 shows a Nickel mesh with a period of 12.7 μm that was imaged at 12 keV by 91 rotationally parabolic beryllium lenses with R = 200 μm and a magnification factor L2 / L1 of 10 onto a high resolution film (from the article "Refractive x-ray lenses"). The distance of the objective CRL from the sample was L1 = 546 mm, yielding an image distance of L2 = 5460 mm. It is obvious that the image is practically free of aberrations. Figure 3 shows a Ta Siemens star that is imaged at 46 keV by rotationally parabolic Al lenses with a magnification factor L2 / L1 of 13 (private communication with M. DiMichiel, M. Scheel, A. Snigirev, I. Snigireva, ESRF). This CRL was made up of 60 lenses with R = 50 μm and 321 lenses with R = 200 μm. The distance of the objective CRL from the sample was L1 = 906 mm, resulting in an image distance of L2 = 11,778 mm. The condenser CRL, consisting of 125 rotationally parabolic Al lenses with R = 200 μm, was placed 2.4 m from the sample and, thus, produced a virtual focal spot inside the objective lens (see Figure 1).

Ni mesh x-ray microscopy
Fig. 2. Ni mesh (Lengeler et al)
Siemens star x-ray microscopy
Fig. 3. Ta Siemens star (DiMichiel et al)

Note that for CRL containing such a large number of lenses it is important to take into account thick lens effects; in particular, sample and image distance have to be understood with respect to the primary and the secondary principal plane, respectively.

Another major application of refractive lenses from RXOPTICS is x-ray diffraction. Apart from the usual configuration employing a collimated beam, high-resolution x-ray diffraction can be performed by removing the objective lens in the configuration in Figure 1 and placing a large area detector in the back focal plane of the condenser (see Figure 4). By Fresnel theory, the detector measures the Fraunhofer diffraction pattern.

Imaging
Fig. 4. Diffraction

This particularly compact experimental setup has been used by M. Drakopoulos and collaborators to investigate a two-dimensional photonic crystal fabricated into a 150 μm thick Si wafer (see Figure 5 and the article "X-ray high-resolution diffraction using refractive lenses"). The CRL consisted of 112 rotationally parabolic Al lenses with R = 200 μm and a focal length of 1334 mm at 28 keV. CRL and sample were located 58 m from the undulator source of beamline ID18F at ESRF. The two vectors a and b defining the hexgonal grid of the photonic crystal have a length of 4.2 μm. The two easily resolved lattice vectors Q01 and Q11 in reciprocal space have a length of 1.75 × 10-3 nm-1 and 2.99 × 10-3 nm-1, respectively (see Figure 6). In this configuration, resolution is not limited by the divergence of the x-ray source but by its small angular size of about 1 μrad; the achieved resolution was of the order 10-4 nm-1.

Photonic crystal
Fig. 5. SEM image of photonic crystal (Drakopoulos et al)
X-ray diffraction pattern
Fig. 6. X-ray diffraction pattern (Drakopoulos et al)