Fig. 1. Focusing

Focusing of the x-ray beam is one of the major applications of refractive x-ray lenses from RXOPTICS. Focusing maps the primary x-ray source to a focal spot, the so-called secondary source (see Figure 1). This is done, for instance, to adjust the beam to the sample size and to increase the photon flux on the sample in x-ray diffraction, absorption, and fluorescence experiments. The gain in intensity, that is, the ratio of the intensities in focal spots of the same size produced by the CRL on the one hand and by a pinhole on the other hand, can be of the order of 104 and above. For instance, a CRL consisting of 52 ideal, rotationally parabolic (2D) beryllium lenses with R = 200 μm maps a source at 15 keV with a size of 300 μm (FWHM, horizontal) × 15 μm (FWHM, vertical) at a distance L1 = 40 m to a secondary source at a distance L2 = 1330 mm with a size of 9972 nm × 511 nm; the gain is 46,946. Rotionally symmetric focusing is achieved by using rotationally parabolic (2D) lenses. On the other hand, astigmatic focusing or focusing in only one direction is possible by employing cylinder parabolic (1D) lenses (see also the section on preconditioning).

Figure 2 and Figure 3 compare the intensity profiles of the beam of the ID18 at ESRF, Grenoble, at 14.41 keV with and without a CRL in the vertical and the horizontal direction (private communication with A. Chumakov, ESRF). Here, the source is mapped by a CRL made up of 39 rotationally parabolic beryllium lenses with R = 1500 μm. The secondary source is well fitted by a Gaussian profile (solid red lines) and hence shows very low background in the wings. The Gaussian intensity profile is a result of the parabolic form of the lenses.

Vertical intensity profile
Fig. 2. Vertical intensity profile (A. Chumakov, ESRF)
Horizontal intensity profile
Fig. 3. Horizontal intensity profile (A. Chumakov, ESRF)

The absence of so-called ringing, that is, significant parts of the intensity residing in oscillations apart from the main focal spot, is an important advantage of parabolic lenses over other x-ray optics and plays a crucial role in many experiments.

Fig. 4. Collimation

Collimation of divergent x-ray sources, which is particularly important in diffraction experiments, is in a sense the inverse operation to focusing. For collimation, the CRL is placed at a distance from the source which (roughly) equals its focal length; the angular size of the source, that is, the ratio of its lateral extent and its distance to the CRL, then translates into a residual divergence of the collimated beam (see Figure 4).

In some techniques, like scanning transmission x-ray microscopy (STXM) and ptychography (scanning x-ray diffraction microscopy, SXDM), the secondary source is scanned over the sample (see Figure 5). A small secondary source may also be used in x-ray microscopy (see Figure 6). Placing the object close to the focus yields a strong magnification M = L2 / L1. The smaller the focus, the sharper is the image.

Fig. 5. Scanning
Fig. 6. Microscopy