ABSTRACT
The interaction of X-rays with matter is very weak. The real part of the index of refraction can be written as n = 1-d, where d is the refractive index decrement. For X-rays with a photon energy of several keV (l of the order of 0.1 nm), which penetrate an air-solid or vacuum-solid interface, it will be d ª 10-6, i.e. n is only slightly less than unity [3]. For visible light, this value is considerably larger than unity, that is, n ª 1.6 for an air-glass interface. The effect of the small deviation from unity is that a refractive X-ray optical element (e.g., a single lens) will provide only a very small deflection angle, leading to an extremely long focal distance, in strong contrast to lenses for visible light. As n < 1, an X-ray focusing lens will be concave, rather than the convex shape of focusing lenses for visible light. Although the concept of using refractive optics for X-ray focusing was already addressed over 60 years ago [4], it was put into practice for the first time only almost 50 years later [5]. As a consequence of the inherent weak refractive power, many single lenses need to be stacked along their optical axes. Consequently, to maximize the transmission of the lens stack, it is crucial to use a material with a low electron number (Z) as for low-energy X-rays the photoelectric absorption is dominant and proportional to Z4 while d is proportional to Z. In the high-energy X-ray range, however, Compton scattering is dominant also being proportional to Z [6]. 3.2.1.1 Metal compound refractive lenses
In the thin-lens approximation, the focal length f0 of a stack of N biconcave, parabolic lenses with an apex curvature radius R is f0 = R/2Nd. If the lens thickness is nonnegligible (i.e., high N), then the deviations can be corrected by applying the thick lens formula (see [7]). The first compound refractive lens (CRL) was realized by drilling a row of 30 holes each with a radius of 300 µm into a block of aluminum, as shown schematically in Fig. 3.1. This simple, low-cost approach led to a one-dimensionally focusing CRL with a focal length of 1.8 m for 14 keV radiation, which is sufficient to produce a focal line of 8 µm width (FWHM) [5]. The CRLs available today are much more sophisticated as they have a rotational parabolic shape (see Fig. 3.1), thereby providing
focusing in both directions free of spherical aberrations, just as their glass counterparts for visible light. Being manufactured by embossing in low-Z metals such as aluminum (Z = 13) or beryllium (Z = 4), they can readily handle even the high heat load of an undulator beam. CRLs are easy to align and robust, and no deterioration of beryllium or aluminum has been observed even after years of operation. They can be used over a wide energy range of 5 keV to about 120 keV and for the apex radius of curvature R a range of 50-1000 µm is available. The geometrical aperture A of these lenses is typically about 1 mm; however, it has to be borne in mind that the effective aperture Aeff is smaller than the geometrical aperture due to the increased absorption in the outermost parts of the lenses. The focal length is a function of the number of single lenses comprising the lens stack (N typically 20-200) and typically lies within the range of 30-0.5 m.
