the inside of the tubes. The array is tapered so that one end of the capillaries points at the X-ray source and the other at the sample. Polycapillary optics are achromatic and thus suitable for scanning fluorescence imaging and other applications where a broad X-ray spectrum is useful. They collect X-rays efficiently for photon energies of 0.1 to 30 keV and can achieve gains of 100 to 10000 in flux over using a pinhole at 100 mm from the X-ray source. Since only X-rays entering the capillaries within a very narrow angle will be totally internally reflected, only X-rays coming from a small spot will be transmitted through the optic. Polycapillary optics cannot image more than one point to another, so they are used for illumination and collection of X-rays. Zone plates Zone plates consist of a substrate with concentric zones of a phase-shifting or absorbing material with zones getting narrower the larger their radius. The zone widths are designed so that a transmitted wave gets constructive interference in a single point giving a focus. Zone plates can be used as condensers to collect light, but also for direct full-field imaging in e.g. an X-ray microscope. Zone plates are highly chromatic and usually designed only for a narrow energy span, making it necessary to have monochromatic X-rays for efficient collection and high-resolution imaging. Compound refractive lenses Since refractive indices at X-ray wavelengths are so close to 1, the focal lengths of normal lenses get impractically long. To overcome this, lenses with very small radii of curvature are used, and they are stacked in long rows, so that the combined focusing power gets appreciable. Since the refractive index is less than 1 for X-rays, these lenses must be concave to achieve focusing, contrary to visible-light lenses, which are convex for a focusing effect. Radii of curvature are typically less than a millimeter, making the usable X-ray beam width at most about 1 mm. To reduce the absorption of X-rays in these stacks, materials with very low atomic number such as beryllium or lithium are typically used. Since the refractive index depends strongly on X-ray wavelength, these lenses are highly chromatic, and the variation of the focal length with wavelength must be taken into account for any application. Reflection The basic idea is to reflect a beam of X-rays from a surface and to measure the intensity of X-rays reflected in the