Refractive lenses allow compact, precision focusing of x-rays

Conventional lenses made of glass are quite good at slowing down visible light that passes through it, causing it to bend or refract. Refractive glass lenses are among the most widely used optical components, with a wide variety of applications in focusing and imaging. But they do not work well with light at the much-higher frequency, much-higher-energy end of the spectrum: x-rays. Refractive lenses for x-rays were considered unfeasible for a long time because the x-rays' energy lets them pass through most materials with very little reduction in speed. In the parlance, they exhibit weak refraction and strong absorption. However, in 1996¹ we showed that these obstacles can be circumvented and that focusing x-rays by refractive lenses would be possible.

Although our lenses function in the same way as do those for visible-light optics, there are some differences. First, as opposed to visible light, the x-ray refractive index of a material (the ratio of its speed of propagation though the material to the speed of light in a vacuum) is smaller than in air. To deal with this, our focusing lenses feature a double concave shape for x-rays (see Figure 1). Second, because the refractive index is very close to unity for x-rays, usually the refraction is very small, and many lenses are put in series to achieve reasonably short focal lengths. To keep the absorption to a minimum, we make these compound refractive lenses from low-atomic-number (‘low-Z’) materials such as beryllium, carbon, aluminum, and silicon. Third, to reduce spherical aberrations, our x-ray lenses have a parabolic shape.²

Figure 1. Parabolic compound refractive transfocator. Left: A single refractive lens illustrating the rotational symmetry about the optical axis. Right: A compound refractive lens with six elements (three lenses are shown cut in half). Putting N lenses in line reduces the focal length by a factor of N with respect to a single lens. F: Focal length. R: Radius of the parabola apex. N: Number of lenses. δ: Decrement of refractive index.

Compared to other x-ray focusing elements, refractive lenses present several attractive features. They are simple to align and relatively insensitive to misorientations. Since refractive lenses are in-line optics, they are more stable with respect to angular vibrations in comparison to deflecting optics. They can be adapted to very high x-ray energies by modifying their composition and number, and can be inserted and removed from the beam to allow fast switching of the beam size.

Transfocators—systems with a variable number of lenses— provide permanent energy and focal-length manageability.^{3, 4} Transfocators comprise several cartridges containing different numbers of lenses, such that the focal distance can be adjusted by insertion or retraction of one or more of the lens cartridges. In-air transfocators (IATs) and in-vacuum transfocators (IVTs) have now been designed, built, and installed at the European Synchrotron Radiation Facility beamlines (see Figure 2). The IVTs are water cooled to allow use in the polychromatic ‘white’ beam. They are installed closer to the x-ray source (∼30m away) where they capture a larger proportion of the diverging x-ray beam. The variable focal length of the transfocator-focused beam means that it can be exploited at all of the beamline experimental stations, leading to enormous energy-flux gains (up to 10⁵) with respect to an unfocused beam.

Figure 2. The transfocator concept (left). Pneumatically actuated cartridges contain a geometrical progression of numbers of lenses allowing between two and 254 lenses (in steps of powers of two). The in-air transfocator installed on the beamline at the European Synchrotron Radiation Facility (right).

Transfocators are very flexible and have been used in several different configurations, including as stand-alone focusing devices in the monochromatic beam, producing micrometer spot sizes. Transfocators can also act as prefocusing devices to be used in conjunction with a downstream micro- or nano-focusing element. As a single optical device in the white beam, the IVT can act as a fundamentally new kind of monochromator, delivering impressive flux in an ∼1% bandpass beam. Such ultra-intense, stable, and focused moderate-bandpass beams are useful for several applications in which high-energy resolution is not necessary, such as scattering from liquids or poorly crystalline materials. The bandpass of this monochromator is well matched to exploit the spectrum of the harmonic peaks of an undulator insertion device at a third-generation storage ring.

Successful developments of tunable refractive optics are not limited by developments of the optics themselves but also generate new, innovative coherent imaging techniques such as high-resolution microscopy.⁵ High-resolution microscopy based on compact table-top transfocators—condenser and objective—is under development now or being built.