Hard X-rays have exceptional properties that are useful in the chemical, elemental and structure analysis of matter. Although single-nanometre resolutions in various hard-X-ray analytical methods are theoretically possible with a focused hard-X-ray beam, fabrication of the focusing optics remains the main hurdle. Aberrations owing to imperfections in the optical system degrade the quality of the focused beam 1 . Here, we describe an in situ wavefront-correction approach to overcome this and demonstrate an X-ray beam focused in one direction to a width of 7 nm at 20 keV. We achieved focal spot improvement of the X-ray nanobeam produced by a laterally graded multilayer mirror 2 . A grazing-incidence deformable mirror 3 was used to restore the wavefront shape. Using this system, ideal focusing conditions are achievable even if hard-X-ray focusing elements do not achieve sufficient performance. It is believed that this will ultimately lead to single-nanometre spatial resolution in X-ray analytical methods.Synchrotron radiation facilities produce high-quality light with wavelengths ranging from the infrared to hard-X-ray regions. The use of hard X-rays with energies higher than several kiloelectronvolts in conjunction with analysis methods such as X-ray diffraction, X-ray fluorescence, X-ray absorption and X-ray photoelectron spectroscopy offers unique advantages for the investigation of the structure, elemental distribution and chemical bonding state of advanced materials and biological samples. In these analytical methods, the resolution, signal strength and contrast must be as high as possible. In this regard, the development of a hard-X-ray focusing device is important for meeting these demands. To focus light, it is necessary to take advantage of its interactions with matter, such as diffraction, reflection and refraction. There are a variety of hard-X-ray focusing optical systems such as mirrors 4 , zone plates 5 , refractive lenses 6 and multilayer Laue lenses 7 . The minimum achievable spot size has been theoretically investigated by many researchers 8-10 , and it has been concluded that sizes below 10 nm are feasible with kiloelectronvolt X-rays. That is, hard-X-ray analytical techniques have the potential for single-nanometre spatial resolution.However, in such discussions, the imperfections of the focusing elements have not been entirely considered. Rayleigh's quarterwavelength rule 1 states that if the wavefront aberration exceeds a quarter of a wavelength, the quality of the retinal image will be significantly impaired. This rule is also applicable to simple light-focusing optical systems. The wavefront error of the focused beam distorts the shape of the intensity profile on the focal plane and spreads the beam. The short wavelength of X-rays demands unprecedented accuracy in the manufacturing of the LETTERS 1.43 nm (r.m.s.) over a 500-nm-square area, which was directly confirmed by atomic force microscopy. A phase shift occurred at the boundary between the X-rays propagating inside and outside the phase ...

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Since the invention of the first lasers in the visible-light region, research has aimed to produce short-wavelength lasers that generate coherent X-rays; the shorter the wavelength, the better the imaging resolution of the laser and the shorter the pulse duration, leading to better temporal resolution in probe measurements. Recently, free-electron lasers based on self-amplified spontaneous emission have made it possible to generate a hard-X-ray laser (that is, the photon energy is of the order of ten kiloelectronvolts) in an ångström-wavelength regime, enabling advances in fields from ultrafast X-ray spectrosopy to X-ray quantum optics. An atomic laser based on neon atoms and pumped by a soft-X-ray (that is, a photon energy of less than one kiloelectronvolt) free-electron laser has been achieved at a wavelength of 14 nanometres. Here, we use a copper target and report a hard-X-ray inner-shell atomic laser operating at a wavelength of 1.5 ångströms. X-ray free-electron laser pulses with an intensity of about 10(19) watts per square centimetre tuned to the copper K-absorption edge produced sufficient population inversion to generate strong amplified spontaneous emission on the copper Kα lines. Furthermore, we operated the X-ray free-electron laser source in a two-colour mode, with one colour tuned for pumping and the other for the seed (starting) light for the laser.