The manufacture and properties of compound refractive lenses (CRLs) for har
d X-rays with parabolic profile are described. These novel lenses can he: u
sed up to similar to 60 keV. A typical focal length is Im. They have a geom
etrical aperture of 1 mm and are best adapted to undulator beams at synchro
tron radiation sources. The transmission ranges from a few % in aluminium C
RLs up to about 30% expected in beryllium CRLs, The gain (ratio of the inte
nsity in the focal spot relative to the intensity behind a pinhole of equal
size) is larger than 100 for aluminium and larger than 1000 for beryllium
CRLs. Due to their parabolic profile they are free of spherical aberration
and are genuine imaging devices. The theory for imaging an X-ray source and
an object illuminated by it has been developed, including the effects of a
ttenuation (photoabsorption and Compton scattering) and of the roughness at
the lens surface. Excellent agreement between theory and experiment has be
en found. With aluminium CRLs a lateral resolution in imaging of 0.3 mu m h
as been achieved and a resolution below 0.1 mu m can be expected for beryll
ium CRLs. The main fields of application of the refractive X-ray lenses are
(i) microanalysis with a beam in the micrometre range for diffraction, flu
orescence, absorption, scattering; (ii) imaging in absorption and phase con
trast of opaque objects which cannot tolerate sample preparation; (iii) coh
erent X-ray scattering.