Optimization of compound refractive lenses for X-rays

The theory of compound refractive lenses for the focusing of Synchrotron radiation X-ray beams is reviewed. The optimization of the transmission and minimization of the image size is discussed for both circular and parabolic holes. A comparison is made with ray tracing. The small-angle scattering expected from the surface roughness and the density fluctuation of the material is addressed. A successful comparison is made with the transmission and spot sizes measured on focusing lenses made of beryllium and Pyrocarbone between 20 and 30 keV on the ID6 undulator beamline of the ESRF. A rms spot size of 6.8 mu m x 100 mu m has been recorded at a photon energy of 23.8 keV in a two plane focusing geometry. The peak spectral flux per unit surface in the focused beam is 26 times higher than that observed without lens. The expected transmission of such lenses placed at a distance of 24 m from an undulator or a bending magnet source point of the ESRF is given in the 1-100 keV energy range for focal length varying between 1 and 24 m. These lenses are inexpensive, very flexible and insensitive to heat load. They are particularly well suited to the undulator beamlines of the third generation sources in the 1-200 keV range. Future developments are discussed. (C) 1998 Elsevier Science B.V. All rights reserved.