Imaging by parabolic refractive lenses in the hard X-ray range

Abstract

The manufacture and properties of compound refractive lenses (CRLs) for hard X-rays with parabolic pro®le are described. These novel lenses can be used up to $60 keV. A typical focal length is 1 m. They have a geometrical aperture of 1 mm and are best adapted to undulator beams at synchrotron radiation sources. The transmission ranges from a few % in aluminium CRLs up to about 30% expected in beryllium CRLs. The gain (ratio of the intensity 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 pro®le 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 attenuation (photoabsorption and Compton scattering) and of the roughness at the lens surface. Excellent agreement between theory and experiment has been found. With aluminium CRLs a lateral resolution in imaging of 0.3 mm has been achieved and a resolution below 0.1 mm can be expected for beryllium CRLs. The main ®elds of application of the refractive X-ray lenses are (i) microanalysis with a beam in the micrometre range for diffraction,¯uorescence, absorption, scattering; (ii) imaging in absorption and phase contrast of opaque objects which cannot tolerate sample preparation; (iii) coherent X-ray scattering.

X-ray Echo Spectroscopy

“…There are no principal preferences of using either curved mirrors or compound-refractive lenses (CRL) for this purpose. However, in practical terms, mirrors maybe a preferable choise ensuring higher efficiency, because photoabsorption of 9.1-keV and especially of 4.5-keV photons is substantial in the CRLs [19,20].…”

Correcting lateral chromatic aberrations in non-monochromatic X-ray microscopy

“…It can be shown that the CRL focal length, f / E 2 , where E is the photon energy. 13 Consider E 0 as the reference energy at which the microscope is in focus. Photons with energy E 6 ¼ E 0 will produce defocused and scaled variants of the in-focus image.…”

“…However, the CRLs employed here are not long enough to make a significant deviation from the thin lens approximation. Therefore, a more comprehensive treatment, accounting also for lens lengths, 13,[15][16][17][18] has been omitted from Eqs. (2)- (5) but can be found as supplementary material.…”

Large aperture x-ray refractive lens from lithium

“…A recent article [3] summarizes the accomplishments of a most active group in this field. Their lenses are parabolas because these lack spherical aberration, and the lens curvature decouples from the aperture [4]: N lenslets with a radius of curvature R 0 in series have a focus at f = R 0 /2Nδ . Without optical equivalent is Cederstrom's multi-prism [5].…”

“…the ratio of the index of refraction decrement over the absorption coefficient. Because lithium produces the largest phase shifts per unit absorption length of all solids, we [6,7,8,9] and others [10,11] use lithium in the best available lens designs [4,5].…”