Diffraction.theory of imaging with X-ray compound refractive lens

Specific features of X-ray compound refractive lens (XCRL) with parabolic profile of concave surfaces for hard X-ray focusing and micro-imaging are analyzed theoretically. Large longitudinal size L of the XCRL requires a verification of the thin lens approximation widely used in the literature. We show that the parabolic XCRL can be treated as a thin lens placed in the middle of the XCRL with the focal length F-1 = F + L/6, where F is the XCRL focal distance in the thin lens approximation. The relatively small aperture of XCRL due to the absorption of X-rays leads to finite resolution and phase effects (or artifacts) of the images. This feature reveals itself as a visibility of transparent objects. It is shown that XCRL allows one to visualize the local phase gradient of the radiation wave field produced by the object. This opens quite a new technique of micro-imaging for purely phase objects which is different from the traditional phase contrast micro-imaging techniques. Optical properties of XCRL as a Fourier transformer are considered as well. (C) 2002 Elsevier Science B.V. All rights reserved.