Refraction and ultra-small-angle scattering of X-rays in a single-crystal diamond compound refractive lens

In this work a double-crystal setup is employed to study compound refractive lenses made of single-crystal diamond. The point spread function of the lens is calculated taking into account the lens transmission, the wavefront aberrations, and the ultra-small-angle broadening of the X-ray beam. It is shown that, similarly to the wavefront aberrations, the ultra-small-angle scattering effects can significantly reduce the intensity gain and increase the focal spot size. The suggested approach can be particularly useful for the characterization of refractive X-ray lenses composed of many tens of unit lenses.