Fresnel and refractive lenses for X-rays

Abstract

We present a Gaussian beam analysis of X-ray refractive and Fresnel lenses. The X-ray refractive lens is featured by an intrinsic soft (Gaussian) aperture due to strong absorption of X-rays by materials. We defined a parameter N 0, the critical Fresnel number (CFN), to describe this optical property. The values of N 0 for all practical materials are below 1000 for photon energies exceeding 30 eV, still lower for high- Z materials. The maximum effective Fresnel number of a lens is determined by its material to be 2 N 0 and its maximum enhancement of X-ray intensity is limited to (2 πN 0) 2, independent of its shape. We found that the refractive lens is likely to be useful for manipulating nearly diffraction limited beam in the hard X-ray region and its application is severely restricted by available fabrication capabilities today. X-ray Fresnel lenses, both in cylindrical and linear forms, are proposed as superior focusing elements for hard X-rays. Their high efficiency, up to 100% in optimal construction, will enable us to manipulate beams with multiple lenses and obtain higher performance optics. Their design and fabrication are discussed in reference to those of X-ray Fresnel zone plates and micro Fresnel lenses for optoelectronics.