Theoretical Analysis of X-ray Compound Refractive Lens Optical Properties

Abstract

We present a theoretical analysis of optical properties of parabolic compound refractive lenses (CRL). The parabolic CRL with a large number of elements is considered as a parabolic medium along the x‐ray path. The problem of x‐ray coherent wave propagation inside such a medium is solved exactly. The analytical formula is obtained for the parabolic CRL imaging propagator as a parabolic wave with complex parameters due to absorption of x rays inside the lens. The fast and universal computer program is developed for simulating the CRL generated images. An imaging example of a test object as a silicon plate of 3 μm thickness with a round hole of 3 μm diameter is presented and discussed in details. The main optical parameters of parabolic CRL such as an effective aperture, a diffraction limited resolution and a focal distance are calculated analytically and discussed. It is shown that parabolic CRL has no spherical aberration while long single plano‐concave and bi‐concave lenses have.