Simulating and optimizing compound refractive lens-based X-ray microscopes

A comprehensive ray-transfer matrix formalism for the use and design of compound refractive lens-based X-ray microscopes is presented, including closed analytical expressions for key optical parameters. These form the basis of an optimization, which reveals that thick-lens imaging geometries are ideal in terms of spatial resolution and achromaticity. A comprehensive optical description of compound refractive lenses (CRLs) in condensing and full-field X-ray microscopy applications is presented. The formalism extends ray-transfer matrix analysis by accounting for X-ray attenuation by the lens material. Closed analytical expressions for critical imaging parameters such as numerical aperture, spatial acceptance (vignetting), chromatic aberration and focal length are provided for both thin- and thick-lens imaging geometries. These expressions show that the numerical aperture will be maximized and chromatic aberration will be minimized at the thick-lens limit. This limit may be satisfied by a range of CRL geometries, suggesting alternative approaches to improving the resolution and efficiency of CRLs and X-ray microscopes.