Extended formalism for simulating compound refractive lens-based x-ray   microscopes
  We present a comprehensive formalism for the simulation and optimisation of CRLs in both condensing and full-field imaging configurations. The approach extends ray transfer matrix analysis to account for x-ray attenuation by the lens material. Closed analytical expressions for critical imaging parameters such as numerical aperture, vignetting, chromatic aberration and focal length are provided for both thin- and thick-lens imaging geometries. 
Hugh Simons, Sonja Rosenlund Ahl, Henning Friis Poulsen and Carsten   Detlefs
physics.optics