Ray-tracing simulation of parabolic compound refractive lenses

X-ray compound refractive lenses (CRL) are becoming a widespread tool for the generation of microfocus spot sizes at synchrotron beamlines. The calculation of their performance by means of ray-tracing is useful for a rapid estimation of flux, resolution and focusing properties achievable in a beamline, when other optics are present, or simply to study the lens acceptance and focusing in the presence of a particular bending magnet, wiggler or undulator X-ray source. The ray-tracing method presented in this paper has been used to calculate the efficiency of beryllium CRLʹs using, for the instrument layout, realistic source size and divergence, and usual optics like perfect crystal monochromators. It is shown that the intensity transmitted by the lens, the effective aperture and the gain are in good agreement with analytical formulas. Additional information provided when running the program are the precise shape of beam at the focus, and at any position along the optical axis. For instance the intensity distribution at the CRL entrance and exit planes allows a comparison between the effective and the geometrical apertures. Finally, the method provides a precise value for the lens focal distance, which depends on the CRL length.