Effect of x-ray mirror figure error on the focus profile: comparison of measurements with physical and geometric optics simulations

Mirrors operating at grazing angles utilising total external reflection are commonly used for focusing X-ray at synchrotron radiation sources. Figure error on the mirror causes distortion of the focus profile. We have modeled a well characterized test mirror which has three different modifications of the elliptical figure laid down in parallel lanes running the length of the mirror. The focusing of the mirror was simulated using geometric optics (ray tracing) and physical optics (wave propagation). The mirror was then tested with X-rays on a beamline at a synchrotron radiation facility. The comparison between the two simulation methods and the measured data elucidates the origins of structures on the intensity profile of the focused beam and demonstrate that for quantitative agreement between simulation and experiment, interference and diffraction effects must be modeled.