Fast convolution-based performance estimation method for diffraction-limited source with imperfect X-ray optics.

Although optical element error analysis is always an important part of beamline design for highly coherent synchrotron radiation or free-electron laser sources, the usual wave optics simulation can be very time-consuming, which limits its application at the early stage of the beamline design. In this work, a new theoretical approach has been proposed for quick evaluations of the optical performance degradation due to optical element error. In this way, time-consuming detailed simulations can be applied only when truly necessary. This approach treats the imperfections as perturbations that convolve with the ideal performance. For simplicity, but not by necessity, the Gaussian Schell-model has been used to show the application of this theoretical approach. The influences of the finite aperture size and height error of a focusing mirror are analysed using the proposed theory. The physical explanation of the performance degradation acquired from the presented approach helps to give a better definition of the critical range of error spatial frequencies that most affect the performance of a mirror. An example comparing two mirror surface errors with identical power spectral density functions is given. These two types of mirror surface errors result in very different intensity profiles. The approach presented in this work could help beamline designers specify the error tolerances on general optical elements more accurately.