Abstract
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.
Highlights
Ever since the novel design of multiple-bend achromatic lattices (Einfeld et al, 2014) made diffraction-limited synchrotron radiation sources possible, many synchrotron radiation sources are being upgraded in order to provide more coherent X-ray beams (Chenevier & Joly, 2018; Leemann et al, 2018; Pellegrini, 2016; Shi et al, 2017)
For diffractionlimited synchrotron radiation (DLSR) or X-ray free-electron lasers (FEL), because of the low emittance of the source, the wave optics need to be taken into consideration
We have developed a tool to rapidly evaluate the performance degradation due to the imperfection of an optical element
Summary
Ever since the novel design of multiple-bend achromatic lattices (Einfeld et al, 2014) made diffraction-limited synchrotron radiation sources possible, many synchrotron radiation sources are being upgraded in order to provide more coherent X-ray beams (Chenevier & Joly, 2018; Leemann et al, 2018; Pellegrini, 2016; Shi et al, 2017). Raimondi & Spiga (2015) have done similar work They investigated the performance degradation from imperfect mirrors in detail through both analytical expression and numerical simulation in terms of the point spread function (PSF) of the mirror. A theoretical approach to evaluate the optical performance degradation caused by imperfect optical elements without using wave optics simulations is given. The proposed theory could be used to evaluate the impacts of finite size aperture, surface height error and other imperfections of optical elements as long as they can be described by a complex transfer function. The presented theory provides physical insights that help to explain the degradation of optical performance These physical explanations will help beamline designers estimate the tolerances on their optical elements more accurately. A summary of the proposed theoretical approach will be given at the end
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