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通过变形反射镜的X射线束整形：所需反射镜轮廓的解析计算

X-ray beam-shaping via deformable mirrors: analytical computation of the required mirror profile

D. Spiga, L. Raimondi, C. Svetina, M. Zangrando

备注：
4th IWXM conference, Barcelona, Jul 2012. Published in NIM-A on May 11, 2013. AAM posted to arXiv as per Elsevier's Article posting policy. Published paper available at http://dx.doi.org/10.1016/j.nima.2012.10.117
发表信息：
Nuclear Instruments & Methods In Physics Research A, Vol. 710, p. 125-130 (2013)
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摘要：

具有高聚焦性能的X射线反射镜用于X射线望远镜的反射镜模块以及同步加速器和自由电子激光（自由电子激光）光束线。聚焦清晰度的劣化通常由几何变形和表面粗糙度引起，前者通常由几何光学描述，后者由物理光学描述。一般来说，技术发展的目标是非常紧密的聚焦，这要求反射镜轮廓尽可能符合标称形状，并将粗糙度保持在可忽略的水平。然而，可以通过压电致动器对反射镜进行有意的变形，以赋予焦点所需的尺寸和分布，如在FERMI@Elettra的EIS-TIMEX光束线上所做的那样。所得到的轮廓可以用长轨迹轮廓仪表征，并通过波前传播代码与预期的光学质量相关。然而，如果粗糙度的贡献可以忽略不计，计算可以通过一个射线跟踪例程，并在适当的假设下，焦斑轮廓（点扩散函数，PSF），甚至可以预测分析。这种方法的优点是，分析关系可以颠倒，即从所需的PSF所需的反射镜轮廓可以很容易地计算，从而避免使用复杂和耗时的数值代码。该方法也可以适用于空间不均匀的光束强度的情况下，通常在同步加速器和自由电子激光器的经验。在这项工作中，我们暴露的分析方法和应用的光束整形问题。

英文摘要：

X-ray mirrors with high focusing performances are in use in both mirror modules for X-ray telescopes and in synchrotron and FEL (Free Electron Laser) beamlines. A degradation of the focus sharpness arises in general from geometrical deformations and surface roughness, the former usually described by geometrical optics and the latter by physical optics. In general, technological developments are aimed at a very tight focusing, which requires the mirror profile to comply with the nominal shape as much as possible and to keep the roughness at a negligible level. However, a deliberate deformation of the mirror can be made to endow the focus with a desired size and distribution, via piezo actuators as done at the EIS-TIMEX beamline of FERMI@Elettra. The resulting profile can be characterized with a Long Trace Profilometer and correlated with the expected optical quality via a wavefront propagation code. However, if the roughness contribution can be neglected, the computation can be performed via a ray-tracing routine, and, under opportune assumptions, the focal spot profile (the Point Spread Function, PSF) can even be predicted analytically. The advantage of this approach is that the analytical relation can be reversed; i.e, from the desired PSF the required mirror profile can be computed easily, thereby avoiding the use of complex and time-consuming numerical codes. The method can also be suited in the case of spatially inhomogeneous beam intensities, as commonly experienced at Synchrotrons and FELs. In this work we expose the analytical method and the application to the beam shaping problem.

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