PSI - Issue 40

A. Barannikov et al. / Procedia Structural Integrity 40 (2022) 40–45 A. Barannikov at al. / Structural Integrity Procedia 00 (2022) 000 – 000

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1. Introduction The most advanced X-ray sources, such as fourth-generation synchrotrons and free-electron lasers, can generate high brightness coherent radiation, especially in the hard X-ray region. X-ray optics are developing to fully utilize these beams of unprecedented brightness and coherence by Snigirev et al. (1996), Snigirev and Snigireva (2008). Due to the significant improvement in manufacturing and preparation techniques, all types of X-ray focusing optics: Fresnel zone plates (FZPs), refractive lenses, and mirrors reached 10 to 50 nm spatial resolution. However, today the further direction of X-ray optics development is mainly determined by the evolution of synchrotron radiation sources expressed in the desire to achieve their theoretical limiting characteristics. The laser-like properties of the sources and modern technologies contribute to creating a new generation of X-ray optics, whose optical properties allow going far beyond simple collimation and focusing functions. This optics makes it possible to form amplitude and phase of the wavefront with almost complete freedom, using the most outstanding properties of synchrotron and X-ray laser radiation. For instance, one of the clearest demonstrations of X-ray beam-shaping optics is a parabolic refractive axicon capable generate a Bessel beam along the optical axis and ring-shaped beam at the imaging distance (see Zverev et al. (2017)). Another example is multilens interferometers which under coherent X-ray illumination from the periodic patterns of the interference fringes in Snigirev et al. (2014) and Snigirev et al. (2009). These optics can provide beam-conditioning and beam-shaping functions for special illumination, beam expanding, or higher harmonics suppressors (see Narikovich et al. (2019) and Snigirev et al. (2021)). This opens up new opportunities for modern X-ray studies in the field of coherent diffraction and scattering, phase-contrast microscopy, and imaging by Zverev et al. (2020) and Zverev et al. (2020). It should be noted that diffractive optical elements (DOEs) can also perform complex optical functions in the X ray regime (see Di Fabrizio et al. (2003)). Previously, based on DOEs, beam-shaping condenser lenses for full-field transmission X-ray microscopes were proposed by Jefimovs et al. (2007) and Vogt et al. (2006). However, to achieve complicated amplitude-phase distribution of forming wave, the design of DOEs is challenging due to fabrication limitations. For instance, efficient focusing of hard X-rays using diffractive optics such as FZP is limited by the ability to manufacture diffracting structures with small outermost zone width and the large thicknesses imposed by the weak interaction of X-rays with matter. With increasing photon energy, the required thickness of phase-shifting material increases. For hard X-rays with silicon FZP, the required structure thickness is several tens of micrometers. Recently, silicon FZPs made by Micro Electro Mechanical Systems (MEMS) technology to achieve a small structure period and high aspect ratios were proposed in Snigirev et al. (2007) and Snigireva et al. (2007). Manufactured FZPs have an outermost zone width of 0.4 μm with the structure's thickness up to several tens of micrometers. The aspect ratio is more than 50, demonstrating the state-of-the-art of the modern Si microfabrication technology. In this paper, we experimentally demonstrate the influence of the diffraction structure of the circular silicon FZP made by MEMS technology on its deformation. The deformation field mapping was taken by the X-ray diffraction imaging technique. The results allowed reconstructing the profile of the FZP curvature. The considered approach can be used to study the more complex DOE structures and improve their manufacturing technology.

Nomenclature 2 θ diffraction angle (Bragg) ⃗ ū unit vector in Cartesian T m membrane thickness

deformation profile of the thin plate

depth of the channels (zones) diameter of the FZP area (aperture)

h A