The most advanced X-ray sources, such as third-generation synchrotrons and free electron lasers (XFEL), are capable to generate high brightness coherent radiation, especially in the hard X-ray region. The availability of such beams facilitates the development of 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 wave front with almost complete freedom, using the most outstanding properties of synchrotron and X-ray laser radiation such as brightness, monochromaticity, and coherence.
Like in visible light optics, beam-shaping functions can be implemented in an X-ray regime based on both diffraction and refractive optical elements. For example, the beam-shaping optics based on diffraction optical elements (DOEs) allows realizing almost any complex optical transformation. However, due to the high penetrating power of X-rays through DOEs their use is significantly limited in the hard energy range. In addition, since many unknown beam parameters must be defined in advance, the design of such beam-shaping optical elements is a challenging task. As for the beam-shaping elements based on refractive optics , they are deprived of the disadvantages which are inherent in DOEs. This optics allows for some beam transformations, and the possibilities of its applications cover various areas of modern X-ray optics, such as interferometry and coherent diffraction, phase-contrast microscopy and imaging, and ultrafast and nonlinear optics studies.
For example, one of the most vibrant demonstrations of the beam-shaping optics is a special class of refractive optical elements that have axial symmetry and are capable to convert a point-like source to a narrow axial straight line segment. These optical elements are called axicons. Recently, we demonstrated an X-ray parabolic refractive axicon lens as a novel type of X-ray beam-shaping element . Under coherent X-ray illumination, the parabolic axicon generates Bessel-like beam propagated along the optical axis in the near field and ring-shaped beam in the far field.
The optical transformations produced by axicon can be used in areas requiring special illumination, as well as extended focused beams, for instance, in diffraction and imaging techniques, in metrological applications, as well as for source diagnostics and beamline alignment. Moreover, such beam-shaping capabilities can significantly simplify some existing experimental layouts or lead to completely new optical schemes for X-ray techniques based on synchrotron and XFEL sources. Most recently, we proposed an optical scheme of phase-contrast microscopy technique based on the axicon optics . Due to the unique optical properties of the parabolic refractive axicon lens, the new approach turned out to be more efficient for visualization of weakly absorbing samples as compared with the traditional microscopy technique.
In addition to new X-ray axicon refractive optics, it is also worthwhile to consider other beam-shaping elements, called interferometers, whose optical functions are well known and successfully used. These devices allow realizing the paraxial optical schemes of interferometry based on the coherent properties of modern X-ray sources. Recently, we demonstrated bilens and multilens interferometers based on refractive optics which under coherent illumination generate an array of mutually coherent beams focused at some distance [4-5]. The size of the focal spots is restricted to the diffraction limit and can be less than tens of nanometers. When the beams overlap they produce a steady interference pattern of fringes in the far field.
The proposed interferometers can be used in a wide X-ray energy range while maintaining high efficiency. The field of applications of their optical functions is not limited only to the interferometry techniques and can be extended in the area of beam diagnostics and beam conditioning. Moreover, such lens systems open up new opportunities for the development of phase-contrast imaging technique, which was recently demonstrated .
 Snigirev, A., Kohn, V., Snigireva, I., & Lengeler, B. (1996). A compound refractive lens for focusing high-energy X-rays. Nature, 384(6604), 49-51.
 Zverev, D., Barannikov, A., Snigireva, I., & Snigirev, A. (2017). X-ray refractive parabolic axicon lens. Optics Express, 25(23), 28469-28477.
 Zverev, D., Snigireva, I., & Snigirev, A. (2018). X-ray Phase Contrast Microscopy Based on Parabolic Refractive Axicon Lens. Microscopy and Microanalysis, 24(S2), 296-297.
 Snigirev, A., Snigireva, I., Kohn, V., Yunkin, V., Kuznetsov, S., Grigoriev, M. B., ... & Detlefs, C. (2009). X-ray nanointerferometer based on Si refractive bilenses. Physical review letters, 103(6), 064801.
 Snigirev, A., Snigireva, I., Lyubomirskiy, M., Kohn, V., Yunkin, V., & Kuznetsov, S. (2014). X-ray multilens interferometer based on Si refractive lenses. Optics express, 22(21), 25842-25852.
 Zverev D., Snigireva I., Kohn V., Kuznetsov S., Yunkin V., Snigirev A., (2020) X-ray phase-sensitive imaging using a bilens interferometer based on refractive optics. Accepted for publication in journal Opt. Express