X-ray beams reflected from a single layer or multilayer coating are widely used for X-ray tomography, holography, and X-ray phase contrast imaging. However, the observed irregular stripe patterns from either unfocused or defocused beams often cause disturbing artifacts and seriously deteriorate the image quality. In this work, we investigate the origin of these irregular fine structures using the wave optics theory. The connection to similar results obtained by the geometric optics theory is also presented. The proposed relation between the second derivative of the wavefront and the irregular structures was then verified by conducting at-wavelength metrology with the speckle-based wavefront sensing technique. This work will not only help to understand the formation of these irregular structures but also provide the basis for manufacturing future ‘stripe-free’ refection optics.

The multilayer Laue lens (MLL) is essentially a linear zone plate with large aspect ratio, which can theoretically focus hard X-rays to well below 1 nm with high efficiency when ideal structures are used. However, the focusing performance of a MLL depends heavily on the quality of the layers, especially the layer placement error which always exists in real MLLs. Here, a dynamical modeling approach, based on the coupled wave theory, is proposed to study the focusing performance of a MLL with layer placement error. The result of simulation shows that this method can be applied to various forms of layer placement error.

High-speed adaptive correction of optics, based on real-time metrology feedback, has benefitted numerous scientific communities for several decades. However, it remains a major technological challenge to extend this concept into the hard x ray regime due to the necessity for active mirrors with single-digit nanometer height errors relative to a range of aspheric forms. We have developed a high-resolution, real-time, closed-loop “adaptive” optical system for synchrotron and x ray free electron laser (XFEL) applications. After calibration of the wavefront using x ray speckle scanning, the wavefront diagnostic was removed from the x ray beam path. Non-invasive control of the size and shape of the reflected x ray beam was then demonstrated by driving a piezoelectric deformable bimorph mirror at ∼ 1 H z . Continuous feedback was provided by a 20 kHz direct measurement of the optical surface with picometer sensitivity using an array of interferometric sensors. This enabled a non-specialist operator to reproduce a series of pre-defined x ray wavefronts, including focused or non-Gaussian profiles, such as flattop intensity or multiple split peaks with controllable separation and relative amplitude. Such changes can be applied in any order and in rapid succession without the need for invasive wavefront diagnostic sensors that block the x ray beam for scientific usage. These innovations have the potential to profoundly change how x ray focusing elements are utilized at synchrotron radiation and XFEL sources and provide unprecedented dynamic control of photon beams to aid scientific discoveries in a wide range of disciplines.

We developed a novel numerical simulation method for volume diffractive optics based on the Takagi–Taupin (TT) dynamical theory of diffraction. A general integral system of equations with a powerful and convenient distortion function was developed for finite-element analysis (FEA). The proposed framework is promising with regard to flexibility, robustness, and stability and has potential for solving dynamical X-ray diffraction problems related to diffractive optical elements of arbitrary shape and deformation. This FEA method was used for evaluating laterally graded multilayer (LGML) mirrors, and a general coordinate system was introduced to make the geometric optimization simple and effective. Moreover, the easily implemented boundary conditions inherent in FEA, combined with the analysis of the energy resolution derived from the TT theory, can make the simulation of volume diffractive optics, including LGML mirrors, more accurate. Thus, a comprehensive and highly efficient computation of LGML mirror diffraction problems was performed. The evaluation of the effects of the figure errors can provide practical guidance for the fabrication of X-ray optical elements.