A Precision Grazing-incidence Angle Error Measurement of a Hard X-ray Condenser Mirror Using Single-grating Interferometry

Abstract

Third-generation synchrotron radiation facilities enable us to use X-rays of extremely high brightness and low emittance, which are efficiently concentrated into a nanoscale area by a focusing device. Such progress has significantly enhanced the throughput of X-ray analyses based on scanning microscopy. On the other hand, the spatial resolution of scanning microscopy directly depends on the focal spot size. Many diffractive [1, 2], refractive [3, 4], and reflective [5, 6] focusing devices are currently available for producing small focal spots. Reflective optics realize the highest throughput with a sufficiently long working distance. Furthermore, among the above-listed focusing devices, reflective devices produce the smallest focal spot size in the hard X-ray region. A total reflection mirror may attain sub-30 nm focal spot size [7], while a multilayer mirror may attain sub-10 nm focal spot size [8]. The achievable focal spot size is significantly degraded by errors in the mirror shape and misalignment of grazing-incidence angle. In the hard X-ray region, the focusing mirror surface requires accuracies below 2 nm PV and 1 nm PV for sub-30 nm and sub-10 nm focusing, respectively. The error in the grazing-incidence angle must not exceed 0.5 × 10−6 rad and 0.1 × 10−6 rad for sub-30 nm and sub-10 nm focusing, respectively. Current advances in fabrication and mirror testing technologies have realized highly accurate deterministic figuring processes that can meet these requirements. Fabrication techniques include ion beam figuring [9, 10] and elastic emission machining (EEM) [11], while figure testing is achieved using optical interferometers [12, 13] or slope profilers [14, 15, 16]. In contrast, alignment accuracy is still evaluated by conventional beam profiling methods such as knife-edge scanning methods. The alignment is optimized by an iterative procedure of beam profiling and glazing-incidence angle adjustment. This procedure is very time-consuming and frequently introduces a significant profiling error from shape imperfections and/or vibration of the object to be scanned. Accordingly, the grazing-incidence alignment often determines the achievable focal spot size. The error in the grazing incidence angle generates a coma aberration, which is essentially a wavefront distortion with a cubic function. Hence, adjusting the grazing-incidence angle by monitoring the wavefront shape is possible. The wavefront shape can be characterized by several methods, such as phase retrieval [17] or ptychography [18, 19]. However, to obtain a wavefront shape of accuracy smaller than λ/4, the limit imposed by Rayleigh's criterion, large amounts of intensity information are required. In addition, these methods are unsuitable for the shot-by-shot measurements demanded in X-ray free-electron laser (XFEL) focusing.