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

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 Chen, T.-Y. 2011. Opt. Express, 19(21): 19919–19924. [Crossref], [PubMed] , [Google Scholar], 2 Kang, H. C. 2008. Appl. Phys. Lett., 92(22): 221114[Crossref], [Web of Science ®] , [Google Scholar]], refractive [3 Snigirev, A. A. 2002. SPIE Proceedings, 4783 [Google Scholar], 4 Schroer, C. G. 2005. Appl. Phys. Lett, 87(12): 124103[Crossref], [Web of Science ®] , [Google Scholar]], and reflective [5 Hignette, O. 2005. Rev. Sci. Inst., 76: 063709[Crossref], [Web of Science ®] , [Google Scholar], 6 Liu, W. 2011. J. Synchrotron Rad., 18: 575–579. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]] 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 Mimura, H. 2007. Appl. Phys. Lett., 90(5): 051903[Crossref], [Web of Science ®] , [Google Scholar]], while a multilayer mirror may attain sub-10 nm focal spot size [8 Mimura, H. 2010. Nat. Phys., 6(2): 122–125. [Crossref], [Web of Science ®] , [Google Scholar]]. 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 Preda, I. 2013. Nuclear Instruments and Methods in Physics Research A, 710: 98–100. [Crossref], [Web of Science ®] , [Google Scholar], 10 Schindler, A. 2002. Ion Beam Finishing Technology for High Precision Optics Production, 64–66. Washington, DC: OSA Technical Digest, Optical Society of America. [Google Scholar]] and elastic emission machining (EEM) [11 Yamauchi, K. 2002. Rev. Sci. Instrum., 73(11): 4028–4033. [Crossref], [Web of Science ®] , [Google Scholar]], while figure testing is achieved using optical interferometers [12 Yamauchi, K. 2003. Rev. Sci. Instrum., 74(5): 2894–2898. [Crossref], [Web of Science ®] , [Google Scholar], 13 Mimura, H. 2005. Rev. Sci. Instrum., 76(4): 045102[Crossref], [Web of Science ®] , [Google Scholar]] or slope profilers [14 Takacs, P. Z. 1989. “Advances in Fabrication and Metrology for Optics and Large Optics”. In Proc. SPIE Edited by: Arnold, J. B. and Parks, R. A. 354–364. 966 [Google Scholar], 15 Siewert, F. 2012. Optics Express, 20(4): 4225–4536. [Crossref], [PubMed] , [Google Scholar], 16 Senba, Y. 2010. Nuclear Instruments and Methods in Physics Research A, 616: 237–240. [Crossref], [Web of Science ®] , [Google Scholar]]. 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 Kimura, T. 2010. Rev. Sci. Instrum., 81(12): 123704[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]] or ptychography [18 Schropp, A. 2010. Appl. Phys. Lett., 96(9): 091102[Crossref], [Web of Science ®] , [Google Scholar], 19 Kewish, C. M. 2010. Opt. Express, 18(22): 23420–23427. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]]. 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.