title: Stitching interferometry for ellipsoidal x-ray mirrors.
abstract: Ellipsoidal mirrors, which can efficiently produce a two-dimensional focusing beam with a single mirror, are superior x-ray focusing optics, especially when compared to elliptical-cylinder mirrors in the Kirkpatrick-Baez geometry. However, nano-focusing ellipsoidal mirrors are not commonly used for x-ray optics because achieving the accuracy required for the surface metrology of nano-focusing ellipsoidal mirrors is difficult due to their small radius of curvature along the short ellipsoidal axis. Here, we developed a surface metrology system for nano-focusing ellipsoidal mirrors using stitching interferometric techniques. The developed system simultaneously measures sub-aperture shapes with a microscopic interferometer and the tilt angles of the sub-aperture shapes with a large Fizeau interferometer. After correcting the systematic errors included in the sub-aperture shapes, the entire mirror shape is calculated by stitching the sub-aperture shapes based on the obtained relative angles between partially overlapped sub-apertures. In this study, we developed correction methods for systematic errors in sub-aperture shapes that originated from off-axis aberrations produced in the optics of the microscopic interferometer. The systematic errors on an ellipsoidal mirror were estimated by measuring a series of tilted plane substrates and the ellipsoidal substrate. From measurements of an ellipsoidal mirror with a 3.6-mm radius of curvature at the mirror center, we obtained a measurement repeatability of 0.51 nm (root-mean-square) in an assessment area of 0.5 mm × 99.18 mm. This value satisfies the requirements for surface metrology of nano-focusing x-ray mirrors. Thus, the developed metrology system should be applicable for fabricating nano-focusing ellipsoidal mirrors.
authors.affiliation: Japan Synchrotron Radiation Research Institute/SPring-8, 1-1-1 Kouto, Sayo-cho, Sayo-gun, Hyogo 679-5198, Japan.
authors.forename: Hirokatsu
authors.initials: H
authors.lastname: Yumoto
authors.affiliation: Japan Synchrotron Radiation Research Institute/SPring-8, 1-1-1 Kouto, Sayo-cho, Sayo-gun, Hyogo 679-5198, Japan.
authors.forename: Takahisa
authors.initials: T
authors.lastname: Koyama
authors.affiliation: Department of Precision Science and Technology, Graduate School of Engineering, Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871, Japan.
authors.forename: Satoshi
authors.initials: S
authors.lastname: Matsuyama
authors.affiliation: Department of Precision Science and Technology, Graduate School of Engineering, Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871, Japan.
authors.forename: Kazuto
authors.initials: K
authors.lastname: Yamauchi
authors.affiliation: Japan Synchrotron Radiation Research Institute/SPring-8, 1-1-1 Kouto, Sayo-cho, Sayo-gun, Hyogo 679-5198, Japan.
authors.forename: Haruhiko
authors.initials: H
authors.lastname: Ohashi