Development of a Shape Evaluation Apparatus for Wolter Mirrors in X-ray Telescopes

High-precision metrology is essential in manufacturing, as reliable fabrication requires accurate measurement. In optical systems, the surface figure accuracy and surface roughness of lenses and mirrors have a strong impact on optical performance, driving continuous advances in shape measurement techniques. Among optical components, X-ray mirrors used for focusing and imaging require particularly high accuracy. While nanometer-scale fabrication and interferometric measurement techniques have been established for planar and near-spherical aspherical mirrors, accurate measurement of the inner surfaces of tubular mirrors remains challenging. This paper presents a non-contact shape measurement method for the inner surface of Wolter mirrors, which have a rotationally symmetric tubular geometry composed of ellipsoidal and hyperboloidal surfaces and are used in X-ray telescopes such as the Focusing Optics X-ray Solar Imager (FOXSI). The measurement system combines a roundness measuring instrument equipped with an air-bearing rotary stage and a motion error compensation technique. A fork-shaped jig holding laser displacement sensors was newly designed to enable axial scanning inside the mirror, while reference mirrors were simultaneously measured to suppress motion errors of the scanning stage. Using the developed system, non-contact measurements of both axial and circumferential shape profiles of Wolter mirror inner surfaces were achieved. Measurement repeatability of approximately 1 nm RMS in both axial and circumferential directions was confirmed through repeated measurements using a flat reference mirror to evaluate intrinsic system performance, as well as repeated measurements of a Wolter mirror.