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An X-ray ellipsoidal mirror requires nanometer-level shape accuracy for its internal surface. Owing to the difficulty in processing the surface, electroforming using a high precision master mandrel has been applied to mirror fabrication. In order to investigate the replication accuracy of electroforming, a measurement method for the entire internal surface of the mirror must be developed. The purpose of this study is to evaluate the shape replication accuracy of electroforming. In this study, a three-dimensional shape measurement apparatus for an X-ray ellipsoidal mirror is developed. The apparatus is composed of laser probes, a contact probe, reference flats, a z-axis stage, and a rotation table. First, longitudinal profiles of a mandrel or mirror placed vertically on the rotation table are measured at several angular positions. Subsequently, without realignment of the measured sample, circularity at every height is measured at regular intervals of 0.1 mm. During each measurement, the effect of motion errors is calculated and subtracted from each profile by referring to the distances between the probes and reference flats. Combining the circularity data with the longitudinal profiles, a three-dimensional error distribution of the entire surface is obtained. Using a mandrel with nanometer-level shape accuracy and a replicated mirror, the performance of the measurement apparatus and the replication accuracy are evaluated. Measurement repeatability of single-nanometer order and replication accuracy of sub-100-nm order are confirmed.
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