Stitching interferometric characterization of geometric errors of hemispherical shells

•Complete characterization of surface error and thickness variation for hemispherical shells.•Interpretation and correction of pixel misalignment and mapping distortion.•Full aperture error map available through subaperture stitching.•Polar harmonics decomposition related to resonator performance. Geometric errors including the surface error and thickness variation of a hemispherical shell are determinant of the system performance, e.g. the frequency splitting of a hemispherical resonator gyroscope. Therefore, complete characterization at 0.1 µm level of accuracy is required which is difficult with current roundness measuring instruments. This paper presents an interferometric method for axially eccentric hemispherical shells. The outer surface and inner surface are measured individually by simply translating the shell along its anchor axis. The two measurements are registered after correction of pixel misalignment and mapping distortion through ray tracing. Thickness variation is then calculated from their difference. A multi-axis platform is designed to scan multiple subapertures covering the hemispherical shell. All subapertures are stitched together with misalignment corrected, according to the minimized inconsistency in the overlapping region of neighboring subapertures. The full aperture map is thus obtained for both the surface error and thickness variation. Polar harmonic representation is suggested by applying annular Zernike polynomial fitting. The method is experimentally demonstrated and validated with roundness cross test.