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Interferometric test of large convex aspheres with high accuracy is still an urgent problem. Adopting a large-aperture null corrector is usually inevitable, and it is imperative to certify the large-aperture null optics in case incorrect final shape of the aspheric mirror is obtained. Moreover, it is necessary to calibrate and remove errors of the large-aperture null lens and trace errors to surfaces that are easy to obtain high accuracy. For these purpose, this paper presents an in situ calibrated null test method. The large-aperture null corrector for convex aspheric mirror is verified and calibrated by a wisely designed small aperture certifying null whose surfaces are either flat or spherical which are easy to be fabricated, measured and assembled. A redundant test is implemented by a Zygo VeriFire Asphere interferometer for cross test. Compared with existing methods of certificating null correctors which utilize an expensive CGH or a self-aligning aspherical mirror, the presented method finally traces errors of a large-aperture null corrector to small aperture flat and spherical surfaces thus costs are expected to be saved dramatically. [ABSTRACT FROM AUTHOR]

• Multi-scale measurement of DOEs based on stitching interference microscopy. • Inherited advantages of high resolution and high accuracy. • Extended lateral range of measurement to 10 mm scale via subaperture stitching. • Simultaneous correction of 6-dof scanning motion error for seamless data fusion. • Full aperture fabrication error map obtained with undercut effect verification. The development of diffractive optical elements (DOEs)enables fascinatingly compact design and chromatic aberration correction. Fabrication errors of DOEs include periodic pattern error, relief profile error and roughness which affect imaging quality and diffraction efficiency. Characterization of the DOE requires thus multi-scale measurement of the surface topography over the full aperture of 10 mm scale. This paper presents a method based on the white light interferometry in combination of subaperture stitching. Firstly, the principle of measurement and subaperture layout design is introduced. The measuring system is easily set up by integrating a scanning platform with the interference microscope. Subaperture stitching algorithm is developed based on the surface height change related to the scanning motion error. The slope of the relief profile is used to model the deviations of overlapping point pairs induced by lateral shift and rotation. Finally, the topography and fabrication error of a Fresnel lens surface are experimentally obtained and characterized over the full aperture through stitching of totally 67 subapertures. [ABSTRACT FROM AUTHOR]

Aiming to develop a prototype swing arm profilometer for several meter-class aspheres, we first present detailed error analysis including error motions of the swing rotary table and the part rotary table, and misalignment of the axes of the two rotary tables. The induced probing error in the normal direction of the reference sphere is calculated by considering the error motions in the coordinate transformation. A surface reconstruction algorithm is then proposed to separate the error motions of the part rotary table by stitching multiple traces. The error motions are optimally recognized and then removed from the trace measurement based on the least squares principle. We model the objective function by relating the normal error to the rigid body transformation of each trace. The basic idea is to minimize the inconsistency of all intersection points of different traces simultaneously. Finally the algorithm is verified through simulations. It shows that error motions of sub-milliradian scale are even tolerant with the surface reconstruction algorithm. [ABSTRACT FROM AUTHOR]

• 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. [ABSTRACT FROM AUTHOR]