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Limited by the aperture and f/number of the transmission sphere (TS), large convex spheres with very small R/number (ratio of the radius of curvature to the aperture) cannot be tested in a single measurement with a standard interferometer. We present the algorithm and troubleshooting for subaperture stitching test of a half meter-class convex sphere with R/0.61. Totally 90 off-axis subapertures are arranged on 5 rings around the central one. Since the subaperture is so small, its surface error is comparable with that of the TS reference error. Hence a self-calibrated stitching algorithm is proposed to separate the reference error from the measurements. Another serious problem is the nonlinear mapping between the subaperture's local coordinates and the full aperture's global coordinates. The nonlinearity increases remarkably with the off-axis angle. As a result, we cannot directly remove power from the full aperture error map as we usually do. Otherwise incorrect spherical aberration will be generated. We therefore propose the sphericity assessment algorithm to match the stitched surface error with a best-fit sphere. The residual is true surface error which can be used for corrective figuring or for tolerance assessment. The self-calibrated stitching and troubleshooting are demonstrated experimentally.

Material removal rate has greatly relied on the distribution of shear stress and dynamic pressure on the workpiece surface in hydrodynamic effect polishing (HEP). Fluid dynamic simulation results demonstrate that the higher rotation speed and smaller clearance will cause the larger material removal rate. Molecular dynamic (MD) calculations show the bonding energy of Si-O in the silicon-oxide nanoparticle is stronger than that in the quartz glass, and therefore the atoms can be dragged away from the quartz glass surface by the adsorbed silicon-oxide nanoparticle. The deep subsurface damage cannot be efficiently removed by HEP due to its extremely low removal rate. However, the subsurface damaged layer can be quickly removed by ion beam figuring (IBF), and a thinner layer containing the passivated scratches and pits will be left on the surface. The passivated layer is so thin that can be easily removed by HEP process with a low material rate under the large wheel-workpiece clearance. Combined with the IBF process, the subsurface damage and surface scratches have been efficiently removed after the HEP process. Meanwhile there are not obvious duplicated marks on the processed surface and the surface roughness has been improved to 0.130nm rms, 0.103nm Ra.

A translation-reduced ion beam figuring (TRIBF) technique for five-axis ion beam figuring (IBF) plants is proposed to process large size components which cannot be processed in the traditional way. This novel technique enhances the capability of five-axis IBF plants by taking advantage of their rotation axes. The IBF kinematic model is described and the TRIBF processing technique is established by solving the motion parameters. Verification experiments are conducted on a 150 mm diameter planar mirror. This mirror was processed by TRIBF technique with only a 100 mm translation stage. The surface error was reduced from initial 10.7 nm rms to 1.3 nm rms within 97 minute processing time. The result indicates that the TRIBF processing technique is feasible and effective.

In off-axis subapertures of most aspheres, astigmatism and coma dominate the aberrations with approximately quadratic and linear increase as the off-axis distance increases. A pair of counter-rotating Zernike plates is proposed to generate variable amount of Zernike terms Z4 and Z6, correcting most of the astigmatism and coma for subapertures located at different positions on surfaces of various aspheric shapes. The residual subaperture aberrations are then reduced within the vertical dynamic range of measurement of the interferometer. The plates are fabricated with computer generated holograms and the experimental results show the variable aberration correction effect without ghost fringes. The same plates are reconfigurable by counter-rotating to enable near-null test of various aspheres flexibly.

Applying the iterative stitching algorithm, we demonstrate the power of subaperture testing through experiments. Naturally the algorithm applies to flats, spherical or aspheric surfaces. We first apply it to a silicon carbide flat mirror with larger aperture than the interferometer's. The testing results help to obtain a high-precision mirror through five iterations of ion beam figuring. The second experiment is 37-subaperture testing of a large spherical mirror. Good consistence is observed between the stitching result and the full aperture test result using a Zygo interferometer. Finally we study the applicability of the algorithm to subaperture testing of a parabolic surface. The stitching result is consistent with the auto-collimation test result. Furthermore, the surface is tested with annular subapertures and also retrieved by our algorithm successfully.