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We present an algorithm for surface reconstruction from the second-derivative data for free-form aspherics, which uses a subaperture scanning system that measures the local surface profile and determines the three second-derivative values at those local sampling points across the free-form surface. The three second-derivative data were integrated to get a map of x-and y-slopes, which went through a second Southwell integration step to reconstruct the surface profile. A synthetic free-form surface 200 mm in diameter was simulated. The simulation results show that the reconstruction error is 19 nm RMS residual difference. Finally, the sensitivity to noise is diagnosed for second-derivative Gaussian random noise with a signal to noise ratio (SNR) of 16, the simulation results proving that the suggested method is robust to noise.

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The increasing level of demand for multi-tasking machines requires a saddle with an ultra-precise machining accuracy level of 15μm, as such a saddle is one of the main components of these machines. The manner of achieving ultra-precise machining accuracy mainly depends on the fixed forces. In this paper, we optimized the number of contact points and the contact positions to reduce the deformation of the saddle while it is machined. The performance levels of the proposed optimal jig and fixture are determined by measuring the flatness, parallelism and perpendicularity of a machined saddle. The machining accuracy is found to be lower than 15μm at all measured points.