Abstract
Monolithic multi-surfaces workpieces (MMSWs) are widely used in aerospace, advanced optics, and other fields. The complete topographic measurement of each sub-surface in MMSWs requires high measurement flexibility and strong space constraints since each sub-surface is located in an inner cylindrical cavity. This paper proposes a complete topographic measuring method for MMSWs based on a four-axis measuring system with a rotating single-point probe. Several basic geometric parameters of the measuring system are identified in the calibration. The mapping relation between the theoretical surface equations and measuring system coordinates is established by searching for reference points. The measurement scanning paths with different orientations are designed for each sub-surface. The iterative measurement and optimization are adopted to compensate for the measurement errors from the coupling of the probe and the four-axis measuring system. A standard sphere is measured, and the deviation of the fitting radius is below 0.5 μm. Besides, a freeform four-mirror optical system is selected as the experimental study case, where the complete topographic measurement of each sub-surface is completed on an ultra-precision machine tool. The form error and the standard deviation of each sub-surface can reach the micron level.
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