In-situ deflectometric measurement of optical surfaces for precision manufacturing

The in-situ measurement of complex optical surfaces is a challenging task in precision engineering. The phase measuring deflectometry is a powerful measuring method for complex specular surfaces, and it has higher measuring efficiency, stability and dynamic range compared to interferometry. Consequently it is promising to widespread applications in various fields. Deflectometry is essentially a calibration problem, and the measuring accuracy is directly determined by the quality of geometrical calibration. An in-situ deflectometric measuring system is designed based on the single point diamond turning machine. A self-calibration method is developed to specify the relative positions of the camera and screen. Ray tracing is conducted at two positions of an auxiliary reflecting mirror, which is mounted on an air bearing spindle. The accuracy of the geometrical positions can be improved by an order of magnitude by minimizing the deviations of the traced points with respect to the true correspondences. According to the statistical properties of the deviations in reverse ray tracing, the form errors and the position errors can be separated, and the positioning error of the workpiece can be corrected accordingly. Henceforth, the nominal shape of the fabricated workpiece can be fully utilized, and the conventional one-way position-form mapping can be converted into a two-way mapping problem. As for the complex shapes, the whole surface can be covered by sub-aperture measurement. Precise localization of a local region under test is achieved by multi-position imaging, so that correct convergence of the iterative reconstruction process can be guaranteed. Several typical optical surfaces including an off-axis paraboloid mirror are measured, and the measuring accuracy of the proposed method is proved better than 150 nm RMS.