In-situ high-accuracy figure measurement based on stereo deflectometry for the off-axis aspheric mirror

The misalignment between the geometric and optical axes, combined with rotational asymmetry, poses significant challenges for achieving high-accuracy measurement of the off-axis aspheric mirror during the fabrication and polishing processes. To address this issue, this paper presents a method based on stereo deflectometry for measuring the figure of the off-axis aspheric mirror. In this method, point cloud of the off-axis aspheric mirror is first obtained using stereo deflectometry. Subsequently, the point cloud is transformed into the parent mirror coordinate system using the final-optimized transformation matrix via the nonlinear least-squares algorithm, and the figure of the off-axis aspheric is determined by subtracting the conic formula. To verify the feasibility and high accuracy of the proposed method, measurements are conducted in both simulations and experiments on an off-axis parabolic mirror with a diameter of 142 mm. The simulation results indicate that the difference between the calculated results of the proposed method and the ground truth is 3.01 nm PV (peak-to-vally), and the experimental results are consistent with those obtained using the interferometer, demonstrating the feasibility and high accuracy of the proposed method.