High-accuracy synchronous distortion-compensated stereo phase measuring deflectometry with orthogonal geometric constraints

For applications such as the fabrication and in-situ inspection of reflective optical components, phase measuring deflectometry (PMD) is widely used for surface figure measurement due to its simple setup and large dynamic range. However, as the measurement accuracy advances from the micrometer to the nanometer scale, systematic geometric errors increasingly dominate the measurement deviations and manifest as pronounced low-spatial-frequency figure errors. To address this issue, we propose a high-accuracy synchronous distortion-compensated stereo phase measuring deflectometry (SDC-PMD) system with orthogonal geometric constraints, in which lens distortion is explicitly incorporated into a system-level geometric modeling and parameter estimation framework, stable initial values are established under co-located orthogonal constraints, and a unified nonlinear optimization is performed in the original observation space using reprojection residuals. Numerical simulations demonstrate that the proposed method can significantly suppress the geometric errors of the extrinsic parameters and mirror pose, with the reprojection error converging to the order of 5.6 × 10 −5 pixels. Experimentally, the root-mean-square (RMS) figure error is improved to 0.027 μm for a 70-mm high-precision flat mirror, corresponding to a 74.5% improvement over a classical calibration method, while for spherical mirror testing, the RMS absolute deviation from a Zygo interferometer is 0.007 μm. By preserving the physical consistency and engineering controllability of the pinhole model, the proposed system-level modeling and synchronous compensation suppress geometric biases induced by distortion–extrinsic coupling, thereby improving both the measurement accuracy and engineering applicability of stereo PMD.