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

Area of Science:

• Optical Metrology
• Precision Engineering
• Surface Metrology

Background:

• Phase measuring deflectometry (PMD) is crucial for surface figure measurement of optical components, offering a simple setup and large dynamic range.
• Advancements to nanometer-scale accuracy reveal that systematic geometric errors, particularly low-spatial-frequency figure errors, limit PMD precision.
• Existing methods struggle to mitigate complex geometric deviations arising from lens distortion and extrinsic parameter coupling.

Purpose of the Study:

• To develop a high-accuracy stereo phase measuring deflectometry (SDC-PMD) system capable of compensating for systematic geometric errors.
• To improve the nanometer-scale surface figure measurement accuracy for reflective optical components.
• To address the limitations of classical calibration methods in the presence of lens distortion and extrinsic parameter coupling.

Main Methods:

• Proposed a synchronous distortion-compensated stereo phase measuring deflectometry (SDC-PMD) system incorporating orthogonal geometric constraints.
• Explicitly modeled lens distortion within a system-level geometric framework for parameter estimation.
• Employed a unified nonlinear optimization using reprojection residuals in the original observation space with stable initial values.

Main Results:

• Numerical simulations showed significant suppression of extrinsic parameter and mirror pose errors, with reprojection error converging to 5.6 × 10^-5 pixels.
• Experimental results demonstrated a 74.5% improvement in RMS figure error for a 70-mm flat mirror (0.027 μm).
• Achieved an RMS absolute deviation of 0.007 μm compared to a Zygo interferometer for spherical mirror testing.

Conclusions:

• The SDC-PMD system effectively suppresses geometric biases caused by distortion-extrinsic coupling, enhancing measurement accuracy.
• The proposed system-level modeling preserves the physical consistency and engineering controllability of the pinhole model.
• This approach significantly improves both the measurement accuracy and engineering applicability of stereo PMD for high-precision optical metrology.