Wafer-level thin-film stress measurement is essential for reliable semiconductor fabrication. However, existing techniques present limitations in practice. Interferometry achieves high precision but at a cost that becomes prohibitive for large wafers. Meanwhile laser-scanning systems are more affordable but can only provide sparse data points. This work develops a phase-measuring deflectometry (PMD) system to bridge this gap and deliver a full-field solution for wafer stress mapping. The implementation addresses three key challenges in adapting PMD. First, screen positioning and orientation are refined using an inverse bundle-adjustment approach, which performs multi-parameter optimization without re-optimizing the camera model and simultaneously uses residuals to quantify screen deformation. Second, a backward-propagation ray-tracing framework benchmarks two iterative strategies to resolve the slope-height ambiguity which is a fundamental challenge in PMD caused by the absence of a fixed optical center on the source side. The reprojection constraint strategy is selected for its superior convergence precision. Third, this strategy is integrated with regional wavefront reconstruction based on Hermite interpolation to effectively eliminate edge artifacts. Experimental results demonstrate a peak-to-valley error in the reconstructed topography of 0.48 µm for a spherical mirror with a radius of 500 mm. The practical utility of the system is confirmed through curvature mapping of a 12-inch patterned wafer and further validated by stress measurements on an 8-inch bare wafer, which show less than 5% deviation from industry-standard instrumentation. These results validate the proposed PMD method as an accurate and cost-effective approach for production-scale thin-film stress inspection.

Thin electronic-packaging films can develop substantial warpage during heating. Three-dimensional digital image correlation (3D-DIC) reconstructs the full displacement field, yet displacement-plane fitting still introduces curvature-dependent projection errors into the calculated strain. The proposed estimator differentiates matched reference and heated surfaces in common material coordinates and compares their first fundamental forms. Directional Green–Lagrange strains are then averaged over a fixed region of interest before temperature regression. Both global-coordinate and local-plane DPF varied with curvature in the cylindrical benchmarks. The surface-metric CTE remained invariant at the reporting resolution across the tested bending directions and regions of interest. Coordinate-noise simulations quantified precision after field averaging and regression. In the reported copper-foil sequence, the surface metric gave an RMSE of $0.170$ $\mathrm{ppm}{\mathrm{K}}^{-1}$ relative to the NIST copper reference, which was lower than either DPF baseline. The method measures directional CTE during smooth developable warpage without prescribing its shape, curvature, or bending direction.