B-spline-assisted deflectometry with a concave mirror for large-order differences specular surface

• A concave mirror is introduced into the PMD system to extend the effective DOF. • An iterative feature-point localization using geometry and SUT traits. • A B-spline method for precise in-situ measurement of large-order specular surfaces. Due to the influence of the non-ideal collimated rays emitted by the display screen and the limited camera's depth of field (DOF), the imaging quality on the camera target surface is degraded in traditional phase measuring deflectometry (PMD), resulting in blurred imaging. This is particularly problematic when measuring objects with large-order differences, as inaccurate phase extraction will case failed measurement ultimately. To overcome these limitations, this paper puts forward a B-spline-based concave mirror-assisted imaging PMD (B-CM-PMD) method. By incorporating a concave mirror and utilizing its reflective characteristics, the captured fringe quality is markedly improved and the effective DOF is substantially expanded. Furthermore, to satisfy the requirement for high-precision in-situ measurement with large-order differences, a B-spline surface reconstruction method incorporating Levenberg-Marquardt optimization for feature points localization is developed, which enables high-precision reconstruction of mirror surfaces using image acquisition at only a single system position. The feasibility and reliability have been verified through both simulations and experiments, and the results show that the B-CM-PMD method enhances reconstruction completeness and reducing reconstruction error by 68.18% in the measurement of the large-order difference surface.