A robust iterative reconstruction technique for deflectometry

We present an iterative surface-reconstruction approach based on vision rays that achieves not only higher reconstruction accuracy than the Delaunay/Möller–Trumbore method but also a significant reduction in computation time. The peak-to-valley value of the reconstruction error is decreased from 4.190 to 0.347 nm, while the time for a single iteration drops from 16 to 0.12 s. By aligning the camera’s optical axis with the z axis of the coordinate system, the need for the Delaunay/Möller–Trumbore surface-updating process is eliminated, preventing errors in surface-normal computation during reconstruction. This alignment leads to an iterative reconstruction method based on vision rays within the optical-axis-based coordinate system that is fast, accurate, and robust. The robustness of this technique is further evaluated by studying the effects of the angle θ between the camera’s optical axis and the z axis, as well as the angle φ of the initial iteration-plane normal. Experimental results show that reconstruction errors introduced by the angle θ are typically in the nanometer range; however, as θ approaches a certain critical angle, reconstruction errors can increase to the micrometer level, potentially leading to reconstruction failure. In contrast, errors introduced by the angle φ remain at the picometer level and can be considered negligible. These findings demonstrate that aligning the camera’s optical axis with the z axis not only ensures the robustness of the iterative process but also achieves the highest reconstruction accuracy.