Self-Correcting and Globally-Consistent 3D Cross-Ratio Invariant Model for Multi-View Microscopic Profilometry

This article introduces a multiview 3-D microscopic profilometry system equipped with tilted cameras adhering to the Scheimpflug condition and a vertically aligned projector. It utilizes a novel 3-D cross-ratio invariant (3D-CRI) model that offers inherent self-correction, enhanced global consistency, and computational efficiency. The inherent self-correction mitigates optical contaminations like multiple reflections by using deviations from the epipolar line for optimal candidate selection. The model is also designed as spatial lines to associate the approximate linear error distribution across depths, thereby facilitating its further correction (e.g., proposed embedded linear compensation method to address data inconsistency among various binocular projector-camera setups). Additionally, the model simplifies computational demands by directly correlating phase differences to spatial coordinates. Furthermore, a conversion method from the triangular stereo to the 3D-CRI model is developed, avoiding the complex per-pixel calibration. The experiments are conducted to verify robustness, globally consistent accuracy, and speed performance. The experimental results validate that the system is robust to multiple reflections by testing on the printed circuit boards with dense components. The global consistency is also verified by the experiments with better quantitative metrics within the whole measurement range over ten times the depth of field. In particular, the quantitative metrics of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</i>-axis are halved. The speed performance shows that our method is the fastest among competing techniques.