Robust white light interferometry reconstruction addressing three-degree-of-freedom disturbances and non-ideal...

White light interferometry (WLI) often faces performance degradation in industrial environments due to three-degree-of-freedom (3-DOF) mechanical disturbances and non-ideal spectral characteristics. This paper proposes a robust hierarchical reconstruction framework, termed "Trinity", to address these challenges. The framework incorporates a Gaussian mixture model (GMM) to accurately represent the source spectrum and utilizes an iterative strategy to decouple height refinement, multi-DOF vibration estimation, and physical model calibration. A zero-mean prior is enforced to resolve parameter coupling ambiguities, while a coordinate transformation strategy ensures numerical stability during the estimation process. Numerical simulations and experimental measurements on a non-isolated optical bench demonstrate that the proposed method effectively suppresses topography ripples and artifacts compared to conventional 1-DOF compensation algorithms. The implementation of GPU-accelerated batch processing further ensures computational efficiency, providing a reliable and practical solution for high-precision metrology in dynamic industrial environments.