Alignment method based on direct establishment of global world coordinate system for 3D Laser Vibrometry

Three-dimensional (3D) full-field scanning laser Doppler vibrometry represents one of the most significant non-contact vibration measurement technologies currently available. Among its core components, 3D alignment and laser vibrometry constitute the two most critical technical elements. 3D alignment obtains the rotation matrices from the local probe coordinate system (PCS) to the global world coordinate system (WCS), thereby mapping non-orthogonal vibration components measured along three laser beam directions by three probes into the orthogonal WCS. However, existing alignment methods demonstrate significant dependence on calibration plates or additional measurement equipment, while exhibiting limited adaptability to complex curved structures, thus constraining their engineering applications. To address this issue, this paper proposes a 3D alignment algorithm based on the developed mathematical model of 2D rotating mirror outgoing light rays that directly establishes the global WCS on the measured object surface. This method utilizes the geometric constraint relationships between multiple laser beam’s direction vectors and the WCS when multiple probes illuminate the same point, thereby solving for the transformation matrix from the PCS to the WCS. This approach eliminates the dependence on calibration plates or feature points that is characteristic of conventional methods. Experimental results demonstrate that the method achieves maximum average relative errors of 2.85% and 6.53% in planar and curved surface alignment scenarios, respectively, while simultaneously enabling 3D full-field laser scanning. Compared to existing technologies, the proposed method exhibits significant advantages in terms of scenario adaptability and engineering practicality.