A Mathematical Model for Determining the Pose of a SLDV

Abstract

A laser Doppler vibrometer (LDV) combined with a pair of orthogonal scan mirrors is a scanning LDV (SLDV). A mathematical model based on the scan mirrors configuration for determining the orientation and position of a SLDV in a structure coordinate system (SCS) is presented in this work. Coordinates of a scan point in a scan mirrors coordinate system (SMCS) are derived from the mathematical model and the relation of coordinates of the same scan point in the SMCS and SCS is derived using the rigid transformation theory. A rotation matrix and a translation vector from the SMCS to SCS are obtained by applying the least squares method and singular value decomposition. An experiment to scan a 3D structure was performed with three SLDVs placed at three different locations. Rotation matrices obtained from two different sets of reference points are almost the same at the three locations, which validates that the proposed methodology is reliable. Another experiment to scan a 2D clamped plate was performed and the rotation matrices were calculated from the proposed methodology as a special case, which shows universal applicability of the proposed methodology and extends its application scope from 3D structures to 2D structures.