22 D.-M. Chen and W. D. Zhu After velocity response along the prescribed scan trajectory is measured by a CSLDV, an ODS in the laser line-of-sight direction can be obtained from velocity response by the demodulation method. Details of the demodulation method can be seen in Ref. [8]. Rotation angles of scan mirrors of the Top CSLDV to direct the laser spot to point Pk on the prescribed scan trajectory are obtained by the proposed algorithm in Sect. 3.2.2. The third variable rk Top in Eq. (3.1), which is the distance from point P0 on the X mirror of the Top CSLDV to point Pk, can be calculated by rk Top D r0 Top cos.˛k Top/cos.ˇ k Top/ (3.3) where r0 Top is the distance from point P0 to the point on the prescribed scan trajectory with ˛Top D0 and ˇTop D0 and can be obtained by the geometrical scan unit of the Top CSLDV, and ˛k Top andˇ k Top are corresponding rotation angles of X and Y mirrors of the Top CSLDV for point Pk, respectively. Hence, coordinates of point Pk in the VCS of the Top CSLDV can be obtained by Eq. (3.1). Since the position of the Top CSLDV with respect to the MCS is obtained by the method described in Sect. 3.2.1, coordinates of point Pk in the MCS can be obtained by Pk MCS DTTop CRTopPk VCS.Top/ (3.4) where TTop and RTop are the translation vector and the direction cosine matrix of the Top CSLDV with respect to the MCS, respectively. Since coordinates of point Pk is constant in the MCS, in order to let laser spots from Left and Right CSLDVs direct to the same point Pk, positional relations among three CSLDVs for point Pk are established by TTop CRTopPk VCS.Top/ DTLeft CRLeftPk VCS.Left/ DTRight CRRightPk VCS.Right/ (3.5) where TLeft and RLeft are the translation vector and the direction cosine matrix of the Left CSLDV with respect to the MCS, respectively, andTRight andRRight are the translation vector and the direction cosine matrix of the Right CSLDV with respect to the MCS, respectively. Hence, coordinates of point Pk in VCSs of Left and Right CSLDVs can be obtained by Pk VCS.Left/ DR 1 Left.TTop TLeft/ CR 1 LeftRTopPk VCS.Top/ (3.6) and Pk VCS.Right/ DR 1 Right.TTop TRight/ CR 1 RightRTopPk VCS.Top/ (3.7) respectively. Further, rotation angles of X and Y mirrors of Left and Right CSLDVs for point Pk can be obtained by ˛ k Left Darctan.z k VCS.Left/=y k VCS.Left//;ˇ k Left Darctan.x k VCS.Left/=.y k VCS.Left/=cos.˛ k Left/ d// (3.8) and ˛ k Right Darctan.z k VCS.Right/=y k VCS.Right//;ˇ k Right Darctan.x k VCS.Right/=.y k VCS.Right/=cos.˛ k Right/ d// (3.9) respectively. With the proposed methodology described above, three laser spots from three CSLDVs can synchronously scan the same point on the prescribed scan trajectory. After velocity response of point Pk is measured by three CSLDVs, vibration information of point Pk in three laser line-of-sight directions can be obtained by the demodulation method. Then vibration information of point Pk in the MCS can be obtained by ŒV k x; V k y; V k z T D ŒRTope k Top; RLefte k Left; RRighte k Right T 1 ŒV k Top; V k Left; V k right T (3.10)
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