3 Rapid and Dense 3D Vibration Measurement by Three Continuously Scanning Laser Doppler Vibrometers 21 Fig. 3.2 Prescribed scan trajectory for a structure by the Top CSLDV where r is the distance from point P0, which is the incident point of the X mirror, to point P. The relation between PMCS and PVCS can be established by PMCS DTCRPVCS D 2 4 xo0 yo0 zo0 3 5C 2 4 cos.x; x0/ cos.x; y0/ cos.x; z0/ cos.y; x0/ cos.y; y0/ cos.y; z0/ cos.z; x0/ cos.z; y0/ cos.z; z0/ 3 5 PVCS (3.2) where TDŒxo0 ; yo0 ; zo0 T is a translation vector that specifies coordinates of origin o0 in theMCS, Ris the direction cosine matrix from the VCS to the MCS. The translation vector Ttogether with the direction cosine matrix Rcan determine the position of a CSLDV with respect to the MCS. Tand Rcan be obtained by the method in Ref. [16]. 3.2.2 Constant-Speed Scan for the Top CSLDV In order to use the demodulation method to obtain an ODS of a structure from velocity response measured by a CSLDV, a constant-speed scan algorithm is proposed for a prescribed scan trajectory, as shown in Fig. 3.2. The shape of a surface is controlled by four boundary points Pll, Prl, Plu, andPru, which are located at left lower, right lower, left upper, and right upper corners of the surface, respectively. Boundaries of the surface in Fig. 3.2 are four lines formed by four boundary points. The laser spot from the Top CSLDV starts at point Pll and simultaneously moves in right and upward directions until reaching point Pr2, which completes a scan of line PllPr2. If multiple scans for line PllPr2 are required, the laser spot moves back to point Pll and repeats the same scan process between points Pll and Pr2 until multiple scans are completed. At the time when multiple scans are completed, the laser spot is at point Pr2 and continues to simultaneously move in left and upward directions until reaching point Pl2. The laser spot repeats the above scan process and finally reaches point Pru to complete the whole prescribed scan trajectory. Note that if multiple scans are applied to a scan line, the number of multiple scans should be odd to ensure that the laser spot is at the other end of the scan line that is different from the start point when multiple scans are completed.
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