2 1 (,,) 2 (,,) K(,,) K(,,) L(,,) K(,,)L(,,) x y z n x y z x y z x y z x y z x y z x y z S ª º : ¬ ¼ JK JK JK JK JK (3) where ( , , ) n x y z is the fringe order at the ( , , ) x y z location of the image plane, K( , , ) x y z JK is the sensitivity vector, 1K ( , , ) x y z JK is the propagation vector of light from a point source of illumination to a point on the object, 2K ( , , ) x y z JK is the propagation vector of light from a point on the object to a point on the CCD sensor, and L( , ) x y K is the displacement vector. 2.3 Deformation measurement in the stroboscopic mode Stroboscopic mode is used for deformation measurements of the TM at a controlled sound input. This mode gives information about the phase difference [8] ' ( , ) x y I which is related to the complex distribution phase of the reference and deformed states respectively, given by ' ' ' ' ' 2 3 1 4 ' ' ' ' 2 4 1 3 ( , ) ( , ) ( , ) ( , ) ( , ) arctan ( , ) ( , ) ( , ) ( , ) a xya xy a xya xy x y a xya xy a xya xy I (4) where ' 1 ( , ) a x y , ' 2 ( , ) a x y represent the real and imaginary part of the reference state, and ' 3 ( , ) a x y , ' 4 ( , ) a x y represent the real and imaginary part of the deformed state. The out of plane displacement after image processing is a relative value with respect to the reference measurement. However, no displacement information along x and y axes from the processed image is obtained. In order to calculate these displacements, we need to first decompose the normal vector of the object surface based on the shape measurement shown in Figure 3. Then using the sensitivity vector K( , , ) x y z JK , we can calculate the displacements along x and y axes [9]. Fig. 3 Schematic drawing of the decomposition of normal vector along three axes. 3. RESULTS 3.1 Shape measurement 203
RkJQdWJsaXNoZXIy MTMzNzEzMQ==