**3. Experiment**

We built the measurement system according to the light path diagram, as shown in Figure 6. The light source is a single longitudinal mode laser with a wavelength of 532 nm and an output power of 100 mW. The spatial resolution of CCD is 640 × 480. The pixel size of the CCD is 4.8 μm × 4.8 μm. The exposure time in the experiment is 200 microseconds and the acquisition frame rate is 70 frames/s. The numerical aperture of the microscope objective is 0.1 and the magnification is 4×. The focal length of the doublet lens is 50 mm.

**Figure 6.** The measurement system diagram with the introduction of doublet lens group.

The traditional Mach–Zehnder uses two mirrors, and the utilization rate of light is really high. Considering that the measured object is not transparent, we use two beam splitters to replace the two mirrors in our optical path, resulting in only half of the light entering the transmission optical path. However, this phenomenon has little effect, for the current laser power is very high. As in our experiment, the CCD exposure time is only 200 microseconds, and a clear and bright interferogram can be observed.

The measured object and reference object in the experiment are microchips with the size of 5 mm × 6 mm × 1 mm (W × L × H), as shown in Figure 7. We need to measure the displacement of the whole microchip. Because the microchip is similar to a rigid body, it is difficult to generate deformation by heating or loading force. The method we adopt here is to place the measured object on the hinge, the hinge axis is fixed, and the blade is pushed by the Physik Instrumente (PI) displacement platform to simulate the displacement of the measured object. The accuracy of the PI displacement platform is 10 nm. The specific process is shown in Figure 8.

**Figure 7.** Two identical microchips.

**Figure 8.** The process of introducing the displacement by hinge.

The entire displacement process is 4 s, and 280 speckle interferograms can be collected. One of the speckle interferogram collected by CCD during the displacement process is shown in Figure 9, and the interference fringe patterns obtained by the subtraction mode are shown in Figure 10.

**Figure 9.** The speckle interferogram collected by CCD.

**Figure 10.** The interference fringe pattern obtained by the subtraction mode. (**<sup>a</sup>**–**d**) represent the 70th, 140th, 210th, and 280th speckle interferogram subtracting the first one, respectively.

Using the WT phase extraction algorithm mentioned above, the time series phase value of each pixel can be calculated. Then, the continuous phase value is obtained by unwrapping, and the corresponding displacement value is finally obtained.

Taking pixels A (100, 260), B (190, 260), C (280, 260), D (370, 260) as examples, we show the phase and displacement maps of these four pixels over time, as shown in Figure 11. The acquisition frame rate of CCD is 70 frames/s. We can obtain the displacements of these four points at 1, 2, 3, and 4 s from the displacement diagrams. The corresponding dynamic displacement map of the microchip is shown in Figure 12.

**Figure 11.** Truncated phase diagrams and displacement diagrams of the 4 pixels. (**<sup>a</sup>**,**b**) correspond to pixel A; (**<sup>c</sup>**,**d**) correspond to pixel B; (**<sup>e</sup>**,**f**) correspond to pixel C; and (**g**,**h**) correspond to pixel D.

**Figure 12.** The dynamic displacement map of the microchip over time: (**a**) left view; (**b**) front view.

It should be noted here that when imaging with a doublet lens group, the object and the image are in opposite directions. Therefore, the smaller the *x* coordinate of the pixel, the closer to the fixed axis of the hinge it is, and the displacement value of the four pixels gradually becomes smaller. The final displacement range calculated from the experimental results is 5.75–10.47 μm, which, respectively, corresponds to the displacement value of the low end and the top end of the microchip.

In order to verify the accuracy of the results, we first use the displacement value introduced by the PI displacement platform to judge whether the displacement range of the measured object is reasonable. The width of the hinge is 16 mm, the width of the measured object is 5 mm, and the distance between the measured object and the low end and top end of the hinge is 6 and 5 mm, respectively; the displacement value introduced by the PI displacement platform at the top of the hinge is 15 μm, which can be used to judge that our measurement range is generally reasonable.

Then, the linear relationship of four points is used in further judgment. Because the four points are selected with an equal pixel interval, and the measured object is approximate to the rigid body and will not deform easily, so the four points should have a linear correlation. The final displacement values of the four points are connected and the correlation coefficient R<sup>2</sup> is calculated to be 0.9994, as shown in Figure 13, which indicates that the linearity is very good. That is, our experimental results have high accuracy.

**Figure 13.** The linear relationship of the displacement of 4 pixels.

In order to verify the full-field performance of the system and the measurement accuracy of different positions, 16 arbitrary pixels were selected to display their displacement values, as shown in Figure 14. Among them, 12 points are in the same row with points A, B, C, D, respectively. According to the displacement direction, the displacement values of these pixels in the same row should be the same. The measuring result is shown in

Figure 14, and the maximum relative error of the 12 points is 0.46%. After traversing all the pixels that record the interference information, the full-field displacement map of the object can be obtained. After calculating the displacement values of all pixels and removing individual dead pixels through smoothing operations, the overall displacement map can be obtained, as shown in Figure 15. In our research, we use MATLAB to calculate the displacement information of each pixel and finally realize the full-field measurement. The entire processing process takes less than 15 s.


**Figure 14.** The final displacement map of the selected 16 pixels.

**Figure 15.** The overall displacement diagram of the measured object.
