# Frequency-Shifted Optical Feedback Measurement Technologies Using a Solid-State Microchip Laser
## 4 Applications of the Laser Confocal Feedback Tomography  
### Microstructure Imaging and Measuring  
The schematic diagram of the laser confocal feedback tomography is shown in Figure 4 above. To realize the three-dimensional scanning in the inner structure of the sample, we fix the objective lens in a vertical translation stage to scan in the longitudinal direction, while the sample is set in the two-dimensional translation stage to get the horizontal movement. The theoretical lateral resolution of the system is approximately given by \(\Delta x=0.61\lambda/(\surd 2\times NA)\), for the objective with the \(NA=0.42\) utilized in the experiment, corresponding to \(1.1\)\(\upmu\)m. The vertical resolution is evaluated via scanning the defocus curve and measuring the full width at half maximum (FWHM), which is about 15-20 \(\upmu\)m. The system can be applied in the imaging of the structure of the micro-electro-mechanical system [80; 81]. For example, the sandwich type sample with the patterned layer etched in a silicon film of 1 mm and two pieces of 0.5 mm thick glass is measured. The 2-D cross-sectional imaging with the depth of 3 mm and lateral range of 6 mm is obtained as shown in Figure 17.  
Figure 16: (a) Experimental system for the gear measurement; \(\theta\), rotation angle; \(H\), eccentricity distance. (b) Experimental result with the \(\theta=25^{\circ}\) and \(H=20\) mm. A biological sample, such as onion inside water, can also be measured using the laser confocal feedback tomography [39]. Two onion samples are adopted, one (named onion-1) containing a pin that is inserted 0.5 mm beneath its surface, and the other (named onion-2) containing two separated pins inserted 1 mm below its surface. The section of the pin's tip immerged into the onion is selected to obtain its 2-D cross-sectional image in the X-Y plane. As illustrated in Figure 18, the cross-sectional images denoted by the double-dot-dash lines clearly indicate the profile of the pins' tip. What is more, the position of the pins in the onions can also be confirmed. Furthermore, [PERSON] [82] improved the axial resolution to nanometers when measuring the microstructure inside the sample based on the laser confocal feedback tomography by using the linear region EF in the defocusing curve as shown in Figure 19. It should be noted that the linear region EF needs to be calibrated experimentally. First, the light is focused on the sample surface; then the objective is moved at a certain step in the longitudinal direction using a one-dimensional motorized scanning stage with the resolution of 0.5 nm, and simultaneously detects the amplitude A. The fitted line is obtained between the amplitude and the defocus distance. With the different objective lenses utilized in the system, different linear ranges and different axial resolutions are realized. The experimental measurement axial resolutions are 2, 5, and 11 nm with the objective NA values of 0.65, 0.55, and 0.3, respectively. Figure 17: Measurement of the sandwich type sample: (**a**) the profile of the sample, and (**b**) the scanning image of the sandwich type sample. (Figure reproduced from Ref. [81]). Figure 18: Cross-sectional imaging of the pins in the onions: (**a**) the pin’s tip image, and (**b**) two parallel pin’s image. (Figure reproduced from Ref. [39]). When measuring the samples, the light is focused on the interesting point first, and then the sample is scanned in the horizontal direction. During the scanning, the amplitude of the feedback light intensity varies with the structure variation. The amplitude variation can be converted to the distance according to the calibrated line. Thus, the structure of the sample is measured at last. A micro-gyroscope is measured as shown in Figure 20. The system can realize the noninvasive inner structure measurement through the protection glass. The tilt angle of the inner side of the rotor should be tested according to actual demands.