# Frequency-Shifted Optical Feedback Measurement Technologies Using a Solid-State Microchip Laser
## 3 Applications of the Laser Feedback Interferometer
### Displacement Sensing
On the other hand, the position of the M\({}_{\mathrm{R}}\) limits the compensation effect when sensing the displacement over a long distance. [PERSON] [46] proposed a ring optical path configuration of the laser feedback interferometer. The paths of the reference light and the measured light coincide completely; thus, the thermal compensation effect is improved. [PERSON] [47; 48; 49] demonstrated a common-path heterodyne self-mixing interferometry with polarization and frequency multiplexing. The two mutual independent orthogonal polarized lights are used as the measuring and reference lights, of which the optical paths completely coincide in space; thus, the effect of the AOMs thermal creep and air disturbance can be eliminated. The short-term resolution is better than 2.5 nm, and the long-term zero drift is less than 60 nm over 7 h. [PERSON] [50] proposed a novel approach to realize full path compensation laser feedback interferometry for remote sensing. The displacement of a steel block at a distance of 10 m is measured, of which the stability is \(\pm\)12 nm over 100 s and \(\pm\)50 nm over 1000 s, and the short-term resolution is better than 3 nm. More recently, the two-dimensional (2-D) displacement measurement based on the self-mixing interferometry is revealed [14]. The system is shown in Figure 7. Two measuring beams at the different shift frequencies are incident on the same spot on the target. By heterodyne demodulating the phases of the two beams and deriving the relationship between the phases' variations and the change of the in-plane and out-of-plane displacement, 2-D displacement measurement can be realized. Various movements in the track of Lissajous figures and random motion are measured in the experiments. The results show that the resolutions of the two dimensions are better than 5 nm and the standard deviation can be better than 0.1 \(\upmu\)m.  
Figure 6: Results of the displacement measurement: (**a**) phase stability test results, and (**b**) measurement result of PZT vibration. The bottom curve shows the PZT driving signal. (Figure reproduced from Ref. [13]). The simultaneous measurements of in-plane and out-of-plane displacements are a significant issue to be researched, such as the grating interferometry [51; 52], speckle pattern interferometry [53; 54], digital image correlation [55; 56], and laser Doppler distance sensing [57]. The resolution of the grating interferometer is a few nanometers, and the accuracy can reach a submicron scale. However, the 2-D grating needs to be set on the target, which limits the application. A laser Doppler distance sensor is appropriate for the dynamic position measurements of the fast-moving object, and the resolution of which is only on the submicron order. Speckle pattern interferometry and digital image correlation are two noncontact and full field displacement measurement methods, which are widely used in industrial nondestructive detection. However, they are limited to the static and quasi-dynamic displacement measurement field; the measurement range and accuracy are related to the speckle size obtained and come to a compromise in the application. Compared with other methods, laser feedback interferometry has the advantages of compactness, non-contact, high resolution, and high accuracy. However, the characteristic of the single-spot measurement limits the application in the full field measurement. It is a promising method to be applied in the 2-D deformation of materials measurement and 2-D thermal expansion measurement, among others.