# Frequency-Shifted Optical Feedback Measurement Technologies Using a Solid-State Microchip Laser
## 3 Applications of the Laser Feedback Interferometer  
### Displacement Sensing  
Displacement measurement is the basic application of the laser feedback interferometer. According to Equation (6), one cycle in the laser intensity modulation corresponds to half the wavelength in the length of the external cavity, which is similar to the traditional laser interferometer. Due to the existence of the amplification factor \(G\), the laser feedback interferometer has a high sensitivity that it does not need a retroreflector or corner prism set on the target. Therefore, it is advantageous to realize the axial displacement measurement where no additional optical devices are installed. [PERSON] [13] proposed a quasi-common-path configuration based on frequency shifting and multiplexing to compensate the air disturbance and the thermal effects of the components. The system structure is shown in Figure 5. It is innovative to put a reference mirror after the two AOMs to generate a feedback light. The original optical path without diffraction and the diffractive optical path with the shift frequency of \(\Omega/2=|\Omega_{1}-\Omega_{2}|\) constitute a round-trip as the reference light, which is shown in blue arrows. The displacement information of the measuring light and reference light can be demodulated at the frequency \(\Omega/2\) and \(\Omega\), respectively. The change of the displacement \(\Delta L\) is related to the phase variation \(\Delta P\) by:  
\[ \begin{array}{c}\Delta L_{m}=(c/2n\omega)\Delta P_{m}\\ \Delta L_{r}=(c/2n\omega)\Delta P_{r}\\ \Delta L_{f}=\Delta L_{m}-\Delta L_{r}=(c/2n\omega)\Delta P_{f}\\ \end{array}  \tag{10}\]  
where \(\Delta P_{m}\) is the phase variation of the measuring light, \(\Delta P_{r}\) is the phase variation of the reference light, \(\Delta L_{m}\) is the corresponding measurement displacement, \(\Delta L_{r}\) is the corresponding reference displacement, \(\Delta P_{f}\) is the final phase variation, and \(\Delta L_{f}\) is the final displacement. The piezoelectric transducer (PZT) is tested in the system as the T in Figure 5. The reference mirror (M\({}_{\text{R}}\)) is placed 10 mm before the PZT. In the experiment, the PZT is driven by a ramp wave signal. The measured \(\Delta P_{m}\) and \(\Delta P_{r}\), and the corresponding \(\Delta L_{m}\), \(\Delta L_{r}\), \(\Delta P_{f}\), and \(\Delta L_{f}\) are shown in Figure 6. It is noted that the PZT vibration waveform cannot be revealed from \(\Delta L_{m}\); however, it can be revealed from \(\Delta L_{f}\) accurately. The maximum nonlinear error of the \(\Delta L_{f}\) data is 1.8 nm, indicating that its short period resolution is better than 2 nm. Figure 5: Configuration of the quasi-common-path laser feedback interferometer. LD: laser diode; ML: microchip Nd: YAG laser; BS: beam splitter; PD: photon detector; L\({}_{1}\), L\({}_{2}\): lens; AOM\({}_{1}\), AOM\({}_{2}\): acousto-optic modulators; M\({}_{\text{R}}\): reference mirror; T: target. The quasi-common-path configuration has dramatically improved the performance of the laser feedback interferometer. However, two shortcomings remain to be improved. One is the measuring speed. The signal demodulation is based on the Lock-in in Ref. [13], which limits the measuring speed to be 100 \(\upmu\)m/s. [PERSON] and [PERSON] [44] proposed a new signal processing method replacing the Lock-in to a phase meter, and the measuring speed is improved to 10 mm/s. Then, [PERSON] [45] improved the performance of the system by replacing the laser source with a Nd: YVO\({}_{4}\) crystal. The relaxation oscillation frequency increased from 300 kHz to 4.5 MHz, and the shifted frequencies were 2 MHz and 1 MHz, respectively. Finally, the measuring speed was improved to 120 mm/s. The other shortcoming is the common path compensation. Due to the difference of the optical path between the measuring light and the reference light, the thermal effect produced by the AOMs is different; thus, quasi-common compensation cannot be completely eliminated.