# Frequency-Shifted Optical Feedback Measurement Technologies Using a Solid-State Microchip Laser
## 3 Applications of the Laser Feedback Interferometer
### Vibration Sensing  
Besides the displacement sensing, the precise measurement of vibration has attracted wide attention as well. Vibration sensing can be utilized to analyze the dynamic characteristics of mechanical structures, fault diagnosis of mechanical systems, target identification, and sound visualization [58]. However, it is difficult to detect small vibration and displacement in many cases, especially the micro-vibration of non-cooperative targets at long distance. [PERSON] [16] proposed the real time nanometer vibration measurement using a self-mixing microchip solid-state laser. The experimental configuration is shown in Figure 8. The LiNdP\({}_{4}\)O\({}_{12}\) (LNP) crystal with a 1-mm-thick plane-parallel Fabry-Perot cavity that is utilized as the microchip laser. The pump light is transformed into a circular beam using the anamorphic prism pairs and is focused onto the LNP crystal via an objective microscope lens. The output light is frequency-shifted by two AOMs and impinged upon a speaker with the Al-coated surface that is placed 90 cm from the laser. A frequency demodulation circuit, a digital oscilloscope, and a radio-frequency spectrum analyzer are utilized in the signal processing. Figure 7: Schematic diagram of the 2-D displacement measurement system. ML is the microchip laser; BS\({}_{1}\), BS\({}_{2}\), and BS\({}_{3}\) are the beam splitters; L is the optical lens; AOM\({}_{1}\), AOM\({}_{2}\), and AOM\({}_{3}\) are the acousto-optic modulators; R\({}_{1}\), R\({}_{2}\), R\({}_{3}\), and R\({}_{4}\), are reflectors; Iso is the optical isolator; T is the target; and PD is the photodetector. (Figure reproduced from Ref. [14]). Figure 9a shows the power spectra for several voltages applied to the speaker. The measured vibration amplitudes (A\({}_{v,m}\)) at the modulation frequency of 8.42 kHz with the carrier frequency of 500 kHz are plotted in Figure 9b. The linear relation was A\({}_{v,m}\)/V\({}_{a}\) = 59 nm/V for the speaker we used. The measurable minimum vibration amplitude was 1 nm according to the carrier-to-noise ratio in the absence of a voltage to the speaker. The velocity range in the present vibrometry was 1 \(\upmu\)m/s to 10 cm/s in the vibration frequency range 20 Hz to 20 kHz. The temporal evolutions of nanometer vibrations were measured by analyzing modulated output waveform using the Hilbert transformation. The almost unheard sound of music below a 20-dB pressure level is reproduced by the system. Furthermore, three-channel real time nanometer vibration [59] was successfully developed with three pairs of acoustic optical modulators and a three-channel frequency-modulated wave demodulation circuit, realizing simultaneous independent measurement of three different nanometer-vibrating targets. On the other hand, the vibration of targets placed 2.5 km away through single-mode optical fiber access was successfully measured [60], due to the effective long-haul self-mixing interference. There are also other researchers applying self-mixing interference effects in the vibration sensing. [PERSON] [61] proposed a vibration system extreme points model and self-mixing vibration sensor based  
Figure 8: Experimental configuration of self-mixing laser-Doppler vibrometry. LD, laser diode; APP, anamorphic prism pairs; OL, objective microscoppelens; BS, glass-plate beam splitter; PD, photodiode receiver; SA, radio frequency spectrum analyzer; VA, variable attenuator; DO, digital oscilloscope; DC, frequency demodulation circuit; PC, personal computer. (Figure reproduced from Ref. [16]). Figure 9: (**a**) Power spectra (long-time average) for several applied voltages. (**b**) Maximum vibration amplitude versus voltage applied to the speaker. Carrier frequency, 500 kHz; modulation frequency, 8.42 kHz. (Figure reproduced from Ref. [16]). on the effect of LD; the amplitude-frequency response curve of the loudspeaker is drawn, and the value of the piezoelectric coefficient of PZT was obtained.