Mechanical waves, especially sound waves, play vital roles in our everyday communications and have facilitated many advanced technologies such as sonar [1,2], seismic detection [3,4], and feature recognition[5]. And the sensitive detection of sound waves is often a fundamental and crucial part in these fields. There are currently many emerging technologies used for sensitive acoustic displacement detection, including AFM nanocantilevers [6], micro-electromechanical systems (MEMS) [7], nano-electromechanical systems (NEMS) [8], optical tweezers [9], and other technologies [10,11]. For example, by combining an AFM and an interferometer, a high displacement sensitivity of $\mathrm{fm}/{\mathrm{Hz}}^{1/2}$ can be reached [12]. However, these technologies often have strict environmental requirements [10] and are difficult to detect information of remote weakly vibrating objects, which leads to some limitations in practical applications. At room temperature, Ohlinger et al. reported a technique for capturing individual gold nanoparticles with a displacement sensitivity of $3\mathrm{nm}/{\mathrm{Hz}}^{1/2}$ by using optical tweezers [9], which can be improved to the level of $\mathrm{fm}/{\mathrm{Hz}}^{1/2}$ by using a dual-beam optical tweezer in air [13]. Nevertheless, it is also difficult to use for long-distance vibration displacement detection and has relatively strict requirements for surrounding environmental conditions with complicated setups.

In addition, voice signal, as one of the most common acoustic vibrations, is an important carrier for humans to obtain information. Therefore, the acquisition and analysis of voice signals are also of great significance in public security [14,15], audio surveillance [16], and many other fields [17–20]. In most above scenes where voice acquisition is required, the large range effective working distance and concealment of the voice acquisition systems are extremely critical. However, conventional voice detection means usually using traditional voice sensors. Dinh Le et al. proposed a skin-attachable voice recognition system that can detect physiological mechanoacoustic signals directly based on the vibrations of vocal cords [21]. However, this method requires the sensor to be fitted to the human body in advance, which is not suitable for long-distance acoustic vibration monitoring. Davis et al. used only high-speed video of the target to extract the minute vibrations and recover the nearby sound [18]. Nevertheless, this method of using images to restore vibration will be greatly affected by ambient light. In addition, vibration analysis based on images requires complex algorithms, which is difficult to ensure real-time performance. Moreover, in order to obtain clear pictures, the working distance may also be limited.

Since the above methods have limitations in long-distance detection, it is undoubtedly necessary to develop a concealed and sensitive long-distance vibration signal acquisition technology. A laser is usually used for long-distance detection because of its good directivity, and the use of lasers to obtain vibration information has also received extensive attention. Sami et al. used the lidar sensors equipped in popular commodity robot vacuum cleaners to realize the voice acquisition of the surrounding environment [22]. However, the working distance is limited to about the size of an ordinary room. In addition, the laser Doppler vibrometer (LDV) is proved to be used to detect the vibration information of non-cooperative targets at 150 m [23,24] or retroreflective tapes at 300 m [25], but there is still huge room for further improvement in the sensitivity of traditional LDVs to the weak light signals returned by long-distance non-cooperative targets. And one of the main challenges in using an LDV as a remote vibration sensor is the low signal-to-noise ratio of the reflected signals [26].

Here, we propose a polarization-modulated laser feedback vibrometer (PLFV) for remote vibration information acquisition. Different from the traditional Mach-Zehnder LDV, in PLFV, the cavity emitting laser irradiates the measuring target; the optical signal backscattered by the target returns to the laser cavity and interferes with the intracavity light field, which modulates the light field in the cavity and makes the re-output laser loaded with external vibration information [27]. Since the feedback process occurs in the laser cavity, the external return optical signal is affected by the laser intracavity dynamic behavior while interfering with the intracavity light field. During this process, the weak return signal can be magnified up to ${10}^6$ through the intracavity resonance before outputting again, which is not available in the traditional LDV. The laser cavity itself is equivalent to an amplifier of the weak light signal, and this can perfectly solve the problem of low signal-to-noise ratio in long-distance detection while retaining the advantages of coherent detection without interference from ambient light. Xu et al. successfully achieved voice signal acquisition at 200 m using a laser feedback system [28], but they did not consider the impact of the parasitic noise in the system, which results in the signal being further weakened below the intensity of the parasitic noise, making it difficult to achieve detection at longer distances.

The parasitic noise can be understood as the light reflected from the surface of various components in the system into the laser cavity. When the signal itself is extremely weak, this part of the noise is a key factor restricting the signal-to-noise ratio of the system. In this paper, we add different polarization modulations to the parasitic noise and the optical signal of interest to make them convert into the feedback insensitive state and the sensitive state, respectively, which further improves the actual response ability of the system to weak optical signals. The vibration detection of non-cooperative targets (cartons, plastics, etc.) at 300 m is achieved, and the effective response energy of each feedback cycle is as low as 2.3 photons’ energy. The vibration amplitude detection sensitivity at 300 m reaches $0.72\mathrm{nm}/{\mathrm{Hz}}^{1/2}$ at 1 kHz. The proposed system is prospect in remote sensitive acoustic vibration detection.

The structural diagram of the proposed method for remote non-contact measurement of the vibration information is shown in Fig. 1.

The laser source is a 1064 nm $\mathrm{Nd}\text{:}{\mathrm{YVO}}_4$ microchip laser, whose resonator is formed by a $3\mathrm{mm}\times 3\mathrm{mm}\times 0.75\mathrm{mm}$$\mathrm{Nd}\text{:}{\mathrm{YVO}}_4$ crystal plate with the coating on both surfaces. The surface near the pump light is coated to be antireflective at the pump wavelength of 808 nm and highly reflective ($\mathit{R}>99.8\%$) at the lasing wavelength of 1064 nm, and the output surface is coated with 5% transmittance at the wavelength of 1064 nm. The output beam is first collimated by a lens, and divided into two beams by a BS. The transmitted light passes through the Faraday rotator (FR1064-3-1.5W, LBTEK), whose polarization state is rotated by 45 deg. Next, it transmits through a half-wave plate, whose purpose is to rotate the polarization state of the laser beam to the same direction as the main axis of the acousto-optic crystal to avoid the additional influence of thermal effects on the light phase and amplitude. Then, the light passes through AOM1, AOM2 (CAFS-070/1-010-TEC-1064-AF-A17, Castech), and the lens group. Some part of the beam directly passes through the two AOMs, and is differentially frequency shifted by AOMs (the frequency shift is $\mathrm{\Omega }$). After being shaped by the lens group and passing through the quarter-wave plate for the second polarization state adjustment, it can further be used for long-distance transmission. The light beam is irradiated on the target to be measured at a long distance. And the backscattered light returns to the laser cavity through the original path, and is modulated again by various components on the path. It is worth pointing out that in the whole process, the total frequency shift of the light is $2\mathrm{\Omega }$ due to the beam going through the AOMs twice. However, there is still another part of the light returned to the laser cavity from the surface of the AOMs and the lens, which can be regarded as the parasitic noise of the system. They return to the laser cavity together with the weak light signal of interest, causing severe interference.

The light field in the laser cavity is modulated by the light returned from the outside to reach a new stable state. The re-output laser is loaded with the vibration information of the external target, and after being reflected by the BS, it is received by the PD and converted into an electrical signal for subsequent analysis of the vibration information. Below is an explanation of how the system suppresses parasitic noise and obtains vibration information.

The Jones matrices of the Faraday rotator, half-wave plate, and quarter-wave plate placed in the proposed PLFV as shown in Fig. 1 are ${\mathbf{T}}_{\mathbf{1}}$, ${\mathbf{T}}_{\mathbf{2}}$, and ${\mathbf{T}}_{\mathbf{3}}$, respectively. The specific expressions are as follows: $${\mathbf{T}}_{\mathbf{1}}=\frac{1}{\sqrt{2}}\left[\begin{array}{cc}1& 1\\ -1& 1\end{array}\right],{\mathbf{T}}_{\mathbf{2}}=\frac{1}{\sqrt{2}}\left[\begin{array}{cc}1& 1\\ 1& -1\end{array}\right],{\mathbf{T}}_{\mathbf{3}}=\frac{1}{\sqrt{2}}\left[\begin{array}{cc}1& -i\\ -i& 1\end{array}\right].$$(1)

In the proposed PLFV, the parasitic light passes through the Faraday rotator and the half-wave plate twice during its round trip, while the signal light passes through the Faraday rotator, the half-wave plate, and the quarter-wave plate twice during the round trip. Since the laser source we use is horizontally polarized output (the polarization state is $\mathbf{A}=\left[\begin{array}{c}1\\ 0\end{array}\right]$), it can be regarded as a natural polarization filter matrix inside the laser cavity and the polarization filter matrix can be written as $\mathbf{F}=\left[\begin{array}{cc}1& 0\\ 0& 0\end{array}\right]$, which means that only the return light with the same polarization state as the intracavity light can have the feedback interference and be amplified by the feedback enhancement effect. So, after considering the polarization modulation, we can get the output of the signal light carrying the vibration information of the external target as [29] $$\begin{gathered} \frac{\mathrm{\Delta }{I}_{\text{signal}}}{I}={\mathbf{FT}}_1{\mathbf{T}}_2{\mathbf{T}}_3{\mathbf{T}}_3{\mathbf{T}}_2{\mathbf{T}}_1\mathbf{A}\kappa G(2\mathrm{\Omega })\cos (4\pi \mathrm{\Omega }t-{\phi }_0+\mathrm{\Delta }\phi ) \\ =\left[\begin{array}{c}-\mathit{i}\\ 0\end{array}\right]\kappa G(2\mathrm{\Omega })\cos (4\pi \mathrm{\Omega }t-{\phi }_0+\mathrm{\Delta }\phi ) \\ \to \kappa G(2\mathrm{\Omega })\cos (4\pi \mathrm{\Omega }t-{\phi }_0+\mathrm{\Delta }\phi -\frac{\pi }{2}). \end{gathered}$$(2)

Here, $\mathrm{\Delta }{I}_{\text{signal}}$ represents the intensity modulation of the measurement signal, $I$ is the steady laser output power without feedback, $\kappa$ represents the effective reflection coefficient of the external cavity, and $G(2\mathrm{\Omega })$ is the gain caused by the laser frequency-shifted feedback effect, which traditional LDVs do not have. The gain factor $G(2\mathrm{\Omega })$ is jointly determined by various parameters of the laser and the frequency shift. It can be expressed as [30] $$G(2\mathrm{\Omega })=2{\gamma }_c\frac{{({\eta }^2{\gamma }^2+4{\pi }^2{(2\mathrm{\Omega })}^2)}^{1/2}}{{(4{\eta }^2{\gamma }^2{\pi }^2{(2\mathrm{\Omega })}^2+{(4{\pi }^2{f}_{\mathrm{RO}}^2-4{\pi }^2{(2\mathrm{\Omega })}^2)}^2)}^{1/2}},$$(3)where ${\gamma }_c$ is the decay rate of the photon inside the cavity, $\eta$ is the relative pump level (the ratio of actual pump power to threshold pump power), $\gamma$ is the decay rate of the population inversion, and $f_{\mathrm{RO}}$ is the relaxation oscillation frequency of the laser.

According to Eq. (3) it can be known that the nearer the frequency shift $2\mathrm{\Omega }$ is to the relaxation oscillation frequency $f_{\mathrm{RO}}$, the larger the gain factor $G(2\mathrm{\Omega })$ is, which can be understood as resonance enhancement between the two frequencies. However, when the two frequencies are too close, the laser will be in chaotic status, which cannot be applied for measurement. Therefore, the frequency shift $2\mathrm{\Omega }$ should be appropriately selected so that it can obtain sufficient gain, and the laser will not enter chaos due to excessive resonance, making it impossible to measure. In the experiment, we use a $\mathrm{Nd}\text{:}{\mathrm{YVO}}_4$ laser, whose relaxation oscillation frequency $f_{\mathrm{RO}}$ is 2.7 MHz. Based on the above principles, we choose a frequency shift of 4 MHz, which is moderate to the $f_{\mathrm{RO}}$. In addition, the other parameters of the $\mathrm{Nd}\text{:}{\mathrm{YVO}}_4$ laser are $\gamma \approx 1.11\times {10}^4{\mathrm{s}}^{-1}$, ${\gamma }_c\approx 2.75\times {10}^{10}{\mathrm{s}}^{-1}$, and $\eta =3$. By inputting all parameters into Eq. (3) we can obtain that the value of the gain factor $G(2\mathrm{\Omega })$ is 4020. ${\phi }_0$ in Eq. (2) is the initial fixed phase, and $\mathrm{\Delta }\phi$ is the phase change in the external cavity. The relationship between $\mathrm{\Delta }\phi$ and the change of the external cavity length $\mathrm{\Delta }L$ can be obtained by Eq. (4): $$\mathrm{\Delta }\phi =\frac{4\pi }{\lambda }n\mathrm{\Delta }L,$$(4)where $\lambda$ is the laser wavelength, and $n$ is the air refractive index. By obtaining the phase change $\mathrm{\Delta }\phi$, we can get the external cavity length change $\mathrm{\Delta }L$ caused by the vibration of the surface of the target, and then restore the vibration information. Furthermore, if the vibration of the target is caused by the sound pressure, we can also restore the voice information through appropriate reconstruction algorithms.

At the same time, the demodulation result of the parasitic light in the system is $$\begin{gathered} \frac{\mathrm{\Delta }{I}_{\text{noise}}}{I}={\mathbf{FT}}_1{\mathbf{T}}_2{\mathbf{T}}_2{\mathbf{T}}_1\mathbf{A}\kappa G(2\mathrm{\Omega })\cos (4\pi \mathrm{\Omega }t-{\phi }_0+\mathrm{\Delta }\phi ) \\ =\left[\begin{array}{c}0\\ 0\end{array}\right]\kappa G(2\mathrm{\Omega })\cos (4\pi \mathrm{\Omega }t-{\phi }_0+\mathrm{\Delta }\phi ) \\ \to 0. \end{gathered}$$(5)

Through Eqs. (2) and (5) it can be found that the parasitic light is transformed into a feedback-insensitive state after polarization modulation, enabling the suppression of parasitic noise output to zero, while the signal light remains in a feedback-sensitive state, which can be amplified by the feedback effect and then output. Therefore, after eliminating the influence of the parasitic noise, even if the returned optical signal is extremely weak, the system can still have enough signal-to-noise ratio to demodulate the vibration information. Next, we conduct a series of experiments to test the ability of the proposed PLFV to acquire and demodulate remote vibration signals.

In order to verify the feasibility and effectiveness of the proposed system, the PLFV is placed in a corridor with a length of 80 m. The light emitted by the PLFV is folded three times by the reflective mirror, and finally irradiates on the carton about 300 m away from the PLFV, as shown in Fig. 2.

When the PLFV is ready, a Bluetooth speaker is placed about 30 cm away from the carton. The speaker plays sound to vibrate the surface of the carton. The vibration changes the phase of the laser. After backscattering, the light returns to the PLFV, and is amplified by the feedback process.

First, we obtain the signal-to-noise ratio of the target at 300 m by observing the frequency spectral information output by the laser. The result is shown in Fig. 3 where the signal-to-noise ratio can reach about 28 dB, ensuring effective acquisition and demodulation of vibration information for the next steps.

When the distance between the target and the PLFV is about 300 m, we can obtain the light energy $E_r$ received by the PLFV returned from the target in each feedback modulation cycle by the following equation [28]: $$E_r=P_0{\eta }^2{\mathrm{\Omega }}_{r}T/{\mathrm{\Omega }}_0.$$(6)

Here, $P_0=15\mathrm{mW}$ is the laser output power, $\eta ={\eta }_{\mathrm{BS}}{\eta }_{\mathrm{AOMs}}{\eta }_{\mathrm{lens}}^3{\eta }_{\mathrm{WP}}^2{\eta }_{\mathrm{FR}}$ is the one-way light transmittance of the PLFV, and each element’s transmittance is listed in Table 1. Since the laser beam passes through the system twice, the total transmittance is ${\eta }^2$. ${\mathrm{\Omega }}_r=A_r/L^2$ is the system’s entrance pupil angle, and $A_r=\pi r_0^2$ is the system’s receiving aperture area. $r_0=10\mathrm{mm}$ is the outputting spot radius of the PLFV. $L=300\mathrm{m}$ is the distance between the target and the PLFV. $T=1/f$ is the feedback modulation cycle, and $f=4\mathrm{MHz}$ is the modulation frequency. ${\mathrm{\Omega }}_0=\pi$ is the backscattering angle of the target (assuming that it is scattered by full-angle).Table 1.

Transmittance of Each Element of the PLFV

Substituting all the parameters, we can obtain $E_r=4.4\times {10}^{-19}\mathrm{J}$, which is equivalent to 2.3 photons’ energy per feedback modulation cycle. The ability to respond to such low returned light power is due to the effective suppression of the parasitic noise, so that the ultraweak signals of interest can be effectively amplified by the feedback enhancement effect, allowing remote vibration information to still be captured. The performance of the proposed PLFV is then fully tested via measuring its vibration frequency detection accuracy, vibration response sensitivity, support range for detection angle, anti-interference, and accuracy of frequency response to different non-cooperative targets at 300 m.

The vibration frequency detection accuracy describes the accuracy of the PLFV to restore the frequency of the target’s vibration. We use the speaker to play the standard scale from 250 Hz to 3000 Hz with an interval of 250 Hz, and the vibration duration of each frequency is 1 s to make the carton vibrate; meanwhile, the PLFV captures these vibration frequencies and restores them. In addition, since the sound played through the speaker slightly deviates from the set value, we use a commercial sensor (GRAS 46AZ) near the speaker to directly collect and restore the sound, and use it as the corresponding standard frequency to be compared with the frequency obtained by the PLFV. The restoration result is shown in Fig. 4.

Figure 4(a) shows the spectrogram obtained by short-time Fourier transformation of the frequency information collected by the PLFV. The frequency changing with time (each frequency lasts for 1 s) can be seen from the figure. Figure 4(b) shows the results of the comparison between the frequency measured by the PLFV and the standard frequency. For all tested frequencies, the deviation between the measurement results and the standard frequency is at most 0.05%, which appears at 2 kHz.

The vibration amplitude response sensitivity describes the system’s ability to detect the smallest vibration amplitudes. A carton is placed at 300 m away from the PLFV and keeps still for detecting the displacement noise spectral density (NSD). The NSD is a widely used method in precision metrology to evaluate system sensitivity (such as in gravitational wave detection [31,32]). It can intuitively reflect the noise limit of the system at different frequencies, which is quite suitable for evaluating the minimum vibration amplitude that the PLFV can detect at different frequencies. In terms of specific calculation method, we first measure the displacement obtained by the PLFV when the target is stationary (because vibration is essentially a periodic displacement change). At this time, the target does not vibrate, and the obtained displacement can be regarded as the noise synthesis of the PLFV. Then we perform autocorrelation on the measured displacement, making Fourier transform and square root operations to the result obtain the NSD calculation result, which is the commonly used NSD calculation method [33]. The NSD result based on 120 s displacement drift is given in Fig. 5 to find the PLFV vibration amplitude sensitivity limit. The results show that at a working distance of 300 m, the spectrum density of vibration amplitude can reach up to $0.72\mathrm{nm}/{\mathrm{Hz}}^{1/2}$ at 1 kHz.

When acquiring remote acoustic vibration information through a non-cooperative target, it is impossible to ensure that the light beam can vertically irradiate on the target surface every time, and the signal quality will decrease to a certain extent during oblique incidence. Therefore, it is necessary to study the ability of the PLFV to accurately recover the vibration frequency under different light incident angles. The standard frequencies from 250 to 3000 Hz at an interval of 250 Hz are used to excite the carton 300 m away from the PLFV to vibrate at different incident angles; then, the PLFV obtains the corresponding frequency information. The detection schematic diagram and results are shown in Fig. 6.

Figure 6(a) shows the test schematic diagram under different incident angles. It should be pointed out that in actual testing, we rotate the target by 30 deg and 45 deg, instead of rotating the beam direction. Figures 6(b) and 6(d) show the spectrograms of frequencies recovered by PLFV at 30 deg and 45 deg incidence angles, respectively. It can be seen that each frequency appears at the correct time. Figures 6(c) and 6(e) show the results of the comparison between the frequencies measured by PLFV and the standard frequencies at 30 deg and 45 deg incidence angles. And the corresponding maximum frequency deviation ratios are 0.0761% and 0.0896% under the conditions of incident angles of 30 deg and 45 deg, respectively. The test results show that the PLFV has an accurate response to the vibration of the carton at 300 m within the range of 45 deg incident angle.

In the actual long-distance vibration measurement applications, due to the very long distance from the target to the PLFV, there may be various complex disturbances, such as wind interference on the optical propagation path, so, we test the PLFV’s ability to detect the standard vibration frequencies in the presence of wind. The test schematic diagram and test results are shown in Fig. 7.

Figure 7(a) shows the testing method. An ordinary electric fan is placed perpendicular to the direction of beam propagation and used to generate wind interference. In this case, the PLFV detects a series of standard vibration frequencies of a carton 300 m away. The restored spectrogram result is shown in Fig. 7(b). It can be seen that in the presence of wind interference, a wide range of noise points appears mainly below 1 kHz, which corresponds to wind disturbance. However, at this time, the tested frequencies below 1 kHz can still be distinguished, and their signal-to-noise ratio in the spectrogram can reach 25 dB. This indicates that even with the introduction of wind interference, the long-distance vibration frequency can still be detected for the PLFV. In the future, by introducing wind speed sensors or reference light to record real-time wind interference and subtracting it from the final result, we can obtain a purer vibration signal, further improving the anti-interference ability of the PLFV.

The accuracy of the frequency response to different non-cooperative targets describes the effectiveness and response consistency of the PLFV for different target scenarios. Here, we use two common plastic materials, polycarbonate (PC) and polyethylene terephthalate (PET), as the test targets. We use the same standard excitation audio as above to stimulate these two types of targets, and obtain the corresponding demodulation spectrogram and the comparison result between the measured frequency and the standard frequency. The detection results are shown in Fig. 8.

Both spectrograms in Figs. 8(a) and 8(d) show a series of clear frequency steps, and the comparison results between the measured frequency and the standard frequency are also shown in Figs. 8(b) and 8(e). According to the comparison results, we get that for the PC plastics and PET plastics, the maximum deviation ratios between the measured frequency and the standard frequency are 0.0669% and 0.1%, respectively. The above measurement results show that for the PC and PET two different targets, the PLFV can accurately respond to their vibration frequencies.

The voice signal is also generated by the vibration of the object. The sound wave as the excitation source can cause small vibration of the objects nearby. Meanwhile, the PLFV can accurately obtain this complex vibration information. Below we will show the complex voice reconstruction ability of the PLFV at remote working distances.

We place the carton away from the PLFV, and place a Bluetooth speaker about 30 cm near the carton. The voice content played by the speaker is “Is this your handbag?” When the carton vibrates, the PLFV captures these weak vibrations. After a series of voice recovery algorithms such as band-pass filtering, the content of the voice signal is finally restored and output. Figure 9 shows the corresponding voice reconstruction spectrograms when the carton is 80 m, 240 m, and 300 m away from the PLFV.

We directly input all recovered audio files into a mature audio-text conversion website (NetEase Jianwai). If the audio information can be correctly recognized, it is considered that the obtained voice information is valid. It should be pointed out that we do not conduct any pre-training throughout the entire recognition process. The recognition results under three different distances are shown in Table 2.Table 2.

Recognition Results under Three Different Distances

From the results in the Table 2, it can be seen that the audio recovered by the PLFV can be effectively recognized. This indicates that the proposed system has the ability to capture and restore the remote vibration information (eavesdropping). We have compared the detection distances achievable by current eavesdropping technologies and the proposed method, and the result is shown in Table 3.Table 3.

Comparison of the Current Methods for Eavesdropping

It should be noted that the listed parameters are based on the experimental results of the proposed method and do not equal the performance limits of the listed sensors. Moreover, the eavesdropping distance refers to the distance between the eavesdropping device and the target being eavesdropped on. From the comparison results, it can be seen that the proposed method has advantages over other methods in terms of eavesdropping distance.

In Sections 3.B–3.F, we conduct tests on the recovery of a target’s vibration frequency by the PLFV under different conditions, including different incident angles and materials. We provide the comparison results between the measured values and the standard values, by giving the corresponding measured vibration frequency value at each standard value, as shown in Fig. 4(b), Fig. 6(c), Fig. 6(e), Fig. 8(b), and Fig. 8(e). Next, by calculating deviation results for the corresponding measured value at each standard acoustic vibration frequency, we can obtain the vibration frequency measurement errors at different frequencies, which can be further used to evaluate the ability of the PLFV in acoustic vibration measurement. The results are shown in Figs. 10 and 11.

Figures 10 and 11 show the errors between the measured vibration frequency values of the PLFV and the standard acoustic vibration frequency values at different incident angles and materials, respectively. We can calculate the maximum deviation rates [(deviation/standard value) $\times$ 100%] of the measured values and standard values. For the same target (carton), the maximum deviation rates are 0.05%, 0.0761%, and 0.0896% at 0 deg, 30 deg, and 45 deg, respectively. For PC plastic and PET plastic, the maximum deviation rates are 0.0669% and 0.1%, respectively. Overall, compared to the values measured by the standard acoustic vibration sensor, the vibration frequency measured deviation of the PLFV does not exceed 0.1%.

In the above tests, the PLFVs all work in an ordinary corridor environment, where the temperature is close to the room temperature. And from the test results, it can be concluded that PLFV has the ability of remote vibration measurement and voice recovery. In the future, by optimizing the light source structure to obtain better frequency stability, or by adding a reference light to obtain the phase shift in long-distance transmission to compensate for the test results, we can further improve the response sensitivity of vibration displacement.

In conclusion, the PLFV displayed for non-contact detection of acoustic vibration is free from electromagnetic interference, and can work at room temperature, which can be applied in aerospace, industrial quality inspection, and many other engineering technologies and frontier exploration fields. The PLFV has a single photon level intensity sensitivity, its detection distance can reach 300 m, and the vibration response sensitivity of a non-cooperative target at 300 m can reach $0.72\mathrm{nm}/{\mathrm{Hz}}^{1/2}$ at 1 kHz. With the above characteristics, it provides a very promising method for long-distance and highly sensitive vibration detection.