Study of Point Scanning Detection Mechanisms for Vibration Signals with Wavefront Sensors

Abstract

Seismic wave laser remote sensing is extensively employed in seismic monitoring and resource exploitation. This work establishes a vibration signal point scanning detection system utilizing wavefront sensors, leveraging their high resolution, array detection capabilities, and the independent detection of each microlens based on research into seismic wave laser remote sensing detection. The experiments validate that each microlens of the wavefront sensor possesses autonomous detecting capabilities, enabling the sensor to scan and identify points of vibrational signals. This work also significantly improved the scanning efficiency by increasing the diameter of the scanning spot.

1. Introduction

Seismic wave exploration is the fundamental method of geophysical investigation. Analyzing seismic wave propagation properties in subterranean media elucidates details of the geological structure [1,2]. In recent years, seismic wave laser remote sensing detection technology has advanced swiftly, employing laser-based non-contact monitoring of ground vibration waveforms characterized by high resolution and sensitivity [3]. Due to variations in wave velocity when seismic waves traverse various geological layers, optical remote sensing technology may more precisely analyze seismic waveforms and reveal subsurface structures [4,5]. Analyzing the seismic wave signals in a region can identify its geological features, including rock types, faults, and folds, and assess the distribution and reserves of minerals, oil, and natural gas, providing a foundation for energy development [6,7]. Advancements in high-resolution optical remote sensing technologies have enabled scholars to detect seismic waves and capture minor vibration signals remotely [8,9]. This technology surpasses the conventional seismic research techniques, which is particularly advantageous for oil and gas development. The traditional exploration methods exhibit difficulties in deep and diverse terrain due to the rising requirements for high resolutions, rapid sampling, and weak signal identification. Optical remote sensing, in conjunction with remote sensing [10], GIS [11], and satellite data [12], has markedly enhanced the efficiency and precision of resource exploitation, emerging as a novel option for geophysical research. Compared to the conventional approaches, laser remote sensing technology offers reduced costs and enhanced efficiency in detecting areas with mineral potential, facilitating advancements in deep geological structure study and resource development.

Laser remote sensing detection technology offers advantages such as non-contact measurement, minimal constraints, enhanced efficiency, and long-range detection, making it extensively utilized to detect object vibrations. To address the issues of remote laser echo signal attenuation and vibration waveform analysis, researchers have investigated the application of He–Ne laser interferometers [13] and Michelson interferometers [14] for measuring vibration signals. Nonetheless, these technologies depend on intricate optical systems and the configuration of reference and measuring arms, which possess certain limits. Silvio Bianchi [15] suggested a novel approach for sensing surface vibration signals without employing an interferometer, utilizing speckle patterns generated by laser irradiation on rough surfaces. This approach enables the efficient detection of vibration signals across several hundred meters. Numerous techniques exist for detecting ground vibration signals based on phase, including wavefront sensors [16,17,18] and shear interferometry [19,20]. Jorge Ares [21] et al. employed a Shack–Hartmann wavefront sensor as a positional sensing apparatus to precisely ascertain the location of point or substantially extended planar objects.

Compared to conventional seismic wave laser remote sensing technology, employing wavefront sensors for detecting ground vibration signals offers substantial advantages. The wavefront sensor eliminates the need for an additional reference and measuring arm, resulting in a more compact and easily deployable device. Secondly, mechanical vibration information can be precisely acquired by detecting the phase shift of the wavefront. Moreover, the wavefront sensor possesses array detection capabilities, augmenting its detection precision and scope of application. In 2023, several researchers employed wavefront sensors to identify ground vibration signals, developed a seismic wave laser remote sensing detection system utilizing wavefront sensors [22], and successfully acquired ground vibration information [23]. The existing technology primarily gathers vibration information from a single site; it cannot analyze regional vibration signals and suffers from low detection efficiency. This work proposes a method for laser remote sensing detection of regional vibration signals, utilizing a microlens array’s non-interference properties and array detection capabilities in a wavefront sensor, as indicated by the research in Ref. [22]. Laser point scanning detection is employed to achieve a measurement method characterized by high precision and high resolution for regional vibration signals, thereby improving detection efficiency. The first section introduces the working principle of the point scanning detection system and the changes in wavefront during vibration. Section 2 introduces wavefront reconstruction using the zonal method, the calculation of wavefront phase, and wavefront crosstalk. Section 3 introduces single-point vibration detection, which determines the relationship between amplitude and phase and then performs point scanning on an area to obtain the vibration information of that area. In order to quickly detect the vibration information in an area, the area of the detection spot is expanded for scanning.

2. Vibration Signal Laser Point Scanning Surface Detecting System and Operational Mechanism

During an earthquake, a longitudinal wave is produced, causing the wavefront of the incident light to be altered by the vertical ground vibrations, thereby transmitting pertinent characteristic information of the seismic wave through the backscattered light of the laser. A laser beam irradiates vertically or obliquely in the target area of the item being measured within a wavefront measurement system. The object’s surface irregularities will cause light to scatter and reflect. The laser’s reflected or scattered light is concentrated and imaged by a microlens from a different angle. The vibration-related information is acquired by reconstructing the wavefront via imaging the microlens.

The work presents the design of a remote sensing detecting system for scanning vibration signal points. The system primarily consists of a transmitter and a receiver, as demonstrated in Figure 1. The transmitter comprises a laser, a fiber optic collimator, and a telescope. The laser produces a continuous wave at a wavelength of 635 nm with constant power. The laser output from a fiber passes through fiber-optic collimator 1, then telescope 2 to ensure consistent angle and power irradiation to the target region 3. The receiver consists of telescope 5, filter 4, and wavefront sensor 6. The telescope captures the reflected and dispersed light from target area 3 and eliminates extraneous environmental light using filter 4 to enhance the contrast of the reflected light. This is a bandpass filter that enables light with a wavelength range from 600 nm to 700 nm to pass through, with a center wavelength of 650 nm. The light subsequently strikes the wavefront sensor 6. The wavefront sensor is an instrument capable of accurately detecting wavefront distortion in optical systems. The assembly consists of a microlens array, with each microlens possessing independent detection capabilities. The lens size of the wavefront sensor is 146 microns, the pitch is 150 microns, the focal length is 4 millimeters, the camera is CMOS type, and the software is wavefront sensor software (version number:18183-D03). The microlens array segments the sub-aperture of the incident light spot and concentrates the image in each detection window 8 within the array.

This system detects wavefront distortion caused by vibration, which causes the centroid of the light spot to deviate from the reference centroid coordinates and cause phase changes. By analyzing the phase changes, we obtain vibration information. Based on this principle, we use this system to detect micro-vibrations in the target area. Understanding the correlation between the phase information of the target vibration and the displacement of the receiving spot in the CMOS sensor pixel is essential. When object 3 vibrates, the centroid offset $\Delta S$ of the wavefront sensor transmits the vibration amplitude $\Delta Z$. The literature [22] states that $\Delta Z=\mu \Delta S$, where $\mu$ is a proportional coefficient. Light propagation in the medium between the transmitting and receiving optics is described by the well-known Fourier optics principles [24]. Note that, for this initial study with a short distance (about 10 m) to the target, the non-ideal effect due to atmosphere is neglected. When not vibrating, the wavefront is a plane; when vibrating, the wavefront changes from a plane to a concave surface, as shown in Figure 2. In Figure 2, we simplify the analysis by assuming the ground is flat when not vibrating. This assumption is made to illustrate the basic relationship between the transmitted and reflected wavefronts. In reality, uneven ground may combine with other non-ideal factors to influence the wavefront’s shape.

Shack–Hartmann wavefront sensor (SHWFS) disaggregates the incident wavefront into numerous minuscule spots via a microlens array, with each spot’s centroid position indicating the local wavefront’s tilt angle. Ideally, the microlens produces a perfect spot on the focal plane. However, due to wavefront distortion, the centroid of the spot will wander from its optimal position, as illustrated in Figure 3. The wavefront distortion can be deduced by examining the sub-aperture spot imaging of the microlens array. When an ideal plane wave is incident, the spot distribution remains uniform; nevertheless, wavefront distortion will result in a displacement of the spot. The wavefront slopes $S_x$ and $S_y$ can be determined by the centroid offsets $\Delta x$ and $\Delta y$ ratio to the focal length f of the microlens, facilitating further analysis of the wavefront’s shape and distortion. Figure 4 shows the wavefront sensor used for research.

The amplitude of wavefront distortion in the z direction can be acquired using the wavefront sensor software, as shown in Figure 5a. Simultaneously, the wavefront sensor software may visually monitor the wavefront slope of the complete microlens array in high-speed sampling mode, as illustrated in Figure 5b. When the object under measurement vibrates, the position of the spot and the angle of reflection produced by laser irradiation on the object will vary, resulting in wavefront distortion. The variations in wavefront distortion amplitude and slope precisely correlate with the phase information of object vibrations, hence facilitating precise detection and assessment of vibrations.

3. Theoretical Analysis of Vibration Signal Laser Array Remote Sensing Detection System

3.1. Zonal Wavefront Reconstruction

The zonal method is a frequently employed waveform reconstruction algorithm in SHWFS [25,26,27]. The approach partitions the entire wavefront into multiple small sections, with the wavefront information of each region being measured by individual microlens from the microlens array. Initially, the wavefront slopes of each minor region are computed, followed by the execution of a double integral of these slopes across two spatial dimensions, subsequently reconstructing the wavefront height of each minor region. The reconstructed wavefronts of each region are combined to derive the three-dimensional shape of the complete wavefront. The zonal method offers considerable benefits. This method successfully decreases computational complexity and markedly enhances reconstruction speed by individually reconstructing the wavefront of each microlens region. Secondly, the area approach may effectively address wavefronts with significant local distortion, particularly in uneven wavefront distortion. This approach is extensively employed in practical applications for rapid and efficient wavefront reconstruction [28].

In the vibration signal point scanning detection system, Southwell’s reconstruction method is employed to reconstruct the wavefront using the zonal method, as illustrated in Figure 6. The wavefront reconstruction result $W\prime$ is derived from the findings in the literature [29]:

$$\begin{array}{c}\hfill W\prime =V{D}^{+}{U}^{T}CS\end{array}$$

(1)

Here, $W\prime$ denotes the wavefront data after reconstruction; S signifies the wavefront slope data acquired from the wavefront sensor; $V{D}^{+}{U}^T$ indicates the inversion of the echo derived from the slope data using the generalized inverse; C serves to transform the slope data into wavefront height. Normalization is employed to adjust to the actual grid distance ds:

$$\begin{array}{c}\hfill W=reshape\left(W\prime ,n,n\right)/ds\end{array}$$

(2)

In the above formula, $W\prime$ is the result of wavefront reconstruction, which is stored in the form of a one-dimensional vector. Reshape ($W\prime$,n,n) rearranges this one-dimensional vector into an $n\times n$ two-dimensional matrix, representing the height data of the wavefront. $/ds$ normalizes each element of the wavefront to adapt to the actual grid distance. The formula above enables the derivation of the wavefront’s three-dimensional shape.

Figure 6. Southwell model (circle represents reconstruction point; arrow represents measurement point).

Figure 6. Southwell model (circle represents reconstruction point; arrow represents measurement point).

3.2. Wavefront Phase

The slope data from SHWFS can be utilized to rebuild the wavefront phase [30,31,32,33,34,35,36,37,38,39,40,41]. Assuming that the wavefront slope matrices in the x and y directions have been obtained from the Shack–Hartmann sensor, the wavefront slopes in the x and y directions are defined as

$$S_x\left(x,y\right)={\displaystyle \frac{𝜕W\left(x,y\right)}{𝜕x}},S_y\left(x,y\right)={\displaystyle \frac{𝜕W\left(x,y\right)}{𝜕y}}$$

(3)

Among them, the wavefront slope is $S_x$ (x,y) in the x-direction, and $S_y$(x,y) is the wavefront slope in the y-direction; W(x,y) is a two-dimensional function representing the wavefront phase, which is inversely obtained from the known slopes $S_x$ and $S_y$. The wavefront phase W(x,y) can be determined by resolving these equations. From these two partial derivative equations, we can obtain the Poisson equation that the wavefront phase W(x,y) must satisfy:

$${\nabla }^{2}W\left(x,y\right)={\displaystyle \frac{𝜕S_x\left(x,y\right)}{𝜕x}}+{\displaystyle \frac{𝜕S_y\left(x,y\right)}{𝜕y}}$$

(4)

The issue of resolving the phase is converted into the Poisson equation. The first derivatives (${\displaystyle \frac{𝜕S_x}{𝜕x}}$ and ${\displaystyle \frac{𝜕S_y}{𝜕y}}$) are second-order derivatives used to convert slope data into phase. ${\displaystyle \frac{𝜕S_x}{𝜕x}}$ and ${\displaystyle \frac{𝜕S_y}{𝜕y}}$ reflect the change in wavefront curvature by differentiating the slope data, thus being associated with the Laplacian operator of wavefront phase. In the Poisson equation for wavefront phase reconstruction, the right-hand side of the equation is not equal to zero. In the general Poisson equation, there is a source term $f\left(x,y\right)$ on the right, which can be expressed as the derivative of the wavefront slope. In the wavefront reconstruction problem, this source term is ${\displaystyle \frac{𝜕S_x}{𝜕x}}+{\displaystyle \frac{𝜕S_y}{𝜕y}}$. If the right side is equal to zero, it means that the wavefront is a smooth and undisturbed wavefront, without any phase change. This obviously does not apply to reconstructing the actual wavefront phase with disturbances, so the right side is not equal to zero.

Fourier transform in two-dimensional space can quickly solve Laplace equation and efficiently and accurately reconstruct wavefront phase. To resolve this Poisson equation, we can employ Fourier transform, which converts the differential operation into an algebraic one. In the frequency domain, the Poisson equation can be expressed as

$$F\left({\nabla }^{2}W\left(x,y\right)\right)=k_x^2·F\left(W\right)+k_y^2·F\left(W\right)$$

(5)

Here, F represents the two-dimensional Fourier transform, while $k_x$ and $k_y$ denote the spatial frequencies in the frequency domain, respectively. Consequently, the Fourier transform $W_{ft}\left(k_x,k_y\right)$ of the wavefront phase in the frequency domain can be articulated as

$$W_{ft}\left(k_x,k_y\right)={\displaystyle \frac{-i\left[k_x·F\left(S_x\right)+k_y·F\left(S_y\right)\right]}{k_x^2+k_y^2+\epsilon }}$$

(6)

In the frequency domain, the value at zero frequency will render the denominator zero. To prevent the inaccuracy of zero removal, a minimum value $\epsilon$ is incorporated into the denominator to enhance calculation stability. Upon acquiring $W_{ft}\left(k_x,k_y\right)$, the wavefront phase expression $W\left(x,y\right)$ in the spatial domain is derived through the inverse Fourier transform as follows:

$$W\left(x,y\right)=F^{-1}\left[W_{ft}\left(k_x,k_y\right)\right]$$

(7)

The slope of the vibration wavefront in Figure 2 is shown in Figure 7. Consequently, the phase alteration of the wavefront is derived utilizing the vibration wavefront slope S depicted in Figure 2, as illustrated in Figure 8.

The phase transition of SHWFS during vibration enables the establishment of the correlation between amplitude and phase, as demonstrated in the subsequent formula:

$$\Delta \phi =k\Delta d+c$$

(8)

where $\Delta \phi$ denotes the phase alteration and $\Delta d$ signifies the amplitude variation. In the absence of vibration, the laser echo detected by the wavefront sensor would induce a minor displacement of the spot centroid on the microlens array, resulting in a slight alteration of the wavefront slope and the emergence of a constant term in the equation.

3.3. Wavefront Crosstalk

In the SHWFS employing the zonal method for wavefront reconstruction, the problem of wavefront crosstalk frequently results in measurement inaccuracies. The zonal method segments the detection area into multiple small pieces, each concentrated by an individual microlens, and enables the measurement of the local wavefront slope. When the spot’s area is beyond the optimal range, it encroaches upon the neighboring microlens region, resulting in the erroneous reception of target area information. This phenomenon causes crosstalk in the wavefront information, hence compromising measurement precision. This issue typically arises from high irradiation power, resulting in an overload of the spot power received by the sensor, hence compromising the accuracy of wavefront reconstruction. The spot’s dimensions, the microlens spacing, and the distribution of spot energy are critical elements influencing the precision of wavefront reconstruction. A considerable spot or high energy concentration will amplify measurement error and induce crosstalk between neighboring regions when employing the zonal method, thereby diminishing reconstruction accuracy.

3.3.1. Spot Size

The focal length of each microlens is denoted as f, the diameter as d, and the detector is positioned on the focal plane of the microlens, meaning that the distance from the detector to the microlens array is f. The local tilt angles of the wavefront on the microlens plane are denoted as ${\theta }_x$ and ${\theta }_y$, and the spot offsets can be articulated as

$$\Delta x=f·{\theta }_x,\Delta y=f·{\theta }_y$$

(9)

It deviates from its center when the spot is sufficiently small and concentrated within a single microlens. Ideally, this offset can be accurately measured. Nonetheless, the detector’s restricted resolution and the spot’s defocusing effect may contribute to actual measurement inaccuracies, impacting wavefront reconstruction accuracy.

Consider a scenario where a laser-emitted spot, with a radius $r_1$, is formed at a certain distance d from the telescope. As the light passes through the telescope, which acts as a converging lens, the spot is focused to form a smaller spot with a radius $r_2$, which can be changed to a different value as needed, as shown in Figure 9.

$$\begin{array}{c}\hfill {\displaystyle \frac{1}{F\prime }}={\displaystyle \frac{1}{d}}+{\displaystyle \frac{1}{d\prime }}\end{array}$$

(10)

where $F\prime$ is the focal length of the telescope, d is the object distance, and $d\prime$ is the image distance. As the spot image moves through the focal plane, its size varies depending on whether it is positioned inside or outside the focal length, thus leading to a different spot size at the focal distance. The magnification M is the ratio of the image size to the object size:

$$M={\displaystyle \frac{r_2}{r_1}}={\displaystyle \frac{d\prime }{d}}$$

(11)

By integrating Formulas (10) and (11) above, one can derive the correlation between the spot radius and the receiving distance as follows:

$$r_2=r_1·{\displaystyle \frac{F\prime }{d}}$$

(12)

Among them, $r_1$ denotes the radius of the circular spot captured by the telescope objective, $r_2$ represents the radius of the spot once the telescope is focused, d indicates the receiving distance of the telescope (the distance from the spot to the objective), and $F\prime$ signifies the focal length of the telescope objective.

Figure 9. The target area is divided into 11 × 11 sub-regions, and the laser is focused on one of the sub-regions. The spot signal of the sub-region is received by the telescope and focused on the corresponding microlens in the microlens array.

Figure 9. The target area is divided into 11 × 11 sub-regions, and the laser is focused on one of the sub-regions. The spot signal of the sub-region is received by the telescope and focused on the corresponding microlens in the microlens array.

3.3.2. Microlens Spacing

Assuming that the spacing of the microlens array is p when the diameter of the spot exceeds the spacing p, the spot may be simultaneously captured by many nearby microlenses. Designate the spot radius as r and the spacing as p. When the spot obscures the neighboring microlens, the position of the spot recorded by the adjacent microlens will coincide, leading to an inaccuracy in the computation of the spot centroid, which subsequently induces crosstalk. The local tilt angle $\theta$ of the wavefront will influence the measurement accuracy as the spot traverses many microlenses. Crosstalk shift can be represented by the following formula:

$$D_{cs}=r-p·sin\theta$$

(13)

When the spot is huge and encompasses several microlenses, this phenomenon will considerably impact the precision of wavefront reconstruction.

3.3.3. Spot Energy Distribution

A Gaussian function can define the energy distribution of the spot. The intensity distribution of the spot on the microlens plane is presumed to be

$$I\left(x,y\right)=I_0\left[-{\displaystyle \frac{{\left(x-x_0\right)}^2+{\left(y-y_0\right)}^2}{2{\sigma }^2}}\right]$$

(14)

Among these parameters, $I_0$ denotes the most incredible intensity at the spot center, ($x_0,y_0$) indicates the coordinates of the spot center, and $\sigma$ signifies the standard deviation of the spot, representing its size. A significant local alteration in the wavefront may cause the intensity of the spot on certain microlenses to be insufficient or undetected, leading to heightened local reconstruction error and crosstalk.

4. The Experiment and Results of Analysis of Vibration Signal Laser Point Scanning Detection System

We experimented with a 70 mW laser at a distance of 10 m. The automatic shutter management of the wavefront sensor camera enables it to process optical input power across a broad dynamic range, with sensitivity significantly influenced by wavelength. The Thorlabs WFS-20-5C Shack–Hartmann wavefront sensor features a high sampling rate of 800 frames per second and a wavefront accuracy of $\lambda$/30 rms at 633 nm. The divergence angle of the laser is 0.25 degrees. This experiment employs a Shack–Hartmann wavefront sensor to detect ground vibration signals. In the single-point detection experiment of vibration signals, a controlled shaking table is employed as a vibration source to replicate the features of longitudinal waves in nature by varying the frequencies and amplitudes. Simultaneously, in the vibration signal point scanning experiment, we employ the vibration motor as the vibration source for testing. The vibration of the tent can usually be described by the displacement function $\Delta z\left(x,y;t\right)$. To isolate the reciprocal effect of the vibration source, we affixed the random amplitude vibration motor to the soft white fabric, as indicated in Figure 10. In the experiment, we employ a laser to illuminate the vibration source and capture the laser echo signal reflected from it using a wavefront sensor.

We employ the wavefront sensor software to document the wavefront variations and monitor the real-time alterations in the incident wavefront. Simultaneously, we compute and exhibit the microlens alterations via the LabView software platform, facilitating additional analysis of the wavefront sensor’s variation upon excitation of the vibration source. The program’s flow is illustrated in Appendix A. Utilizing the architecture and recording approaches of the system above, we can precisely monitor and analyze the small alterations in the wavefront sensor induced by the vibration source’s oscillations. The wavefront slope of the wavefront sensor deviates during the activation of the vibration source, with the deviation occurring in both horizontal and vertical orientations. Detecting longitudinal seismic waves results in a very significant offset in the y-direction and a comparatively minor offset in the x-direction [23]. The vibrometer concurrently detects the vibration signal.

During the test of the reception point of an individual microlens, the laser echo signal is concentrated on a microlens inside the microlens array via a telescope. The high-speed sampling mode (800 frames per second) in wavefront sensor software is a feature that enables real-time acquisition and analysis of wavefront data. This mode captures wavefront data at a high sampling rate, enabling the system to monitor rapidly changing wavefronts in real time, especially suitable for dynamic scenes or fast-moving objects. The Beam View mode in wavefront sensors is a display mode used to observe and analyze the distribution of light beams on the sensor. In this mode, the output signal of the wavefront sensor will be displayed in the form of a beam, usually as an image or a visualized light spot. This mode enables intuitive observation of the characteristics of the beam, such as the shape, size, and position of the light spot. In Beam View mode, the various features of the beam can determine the alignment of the optical system, especially whether there are issues such as focal shift, beam expansion, and skewness. We focused the laser echo signal onto the 6 × 6 microlens in the wavefront sensor microlens array using a telescope and enabled the high-speed sampling mode of the wavefront sensor. In the 6 × 6 green square (corresponding to a 6 × 6 microlens), a spot centroid and its location will be displayed, as shown in Figure 11a. Due to the fact that the laser echo signal is only focused on the 6 × 6 microlens, although there are weak signals around the microlenses, they are not displayed. In the Beam View mode of the wavefront sensor, it is observed that the target microlens exhibits a spot signal. At the same time, numerous neighboring microlenses also display comparatively weaker spot signals, as illustrated in Figure 11b. This indicates that the relationship between the laser echo signal and the microlens array is not a perfect ‘one-to-one’ correspondence but rather a ‘one-to-many’ complex relationship.

The laser creates a spot on the vibration table, and the echo signal is directed to the 6 × 6 microlens of the wavefront sensor via the telescope. The wavefront slopes ($S_x$ and $S_y$) of the centroid of the 6 × 6 microlens array are acquired using LabView software, and the related wavefront picture is rebuilt utilizing the zonal method. Figure 12a–d illustrate that, as the vibration amplitude escalates, the extent of wavefront distortion correspondingly intensifies, resulting in mild disturbances to the microlenses around the 6 × 6 microlens array. In the presence of vibration signals of varying amplitudes inside a particular area, the laser echo signal will transmit the vibrational information of that area. The wavefront sensor acquires and evaluates the associated vibration information by capturing these laser echo signals. Analyzing the wavefront phase alterations at varying amplitudes elucidates the correlation between amplitude and phase, as illustrated in Figure 12e. The wavefront’s phase is altered with changes in amplitude, enabling the derivation of the amplitude variation law using phase change measurement, as indicated in the subsequent formula:

$$\Delta \phi =k\Delta d+c,k=0.0143\left(rad/mm\right),c=0.0354$$

(15)

According to the tests above, we partition a 1.2 m × 1.2 m target into 11 × 11 sub-regions, commencing from the upper left corner, designating the initial area as 1 × 1 coordinates, and sequentially constructing the array. A vibration source is randomly positioned within 11 × 11 sub-regions behind the target. The laser sequentially irradiates each sub-region, employing two pan-tilt mechanisms to regulate the laser head and telescope for point scanning throughout each sub-region, as illustrated in Figure 13. Point scanning is conducted for each sub-region to acquire the wavefront slope variations regarding the respective microlenses. During the detection process, we first use pan-tilt 1 to project the collimated laser onto the target area. Then, we use a clamp to fix telescope 1 and manually adjust its objective lens and eyepiece to adjust the spot area on the target area. Then, we use pan-tilt 2 to adjust the receiving angle of telescope 2 and further adjust the objective lens and eyepiece of telescope 2 to ensure the best receiving effect. Subsequently, through the high-speed sampling interface of the wavefront sensor, we manually adjust the position of the wavefront sensor so that the laser echo signal can be accurately focused on the corresponding lens in the wavefront sensor microlens array, thereby achieving vibration signal point scanning detection. Figure 14 shows the physical system. The field of view of the telescope is $16.4^{\circ }-4.1^{\circ }$, and the distance between the telescope and the spot is 10 m. Therefore, the 10 cm spot size is fully within the field of view of the telescope.

The generated spot is directed onto the wavefront sensor using a telescope, with each spot corresponding individually to the microlens array in the sensor. Figure 15a–h illustrate the outcomes of point scanning over all sub-locations, demonstrating that the microlens array in various regions captures the spot, further substantiating the one-to-one correlation between the microlens array and the target area. During single-point detection across several regions, the application of excitation vibrations by the vibration source to the sub-regions of the target object results in synchronous distortion of the laser echo wavefront. The variation in the wavefront gradient calculates the phase alteration during vibration, and the associated vibration amplitude is computed. The anticipated amplitude of Figure 15b is 1.08 mm, that of Figure 15d is 0.86 mm, the amplitude of Figure 15f is 0.88 mm, and the amplitude of Figure 15h is 1.3 mm. The minor root mean square error is 0.00045 for the amplitude measured by the vibrometer.

In order to achieve faster detection of vibration information in an area, the designated area of 1.2 m × 1.2 m is segmented into a 2 × 2 grid, and a laser beam is directed to four sections to create a spot with a diameter of 60 cm. The telescope is utilized to position the laser echo signal onto the microlens array; in the high-speed sampling mode of the wavefront sensor, the microlens array is viewed to capture the spot centroid, as illustrated in Figure 16.

Based on the detection in the area of Figure 16, we randomly arranged multiple vibration sources in the target area of 1.2 m × 1.2 m. The coordinates of the vibration source are marked in Figure 17a,c,e,g. The laser beam shines a 60 cm diameter spot through a telescope onto multiple sub-regions of the target area. In the high-speed sampling mode of the wavefront sensor software, we observed that 36 microlenses received spot signals, with two detection windows showing significant wavefront distortion, as shown in Figure 17. Through LabView software (version number: LabView2020.0 32-bit), we can accurately locate the microlens detection window with significant wavefront distortion, thereby obtaining the corresponding changes in the wavefront slope of the microlens and calculating the wavefront phase. Figure 17b shows the information of the two vibrations detected in the first sub-region. Subsequently, we scanned the next sub-region and successfully obtained the vibration information of that region, as shown in Figure 17d,f,h. For completeness, we include a case where the two sources are not parallel to the horizontal or vertical axis. The wavefront slope of Figure 17 is shown in Appendix B. This indicates that increasing the spot area of the target region can effectively detect the vibration information of the sub-region, thereby improving the detection efficiency. The minimum root mean square error between the vibration amplitude calculated by phase change and the amplitude recorded by the vibrometer is 0.00049112. Figure 18 shows the amplitude and phase changes in surface scanning. The amplitude generated by the vibration sources in Figure 18 is random, so the abscissa of the eight vibration sources does not increase proportionally. The insufficient accuracy and sensitivity of the vibration meter, as well as the failure to firmly adhere to the vibration source, may lead to inaccurate measurements and cause significant errors.

Figure 17 illustrates the variations in the vibration amplitude of the source correspondingly alter the wavefront phase. This indicates that the vibration signal laser point scanning detection system can efficiently identify vibrations across many target regions and can simultaneously detect the vibration information of multiple sub-areas. By examining the wavefront distortion across varying vibration amplitudes, one may deduce the vibration properties of each sub-region and their impact on the overall wavefront. This method confirms that the laser point scanning detection system possesses excellent sensitivity and resolution in intricate situations, enabling precise capture of local vibration information, hence offering robust support for vibration signal identification. Note that focal plane wavefront sensing is used here as an initial approach, although pupil plane wavefront sensing may also be explored for advanced functionality in the future [42].

5. Conclusions

A vibration signal point scanning detection system utilizing Shack–Hartmann wavefront sensor methods for seismic wave laser remote sensing detection has been established. The system’s transmitter leverages the benefits of short laser wavelengths, elevated detection sensitivity, and high measurement resolution for information collecting. The technique of point scanning detection for extensive ground vibration signals is investigated by utilizing the small size, high precision, high resolution, and high sensitivity of the Shack–Hartmann wavefront sensor. This research provides a vibration signal point scanning detection method that enables remote, non-contact, and effective data collection, addressing the limitations of the current laser remote sensing seismic wave detection technology. This method diverges from conventional single-point spot detection by including the whole surface of the spot. Based on the fundamental principle of the wavefront sensor, we analyze and verify the variations in the vibration of the spot across different locations. Upon excitation of the vibration source, the microlens array within the wavefront sensor captures the ground vibration signal. The telescope system focuses the laser echo signal in the target area onto the wavefront sensor, with the microlens array’s sub-aperture corresponding to the received light spot. The experimental results indicate that, at a fixed vibration frequency, each microlens’ wavefront slope within the array varies with different amplitudes. Moreover, by increasing the diameter of the scanning spot and detecting multiple sub-regions, the scanning efficiency has been significantly improved. The point scanning method concurrently detects the vibrations of various target sub-regions, successfully capturing the vibration wavefront. This outcome confirms the validity of our suggested vibration signal point scanning system and demonstrates its capability to detect vibration information across various regions within an extensive range.

In contrast to the conventional single-point spot detection method, the system has markedly enhanced the detection range and comprehensively analyzed the response of each sub-aperture within the microlens array. This paper presents experiments on low-frequency and small-amplitude vibrations. The system’s features are analyzed, and vibration signal point scanning detection and data analysis are performed. With promising seismic wave detection and exploration applications, it can monitor and record minute ground vibrations in real time. Nonetheless, the vibration signal point scanning detection system established in this study faces the issue of laser power attenuation during the detection of seismic waves. To attain more excellent distance detection in the future, we must prioritize the utilization of high-power lasers. Moreover, noise interference constitutes a significant concern. Future studies may explore the application of neural networks to eliminate noise caused by environmental interference.