1 Introduction

Glass is widely used in biomedical, microelectromechanical systems (MEMS), and microfluidic fields owing to its chemical stability, optical properties, and biocompatibility. Although the applications in these fields require microscale patterning, the brittleness of glass renders the fabrication of micromachined parts using conventional tool-based machining challenging. Lasers offer an alternative micromachining method that ablates materials using high energy at their focal points. However, because the absorptivity of glass varies with wavelength, machining with existing laser equipment can be difficult.

Laser-induced backside wet etching (LIBWE) eliminates the need for new equipment, making it a powerful alternative for processing transparent materials. A LIBWE irradiates the rear side of a workpiece in contact with an absorbent liquid. Thermal expansion of the liquid results in the formation of microbubbles at the workpiece–liquid interface. When a laser-induced bubble collapses, the microjet impacts the surface of the locally heated part of the workpiece and breaks it. This results in a higher aspect ratio compared to the direct irradiation methods [1, 2] and debris-free removal of the substrate because the debris dissipates through the surrounding liquid. Several applications of the LIBWE process have been reported, including micro-optic lens arrays [3], microfluidic devices [4], and circuit patterning [5].

Owing to the complex combination of liquid/vapor flows and local thermal effects on the irradiated spot, various factors affect the etching behavior; numerous studies have analyzed these factors using various monitoring methods. Niino et al. [6] captured vapor expansion and bubble collapse signals using a piezoelectric pressure gauge. Cheng et al. [7] proposed a focus alignment and etching threshold method by monitoring blue light emission at the liquid–solid interface. Tsvetkov et al. [8] observed the hydrodynamic pressure generated by a laser-induced bubble collapse by installing a hydrophone beneath an irradiated spot. The hydrodynamic pressure was analyzed under various laser fluences, confirming that supercritical water dominates the etching at low laser fluences, whereas hydrodynamic processes dominate at higher fluences. Long et al. [9] used a high-speed camera to observe the evolution and collapse of laser-induced cavitation bubbles at the liquid–solid interface. They confirmed that larger cavitation bubbles formed at higher laser fluences and produced a powdered material that was deposited on the interface. However, these previous studies focused on parametric experiments or surface characterization limited to shallow boundaries; the etching behavior in high-aspect-ratio structures has not been explored in depth. In the case of a high-aspect-ratio structure, Cheng et al. [10] observed a significant variation in the etching depth and concluded that the debris remained and accumulated at the bottom of the structure, hindering the accurate machining of microscale parts.

One way to increase the accuracy of laser machining is to monitor the dimensions simultaneously during the process. For example, Döring et al. [11] reported in situ imaging of hole shape evolution using a microscope and an edge-pass filter with a wavelength of 1050 nm, which is transparent through the polished surface of the material. Ho et al. [12] designed a vision-based monitoring system with coaxially installed CMOS camera, estimating depth from the plasma region of the hole. Ji et al. [13] demonstrated that inline-coherent imaging (ICI) enables imaging of both deep microchannels and 2D structures. However, microscope-based methods are valid only at the focused point and require adjustments for each target. By contrast, both vision-based and the ICI method utilize the reflectance of the imaging laser at the surface, which is limited to direct ablation.

An alternative method for monitoring the laser machining progress involves acoustic sensing using microphones. Unlike a vibration sensor, a microphone provides an intuitive sense of energy removal without direct contact with a workpiece or tool. Sheng and Chryssolouris [14] estimated the groove dimensions based on the sound generated by the gas jet and groove wall interactions. Kurita et al. [15] experimentally related the sound pressure during the process to the removal characteristics of the particular material. Huang et al. [16] realized an acoustic monitoring system that can prevent damage on the workpiece when removing the surface coating by extracting characteristic frequency parameters. These studies confirmed that the acoustic sensing technique offers high measurement speed and flexibility in sensor positioning, making it a valuable tool for monitoring laser machining processes.

This paper presents a new method for observing the removal process in an LIBWE using a microphone. The process-characteristic frequency was first filtered out from the acoustic signal to overcome its susceptibility to irrelevant noise. Then, the average energy of bubble-driven removal was estimated using statistical features extracted from the refined signal. By accumulating the history of the energy features, we developed an efficient technique for estimating the depth of microchannels and the shift in removal behavior through acoustic sensing.

2 Cavitation Bubble and Sound Generation

In LIBWE, laser-induced cavitation bubbles play a crucial role in removing material. A highly focused laser beam passes through the transparent workpiece and heats the focused area, affecting both the absorbent liquid and the workpiece. When the liquid is irradiated by a laser, thermal expansion forms a bubble, causing it to grow in size. As the encapsulated gas exceeds the ambient pressure of the liquid, the bubble collapses, and a high-pressure jet propagates through the liquid [17]. This strikes and removes the locally heated part of the workpiece and emits sound.

The sound generated during the process depended strongly on the frequency response of the collapse of laser-induced cavitation bubble. Böhme and Zimmer [18] formulated an equation illustrating that the lifetime of a bubble is proportional to the laser fluence in the LIBWE process:

$${T}_{C}=0.915\sqrt{\frac{{p}_{stat}-{p}_{vap}}{\rho }} {R}_{max} , \quad {\text{where }} {R}_{max}\propto \sqrt[3]{{E}_{B}}.$$
(1)

where Tc is the lifetime of the bubble, pstat and pvap are the static pressure of the surrounding liquid and the vapor pressure inside the bubble, respectively, Rmax is the maximum radius of the bubble, and ρ is the fluid’s density. The maximum size of the bubble is proportional to the cube root of EB, where EB is the bubble energy, which is, in turn, proportional to the absorbed laser fluence. When a laser is irradiated on an inhibiting cavitation bubble, it scatters the laser [19], and the degraded laser forms smaller nearby laser-induced bubbles (Fig. 1a). As each bubble has its own lifetime and individual impact on the machining process (see Fig. 1b), the frequency response contains a superposition of multiple bubble dynamics. After the surface is modified, the liquid flows into the vacancy, and the repulsive flow from the microjet strikes the surface, pulling out debris and bubbles (see Fig. 1c). In the actual process, all these phenomena occur simultaneously as each bubble individually collapses, which makes observing the exact existence time of each bubble (see Fig. 1d) challenging. Therefore, we utilized the sound signal generated from the bubble collapse to estimate the removal. The frequency response of the process should be observed within a range that considers multiple bubble dynamics.

Fig. 1
figure 1

Laser-induced bubble beneath the workpiece: a scattering of the laser; b diverse bubble collapse of the bubble and generation of jet-stream; c removal of the part; d in-situ image using high-speed camera

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3 Wavelet Transform

In this study, wavelet transform was performed to filter out the sound amplitudes in the characteristic frequency range. Wavelet transform (WT) is a technique for analyzing time and frequency information. Unlike the short-time Fourier transform (STFT), which has a uniform resolution across the frequency range, the WT provides high resolution at lower frequencies and low resolution at higher frequencies. This is achieved using two factors that govern the waveform of the mother wavelet: scale and location. The scale factor stretches the mother wavelet, increasing the localized time at low frequencies. The location factor shifts the wavelet, which slides through the input time-series signal based on its size. By performing a convolution of various squeezed and stretched mother wavelet waveforms on the time-series signal, the signal is decomposed into frequency features over time.

Discrete wavelet transform (DWT) is a wavelet transform that employs discretized scale factors. The mathematical equation for the discretized mother wavelet can be expressed, as shown in Addison [20]:

$${\psi }_{m,n}\left(t\right)= \frac{1}{\sqrt{{a}_{0}^{m}}}\psi \left(\frac{t-n{b}_{0}{a}_{0}^{m}}{{a}_{0}^{m}}\right),$$
(2)

where a0 and b0 denote the scale and location of the bases, respectively. Instead of directly applying the scale factor to the equation, the power of the a0 notation can be applied as it provides exponential scaling. To implement the DWT, a0 and b0 were set to 2 and 1, respectively. Ψ(t) is called mother wavelet, which is a wave-like oscillation function that begins and ends at zero. It works similar to the sinusoidal function in FFT; however, it is limited in terms of time duration. The final detail coefficient of the DWT can be written as

$${T}_{m,n}= {\int }_{-\infty }^{\infty }x\left(t\right){\psi }_{m,n}\left(t\right)dt,$$
(3)

where Tm,n is the detail coefficient at the scale and location indices (m,n), and x(t) is the time series data. The DWT can be performed using multivariate filter banks, which recursively subdivide the frequency into a coarse approximation (a) and a detailed coefficient (d), as shown in Fig. 2. The coarse approximation follows the lower half of the frequency band, whereas the detailed coefficient covers the upper half. By increasing the number of levels to be divided, the DWT provides a higher resolution in the low-frequency domain. In this study, 8 detail coefficients (d1, d2, d3, d4, d5, d6, d7, and d8) were obtained from the acoustic signal using Haar as the mother wavelet. According to the Nyquist–Shannon theorem, the analyzable frequency range is limited to half the sampling rate.

Fig. 2
figure 2

Frequency band diagram of wavelet decomposition (level = 8). LP refers to a low-pass filter bank, and HP refers to a high-pass filter bank

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4 Experimental Setup and Design

4.1 Experimental Setup

Figure 3 illustrates the experimental setup used to study the LIBWE process. A soda-lime glass workpiece (JMC glass, Korea) measuring 15 × 15 × 1.85 mm3 was used. The workpiece was mounted onto a PMMA reservoir and fixed using a holder with a penetrating cuboidal shape for laser irradiation. An aqueous solution of copper (II) sulfate (CuSO4) was used as the absorbent liquid, and phosphoric acid (H3PO4) was used to suppress crack generation. The concentration of the phosphoric acid was controlled by the weight fraction of the substance in pure water.

Fig. 3
figure 3

Experimental setup. a Schematic of the entire system, b Installation of the microphone, c Top view of the loaded workpiece

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A Yb-doped fiber laser (YLP-V2-1-100-30-30, IPG, Germany) with a wavelength of 1064 nm and a pulse duration of 100 ns was employed as the laser source. The laser pulses were focused on the back side of the glass workpiece using an XYZ stage. At the focal length, the spot size was 40 µm, and a galvanometer scanner (SCANcube® 10, Scanlab, Germany) was used to scan the designated path with a resolution of 2 μm/pixel.

A cardioid condenser microphone (E205UMK2, Superlux) was used for acoustic sensing. Cardioid microphones are sensitive to sounds coming from the front and reject sounds from the sides and back. Therefore, the microphone was placed 200 mm from the workpiece at a 30° inclination angle facing the workpiece. The sound signal was recorded using an audio-recording program developed in a Python environment with a 96 kHz sampling frequency and 16-bit depth. The observable frequency range was set from 2 to 20 kHz, because the lower range contains ambient noise (such as the noise of fans and other electrical noise) while the higher range was beyond the upper limit of the microphone's frequency response.

The surface-etching characteristics were observed using an optical microscope (BX53MTRF, OLYMPUS, Japan). A focused ion beam system (COBRA FIB, Orsay Physics, France) was used to examine the microchannel morphology. A surface profiler (Surfiew, GLtech, Korea) with interferometry was used to acquire the 3D morphology of the overall structure.

4.2 Experimental Design

The procedure of this study was divided into two steps. The first step involved identifying the characteristic frequency using fast Fourier transform (FFT) as well as short-time Fourier Transform (STFT), whereas the second step involved estimating the final depth based on the features selected from the characteristic frequency.

4.2.1 Process-Related Characteristic Frequency

The sound was generated due to the effect of the hydrodynamic pressure from the laser induced bubble collapse, regardless of surface modification. The criterion for choosing the characteristic frequency depends on the frequency response of the sound that is generated when the actual etching occurs. The laser conditions were explored based on the processable parameters listed in Table 1. The basic laser condition was set as 15 W laser intensity and 50 kHz pulse repetition rate, while the chemical composition of the absorbent liquid was fixed as 0.5 M copper sulfate, 50 wt% phosphoric acid. The number of scans were set to observe the surface modification corresponding to the frequency change.

Table 1 Verification of the characteristic frequency under different laser conditions
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4.2.2 Selection of the Statistic Feature, Estimation of the Depth

To estimate the depth based on the characteristic frequency that was defined in the previous step, wavelet transform was performed to filter out the factors in the characteristic frequency range. Statistical features were then explored to find out the best feature that describes the etch rate.

As measuring the depth of the microchannel in situ during the process was not possible, individual microchannels were fabricated by increasing the number of laser scans in increments of 100. Figure 4 shows the overall process of the experiment. The summation of the statistical features was then compared with the fabricated depth based on the Pearson coefficient, which represents the mathematical correlation between two variables.

Fig. 4
figure 4

Overall experimental procedure of the data acquisition process

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To further validate the model for a given laser condition, two sets of experimental conditions (hard mode and soft mode) were selected (Table 2). In addition, three replicates of the experiment were performed and compared to determine whether the estimation using the sound feature tracked the deviation of each final part.

Table 2 Depth estimation validity test under different laser parameters
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5 Results and Discussion

5.1 Identification of the Characteristic Frequency in LIBWE Process

In this experiment, we observed the characteristic frequency of the LIBWE process, which is revealed when etching occurs. The criterion of the characteristic frequency was based on the common frequency range when the actual removal of the glass occurs. According to the frequency response (Fig. 5), frequencies between 6 and 12 kHz are observed at all values of the process parameters in the beginning of the process, but the frequencies between 3 and 6 kHz starts to unveil at higher laser power and pulse repetition rate as the process proceeds. To match the frequency shift and the etch behavior, four sets of laser power and pulse repetition rate were used for two scan cycles with different numbers of scans.

Fig. 5
figure 5

Short-time Fourier transform (STFT) result for 15 s while increasing power and pulse repetition rate. Green dashed line: when the laser was turned on; yellow line: low frequency response that was not visible in the 15 W, 20 kHz condition. Idle state refers to the state when the laser was not yet turned on

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5.1.1 Laser Power

As can be seen in the right-column images in Fig. 5, the yellow line, which implies the emergence of the lower frequency, becomes closer to the green line at a higher laser power. In the LIBWE process, material removal at the surface is less likely to occur at the first few pulses of laser irradiation due to insufficient copper attachment on the glass surface and insufficient energy absorption. This phenomenon is called the incubation effect. Böhme and Zimmer [18] confirmed that the required number of scans to exit the incubation decreases with increasing laser fluence, as the process proceed with the forming of large bubbles with increasing periods of contact with the hot surface.

Although material removal did not occur, a sound was generated as the jet from the collapsed bubbles hit the glass surface (Fig. 6a). The frequency response of such a minor bubble collapse tended to lie in the higher range (between 6 and 12 kHz) as the low amount of absorbed energy created smaller bubbles with shorter lifetimes. Meanwhile, at higher fluences, the influence of the lower-frequency range increased as larger bubbles with longer lifetimes grew in size and accelerated heat accumulation in a considerably shorter time. The coexistence of the lower- and higher-frequency responses (Fig. 6b) implies that the incubation region is small and starts to remove the material.

Fig. 6
figure 6

Influence of incubation effect under varying power for the first 40 scans with a constant pulse repetition rate of 50 kHz: a incubation stage; b co-existence of incubation and initial etching stage. A fast breakdown of the small bubbles due to the low absorbed energy generates a mild hydrodynamic process and dominates the high-frequency response domain. Larger bubble with longer lifetime due to high absorbed energy generates strong hydrodynamic process and dominates the low-frequency domain

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5.1.2 Pulse Repetition Rate

Another difference in the frequency response could be observed with an increase in the pulse repetition rate (bottom-row images in Fig. 5). To confirm the influence of the pulse repetition rate on the removal behavior and visualize how it affected the frequency response, the pulse repetition rate was varied. Long et al. [9] reported that a high repetition rate causes a substantial increase in the etching rate. According to their study, shorter intervals between pulses at higher repetition rates irradiate the bubble before it collapses, increasing its size and causing effective thermal accumulation on both the liquid and workpiece surfaces. Considering the acoustic response in relation to this finding, the number of scans required to exit the incubation would decrease at a higher pulse repetition rate.

Figure 7a shows the transition of the removal mode based on the frequency response in discrete time intervals. As the process continued, the accumulated copper increased the heat absorption of the laser, and the increased bubble size caused a reduction in frequency response. Higher-frequency features remained in the yellow area shown in Fig. 7a with a decreased amplitude; this is because the irradiated laser on the bubble would be scattered form a smaller bubble nearby [19] and would cause gentle etching. Moreover, the etching results were consistent with the previous work of Long et al. [9], showing that the amount of etched surface increases at higher pulse repetition rates (Fig. 6b–d).

Fig. 7
figure 7

Result from 600 scans (15 W) under varying pulse repetition rate. a Frequency response when the pulse repetition rate was set at 40 kHz. b–d Optical microscopic image of the part when pulse repetition rate was set at 30, 40, and 50 kHz, respectively. No etching occurred at 20 kHz

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To further analyze the temporal changes in the time–frequency domain, we adapted the wavelet transform. Based on the findings obtained with the laser parameters, we matched the observable wavelet transform filter bank to the 4th level (d4), corresponding to a frequency range of 3–6 kHz when the sampling rate was set to 96 kHz (Table 3).

Table 3 Frequency range on the level of the wavelet transform
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5.2 Sound Feature and Etching Rate

Quantification of the sound signal that changes during the process first includes slicing the time series data into 243-ms durations, yielding 23,360 data points with a sampling frequency of 96 kHz. This time duration corresponded to the time spent scanning a 3-mm line at a speed of 150 mm/s, returning at 1000 mm/s for 10 times, with minor jumps and scanning delays. The sliced data were normalized and decomposed into the selected frequency levels using the wavelet transform. Bordatchev and Nikumb [21] confirmed that the normalization procedure of the time signal produced a dimensionless time series with zero mean and unit variance, which excluded the unknown effect of the signal amplitude.

Subsequently, to correlate the etching rate with the sound features, the statistical features that best described the removal process were explored. Table 4 lists the equations used to calculate these features. The maximum, minimum, mean, and root mean square (RMS) values of the energy of the signal were calculated. Variance, skewness, and kurtosis were used to explain the data distribution. The shape and impulse factors were related to the waveform [22].

Table 4 Calculation equation of features
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5.2.1 Statistical Feature Selection and Depth Estimation Mechanism

Feature selection was performed using Pearson’s correlation coefficient, which calculates the correlation between the summation of statistical features during the scan and the depth of the fabricated channel. Table 5 displays the Pearson coefficients between the evaluated statistical features and the final machined depth from 0 to 2000 laser scans in intervals of 100. Among the nine features, the RMS value was the most appropriate for describing the depth trend. The RMS value of the characteristic frequency implies that the removal energy was approximated.

Table 5 Pearson correlation coefficient result of features from 100 to 2000 scans
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Figure 8a shows the relationship between the depth of the microchannel and summed d4 RMS features after a certain number of laser scans. The summation of the data points in Fig. 8b refers to the blue point in Fig. 8a, and the measured microchannel depth in Fig. 8c refers to the red-cross point at the 2000 scans in Fig. 8a. The drawback of the open-loop control with a fixed number of scans is evident at several intervals due to the instability of the process. Despite more laser passes along the path, the machined depth was sometimes smaller than that with fewer scans (1000–1200, 1600–1700, and 1900–2000). Meanwhile, the pattern between the summation of the RMS and measured depth highly matched in the range below 1700 scans, with a Pearson coefficient of 0.98. This indicates the possibility of introducing an arbitrary constant coefficient to convert the summation of sound features into depth units in a limited estimation boundary.

Fig. 8
figure 8

RMS trend in the increasing number of scans. a Summation of RMS value (SRMS) to the measured depth. Yellow-colored area refers to the valid range of the estimation. b d4 RMS curve during 2000 scans and c FIB image of the fabricated microchannel after 2000 scans. Summation of b refers to the blue point in a at 2000 scans. The upper and lower boundaries for the estimation are based on the coefficients calculated from 500 and 1200 scans, respectively

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The calculation of such a coefficient can be derived as

$$\mathrm{\alpha }= \frac{{D}_{N}}{{\int }_{0}^{N}d4 RMS (x) dx},$$
(4)

where α is an arbitrary constant, DN is the depth of the microchannel, and N is the number of scans. Based on this approach, N was set as 500 for the maximum value of alpha and 1200 for the minimum value of alpha, as shown in the pink-colored area in Fig. 8a. The estimation started to show error beyond 120 μm (1400 scans), which implied that another factor accounted for the process that could not be explained through laser-induced bubble growth and sound. This limitation in the estimation may result from machining phase change, as previously discussed by Kwon et al. [23]. The processing state was subdivided into three states: initial state with bubble generation, vapor layer generation state, and crack generation state. The process entered the vapor layer generation state as the gas byproduct produced by thermal decomposition was trapped inside the deep microchannel and hindered the contact of the absorbent liquid with the glass. In our case, it entered the vapor layer generation stage and encountered steady machining at 150 μm as the hydrodynamic force from the bubble could not effectively reach the surface.

5.2.2 RMS Trend and Phase Change in Etching

To verify our proposed mechanism, we considered the variation of the RMS value of the d4 level during etching. According to a previous result from Böhme and Zimmer [18], when observing the etching rate trend with increasing beam passes, the etching rate increased as the incubation period ended, and it fluctuated before it saturated. Accordingly, the RMS value is shown in Fig. 9b, illustrating the etching rate of the process, although the amplitude of the time-series data is greater in the beginning (see Fig. 9a). In addition to the incubation effect, a common trend is observed as shown in Fig. 9b. The d4 RMS value reached a peak at approximately 50 scans and began to decrease thereafter. To determine the causes of this behavior, further observations were conducted by magnifying the range and fabricating microchannels in 10-loop intervals.

Fig. 9
figure 9

Time series acoustic signal and d4 RMS response signal between successive scans: a 10 scan intervals in the increment of 1000 scans. b d4 RMS value trend in three different laser scans

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Based on this observation, the frequency of the sound from the process can be inferred to illustrate the evolution of the removal mode. As the etching progressed, the sound generated changed, reflecting a shift in the etching direction and growth of the microchannel.

Initially, the sound frequency feature captured the removal of the hemisphere, which was responsible for enlarging both the width and depth of the microchannel. As the laser continued to scan the area and the width of the microchannel started to saturate, the sound frequency feature reflected these changes, capturing the machining process that occurred mainly in the axial direction (see Fig. 10).

Fig. 10
figure 10

Width growth with increments in the number of laser scans: a width growth and saturation; b morphology of microchannel after 40, 50, and 70 scans; c high-aspect ratio microchannel with a consistent width

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In summary, the frequency features of the sound generated during the etching process provide valuable insights into the evolution of the removal mode. By analyzing the sound frequency features, it is possible to monitor the etching progress, understand the changes in the etching direction, and improve the overall control of the laser microchannel fabrication process.

5.3 Validity of the Estimation Mechanism

5.3.1 Etching Rate in Different Laser Conditions

The results obtained from testing the additional laser parameter set, referred to as the “soft mode,” further validated the methodology under different etching rates. This soft mode exhibited a narrower etching depth and a distinct transition point of approximately 20 μm. At this transition point, the slope of the average depth trend changed from 0.015 to 0.020 μm/scan, representing a 33% increase (Fig. 11a). Moreover, a change in the removal mode could be observed in the RMS trend, as shown in Fig. 11b. The RMS value increased with fluctuations before starting to saturate, reaching approximately 1200–1300. The saturation points of the RMS trend coincided with the point at which the etching rate increased, further supporting the relationship between the sound features and the etching process.

Fig. 11
figure 11

Etched depth and corresponding RMS trend up to 2000 scans: a depth variation of microchannel under increments of laser scans; b RMS trend of laser scans; c cross-sectional profiles of the microchannel, corresponding to the scans depicted in a. Error bar refers to the maximum and minimum depth of the fabricated microchannel

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5.3.2 Repetition Test of Estimation

To confirm the validity of the estimation method that tracks the deviation of the final part, each process is repeated three times. The coefficient for each condition was then calculated by averaging the coefficients obtained from the set. Hence, each estimation in Fig. 12 shares a common coefficient under a single laser condition.

Fig. 12
figure 12

Repetition test of the depth estimation in the soft mode condition: a hard mode (27 W 50 kHz) condition. The upper and lower boundary are based on the averaged coefficient calculated in the 500 and 1200 scans, respectively. b Soft mode (20 W 65 kHz) condition. The upper and lower boundaries are based on the averaged coefficients calculated from 1300 and 1700 scans, respectively. The valid estimation range covers the full range of the explored number of scans in the soft mode, whereas it starts to fail beyond 120 μm in the hard mode

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The depth estimation for the hard and soft modes was generally well-fitted to the measured depth, with only a few errors (see Fig. 12). Major deviations were consistently tracked in all cases, whereas minor fluctuations remained unresolved. Minor errors were expected to result from the minor bubble collapse above the characteristic frequency identified in Sect. 5.1. In the high-temperature region with a softened surface, the surface will likely be removed due to the low hydrodynamic force generated from the minor bubble collapse. Because the hard mode provides a higher surface-softening effect, it produces more errors, as shown in Fig. 12.

Nevertheless, because the proposed sound feature captured the relative depth, the results are promising and suggest that the proposed mechanism is robust across different laser parameters. This demonstrates the potential of using sound features to monitor and control the laser microchannel fabrication process under various etching conditions. This methodology can be further refined and applied to other material processing techniques to improve process control and accuracy.

5.4 Feedback Control System

The development of a control system based on depth estimation by the proposed mechanism demonstrated its potential for improving the accuracy of microchannel machining in the LIBWE process. An integrated feedback control system was designed by connecting a Python environment, which handled data acquisition and processing, to a C++ environment, which controlled the laser delivery system using socket communication. A flowchart of the integrated feedback control system for microchannel machining in the LIBWE process is shown in Fig. 13. The start signal triggered the laser scanning system to deliver the laser, thereby replacing the data-slicing procedure used in previous experiments. The process parameters were set to be the same as those in the hard mode to verify the deviation from strong ablation, and a constant coefficient was used for the estimation.

Fig. 13
figure 13

Flow chart of the sound-based feedback control LIBWE system

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Figure 14 presents a comparison of the open-loop control system with a fixed number of laser scans determined by the experiment with the closed-loop control system, which uses the proposed feedback control system. The closed-loop system adjusted the number of scans for each target depth based on the RMS value of the sound signal calculated in each case, as shown in Table 6. The mean values in both cases closely matched the target depth, with the closed-loop system converging to a specific value. The maximum error in the feedback system was 5.6% when machining a 90-μm-depth microchannel, which represents better performance than that of the conventional method. These results indicate that the proposed mechanism can enhance the accuracy of LIBWE by monitoring the physical signals generated during the removal process.

Fig. 14
figure 14

Comparison of machining accuracy between open-loop and closed-loop control from 80 to 120 μm

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Table 6 Number of scans of the closed-loop control system about the target depth
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6 Conclusion

In this study, a depth estimation mechanism for LIBWE was developed using acoustic sensing. By exploring the characteristic frequency of the process through FFT, it was determined that frequencies between 3 and 6 kHz were distinct from other frequency ranges. The RMS value of the characteristic frequency was useful for approximating the etching rate and displayed a trend similar to that observed in previous studies. Furthermore, a feedback control system was developed for accurate microchannel fabrication.

To the best of our knowledge, this is the first study to investigate the relationship between the energy features of process sounds and the material removal quantity in LIBWE. The results provide compelling evidence for the wide-depth range involvement within the range of processable laser power and suggest that this approach is effective for the real-time estimation of the current machining depth, which is difficult to obtain through visual inspection.

However, this study has some limitations. As mentioned earlier, synchronizing the depth in a time step and the acoustic energy simultaneously was not possible. Therefore, the hypothesis was supported statistically and through empirical trends from prior work. Future research should evaluate whether the energy value at a specific time step accurately represents the exact amount of removal and whether estimating more complex microstructure geometries is feasible. By addressing these limitations, this approach can be further refined and optimized for a wider range of applications of LIBWE processes.