Φ-OTDR Based on Undersampling Heterodyne Detection

Abstract

We demonstrate a distributed acoustic sensing (DAS) system based on phase-sensitive optical time-domain reflectometry (Φ-OTDR) that employs I/Q demodulation and heterodyne detection. The proposed DAS system utilizes a 90° optical hybrid to obtain in-phase (I) and quadrature (Q) signals. By applying undersampling theory, the system significantly reduces the required analog-to-digital sampling rate. In an experimental demonstration, a 200 MHz heterodyne beat signal is successfully recovered at a sampling rate of 110 MSa/s without any loss of phase information. The system achieves a spatial resolution of 10 m, a signal-to-noise ratio of approximately 63.54 dB at a demodulation frequency of 200 Hz, and a background noise level of −52.27 dB·rad2/Hz. In addition, an amplitude-based analysis of the I/Q data is used to locate vibration events and estimate their effective length, so that an adaptive differential gauge length can be chosen to suppress common-phase fluctuations and restrict phase demodulation to a short fiber segment. This approach effectively reduces data throughput and system complexity while maintaining high sensitivity and resolution, illustrating the potential for more efficient real-time DAS implementations.

1. Introduction

Distributed acoustic sensing (DAS) based on phase-sensitive optical time-domain reflectometry (Φ-OTDR) has attracted substantial interest for applications such as perimeter intrusion detection, structural health monitoring, and pipeline surveillance, due to its long sensing range, low cost, and fully distributed sensing capability [1,2,3,4,5]. Intensity-based Φ-OTDR systems detect vibration events by measuring optical intensity variations, but they suffer from strong nonlinear responses, which distort the reconstructed acoustic signal. Demodulating the phase changes in the Rayleigh backscattering provides a linear response and overcomes this limitation.

Over the years, various phase demodulation methods have been proposed to improve the performance of the Φ-OTDR-based distributed acoustic sensing. Early Φ-OTDR systems employed digital coherent detection to demodulate the signal phase, relying on software for phase computation. However, this approach imposed a significant computational burden and complicated subsequent data analysis [6]. Later, 3 × 3 fiber couplers and unbalanced interferometers combined with phase-generated carrier (PGC) techniques were introduced into Φ-OTDR systems [7,8,9,10,11]. For example, the PGC-Φ-OTDR proposed by Fang et al. achieved significant progress in suppressing phase fading [10]; however, such interferometric configurations are highly sensitive to environmental disturbances. Wang et al. used a 90° optical hybrid with I/Q demodulation to directly recover the baseband phase signal, enabling dynamic strain measurement with a spatial resolution of 10 m over a 12.6 km fiber [12,13]. He et al. further employed a dual-pulse heterodyne architecture, enabling simultaneous recovery of multiple event waveforms and improving the signal-to-noise ratio (SNR) to 49 dB [14]. More recently, S. Liu et al. accelerated the phase demodulation process for heterodyne Φ-OTDR by generating orthogonal components via spatial phase shifting, thereby reducing the computational burden [15]. F. Liu et al. further demonstrated a real-time phase-demodulation scheme for heterodyne Φ-OTDR, enabling GPU-based real-time processing [16]. In addition, Ref. [17] also presents a phase demodulation method using a direct-detection system. Cheng and Shi further improved the phase demodulation quality in direct-detection Φ-OTDR by introducing a multi-position compensation strategy [18].

Despite these advances, a significant challenge in coherent Φ-OTDR is the extremely high data rate required for signal acquisition. The optical signal typically occupies the high-frequency range (e.g., 80–200 MHz), and a very high sampling rate is necessary to fully capture its bandwidth. For instance, a sampling rate of 500 MSa/s or higher is commonly required to accurately cover the phase-modulated heterodyne beat signal. Such high data throughput not only increases system cost, but also imposes a heavy burden on real-time processing.

Homodyne detection overcomes the limitations of heterodyne schemes by directly demodulating the signal to the baseband, thereby significantly reducing the required data acquisition rate and receiver bandwidth. However, this enhanced performance comes at the cost of increased system complexity. A fundamental challenge in homodyne detection is the need to maintain a stable phase relationship, specifically phase locking, between the local oscillator and the signal. To actively control and stabilize this critical phase difference, an additional Acousto-Optic Modulator (AOM) is often introduced into the local oscillator path [12]. This addition makes the optical setup more intricate, requiring sophisticated feedback control loops, and generally demands greater alignment precision and stability compared to simpler heterodyne or direct detection systems.

Undersampling provides an effective solution to alleviate the high sampling rate bottleneck in Φ-OTDR systems by folding the high-frequency beat signal to a lower frequency range. This approach reduces the required sampling rate without losing any information. According to the undersampling theory, when the sampling frequency is carefully matched to the signal’s spectral characteristics, spectral aliasing can be avoided, thereby preserving the complete signal content. Jiang et al. were the first to introduce this concept into the Φ-OTDR field, and demonstrated that a 200 MHz Φ-OTDR heterodyne signal could be accurately demodulated using a sampling rate as low as 71 MSa/s through precise alignment of the sampling frequency with the signal bandwidth [19]. In practice, successful implementation of undersampling demands rigorous front-end filtering and precise frequency planning to prevent unwanted aliasing [20,21].

Undersampling-based Φ-OTDR systems typically generate the quadrature component digitally for phase demodulation. In contrast, a 90° optical hybrid provides native I/Q outputs in the optical domain, which simplifies the demodulation chain and reduces sensitivity to digital quadrature-generation imperfections, resulting in more consistent I/Q components.

In this work, we demonstrate a distributed acoustic sensing (DAS) system with a significantly reduced data acquisition rate by combining heterodyne detection with undersampling. The proposed DAS system employs a 90° optical hybrid to obtain in-phase (I) and quadrature (Q) components of the backscattered signal, enabling full complex field recovery. By applying undersampling, the 200 MHz Rayleigh backscatter beat signal is folded to a low frequency, allowing for efficient sampling. In our experiment, a data acquisition card (DAQ) with a sampling rate of only 110 MSa/s is used, yet the vibration signal is accurately recovered without any loss of phase information. We also address the common-phase change that appears when the PZT is placed near the fiber input. A moving-average–moving-difference amplitude analysis is employed to locate vibration events and estimate their effective spatial extent, from which an adaptive differential gauge length is selected to suppress common-phase fluctuations and restrict phase demodulation to a local fiber segment. The system achieves a spatial resolution of 10 m, a signal-to-noise ratio (SNR) of approximately 63.54 dB at a demodulation frequency of 200 Hz, and a background noise level of as low as −52.27 dB·rad²/Hz. The main contributions of this work are threefold: (1) Integrating a 90° hybrid-based heterodyne Φ-OTDR with undersampling, thereby substantially reducing the sampling rate requirement for DAS; (2) experimentally validating phase demodulation at a 200 MHz heterodyne beat frequency with a sampling rate of 110 MSa/s; and (3) introducing an amplitude-assisted adaptive gauge-length strategy to suppress common-phase fluctuations and reduce data throughput.

The remainder of this paper is organized as follows. Section 2 introduces the operating principle of the coherent Φ-OTDR based on heterodyne detection, I/Q demodulation, and undersampling. Section 3 describes the experimental setup and key system configurations. Section 4 presents the experimental results and discusses the performance in terms of signal quality and phase demodulation. Finally, Section 5 concludes the paper.

2. Principle of Operation

2.1. I/Q Demodulation

Figure 1 illustrates the I/Q demodulation scheme using a 90° optical hybrid. The two input ports of the optical hybrid are fed with the Rayleigh backscattered signal light carrying the vibration information and the local oscillator light from the laser. In the experiment, the local oscillator (LO) and the signal light are derived by splitting the same laser using a 95:5 fiber coupler; the signal light is frequency-shifted by 200 MHz using an acousto-optic modulator (AOM) and returns in the form of Rayleigh backscattering. The four pairs of output ports (I+/I− and Q+/Q−) are converted into electrical signals by two balanced photodetectors, filtered by bandpass filters, and sampled by the data acquisition card (DAQ). The overall experimental configuration and the optoelectronic signal chain are summarized in Figure 2. The phase information is obtained by taking the arctangent of the I/Q components, and the phase-unwrapping algorithm is performed offline to eliminate phase jumps. Here, I and Q denote the digitized in-phase and quadrature amplitudes. The complex field is reconstructed as $E(z,t)=I(z,t)+jQ(z,t)$. The instantaneous phase is computed as

$$\varphi (z,t)=\mathrm{atan}2(Q(z,t),I(z,t))-{\varphi }_d$$

(1)

where ϕ_d denotes a constant initial phase offset between the signal and the LO [12].

Figure 1. Block diagram of I/Q demodulation based on 90° hybrid.

Figure 1. Block diagram of I/Q demodulation based on 90° hybrid.

Figure 2. Experimental setup. OC, optical coupler; Cir, circulator; SMF, single mode fiber.

Figure 2. Experimental setup. OC, optical coupler; Cir, circulator; SMF, single mode fiber.

By subtracting the phases of the vibrating and non-vibrating regions, the phase difference along the fiber can be calculated as

$$\Delta \varphi (z_1,z_2,t)=\varphi (z_1,t)-\varphi (z_2,t)$$

(2)

In Φ-OTDR, an externally applied vibration can introduce an almost uniform phase variation along the sensing link because it effectively imposes a global phase modulation on the probe pulses. This response is commonly referred to as a common-phase change in Rayleigh backscattering. Because every Rayleigh backscattered signal carries this common-phase term, the phase response cannot be spatially localized in the same way as in conventional amplitude-based localization; simple differencing does not remove the common-mode contribution. An appropriate differential demodulation scheme can suppress the common-phase term and mitigate its impact.

To suppress the common-phase contribution and enable spatial localization, a spatial phase differencing with a gauge length of N is then performed along the fiber [7,22],

$$\Delta {\varphi }_N(z,t)=\varphi (z+N,t)-\varphi (z,t)=\kappa {\displaystyle {\int }_z^{z+N}}\epsilon (\xi ,t)\mathrm{d}\xi +\Delta {\eta }_N(z,t)$$

(3)

where ε(ξ, t) denotes the spatial distribution of axial strain (or strain rate); $\kappa$ is a proportionality constant related to the refractive index, elasto-optic coefficient, and wavelength; and ∆η(z, t) denotes noise.

Equation (3) shows that the output of the spatial differencing depends only on the strain within the interval [z, z + N], while the common-phase term outside this interval is effectively eliminated.

Suppose that the disturbance is confined to the interval [z₀, z₀ + L], and that its spatial distribution along the distance coordinate can be approximated by the indicator function $g(\xi )={\chi }_{[z_0,z_0+L]}(\xi )$, while its temporal amplitude is described by s(t). This separable form is a rank-1 approximation of the deformation field; assuming that the spatial profile of the disturbance remains approximately constant over time and that the time dependence is the same for all points within the disturbed region, then

$$\epsilon (\xi ,t)=s(t)g(\xi )$$

(4)

$$\Delta {\varphi }_N(z,t)\propto {\displaystyle {\int }_z^{z+N}\epsilon }(\xi ,t)d\xi =s(t){\displaystyle {\int }_z^{z+N}g}(\xi )d\xi =s(t){\displaystyle {\int }_z^{z+N}{\chi }_{[z_0,z_0+L]}}(\xi )d\xi$$

(5)

This approximation has been verified mainly for localized low-frequency disturbances. For extended or traveling-wave cases, the spatial profile may vary over time, and the applicability of this approximation requires further investigation. Therefore, under the above assumption, to correctly compute the phase difference and accurately characterize the local disturbance, the chosen gauge length of the phase-difference sampling, i.e., the spatial spacing N, must be larger than the length of the disturbed region L, that is N ≥ L.

$${\displaystyle {\int }_z^{z+N}{\chi }_{[z_0,z_0+L]}}(\xi )d\xi =|[z,z+N]\cap [z_0,z_0+L]|={\mathcal{l}}_{\mathrm{ov}}(z;N,L)$$

(6)

$$\Delta {\varphi }_N(z,t)=\kappa s(t){\mathcal{l}}_{\mathrm{ov}}(z;N,L)$$

(7)

The above expression indicates that the differential phase is determined by the overlap length between the differencing window and the disturbed interval. When N ≥ L, there exists a window position z ∈ [z₀ − (N − L), z₀], such that the overlap length satisfies ℓ_ov(z; N, L) = L, which enables an undistorted recovery of both the spatial extent of the event and its phase amplitude.

2.2. Undersampling

An acousto-optic modulator (AOM) is commonly used to modulate continuous-wave light into pulses and introduce a frequency shift of several hundreds of MHz. In a heterodyne system, the frequency shift introduced by the AOM will result in a frequency difference between the signal light and the local oscillator (f₀ = Δf), which requires a high sampling rate to capture the full beat signal. By applying undersampling, the sampling rate could be reduced without losing any information, thereby decreasing both the data volume and computational load. To achieve alias-free sampling, the sampling frequency f_S must satisfy the constraints defined by the undersampling theorem, specifically [23]:

$${\displaystyle \frac{2f_U}{n}}\le f_s\le {\displaystyle \frac{2f_L}{n-1}}$$

(8)

where n is an integer constrained by 1 ≤ n ≤ f_U/2f_B; f_U and f_L are the upper and lower cutoff frequencies of the bandpass signal, respectively, and 2f_B is the bandwidth of the bandpass signal.

To obtain a valid bandpass signal, a bandpass filter (BPF) is placed after the balanced photodetector (BPD) to suppress out-of-band noise in the beat signal. After the BPF, the heterodyne beat is confined to a band centered at f₀ with an effective occupied bandwidth B. To avoid spectral overlap among aliased replicas during undersampling, the sampling frequency f_S must be jointly designed with the BPF bandwidth B [19]. According to Equation (8), alias-free sampling is guaranteed when f_S satisfies:

$${\displaystyle \frac{2f_0+B}{n}}\le f_s\le {\displaystyle \frac{2f_0-B}{n-1}}$$

(9)

where n is an integer satisfying 1 ≤ n ≤ (2f₀ + B)/2B.

For an optical pulse with a pulsewidth W, the full width at half maximum (FWHM) is approximately 0.8859/W [19]. In practice, the BPF bandwidth B is usually chosen to be larger than the FWHM of the beat-signal spectrum in order to avoid waveform distortion while still providing sufficient out-of-band noise suppression.

Under the alias-free undersampling condition, the sampled beat signal can be modeled as

$$I_s(t)=A(t)\cos (2\pi f_{c}t+\varphi (t))$$

(10)

where A(t) and ϕ(t) denote the amplitude and phase of the Rayleigh backscattered optical field, respectively. The effective carrier frequency f_c after undersampling is:

$$f_c=\left\{\begin{array}{ll}{f}_0-{\displaystyle \frac{n-1}{2}}{f}_s,\hfill & n=1,3,5,\dots \hfill \\ {\displaystyle \frac{n}{2}}{f}_s-f_0,\hfill & n=2,4,6,\dots \hfill \end{array}\right.,\hspace{1em}\hspace{1em}{f}_c\le {\displaystyle \frac{f_s}{2}}$$

(11)

3. Experimental Setup

The experimental setup for coherent Φ-OTDR is shown in Figure 2. A narrow-linewidth laser (HYLM-E-1550.12-2k-10-PA, UnistarCom, Tianjin, China; 1550.124 nm, ~1.4 kHz linewidth), featuring a polarization-maintaining (PM) output fiber, serves as the light source for the system. The laser output was split into two beams by a 95:5 fiber optical coupler, with 95% of the light directed to an acousto-optic modulator (AOM) (SCTF200-1550-1FH, CETC, Chongqing, China; 200 MHz shift, ER > 50 dB). The AOM modulates the light into optical pulses with a repetition frequency of 5 kHz and a pulse width of 100 ns. An arbitrary waveform generator (AWG) provides the RF drive for the AOM, and the same signal is also used as the trigger for the data acquisition card (DAQ). The optical pulse is amplified by an erbium-doped fiber amplifier (EDFA) (AEDFA-NS-200-20-25-M-FA, Amonics, Beijing, China; Psat ≥ +23 dBm, NF ≤ 6 dB), then launched into port 1 of a circulator and coupled into a 1.07 km sensing fiber via port 2. The Rayleigh backscattered light returns through port 2 and exits via port 3, which is connected to the signal input of a 90° optical hybrid (90°-COH28, Kylia, Paris, France). Meanwhile, the remaining 5% of the original laser light is used as the local oscillator (LO) and is fed into the LO port of the 90° optical hybrid. The interference between the LO and backscattered signal generates a 200 MHz beat signal, which is demodulated into in-phase (I) and quadrature (Q) components by the 90° optical hybrid. Balanced photodetectors (BPDs) (BPD465C, Guangyi, Guilin, China; 400 MHz bandwidth) convert these optical signals into electrical signals, which are then filtered by bandpass filters (BPFs).

The pulse repetition rate and pulse width used in this system are 5 kHz and 100 ns, respectively, which means the FWHM of the beat-signal spectrum is approximately 9 MHz. We therefore select a BPF with a center frequency of 200 MHz, a bandwidth (FWHM) of 18 MHz, and a stopband rejection of 50 dB. The Kylia 90°-COH28 optical hybrid provides eight output ports with dual polarization: ports 1–4 correspond to the X-polarization output and ports 5–8 correspond to the Y-polarization output; for simplicity, only the X-polarization output ports are used in this setup. Accordingly, the BPFs are installed only after the two BPD channels that receive Ix and Qx. The data are acquired by the DAQ (QT1144VG4 series, Kunchi, Beijing, China; 16-bit, up to 250 MSa/s) at a rate of 110 MSa/s and sent to the computer for data processing. According to Equations (8)–(11), with f₀ = 200 MHz and f_s = 110 MSa/s, we choose n = 4, which folds the 200 MHz beat to an effective carrier of 20 MHz after sampling.

In the experiment, a cylindrical piezoelectric ceramic (PZT) is placed at the end of the 1.07 km fiber as a vibration test point, with 30 m of bare fiber wound around the PZT. Another output port of the arbitrary waveform generator (AWG) is used to drive the PZT, generating the vibration signal.

4. Results and Analysis

First, signals were collected over several pulse periods and the distribution of the I/Q scattering-light signal amplitude along the fiber was plotted, as shown in Figure 3. These scattering curves show excellent repeatability and essentially overlap with one another.

To confirm correct phase recovery in phase-demodulated Φ-OTDR, we deliberately chose a single-tone sinusoidal excitation as a standard validation signal. Under the present acquisition and processing settings, a stable sinusoid in the time domain together with a dominant spectral component at the known drive frequency provides a direct validation of correct phase demodulation. In the experiment, a sinusoidal electrical signal with an amplitude of 5 V and a frequency of 200 Hz was applied to the PZT, producing a deformation of 0.25 με.

Before phase extraction, the raw I and Q waveforms are digitally calibrated. In our setup, the main nonidealities include residual DC offsets, gain imbalance between the two channels, and quadrature error caused by imperfect 90° hybrid responses and unequal cable delays. We therefore apply a three-step calibration: (i) DC-offset removal for each channel; (ii) gain normalization by matching the RMS amplitudes of I and Q; and (iii) quadrature correction via a linear decorrelation (Gram–Schmidt type) procedure to enforce statistical orthogonality. The phase is then calculated using atan2(Q, I) on the calibrated I/Q pair. As shown in Figure 4, the I-Q constellation before calibration appears as a tilted ellipse with an offset from the origin, whereas after calibration, it becomes a near-centered, nearly circular distribution. Consistently, the I–Q correlation coefficient decreases from −0.15012 to −2.1851 × 10⁻¹⁴.

Φ-OTDR scattering traces were continuously collected for phase demodulation. Figure 5a shows the spatio-temporal waterfall plot of the demodulated phase difference, where the horizontal axis represents fiber length and the vertical axis represents time. The sinusoidal vibration trace generated by the PZT at the end of the 1.07 km fiber can be clearly observed. The time-domain demodulated experimental results are shown in Figure 5b. The red solid curve denotes the demodulated phase difference at the vibration point in the time domain, exhibiting a clear sinusoidal variation over time with an amplitude of approximately 16 rad; the blue solid curve denotes a reference sinusoid at the excitation frequency. The demodulated waveform matches a reference sinusoid at the excitation frequency well, with a Pearson correlation coefficient of r = 0.999 and an RMSE of 0.256 rad over the analyzed time window. Figure 5c shows the frequency-domain demodulated phase signal, with a clear peak at 200 Hz. The signal-to-noise ratio (SNR) is calculated using the formula 10 log₁₀ (P_signal/P_noise), where P_signal is the signal power and P_noise is the background noise power. With this definition, our undersampling heterodyne system achieves an SNR of 63.54 dB with a background noise floor of −52.27 dB·rad²/Hz over a 1.07 km sensing fiber at 10 m spatial resolution. For context, compared with a conventional coherent heterodyne Φ-OTDR that typically digitizes the beat signal at a high sampling rate (e.g., 500 MSa/s), our scheme operates at 110 MSa/s, corresponding to a 78% reduction in DAQ sampling rate. In contrast to a typical homodyne Φ-OTDR scheme [12], which often introduces an additional AOM in the local oscillator (LO) branch to ensure frequency matching between the signal and the LO, our undersampling heterodyne Φ-OTDR eliminates the need for an extra AOM in the LO branch, thereby simplifying the optical layout and reducing system complexity while maintaining a 10 m spatial resolution and a high SNR.

To evaluate the linear response of the system, the PZT driving frequency was kept fixed at 200 Hz and the amplitude of the sinusoidal voltage applied to the PZT was gradually increased. Figure 5d shows the relationship between the phase amplitude and the driving voltage, where the blue circles represent the measured sinusoidal phase amplitudes and the blue solid line represents their linear fit. The phase amplitude increases approximately linearly with the driving voltage, and the coefficient of determination is R² = 0.9998, indicating an excellent linear response within this voltage range.

When the vibration source (PZT) is placed at the input end of the sensing fiber and the demodulated phase is differenced trace by trace along the fiber, the resulting spatio-temporal waterfall plot shows an apparent response across the entire fiber. This behavior is the common-phase change discussed in Section 2 Principle of Operation Section and is illustrated in Figure 6.

In laboratory experiments, the position of the PZT and the length of fiber wound around it are known a priori; thus, the differential spacing can be selected based on Equations (4)–(7) to satisfy N ≥ L according to the physical length of the disturbed region. In practical field applications, however, neither the location of external disturbances nor their effective extent along the fiber is generally known, and it is difficult to properly configure the gauge length based solely on prior geometrical information. To address this issue, we first process the I/Q signals using a moving-average–moving-difference (MA–MD) scheme to obtain an amplitude profile [24], as shown in Figure 7a. This profile is then used to automatically locate vibration events along the fiber and to estimate the effective length L of the disturbed region. Based on this estimate, the differential spacing is adaptively selected to satisfy N ≥ L, so that the phase-differencing window fully covers the actual vibration region. In this way, common-phase perturbations are suppressed while preserving an undistorted reconstruction of the local phase response, as shown in Figure 7b.

After the vibration event is located along the fiber using the MA–MD amplitude profile, both the center position of the event and its effective spatial extent can be obtained, so that a full phase demodulation over the entire fiber is no longer required. Building on this, we propose a local-region phase demodulation strategy: once the amplitude-based localization is completed, the phase of the I/Q data is computed only over a limited fiber segment in the vicinity of the event. In this way, the complete phase information of the target disturbance is preserved, while redundant computations in non-vibrating regions are significantly reduced.

To quantitatively evaluate the computational efficiency of the proposed local-region demodulation, we implemented both a full-fiber demodulation scheme and a local-region demodulation scheme in a MATLAB R2024b (MathWorks, Natick, MA, USA) environment. The acquired I/Q data form a matrix of size 1160 × 1120, and the full-fiber demodulation directly operates on the entire matrix to obtain a phase matrix Φ ∈ ℝ^1160×1120. In contrast, the local-region demodulation performs the same operations only on a 32 × 1120 submatrix corresponding to the interval [z_start, z_end] identified by the amplitude-profile localization (which spans approximately 30 m of fiber), while recording the runtime and memory usage of the phase data for both schemes. Experimental results show that, for the data size considered in this work, the runtime of full-fiber demodulation is about 12 ms with a memory usage of approximately 9.91 MB, whereas the local-region demodulation requires only 2 ms and about 0.27 MB of memory. Thus, the computational time and memory consumption are reduced to roughly 16.67% and 2.72% of those of the original full-fiber scheme, respectively. These results demonstrate that the amplitude-profile-guided local phase demodulation substantially reduces computational time and memory usage compared with full-fiber demodulation, while preserving a complete reconstruction of the vibration event.

5. Conclusions

In summary, the experimental results confirm that, when a 200 Hz sinusoidal electrical signal is applied to the PZT, the demodulated phase difference at the vibration point exhibits a sinusoidal variation with the same frequency, demonstrating that the Φ-OTDR system based on a 90° optical hybrid can accurately recover the dynamic phase of the vibration along the sensing fiber. By introducing undersampling into the heterodyne coherent detection, the 200 MHz beat signal is correctly reconstructed with a sampling rate of only 110 MSa/s, which effectively alleviates the requirement for ultra-high-speed data acquisition and reduces both data volume and computational load. Furthermore, a moving-average–moving-difference amplitude analysis is employed to locate the vibration event and estimate its effective length, enabling an adaptive selection of the differential gauge length that satisfies N ≥ L and suppresses common-phase changes. On this basis, phase demodulation is restricted to a short fiber segment around the event instead of the entire sensing range, leading to a significant reduction in computational burden while preserving the quantitative phase information of the disturbance. Compared with related coherent Φ-OTDR implementations, our undersampling heterodyne scheme reduces the DAQ sampling-rate requirement and avoids an extra AOM in the LO branch, thereby simplifying the optical layout while maintaining 10 m spatial resolution and a high SNR. These results indicate that the proposed scheme not only maintains high sensitivity and spatial resolution with reduced sampling hardware requirements but also provides a practical route towards more data-efficient and potentially real-time phase-demodulated DAS implementations.