Global large-scale infrastructure construction has advanced rapidly over the past few decades. There has been a dramatic increase in the total mileage of high-speed railways, the number of bridges spanning rivers, and the total length of power grid cables. As these infrastructures grow, the need for their status monitoring has become increasingly important and urgent. In this review, distributed fiber optic sensing technology, known for its long sensing distance and high density of sensing points, has seen rapid development and has demonstrated great potential for monitoring large-scale infrastructures^[1–9]. Among the various distributed fiber optic sensors, phase optical time domain reflectometers have garnered considerable attention from scientists and engineers worldwide in recent years, thanks to their high sensitivity and capability for dynamic measurements^[10–17].

In a phase optical time domain reflectometry (Φ-OTDR) system, when an optical pulse is injected into the fiber, it induces Rayleigh backscattering light, which is detected in the time domain. Because the laser source emits highly coherent light with a narrow linewidth, the photodetector captures a distinct coherent Rayleigh backscattering signal characterized by varying intensities over time. When the laser’s frequency remains constant, the temporal features of the coherent Rayleigh curve do not change with the pulse sequence. However, if an external perturbation affects the fiber, the photoelastic effect and elastic deformation cause an optical path difference in the Φ-OTDR, which in turn alters the intensity of the Rayleigh backscattering signal at the point of perturbation. This change affords a precise localization of the event based on the time-distance relationship in the Φ-OTDR^[18–25]. The Φ-OTDR systems in earlier studies were designed based on this principle. However, these early systems were mainly able to detect the occurrence of events, without offering detailed quantitative insights into them.

As research progressed, researchers discovered that changes in the optical path difference within the Φ-OTDR system lead to variations in the intensity of the coherent Rayleigh curve. Conversely, this change allows for the demodulation of the optical path difference using quantitative information from the intensity signal of the Φ-OTDR. Since the change in optical path difference is directly proportional to the phase change, the phase change can be used to quantitatively characterize external perturbation events^[26–30]. This technology, known as the quantitative measurement of the Φ-OTDR, is also referred to as distributed acoustic sensing (DAS)^[31–33]. According to the detection method, distributed fiber optic acoustic sensors are mainly divided into direct detection-based Φ-OTDR and coherent Φ-OTDR (coherent detection, including heterodyne detection and homodyne detection). Compared to direct detection-based Φ-OTDR, the phase change in coherent Φ-OTDR exhibits a linear spatial distribution that is advantageous for subsequent signal processing^[34–43].

Moreover, researchers have conducted in-depth studies on the relevant theories of noise. The literature^[44–51] elaborates on the generation, types, spatial distribution characteristics, frequency-domain characteristics, related statistical characteristics of noise, and other aspects. On the one hand, these studies indicate that, compared to direct detection, coherent detection has an inhibitory effect on common-mode noise, shot noise, low-frequency noise, spatially variable phase noise, etc. This enables coherent detection to have near-quantum limit detection capability^[52] and also makes it a more suitable choice for a phase optical time domain reflectometer. On the other hand, the phase signal of the Φ-OTDR is extracted from the intensity information, and the mechanism of action of the noise on the signal is a complex process, which these studies did not elaborate on in detail.

Therefore, it is necessary and meaningful to review the noise processing in the coherent Φ-OTDR separately. Accordingly, the remainder of this review is structured as follows: first, in Sec. 2.1, the impact of noise on the signal is explained in combination with the coherent detection and the typical demodulation process. Then, in Sec. 2.2, nine pathways to suppress the effect of noise are given based on the concept of signal-to-noise ratio (SNR). Next, each pathway is explained in Sec. 3. Finally, in Sec. 4, the suppression of the noise effect in coherent Φ-OTDR is summarized and prospected.

This section outlines the general demodulation process for quantitative signals in coherent Φ-OTDR. It then delves into the noise present in the system during the demodulation process. Finally, by analyzing the relationship between the noise and the signal, possible approaches to suppress the influence of noise are presented.

Figure 1 illustrates a typical coherent Φ-OTDR. A laser device (LD) emits highly coherent light with a narrow linewidth. This light is split into two paths by a 90:10 coupler: the upper path signal light, which carries 90% of the energy, and the lower path reference light, which carries 10% of the energy. The upper path signal light is frequency-shifted by several tens of megahertz using an acousto-optic modulator (AOM) to produce the probe pulse light. An erbium-doped fiber amplifier (EDFA) amplifies the probe pulse light, which is then injected into the fiber through a circulator. Some of the Rayleigh scattering light generated in the fiber returns to the injection port and is further mixed with the reference light at a 50:50 coupler. The resulting mixed signal is then output and detected by a balanced photodetector (BPD), inducing an intermediate frequency signal. This electrical signal is captured by an oscilloscope (OSC) and displayed in the form of a coherent Rayleigh curve. The curve in coherent Φ-OTDR is an amplitude-based signal, also known as a coherent Rayleigh scattering signal. It undergoes a series of processing steps, including in-phase/quadrature (I/Q) demodulation, to extract the phase information. The specific processing steps are illustrated in Fig. 2^[29,53,54].

In Fig. 2, I_s(t) represents the coherent Rayleigh scattering signal. In the practical system, this signal inherently contains laser phase noise. Moreover, the laser’s frequency fluctuates over time. Unfortunately, the Φ-OTDR system emits a pulse sequence at specific time intervals, and these fluctuations in the laser’s frequency significantly impact the accuracy of the phase measurement. Even with a highly coherent, narrow linewidth light source, laser frequency drift can still affect the precision of phase measurement. Additionally, since the laser source is highly coherent, the coherent Rayleigh scattering signal exhibits fluctuating characteristics over time or along the fiber, which are particularly pronounced due to the modulation of the intermediate frequency carrier. Furthermore, the balanced photodetector and subsequent processing circuits in the Φ-OTDR are inevitably subject to electronic noise such as thermal noise, shot noise, and 1/f noise^[44]. These noises are ultimately, whether in the form of phase, frequency, amplitude, or intensity, incorporated into the noisy coherent Rayleigh scattering signal.

I/Q demodulation is the most commonly employed method in coherent Φ-OTDR to convert amplitude signals into phase signals. In Fig. 2, f represents the frequency shift of the acousto-optic modulator. The coherent Rayleigh scattering signal is multiplied by the sine and cosine of the frequency shift and then passed through respective low-pass filters to generate I/Q components without the frequency shift part. The phase value, also known as the initial phase, is obtained by dividing these two components and applying an arctangent function, which accounts for the correct quadrant. However, the phase value is still wrapped within the range of [−π,π], necessitating a phase unwrapping algorithm to reveal the continuous phase variation.

Due to factors such as the clock jitter of the drive signal for the AOM, the initial phase in the direction of the pulse time at a certain position on the fiber may not accurately reflect external perturbation events. To eliminate this effect, a reference point is typically chosen with mainly two methods being employed. The first method is to choose a fixed reference point and then subtract the initial phase at the reference point from all positions after the reference point to obtain the differential phase. Then, a reference phase is selected to eliminate the inconsistency of the initial phase along the fiber, resulting in a phase change that is consistent with the external perturbation information. When the laser frequency drift is small, the phase change in the undisturbed area shows a linear distribution along the fiber. Although the effects of polarization fading and interference fading do not need to be considered during I/Q demodulation, these effects must be eliminated when solving for the phase change or phase signal. Polarization fading directly causes the phase signal to be demodulation-resistant, and interference fading also affects the SNR of the demodulated phase signal. For phase signals, the fading positions are consistent with those in the amplitude form. Therefore, when choosing a reference point, it is crucial to avoid choosing a position at a fading point, which can be confirmed by the linear distribution characteristic of the phase change.

The other method is to choose non-fixed reference points, dividing the fiber into several equal-length intervals, and then differencing the initial phases at the endpoints of each interval to obtain the differential phase. All the different positions, except the last endpoint, serve as reference points. The advantage of differencing in pairs is that the method is simple and easy to implement, but the difficulty in avoiding fading points is greater, and the differential phase obtained may not accurately represent external perturbation events even after eliminating the inconsistency of initial phases along the fiber. Another scenario for choosing non-fixed reference points is that the reference point changes with the location of the perturbation event. In this case, the initial phases on both sides of the perturbation event area are differenced. Whether fixed or non-fixed, reference points are chosen for phase differencing, and the larger the distance over which the differencing occurs, the greater the influence of laser frequency drift on the differential phase value. Additionally, although I/Q demodulation can theoretically eliminate various noises from the detector and the fiber’s sensing environment, the low-pass digital filters used in I/Q demodulation always have a bandwidth, so the phase values obtained after I/Q demodulation will inevitably retain some influence from these noises.

The significance of noise research lies in the ability to separate or identify the signal from the noise. Therefore, in many engineering applications such as communication systems, the primary concern is not the noise itself but rather the SNR. The higher the SNR, the smaller the impact of noise on the system performance. Suppressing noise components or enhancing signal components, or both, can increase the SNR value, thereby minimizing the impact of noise. In the case of the phase optical time domain reflectometer, the same principle applies. However, as previously mentioned, the ultimate goal is to extract the phase signal, while coherent Φ-OTDR directly detects the amplitude signal. Consequently, the impact of noise on the phase signal should be considered not only in terms of the SNR of the phase signal but also in terms of the SNR of the amplitude signal.

On the one hand, for the phase signal, it is evident that by suppressing the phase noise or increasing the intensity of the phase signal, the SNR can be improved, thereby achieving the goal of minimizing the impact of noise. On the other hand, the SNR of the phase signal is related to the SNR of the amplitude signal. As described in Ref. [55], the SNR of the phase signal in coherent Φ-OTDR can be expressed as SNRphase(i,i′)=2σϕ2σn2[1A2(i)+1A2(i′)],(1)where i and i′ are the index numbers of different resolution cells, σϕ2 is the variance of the phase signal, and A and σn are the signal intensity and noise standard deviation corresponding to the amplitude signal, respectively. For the convenience of analysis, assuming that A(i) is k times A(i′), Eq. (1) can be written as SNRphase(i)=2k2σϕ2k2+1·A2(i)σn2∝2k2σϕ2k2+1·SNRamp(i).(2)From Eq. (2), it can be seen that the SNR of the phase signal is proportional to the SNR of the amplitude signal. It should be noted that Eq. (1) and Eq. (2) focus on the analysis of differencing based on the non-fixed reference point. For the method of differencing with a fixed reference point to solve for the phase signal, the phase value of each sampling point after the reference point is differenced with that of the fixed reference point. This process results in each sampling point owning a phase-related signal value, and the SNR of each signal value is proportional to the SNR of the corresponding amplitude signal. As the SNR of each phase-related signal value increases, so does the SNR of the final phase signal. In other words, the SNR of the final phase signal shows an increasing trend as the SNR of the amplitude signal increases. Therefore, no matter which differencing method is used to obtain the phase signal, in order for the phase signal to have a higher SNR, it is necessary to either increase the intensity of the amplitude signal itself or suppress the noise in the amplitude signal.

Figure 3 summarizes the pathways to suppress noise effects based on the analysis results of the recent literature. Since the effect of noise can be suppressed from both the noise and signal aspects, and separately for amplitude and phase forms, there are four major categories of pathways to suppress noise effects when considered together.

The first major category is to suppress the noise of the amplitude signal. However, for phase optical time domain reflectometers that measure external perturbations using phase signals, there are few specific reports on how to achieve an improved SNR of the phase signal through the suppression of amplitude signal noise. This is because when phase optical time domain reflectometers can only work with amplitude signals, there has already been much research on how to suppress the impact of noise. When using phase signals, suppressing the impact of amplitude noise is simply a prerequisite for demodulating the phase signal. Therefore, for phase optical time domain reflectometers in the form of phase, there is often no need to specifically study the suppression of amplitude signal noise.

The second major category involves suppressing the noise of the phase signal. Phase noise can be categorized into system noise and random noise. System noise primarily originates from laser frequency drift, which introduces a systematic error into the phase signal. The fundamental approach to mitigating the impact of laser frequency drift is to eliminate the drift itself. However, since the stability of commercial laser frequencies may not fully satisfy the demands of precise measurements, the prevalent method to suppress the effects of laser frequency drift is to employ phase compensation. The electronic noise of the detector becomes mixed with the phase signal through various demodulation methods after the conversion from amplitude to phase. Nevertheless, the positions of the noise before and after the conversion remain largely unchanged, so the noise in the phase signal can still be regarded as randomly distributed.

In coherent Φ-OTDR, if systems have a fixed refractive index distribution and a stable laser frequency (or extremely low laser frequency drift), the positions of the interference fading and polarization fading are indeed deterministic. At this point, in the direction of fiber length, the polarization fading causes the failure of phase demodulation, making the phase values generated by the polarization fading significantly different from the random noise at other fiber sampling positions. This allows us to treat polarization fading specially—either finding alternatives for the phase values at the polarization fading locations or directly discarding the phase values at the polarization fading locations. However, since different fibers have different refractive index distributions and even the same fiber can be treated as approximately random for laser frequency drift and environmental change, the positions of interference fading and polarization fading in the amplitude signal can be regarded as approximately random. Regardless of whether it is the amplitude signal or the phase signal, the positions of fading do not alter. Thus, for the phase signal, the positions of fading can be considered random, and the phase noise induced by fading can also be treated as random noise.

The third major category is to enhance the intensity of the phase signal. Increasing the sensing length of the fiber acted on by the perturbation signal, which means increasing the distance between the two points for differencing, can enhance the intensity of the phase signal. However, it will result in a decrease in the spatial resolution. Therefore, although this is indeed a method to increase the intensity of the phase signal, it is relatively rarely reported in the literature. Another method to increase the intensity of the phase signal is to use a sensitivity-enhanced fiber, which increases the conversion coefficient between the phase signal and the external perturbation.

The fourth category involves enhancing the intensity of the amplitude signal. In recent years, one of the most representative methods to achieve this is using weak reflection fibers to boost the intensity of the Rayleigh backscattering signal. Another method, which although does not directly enhance the intensity of the probing signal but has an equivalent effect, is to employ coding schemes to improve the SNR of the amplitude signal.

Furthermore, in recent years, methods utilizing artificial intelligence, such as deep learning, to suppress noise effects based on the data itself have also emerged, and these are listed separately as another major category. As shown in Fig. 3, these five major categories can evolve into nine specific implementation pathways.

This section will describe each of the nine pathways to suppress noise effects, as shown in Fig. 3. In describing each pathway, we first summarize the general development of that pathway and then provide a specific implementation scheme.

In the early stages of Φ-OTDR, the signal was solely in the form of amplitude. Consequently, regardless of whether the noise source originated in the phase or amplitude form, it was essential to suppress amplitude noise to achieve the final solution. Early research efforts not only focused on suppressing noise at the device and equipment level but also employed techniques such as bandpass filtering, wavelet transformation, and empirical mode decomposition to mitigate the impact of amplitude noise. As the research focus of Φ-OTDR evolved from amplitude to phase signals, the suppression of amplitude noise became crucial for the successful extraction of the phase signal since the phase signal is demodulated from the amplitude signal. On the one hand, researchers considered the necessity of amplitude noise suppression for phase signal extraction to be self-evident, which could have led to a scarcity of related reports. On the other hand, extensive research has been conducted on amplitude signal noise suppression in the early stages^[56–60]. However, it is important to note that while many studies on noise suppression of the amplitude signal are beneficial for phase signal extraction^[61], not all methods aimed at amplitude noise suppression for the amplitude signal can be directly applied to the study of amplitude noise suppression for the corresponding phase signal. For instance, the method of spectral subtraction may yield good results when applied to amplitude signals for noise reduction. However, the suitability of spectral subtraction for reducing noise in amplitude signals and then extracting the corresponding phase signal must be carefully evaluated, as the algorithm itself may introduce errors during signal reconstruction^[62], potentially distorting the phase signal.

In summary, this review does not offer a detailed explanation of the suppression of amplitude noise, but rather introduces the recent research conducted by the research group at the Electronic Science and Technology University on the relationship between quantization bits and phase noise^[63]. First, the relationship between the variance of quantization noise (σ2) and the number of quantization bits (b) is as follows: σ2=112·(Vp2b)2,(3)where Vp is the full-scale voltage. It can be observed that the higher the number of quantization bits, the smaller the quantization noise, and this quantization noise is superimposed on the amplitude signal. That is to say, the higher the quantization bits, the smaller the variance of the amplitude noise. Furthermore, the difference in noise power spectral density (PSD) between the pre-quantization and post-quantization (ΔNoise_floor) for the phase noise is related to the quantization noise variance σ2 as follows: ΔNoise_floor=10log(1+σ2σn2).(4)

It can be seen that for the phase noise, the smaller the quantization noise variance, the lower the noise floor. Combining the relationship between Eq. (3) and Eq. (4), it can be concluded that the higher the number of quantization bits, the lower the noise floor for phase noise. This group conducted experimental verification in a similar experiment in Fig. 1, with the difference that the modulated pulse light was chirped. However, the conclusions from this experiment can be applied to other forms of pulses as well. The experiment yielded the comparison of the noise floors for phase noise with a quantization bit of 1 and 12.

Figure 4(a) shows the comparison of demodulated phase signals in the time domain for both 12-bit and 1-bit signals. Additionally, Fig. 4(b) displays the comparison of the PSD between 12-bit and 1-bit signals. It is evident that the noise floor for the phase noise with 12-bit quantization is 11.8 dB lower than that with 1-bit quantization. It proves that the higher the number of quantization bits, the lower the noise floor for the phase noise.

The phase noise of the laser affects the accuracy of the phase signal that is ultimately resolved. However, for coherent Φ-OTDR with the function of quantitative measurement, another important parameter affecting the measurement result is the laser frequency drift. This parameter introduces an additional bias to the phase signal. This causes the phase signal to distort, and there is no direct method to subtract the bias. Furthermore, significant laser frequency drift can prevent the accurate extraction and identification of the phase signal. For example, for low-frequency signals, the pulse interval is often very large, which makes the laser frequency drift value very large. Then the final phase signal cannot be correctly extracted.

Addressing the impact of laser frequency drift on the phase signal, especially the nonlinear effects it causes, currently lacks mature and stable commercial solutions. However, researchers have sequentially attempted to compensate for the distortions of the phase signal using various methods, such as interferometer measurement phase compensation^[64], twice differential phase compensation^[65], phase compensation based on the median-fitting algorithm^[66], and empirical mode decomposition component compensation^[67]. Although these methods differ in approach, their core idea is consistent: they aim to obtain the bias caused by laser frequency drift either through actual measurement or algorithmic decomposition, and then subtract this bias from the distorted phase signal to obtain the compensated phase signal. This review only demonstrates one method from our research group^[65].

Figure 5 illustrates the principle of the twice-differential phase compensation. In this figure, a vibration event (simulated by PZT) is introduced between points A and B, and thus the area between A and B is referred to as the vibration area. The length D of CD is the same as that of AB. However, there is no perturbation event between points C and D, and hence the area between C and D is called the non-vibration area. If laser frequency drift is not considered, and no phase change is caused by the vibration event, the equivalent phase caused by the Rayleigh backscattering light induced by the laser pulse with frequency f is expressed as θR(f(t),z). The phase caused by the external vibration event is φ, and the phase caused by the laser frequency drift at distance D is 4Dπnf/c, where c is the velocity of light in a vacuum. Consequently, the time-dependent phase changes for the AB and CD regions can be, respectively, expressed as ΔΦAB(t)=4πnDABf(t)c+φ(t)+θR[f(t),zB]−θR[f(t),zA],(5)ΔΦCD(t)=4πnDCDf(t)c+θR[f(t),zD]−θR[f(t),zC].(6)

Obviously, by subtracting the two equations mentioned above, we eliminate the phase bias caused by the laser frequency drift. Here, it should be noted that the importance of selecting the reference point was discussed in Sec. 2.1. Although the phase differential method for ΔΦAB or ΔΦCD is similar to the relevant process related to the non-fixed reference points described in Fig. 2, for the convenience of demonstration, it is directly assumed here that the difference points on both sides are chosen at non-fading points. In the experiment, the reconstruction of a sinusoidal perturbation signal with a minimum frequency of 0.1 Hz is demonstrated, as depicted in Fig. 6.

In Fig. 6, due to the influence of the laser frequency drift, the sinusoidal curve from ΔΦAB drifts from above zero to below −20rad, and the curve is significantly distorted. After phase compensation using the twice differential method (differential operation between ΔΦAB and ΔΦCD), the sinusoidal curve changes around zero, which is very close to the actual value. This indicates that the method of twice-differential phase compensation effectively corrects the phase distortion caused by the laser frequency drift.

In coherent Φ-OTDR, due to the highly coherent laser source, the coherent Rayleigh scattering signal generated by the detector will inevitably have coherent fading. Furthermore, due to factors such as thermal stress and mechanical stress in the fiber, irregular birefringence will occur, leading to undetermined polarization fading of the coherent Rayleigh scattering signal. Fading, especially polarization fading, can cause signal distortion and even make the signal fail to be demodulated. For a long time, it has been commonly believed that a simple polarization diversity scheme is needed to eliminate the impact of polarization fading^[68,69]. However, in fact, changes in the polarization state of light are essentially changes in the phase of light. Thus, directly changing the phase state can also change the polarization state. When the frequency of light changes, the accumulated phase over time will naturally change, which can also lead to changes in the polarization state. Additionally, when the spatial propagation path of the light changes, the distribution of the phase factor over time will also change due to the different refractive index distributions along different spatial paths. Therefore, in addition to the polarization diversity scheme, researchers have also studied schemes such as phase complementarity^[70,71], frequency division multiplexing^[72,73], and space division multiplexing^[74]. Although there are subtle differences in the technical solutions, it is essentially consistent. So only our research group’s frequency division and multiplexing scheme is presented here to illustrate the principle of such methods^[73], which is shown in Fig. 7.

In Fig. 7, in addition to using three AOMs to generate a multi-frequency single pulse probing signal light, the rest of the setup is essentially the same as in Fig. 1. Therefore, except for the data processing part, the principle of this setup will not be further described. When the collected data enters the computer, it first separates out the frequency components and then individually demodulates the phase, and its demodulation results and important processes are indicated in Fig. 8.

From Fig. 8, it can be observed that the demodulation of the phase signal fails in areas where the amplitude of the intensity signal is very small. Therefore, by optimizing the amplitude of the strength signals of each frequency component, the occurrence of fading is predicted based on the cross-prediction of the strength signals, and the optimal phase signal is selected. This method reduces the demodulation distortion rate introduced by fading to 1.15%.

Although the occurrence of fading in the direction of the fiber length is relatively random in the distribution of coherent Rayleigh curves and phase curves, from a physical mechanism perspective, fading—especially polarization-induced fading—is a systematic noise that is obviously different from the non-fading random noise in the form of phase. Therefore, when suppressing these random noises to obtain an accurate phase signal, it is best to first eliminate the influence of polarization fading. In 2019, our research group pointed out that in the case of a small laser frequency drift, the phase change in the undisturbed area of the sensing fiber in coherent Φ-OTDR presents a linear distribution feature along the fiber^[75]. In 2021, we provided a rigorous theoretical proof process when the laser frequency drift is less than 50 kHz^[54]. Based on this linear relationship, the phase at the position of polarization fading can be pre-eliminated, and the method of least squares fitting was used to eliminate random noise in the direction of fiber length. Then, in 2024, in addition to emphasizing the use of a low-pass filter to filter out amplitude noise during I/Q demodulation, the wavelet transform was used to reduce noise in the direction of the pulse sequence itself, and then the noise in this direction was suppressed using data fitting of least squares^[76]. The main part of the experimental setup is consistent with Fig. 1 and will not be repeated here.

After I/Q demodulation, the phase changes of coherent Φ-OTDR are shown in Figs. 9(a) and 9(b). The outlier parts indicate the locations of the fading. By removing the fading parts, the phase change values shown in Figs. 9(c) and 9(d) are obtained. The noise in these phase change values is primarily random noise without fading. Figure 9(e) represents a trace at an arbitrary sampling position from Figs. 9(c) and 9(d), where the sinusoidal shape corresponds to the external perturbation signal. Wavelet denoising is performed on such a trace of each sampling position. It is worth noting that in Ref. [76], the choice of decomposition level in the wavelet denoising process exploits the spatial repetition of the sinusoidal traces. The phase changes after wavelet denoising are highly similar to those in Figs. 9(c) and 9(d), so they are not plotted again. Since it has been proven that the trace exhibits a linear characteristic along the fiber, a linear equation with parameters is used for data fitting. Each pulse moment’s trace undergoes data fitting. The data fitting process is also a denoising process. Therefore, the method in Ref. [76] effectively suppresses non-fading random noise in both the fiber length and the pulse sequence directions. Then, the fitted phase value at a specific position is calculated as the phase signal. In the literature, the final calculated result of an experimental measurement is fitted to a parameterized sinusoidal function, yielding a Chi-square coefficient of 0.99996 and a root mean square error of only 0.17832 rad.

In the method of extracting phase signals by differencing in pairs based on the non-fixed reference points, the signal only exists in the direction of the pulse sequence. In this direction, there is environmental noise from the sensing coupling path and electronic noise from the detector, both of which are random noises. Additionally, when the laser frequency drift is very small, different pulse moments at a specific fiber sampling position will either be affected by the fading noise or remain free from it. However, commercial lasers often have difficulty ensuring that the laser frequency drift is very small during long-term operation. Even when a laser with high nominal frequency stability is used in coherent Φ-OTDR, if the duration of the signal being examined is long, the laser frequency drift can become significant, and the trend of this drift often exhibits some degree of randomness. Consequently, for the phase signal in the direction of the pulse sequence, the phase signal at some pulse moments will be affected by fading, while the phase signal at others will not. Therefore, fading can also be considered as a random noise at this point.

Therefore, in qualitative measurements that involve random noise combining fading and non-fading, there have been many proposed schemes^[77,78]. However, in quantitative measurements, the research is still very limited. Chen et al. utilized the combination of empirical mode decomposition (EMD) and correlation calculation to suppress random noise containing fading^[79]. The processing process is roughly as follows: first, perform empirical mode decomposition until the residual component becomes monotonic or constant, thus obtaining a series of intrinsic mode functions. Then, these intrinsic mode functions are correlated with the original signal, and a correlation coefficient is calculated for each correlation. The intrinsic mode functions with correlation coefficients greater than 0.4 are retained to suppress the noise. In the experiment, sinusoidal signals at 200, 300, 400, and 500 Hz, as well as a sawtooth signal at 500 Hz, were applied to the PZT. Then, the phase signals obtained using the method of EMD combined with correlation calculation effectively reproduced the original signals. Here, only the comparison results of various algorithms when PZT was loaded with a 500 Hz sinusoidal signal are displayed.

Figure 10(a) displays the original signal loaded, which is a standard 500 Hz sine waveform. Figure 10(b) shows the result from the ordinary wavelet denoising algorithm. Figure 10(c) presents the result of the EMD-soft denoising method, and Fig. 10(d) is the result obtained using EMD combined with correlation calculation. Clearly, the phase signal from the EMD combined with the correlation calculation method is closer to the original signal than the first two denoising algorithms.

Directly enhancing the intensity of the phase signal can reduce the impact of the phase noise in coherent Φ-OTDR on the reconstruction of the phase signal after demodulation. However, previous research and applications of Φ-OTDR have primarily focused on straight optical fibers^[80], including existing optical cables, without utilizing the fiber itself for any processes related to enhancing the intensity of the phase signal. In recent years, more and more researchers have started studying the production of Φ-OTDR as a fiber hydrophone^[81,82]. When fabricating a fiber hydrophone, the fiber is no longer simply straight, which makes it possible to enhance the strength of the phase signal using the fiber itself. The literature^[83] summarizes the research progress of distributed fiber sensors in the field of fiber hydrophones and provides a theoretical explanation for the enhancement of the phase signal in Φ-OTDR.

For the sake of comparison, we will first discuss the scenario involving the straight bare optical fiber. At this point, the minimum detectable acoustic pressure P for Φ-OTDR is P=YΔϕZ(1+γ)n0kμΔz,(7)where Y, Δϕz, γ, n0, k, μ, and Δz are the Young’s modulus of the fiber, phase demodulation accuracy, photo-elastic coefficient of the quartz fiber, average refractive index of the fiber, angular wave number, Poisson’s ratio of the fiber, and fiber length, respectively. For common optical parameters of Φ-OTDR, when the phase demodulation accuracy is 0.1 rad, the acoustic pressure is 806.2 Pa, corresponding to approximately 178 dB. The noise level of the zero-order sea conditions is 45 dB. At this stage, if the fiber is not treated in any way, the weak signal demodulated by Φ-OTDR will be overwhelmed by noise. To overcome the impact of noise, a hollow cylindrical structure such as polycarbonate pipe is often used to enhance the intensity of the phase signal, allowing the useful signal to be separated and identified from the noise and achieving the purpose of enhancing the acoustic pressure detection capability. The hollow cylindrical structure used is shown in Fig. 11.

After using the fiber sensitization structure shown in Fig. 11, the minimum detectable acoustic pressure Pz for Φ-OTDR can be achieved as Pz=Δϕm,ZYm(1+γ)n0kΔz·(a2+b2a2−b2−μm),(8)where Δϕm,Z, Ym, μm, a, and b are the phase demodulation accuracy, Young’s modulus, Poisson’s ratio, outer radius, and inner radius of the hollow cylinder, respectively. It can be seen that the minimum detectable acoustic pressure can be reduced by adjusting the values of the inner and outer radius. When the Young’s modulus, Poisson’s ratio, outer radius, and inner radius of the hollow cylinder are 2.38 GPa, 0.37 cm, 3.0 cm, and 2.8 cm, respectively, the minimum detectable acoustic pressure is 0.355 Pa, which is 111 dB. At this time, the detection capability of the Φ-OTDR is enhanced, but the weak external perturbation signals are still overwhelmed by the noise of the zero-order sea conditions. If the inner and outer diameters can be set to 2.9999 and 3 cm, respectively, the minimum detectable acoustic pressure can reach 0.00017 Pa, which is 44.7 dB. At this point, the phase signal demodulated by Φ-OTDR can eliminate the impact of the background noise of the zero-order sea conditions and correctly reflect the external perturbation information. However, as mentioned in Ref. [83], this is a significant challenge because it is difficult to achieve a very small difference between the inner and outer diameters of the hollow cylinder. Despite the numerous challenges, research on fiber sensitivity enhancement schemes based on or similar to the hollow cylinder in Fig. 11 has made some progress in applications such as localization.

According to Eq. (2), the increase in the SNR of the amplitude signal leads to an increase in the SNR of the phase signal. Therefore, to suppress the impact of noise on the phase signal in the final demodulated results, one can also start by increasing the intensity of the amplitude signal. For Φ-OTDR, enhancing the intensity of the amplitude signal means increasing the intensity of the Rayleigh backscattering signal detected by the photodetector. There are two main methods to increase the intensity of the Rayleigh backscattering signal: increasing the scattering coefficient of Rayleigh scattering and increasing the collection efficiency of the fiber for backscattered light^[84]. The former is achieved through methods such as fiber irradiation, writing microstructures, and doping nanoparticles, which increases the intensity of the source at the “signal source” level. The latter is achieved by methods such as increasing the numerical aperture and reducing the mode field radius, which increase the collection of the signal at the “collection end” level. However, these methods often face challenges due to limited sensing distances or overly complex structures, making them difficult to apply. In contrast, the method of writing microstructures in ordinary single-mode fibers by embedding weak reflection fiber Bragg gratings (FBGs) has a more mature process and some applicability. Our research group has studied the optical influence mechanism and demodulation methods of Φ-OTDR embedded with weak reflection FBGs. The coherent detection scheme for resolving phase is shown in Fig. 12^[85].

The experimental setup in Fig. 12 is essentially the same as in Fig. 1, with the difference being in the sensing fiber section. In Fig. 12, the sensing fiber is embedded with weak FBGs, each with a bandwidth of 5.5 nm, at intervals of 50 m. This setup can use a double-pulse inquiry to obtain phase information. Each pulse has a width of 300 ns, and the interval between the two pulses is 500 ns, allowing the Rayleigh backscattering light from the two pulses to overlap. The Rayleigh backscattering light mixes with the reference light and is received by the photodetector. The received Rayleigh backscattering signal is further processed using the Hilbert transform method to extract the phase, and the phase difference between the weak FBGs is used to extract the perturbation signal between the two FBGs. The embedding of weak FBGs enhances the Rayleigh backscattering signal, which is in the form of amplitude, by approximately 18 dB compared to the absence of such gratings. Thanks to this increase, combined with the method of twice phase difference, the low-frequency signal of 0.2 Hz is successfully reconstructed.

The Rayleigh backscattering signal detected by the detector at a specific moment comes from a certain spatial range of photons, and this spatial length is proportional to the pulse width. In other words, widening the pulse results in a greater intensity of the signal received by the detector. It boosts the intensity of the signal in the form of amplitude, thereby enhancing the SNR of the phase signal. However, in Φ-OTDR, the increase in pulse width also means a decrease in the spatial resolution of Φ-OTDR. Therefore, simply increasing the pulse width is not an effective method to improve the SNR of the phase signal. The probing signal with the encoding pulse scheme can solve this problem. Although the total length of the encoded pulse is very long, the spatial resolution of the Φ-OTDR based on the encoded pulse depends on the spatial width of the code element, not on the width of the encoded pulse sequence. The increased duration of the probing signal enhances the reception intensity of the received Rayleigh backscattering signal^[86–88], thereby improving the SNR of the resulting phase signal. However, when coding techniques are applied to traditional OTDR systems, only the encoding and decoding of intensity information exist. In Φ-OTDR, it is also necessary to recover the phase information of the single pulse response from the overall response of the coded pulse sequence. This work was previously progressing slowly. In 2018, a research group of systematically proposed a method to linearize the response of the coded Φ-OTDR system, effectively suppressing the influence of inter-code crosstalk and making it possible for Golay codes to be truly and effectively applied to Φ-OTDR systems. This laid the foundation for the subsequent development of the encoding pulse scheme in Φ-OTDR with phase extraction^[89,90].

Assuming in a coherent Φ-OTDR, the encoded pulse sequence injected into the fiber is C=[C0ejφ0,C1ejφ1,C2ejφ2,⋯,CMejφM],(9)where Ci and φi are the intensity (0 or 1) and initial phase of the pulse sequence, respectively. This pulse sequence enters the fiber and generates Rayleigh backscattering light that mixes with the reference light to produce the Rayleigh backscattering signal output by the photodetector. If the scattering signal contains an intermediate frequency term, it is the desired beat frequency signal, and all other components are filtered out by the bandpass filter. The beat frequency signal can be written as I(t)=C*h(t)=C*{B(t)·cos[φ(t)+φc]},(10)where B is the coefficient brought by the scattering light, the local oscillator light, the detector response coefficient, and the coupler; φc is the initial phase difference between the scattering light and the local oscillator light; and φ is the interference phase result of each scattering element. Thus, it can be seen that the response of each individual pulse can be resolved from the aggregate response of the encoded pulse, as represented by the beat frequency signal, leading to the determination of the phase.

However, there are many types of pulse encoding, and different encoding methods have different effects on the system. For the quantitative phase demodulation of Φ-OTDR, researchers have studied the application of various code types, such as unipolar Golay codes^[91], PPA codes^[92], bipolar Golay codes^[93], random codes^[94], and same-frequency orthogonal coding (OCSC)^[95,96]. Although there are differences in the code types of the encoded pulse and the impact on the system performance also varies, the common point is consistent, that is, encoding is used to increase the intensity of the received signal in the form of amplitude. For example, for a Φ-OTDR using M+1 bit code elements of unipolar Golay codes, the gain of the received signal in the form of amplitude is M/2. The SNR of the amplitude signal naturally increases. Thus, according to Eq. (2), the SNR of the phase signal also increases.

Figure 13 illustrates the phase demodulation results of measuring external perturbations using single pulses, single pulses averaged four times, and 128-bit unipolar Golay coded pulses in Ref. [91]. The noise variances of the phase waveforms in Figs. 13(a)–13(c) are 0.0792, 0.0210, and 0.00009046 rad, respectively. It is evident that the employment of the encoded pulses in coherent Φ-OTDR results in the reduction of noise components in the derived phase signal.

Deep learning-based noise suppression involves training a deep learning model on a large amount of training data to automatically learn the features and patterns of the data, enabling the recovery of the original data from the noisy data and thus removing the noise. Since these methods focus on the overall denoising effect of the output relative to the input, rather than on the causes and sources of the noise, deep learning has been widely used in noise suppression in the fields of speech signals and digital images. Clearly, when deep learning is introduced to the denoising of distributed fiber acoustic signals, the denoising is no longer specific to particular fading and laser frequency drift, but directly targets the data itself. Similar to speech signals and digital images, the introduction of deep learning to the denoising process of distributed fiber sensing signals has also experienced one-dimensional (1D) denoising^[97,98] and two-dimensional (2D) denoising^[99,100]. 2D denoising based on deep learning for distributed fiber acoustic signals involves two cases. One is to use methods such as short-time Fourier transform to convert 1D data into two-dimensional data and then use deep learning methods for denoising. The other is to perform denoising based on the inherent 2D temporal and spatial characteristics of the phase optical time domain itself. Each time Φ-OTDR emits a pulse, it generates a data column with a spatial scale, and the timing of the pulse corresponds to the time scale. Therefore, the data captured by the phase optical time domain reflectometer within a certain period of time has temporal and spatial two-dimensional characteristics. With this groundwork, it is now possible to directly transfer advanced deep learning-based two-dimensional denoising techniques, successful in various other fields, for the noise suppression of the distributed fiber acoustic signal.

These deep learning denoising schemes only focus on suppressing the noise in the already demodulated phase signal and do not have the ability to demodulate the phase signal. Recently, Liang et al. proposed a method based on deep learning that can both demodulate the phase signal from the amplitude signal and suppress the noise in the phase signal^[101]. Certainly, it is important to note that the input in this case is the noisy amplitude signal, not the noisy phase signal, and the resulting phase signal is less affected by noise than those obtained from other demodulation and noise reduction techniques. In the reference state, the response of the pulse light can be expressed as hDP(t)=G·∑q=1Naq¯exp(jΦq)δ(t−qΔt),(11)where G is the gain caused by the intrinsic mixing light and the detector, Φq is the delay phase of the q-order scattering center, and N is the number of fiber segments. In the event of a perturbation on the fiber, Eq. (11) can be rewritten as $$\begin{gathered} hDP′(t)=G·∑q=1Naq¯exp[j(Φq+ΔΦq)]δ(t−qΔt) \\ =h(t)·exp[jΘ(t)], \end{gathered}$$(12)where Θ(t) represents the perturbation information.

In Fig. 14, the training data is generated by the model, so when the corresponding data of the two columns enter the network shown in Fig. 14 for training, the phase information can be automatically demodulated. The literature compares the newly proposed method with the traditional SPEA method, and it yields satisfactory results in both cases.

The coherent Φ-OTDR system for measuring phase signals has become one of the most important distributed fiber acoustic sensors. This review analytically describes the mechanism of noise impact based on the general process of phase demodulation and then provides a detailed introduction to several representative methods to suppress the noise impact on phase signals in coherent Φ-OTDR across various pathways, such as noise suppression/signal enhancement of amplitude signals, phase signals, and data itself. They can be subdivided into nine pathways, each presenting a typical implementation case. These implementation cases are estimated in terms of the complexity of the hardware and software solutions, the degree to which cost affects the effectiveness of the solution, and the correlation between execution difficulty and the limitations of practical application scenarios. The evaluation results are shown in Table 1.

As can be seen from Table 1, no implementation case has the best performance in terms of complexity, effectiveness, and implementation difficulty simultaneously. This also means that coherent Φ-OTDR still has many shortcomings that need to be overcome. Therefore, the research on noise processing for phase-extracted signals in coherent Φ-OTDR will remain a hot topic in the field of distributed fiber sensing. Besides those mentioned above, this research at least also includes computational capability and detection capability at far end: