1. Introduction

Fiber-optic hydrophones, developed in the late 1970s, can convert sound signals in water into changes in phase, amplitude and other parameters of light, and transmit over long distances through low-loss optical fibers [1,2]. The unique advantages of fiber-optic hydrophones include high sensitivity, wide response band, good frequency response characteristics, strong immunity to electromagnetic interference and crosstalk, and the ability to use multiplexing technology to form large-scale and large-area arrays [3–5]. Therefore, fiber-optic hydrophones are widely used in many fields [6–9]. Phase interference type fiber-optic hydrophone has the highest detection sensitivity and can realize long-distance relay-free detection [10]; thus, it is of much research value and has become an important research topic. Noise is one of the core indicators of hydrophone, and the noise floor of interferometric systems is mainly limited by the quality of the light [11–16]. The power degradation caused by long-distance transmission causes a serious decrease in the signal-to-noise ratio (SNR) of the received signal, but simply increasing the optical power can excite serious fiber nonlinearity, which also makes the noise floor of the detection deteriorate. To resolve this contradiction, we in previous work applied linear frequency modulated (LFM) optical pulses to an interferometric fiber-optic hydrophone system for the first time. Compared with other heterodyne-type scheme, the LFM technique can improve the power utilization of the light source and effectively suppress the fiber nonlinearity [17]. Experiments showed that the maximum tolerable loss of the fiber-optic hydrophone was improved by 7.1 dB with LFM light source. However, we note that the LFM scheme uses an interferometer with unequal arm lengths as the sensor, thus placing higher requirements on the frequency noise of light source [18,19]. The frequency noise of a laser is manifested as a time variation of its instantaneous frequency. The previous heterodyne-type fiber-optic hydrophone applies equal-arm interferometric sensing, i.e., the two optical pulses that interfere experience equal optical distances, so the influence brought by the laser linewidth is theoretically reduced [20]. However, in the LFM scheme, the frequency change of light source is converted into phase noise after passing through the interferometer with non-zero arm length difference, which brings about the deterioration of the noise floor. Currently, light source frequency noise dominates the noise floor of detection system, so effective means are needed to minimize its negative impact.

Many solutions have been proposed in recent years to overcome the frequency noise of the light source and improve the sensitivity of hydrophone detection. In particular, the interferometric hydrophone system based on phase generation carrier (PGC) technology, which also uses a non-zero arm length difference interferometer for sound signal sensing, is also affected by the light source largely [21–23]. The most straightforward solution to reduce the associated noise is to use a narrow linewidth laser with high frequency stability [24–26]. For example, the emission frequency of the laser can be stabilized by locking it to a reference cavity. However, such lasers are expensive and not suitable for use in large-scale interferometric hydrophone array systems. Kersey et al. proposed to introduce a probe isolated from environmental perturbations as a reference in the sensors array, which can measure the effect of frequency noise from the laser in real time [21]. These effects are then removed during the demodulation of the echo signal from the real sensors, resulting in frequency noise correction. This technique is often used in time-division multiplexed (TDM) array because the sensors and probe involved in the correction process must be illuminated by the same light source [22,23,27]. There are several correction algorithms, and a simple one can be achieved by subtracting the signal of the reference probe from the demodulated phase signal of the real sensor, thus achieving noise reduction. These solutions require the reference probe and the real sensor to have the same arm length difference, otherwise the correction effect will be weakened. Literature [28] proposed a technique that can adaptively perform phase noise cancellation, where an accurate and real-time measurement of the arm length difference for all interferometers, including the reference probe and the real sensors, is achieved by additional frequency modulation of the light source, and the correction algorithm is adjusted using these measured values.

Since the previous correction algorithm of direct subtraction would lead to a significant increase in white noise, leading to a deterioration of at least 3 dB in the detection sensitivity. Correspondingly, we propose a novel TDM array with unbalanced echo power, where the power of reference probe is higher than that of the other real sensors. On the one hand, this power optimization introduces only a negligible loss cost to the real sensors in a large-scale TDM array. On the other hand, the high echo power greatly compresses the noise of the reference probe and thus introduces only much smaller deterioration of white noise in the frequency noise correction algorithm. Experiments show that our proposed new TDM array can reduce the noise floor deterioration caused by existing correction algorithms to within 1 dB while suppressing the laser frequency noise, and the hydrophone signal demodulation based on the LFM technique achieves very close noise performance after correction when the source linewidth is in the range from 1.417 kHz to 338.06 MHz.

2. System design

Our proposed TDM interferometric fiber-optic hydrophone array with reference probe power optimization, as well as the LFM scheme for phase demodulation, are shown in Fig. 1. Unlike our previously proposed LFM system, here we use a transmitter with a common laser that does not have the characteristics of narrow linewidth or low frequency noise. The laser emits light that is modulated by carrier-suppressed single-sideband modulation (CS-SSB) to obtain LFM light pulses [29], and the pulses are amplified by Erbium-doped fiber amplifier (EDFA) and enter the transmission fiber as well as the sensor array. The novel TDM array includes a reference probe and a conventional, uniformly power-distributed TDM array. As shown in Fig. 1, a fiber Michelson interferometer is added as the reference probe in front of a conventional TDM array using a pair of optical couplers (named by “reference couplers” in the following) with the same coupling ratio. Reference probe is in environmentally isolated package. Such TDM array proposed here can still support large-scale networking as usual [15,20], while one can adjust the power of the reference probe by controlling the coupling ratio of the reference couplers. Thus, the reference probe can have a higher echo power than other real sensors, while all of the real sensors have the same echo power. The optical pulses pass through the above-mentioned array as well as the transmission fiber and enter the receiver, where they undergo optical amplification, filtering, and photoelectric conversion and are received by the analog-to-digital converter (ADC). In data processing, the sound modulation as well as the laser frequency drifting can then be learned from the time-domain interference fringes. As always, the system can easily be expanded into larger sensing networks with wavelength-division multiplexing (WDM) technology. The scheme proposed in this paper to suppress laser frequency noise can suppress the deterioration of white noise while suppressing laser frequency noise, which is not only applicable to LFM-based interferometric fiber hydrophone systems, but also to other systems, such as PGC-based hydrophone systems and traditional heterodyne systems, the same applies to systems without frequency modulation. By introducing a reference probe that is isolated from the external environment and has a higher echo power than the real sensor, the laser frequency noise suppression of the real sensor is realized, and the white noise is effectively suppressed. The LFM-based interferometric fiber hydrophone can effectively improve the system reception sensitivity and increase the maximum tolerable loss of the system [17], so this paper mainly analyzes the application of the proposed noise suppression scheme to the LFM-based interferometric hydrophone system.

 

Fig. 1. LFM-based interferometric fiber-optic hydrophone array and demodulation, and a reference probe is added of which the echo power is optimized.

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In the following we theoretically analyze the principle of introducing a reference probe to reduce the frequency noise of the light source in the LFM scheme. We use ${f_{ins}}(t )$ to denote the instantaneous frequency of the light source, then according to [17], the LFM light pulse output by the transmitter can be expressed as follows.

The above theory shows that although the random frequency noise of the light source destroys the strict periodicity of the LFM optical pulse train, the echo beating frequency is still an integer multiple of its repetition rate, which means that the chirp rate or the arm length difference within a certain range of perturbation does not affect the demodulation of the target signal, and ensures the accuracy of the hydrophone phase detection. In the Ref. [17], without considering the frequency noise of the laser, it is concluded that the demodulation signal has strict periodicity, that is, the echo beat frequency is an integer multiple of the repetition rate. When the frequency noise of the laser is taken into account, as can be seen in Eq. (2), the demodulated signal is introduced into the phase noise, which is non-periodic. According to the formula, this noise is related to the arm length difference, so the corresponding correction algorithm is also related to the arm length difference. Equation (3) shows the principle of introducing a reference probe and correcting the additional phase noise of the real sensor. Under the illumination of the same light source, both the reference probe and the real sensor obtain additional phase noise proportional to the same random frequency ${f_{ins}}(t )$ and thus can cancel each other out. Since the reference probe is isolated from the environment, the real sensor after correction will get the desired sound signal, $\varphi (t )$. Mathematically, we assume that the demodulated phase of the ${k^{\textrm{th}}}$ real sensor of the TDM array is ${\varphi _k}(t )$ and that of the reference probe is ${\varphi _r}(t )$. Then the correction algorithm is

Equation (3) shows that the additional demodulated phase noise introduced by the light source frequency noise is proportional to the arm length difference of the interferometer. Due to fabrication errors or environmental disturbances, there are inevitable differences between TDM interferometers. For a more accurate correction of the phase noise, this difference must be considered, as expressed in Eq. (4). Thus, the ratio of the arm length differences between the real sensor and the reference probe needs to be known precisely. If the sensor changes, that is, the arm length difference changes, the effect of the suppression scheme will not be different, and if there is a difference, the arm length difference scale factor between the corresponding real sensor and the reference probe can be adjusted according to Eq. (4), and then the phase noise suppression continues. The laser frequency noise model used in this paper is universal and reasonable, which is the basis for the formula derivation. It can be seen from the formula derivation that regardless of the noise distribution, the conclusion that the additional demodulated phase noise introduced by the frequency noise of the light source is proportional to the arm length difference of the interferometer can be obtained, so the scheme proposed in this paper is effective for a series of laser frequencies and linewidths, and the noise suppression means are independent of the noise distribution. Several related methods have been proposed that can be introduced into the LFM scheme. We note that this scheme of introducing reference probe to eliminate the influence of light sources is already available in hydrophone systems based on PGC technology [21]. However, in [17] we analyzed the advantages of the heterodyne technique over the PGC scheme, especially that based on LFM which has significant advantages in terms of nonlinear suppression. The previous heterodyne-type fiber-optic hydrophone applies equal-arm interferometric sensing, so that the difficulty of high requirements for light source quality is overcome in theory. Here, for the first time in an LFM heterodyne scheme, we achieve a relaxation of the laser requirements by means of a reference probe and correction algorithm.

It is worth noting that the reason for introducing a reference probe and thus removing the effect of laser frequency noise is because of the correlation between the additional phase noises of the sensor and the probe. However, there will be considerable uncorrelated noise between the interferometers during the demodulation process. Particularly, in long-range repeater-free hydrophone systems, both fiber optic transmission and TDM arrays introduce large losses, resulting in very weak echoes from each interferometer when they reach the receiver. As a result, the echo beating will include a large amount of broadband white noise, which is mainly caused by the amplified spontaneous emission (ASE) noise of EDFA. When laser frequency noise removal is achieved using the correction algorithm described above, this white noise will dominate. Since the white noise from each interferometer is not correlated, the subtraction in Eq. (4) will not make them cancel each other; instead, the random noise will be superimposed after the above algorithm. When echo powers of the real sensor and the reference probe are the same, their SNR are also the same, so the correction algorithm will cause the sensor white noise to become twice as large, i.e., causing a 3 dB deterioration in SNR. Thus, an optimal phase noise correction algorithm should take into account the effect of the above-mentioned non-correlated noise and minimize its effect. In order to improve the deterioration of white noise caused by the direct phase subtraction algorithm, we appropriately increase the echo power of the reference probe by controlling the ratio of the reference coupler, as shown in Fig. 1, when the LFM optical pulse power entering the TDM array is fixed. At this time, the SNR of the echo beating generated by the reference probe will be greater than that of other interferometers, and the direct phase subtraction algorithm continues to be applied at the receiving end to suppress the additional phase noise in sensors. The white noise of the sensors after the algorithm will be mainly from itself, which effectively avoids the superposition of white noise and therefore effectively improves the SNR deterioration. Notice that the above uneven power distribution does not affect the previous extra phase noise suppression. In other words, our proposed scheme can successfully remove the effect of laser frequency noise and reduce the deterioration of white noise.

As shown in Fig. 1, the selection of each coupler ratio needs to satisfy the following conditions. Firstly, the echo optical power of each real sensor is the same. Secondly, the echo power of the reference probe is M times that of the real sensor. Finally, the smaller the loss of the whole TDM array, the better. Given the number of interferometers in the TDM array, one can obtain the power ratio of all optical couplers. Since a portion of the optical power entering the array is allocated to the reference probe, additional losses are introduced to the other sensors. Obviously, when the number of interferometers in the TDM array gets higher, the loss will be allocated to more sensors, and thus the additional loss introduced will be smaller. In general, for long-distance systems, the number of interferometers in a TDM array is large in order to observe a large area, so the additional loss is small. Taking the 16-TDM array as an example, we give the extra loss of the sensors in Fig. 2(a) as a function of the reference probe power ratio M. $M = 0$ means that there is no reference probe, or the optical power allocated to the reference probe is zero, and the extra loss at this time is 0 dB. As the reference probe echo power ratio increases, the extra loss introduced to the sensors also increases smoothly. When the power ratio is 4, the additional loss is only 1.1 dB. When the power ratio is as high as 16, the introduced loss is 2.1 dB.

 

Fig. 2. (a) The extra loss of the sensors. (b) The variation of the phase noise floors obtained by demodulation of the TDM array under different echo power ratios.

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We simulate the demodulation results of the hydrophone array shown in Fig. 1 above to observe the suppression of the negative effect of the reference probe on the laser frequency noise and to verify the performance improvement of the non-uniform power allocation on the existing correction algorithm. The average power of the pulse train is 8 dBm and the relative intensity noise (RIN) is uniformly distributed at -150 dBc/Hz. Because of the short duration of the optical pulse, it is reasonable to assume that the instantaneous frequency of the light within the pulse remains constant. However, different optical pulses have different carrier frequencies and satisfy a normal distribution. The TDM array has 16 interferometers, the first of which is a reference probe. The echo power ratio of reference probe over sensor is adjustable from 0 to 16 by adjusting the reference coupler. At the receiver, the EDFA noise figure (NF) is 4.5 dB. Because of the large losses in the fiber and the array (which is 43 dB in total), the ASE noise dominates, and we ignore the noise from the photodetector, the electrical amplifier at the receiver, as well as the ADC in the simulation. The algorithm to recover the phase modulation from the interference fringes can be found in [11,32]. The arm length differences of each interferometer in the simulation are the same, and the scale factor in the algorithm correcting phase noise is 1 according to Eq. (4).

Figure 2(b) shows the variation of the phase noise floors obtained by demodulation of the TDM array under different echo power ratios. These noise floors include the that under laser having zero frequency drift (corresponding to the lowest line in Fig. 2(b)), the laser frequency satisfying a normal distribution with a standard deviation of 1 MHz (corresponding to the highest line), and the noise floor after correction by the reference probe (corresponding to the middle line). These noise floor values, in the simulation, are the average of the frequency offset range from 30 kHz to 70 kHz. The calculations for the other intervals yielded the same conclusion. Firstly, the above simulation verifies the effectiveness of the correction algorithm. When the frequency noise of the laser changes from zero to 1 MHz, the phase noise of the sensor deteriorates sharply by 7 dB. However, when the correction technique is used, the noise floor is pulled back substantially and approaches the case of no frequency noise, regardless of the power distribution factor. Secondly, we see that there is a lift in the noise floor as the power ratio increases, which is related to the increase in additional losses as illustrated in Fig. 2(a). Thirdly, we can observe that when the power ratio is 1, i.e., the traditional reference probe correction technique, although the correction brings about a great suppression of phase noise, the corrected noise floor is still 3 dB higher compared to the zero-frequency noise case, which is consistent with our previous theoretical analysis that the deterioration comes from the superposition of the respective white noise of the reference probe and the sensor. Finally, the simulations show that the corrected phase noise curve exhibits a different trend from the other two cases when the power ratio gradually increases: the noise first decreases and then increases, and the corrected curve obtains a minimum value when the power ratio is around 4. At this point, the corrected noise floor is -91.3 dBc/Hz (a common unit to describe the magnitude of phase noise [33]), a value that is only about 0.9 dB higher than the case without frequency noise, and lower than the results of conventional correction means. This trend is also in agreement with the previous theoretical analysis, i.e., the correction noise is increased by the additional loss on the one hand, and reduced by the reference probe SNR enhancement on the other.

3. Experiment

We demonstrate the noise suppression superiority of the proposed novel TDM array containing a reference probe through a proof-of-concept experiment. The experimental scheme is shown in Fig. 1 and is similar to our previously proposed LFM-based hydrophone, with the difference that here we use a linewidth-tunable laser as the light source. The transmitter outputs an LFM pulse sequence with a pulse duration of 312.5 ns, bandwidth of 1.5 GHz, repetition frequency of about 195.31 kHz, and optical pulse duty cycle of 1/16, which can support the demodulation of a 16-TDM array. The pulse sequence is amplified by EDFA to 8 dBm. Experiments are performed with tunable optical attenuators (VOA) simulating downlink and uplink fibers, placed in front and behind the TDM array, respectively. The total loss of the two attenuators is 16 dB and is used to simulate 100 km of linear transmission (assuming a fiber of G.654D with a loss of 0.16 dB/km). We simulate 16-TDM array using two parallel, environment-isolated Michelson interferometers, each using a pair of Faraday rotation mirrors (FRMs) to eliminate polarization-related fading. These two dummy interferometers are used to simulate the reference probe and the real sensor, respectively, and their insertion loss can be set independently to simulate the array loss, and the power distribution ratio of the reference probe, respectively. In the experiments, the sensor loss is fixed at 27 dB, corresponding to the loss introduced by the conventional 16 TDM. And the access loss of the reference probe is tunable. In practical applications, the reference probe should be environmentally isolated. In this experiment, the real sensor is also environmentally isolated, in order to accurately measure the correction capability of the additional phase noise. The echo is amplified by an EDFA (NF is about 4.5 dB) and then received by the photodetector with a narrowband optical filter previously set to remove the additional ASE noise. It is found that, since the optical power entering this EDFA is very low (around -35 dBm), adjusting the EDFA output optical power within a certain range will not affect the phase demodulation results. The sampling rate of the ADC used in the receiver is 100 MHz and the effective number of bit (ENOB) is 10. A MATLAB program extracts and analyzes the data corresponding to the actual two interferometer time slots. It is worth noting that the optical power entering the photodetector is no longer uniform over time due to the different interferometer echo powers, and a suitable incident optical power needs to be set to keep both the photodetector and the ADC in a linear operating range.

To better evaluate the effectiveness of our proposed scheme in correcting the phase noise introduced by different degrees of frequency noise of the laser, we use a frequency-noise tunable laser in our experiments to avoid inaccurate evaluation results due to other parameters of the source. We use a white-noise source to drive a narrow linewidth laser. The laser has a linewidth of 1.417 kHz, and the noise driver is output from an arbitrary waveform generator (AWG) with a bandwidth of 100 kHz and tunable amplitude. Figure 3(a) shows the phase noise deterioration of the laser after driving with white noise from 0 V to 2 V in amplitude, respectively. The measurements are realized with the HI-QTM Optical Test Measurement System (TMS), which provides fully automated measurements of ultra-low phase noise continuous-wave laser sources using the zero-difference method. As the noise drive increases, the linewidth of the laser increases, from a narrowest 1.417 kHz up to 338.06 MHz. It can be seen that the phase noise of the laser is subsequently raised throughout the offset-frequency band, indicating that it is reasonable to simulate the frequency noise of the laser in this way. Next, we observe the demodulation results of the hydrophone system for different linewidth cases. The measured phase noise and its fit are shown in Fig. 3(b). We apply the “smoothdata” function in MATLAB to smooth the obtained phase noise data to obtain the fitted curve in Fig. 3(b). In agreement with the simulation prediction, as the laser linewidth increases, the demodulated phase noise increases throughout the offset-frequency band. This is because the LFM scheme uses an interferometer with non-zero arm length difference, which is severely affected by the laser frequency noise. As the linewidth increases above 1 MHz, the phase noise deteriorates by 14 dB, indicating that conventional light sources for fiber optic communication systems cannot be applied to such interferometric hydrophone systems. It is worth noting that the above multiple comparison experiments were performed only on the laser for linewidth expending, and all other parameters were constant, and this operation ensured the reliability of the experimental results.

 

Fig. 3. (a) The phase noise deterioration of the laser after driving with white noise from 0 V to 2 V in amplitude, respectively. (b) The measured phase noise and its fit.

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We next verified the enhancement of the frequency noise suppression by increasing the reference probe power. Before the correction is implemented, we measure the arm length differences of the two interferometers, 0.252 m and 0.247 m for the reference probe and sensor, respectively. Thus, the coefficient of the correction algorithm in Eq. (4) is 0.98. The light entering the sensing unit and the reference probe are all from the same laser, and the design value of the length difference between the real sensor and the reference probe arm is the same, but in practice there will be a slight difference, and this difference can be adjusted according to the coefficient of the algorithm modified in Eq. (4), so as to ensure the denoising performance of each sensing unit. As seen in Fig. 2(b), the phase noise correction is best when the echo power ratio is 4. Therefore, in the experiments, we compared the reference probe and sensor probe return power ratios of 1 and 4, respectively of the cases. Since the access losses of the two interferometers are set independently, thus in the following experiments, only the loss of the reference probe needs to be adjusted, keeping the loss of the sensor unchanged. To ensure the accuracy of the power ratio adjustment, we use an oscilloscope to observe the amplitude values of the two echoes after the photodetector. When the noise drive of the laser is turned off, we measure the obtained phase noise floor as shown in Fig. 4(a). At this time, the linewidth of the laser is 1.417 kHz, corresponding to the optimal demodulation effect obtained, and the phase noise at 1 kHz frequency bias is -97.6 dBc/Hz, and can be used as a benchmark for subsequent comparison experiments. Subsequently, a white noise drive with an amplitude of 1 V is applied to the light source, and the linewidth is widened to 25 MHz, which raises the demodulated phase noise by 20 dB. Then, the phase is demodulated and the corresponding corrected phase noise is obtained by setting the return power ratio of the reference probe to 1 and 4, respectively, and applying the noise suppression method. The above results are shown in Fig. 4(a). The fitted curve in Fig. 4(a) is obtained in the same way as Fig. 3(b). As can be seen, simple subtraction can be achieved to suppress the effect of laser frequency noise, but with different effects. At 1 kHz frequency offset, the phase noise is suppressed by 16.76 dB when the return power ratio is 1, and by 19.72 dB when the return power ratio is 4. The corrected phase noise floor at a ratio of 1 is 3 dB higher than in the case of a narrow linewidth source, a result that is consistent with both theory and simulation. At a ratio of 4, the corrected results deteriorate within 1 dB. This improvement in the correction effect can be seen throughout the frequency offset band. After suppressing the laser frequency noise, the number of probes in the system does not increase or decrease, and the noise floor of the corresponding real sensor is reduced. In theory, our scheme can completely suppress the frequency noise of the laser, so the same sensing capability can be obtained as if the ideal laser was applied. The sensing capability of our system under narrow linewidth laser has been described in detail in [17], which can suppress SBS noise and improve the sensing capability by 7.1 dB compared to existing coherent systems. It is worth noting that since the real sensor and the reference probe will be affected by the environment, these effects are independent noise, such as sound, oscillation, and thermal noise, and the frequency of these noises is around 100 Hz, so the corrected phase noise is still relatively high at the low-frequency offset, and better isolation packaging can solve this problem.

 

Fig. 4. (a) The demodulated phase noise when the noise drive of the laser is off and the white noise amplitude is 1 V, the corrected phase noise when the echo power ratio is 1 and 4, respectively. (b) Phase noise results obtained experimentally when the power ratio of the reference probe is 1 and 4, respectively, and when the laser noise drive amplitude is adjusted from 0 V to 2 V.

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Finally, we test the performance of the new scheme in the case of different laser linewidths by adjusting the laser noise drive amplitude varying from 0 V to 2 V. When the power ratio of the reference probe is 1 and 4, respectively, the experimentally obtained phase noise results are shown in Fig. 4(b). The lowest -98.8 dBc/Hz is the result when the laser is unperturbed and represents the best performance that the system can achieve. When the reference echo power ratio is 1, the corrected phase noise ranges from -96 to -95 dBc/Hz, with an average value of -95.3 dBc/Hz, which is about 3 dB away from the optimum value. This result further verifies the conclusion that the conventional scheme raises the white noise. When the reference echo power ratio is 4, the corrected phase noise ranges from -99 to -98 dBc/Hz with an average value of -98.6 dBc/Hz, which is within 1 dB of the optimal value. This result shows that even when the laser frequency noise is severe (linewidth maximum of 338.06 MHz), increasing the echo power ratio of the reference probe can effectively suppress the phase noise deterioration while reducing the superposition of white noise. It is worth noting that although this article uses a laser that changes the linewidth by white noise drive, the experimental results will not change at all when comparing lasers with different linewidths (non-white noise drive).

In order to further illustrate that the suppression of laser frequency noise by the proposed scheme is independent of the noise distribution, further simulation is carried out. In the simulation, the laser is treated with white noise and 1/f noise, and the 1/f noise is added to a level of white noise, but the noise of 1/f noise is greater at low frequency, and the noise distribution of the laser under the above two noise treatments is shown in Fig. 5(a), it can be seen that both noise treatments have a significant impact on the noise of the laser. Under the noise distribution of Fig. 5(a), the corresponding demodulation phase noise distribution after the system is given, as shown in Fig. 5(b), when there is white noise or 1/f noise in the laser, it will lead to a large deterioration of the demodulated phase noise, and under these two noise treatments, the demodulated phase noise results obtained after the algorithm correction we propose are almost indifferent, and the difference between the corrected demodulation result and the phase noise result of demodulation without dither in the laser is within 1 dB,which further verifies the effectiveness of our scheme, and also shows that the suppression of laser frequency noise by our proposed scheme has nothing to do with the distribution of noise. The ratio of echo power between the reference probe and the real sensor in the simulation is 4.

 

Fig. 5. (a) Noise distribution of laser without dither, white noise, and 1/f noise. (b) Phase noise distribution after demodulation.

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The principle of eliminating laser frequency noise in the Ref. [34,35] is similar to the principle of our proposed scheme, which is to obtain the frequency noise of the laser by introducing a reference probe, and then use the reference probe to correct the laser frequency noise in the sensing unit. But the difference is that the echo power of the reference probe introduced by our scheme is higher than that of the sensing unit, which makes our scheme not only suppress laser frequency noise, but also solve the problem of white noise superposition in the phase noise correction process, that is, suppress white noise, but this is not in the DAS system mentioned. Compared with the DAS based distributed hydrophones, in general, the interferometric sensor based TDM system has less noise and better consistency [32,36,37], and the scheme proposed in this paper can not only effectively suppress laser frequency noise, but also effectively suppress the superposition of white noise, which further enhances the performance of the system in the previous advantages.

4. Conclusion

In summary, we proposed a novel TDM hydrophone array, which includes a reference probe that can detect the frequency noise of the light source in real time and correct the demodulated phase of the real sensors. We solve the problem of white noise superposition in the previous similar phase noise correction process by appropriately increasing the optical power of the reference probe to minimize the phase noise deterioration. Through simulations and experiments, we demonstrated that the proposed TDM array was able to reduce the noise floor deterioration from 3 dB to within 1 dB compared to conventional correction algorithms. We applied this technique to a hydrophone demodulation system based on LFM, which takes advantage of the high fiber nonlinearity threshold of LFM optical pulses and overcomes the difficulties of narrow linewidth of the laser due to the non-zero arm length difference of the interferometer. Experiments showed that the laser linewidth requirement of LFM demodulation technique could be relaxed to 338.06 MHz after the adoption of the proposal, which will pave the way for the practical application of hydrophone demodulation system based on LFM scheme.