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Abstract
Accurate remote sensing of the sound velocity profile of the upper-ocean mixed layers is of major important in oceanography, especially in underwater acoustic communication. However, the existing technologies cannot realize fast and real-time detection on sound velocity profile, a cost efficiency, flexibility, and real-time remote sensing technique is still highly urgent. In this paper, we propose a novel approach based on stimulated Brillouin scattering (SBS) LiDAR for retrieving the sound velocity profile. The sound velocity profiles in the upper-ocean mixed layer of South China Sea were retrieved theoretically and experimentally. We simulated the sound velocity profile of the upper-ocean mixed layer in South China Sea by using the Del Grosso algorithm and the data of temperature, salinity, depth selected from the World Ocean Atlas 2018 (WOA18). We designed a special ocean simulation system to measure the sound velocity in seawater with different temperatures, salinities, and pressures through measuring the frequency shift of SBS. Based on the measured sound velocities, we built a retrieval equation to express the sound velocity as a function of temperature, salinity, and pressure. Then, we retrieved the sound velocity profile of the upper-ocean mixed layer of South China Sea by using the retrieval equation. The results show that the retrieved sound velocity profile is good agreement with the theoretical simulation, and the difference between them is approximately 1∼2 m/s. Also, we have analyzed the differences between the theoretical simulation and experimental measurement. This work is essential to future application for remote sensing the sound velocity distribution profiles of the upper-ocean mixed layers by using the Brillouin LiDAR technique.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Accurate remote sensing of the sound velocity profile of the upper-ocean mixed layers is of major important in oceanography. One important reason is that acoustic waves are currently the only option for long-range (over 200 m) underwater communications [1]. Acoustic communication is critical for improving ocean exploration and fulfilling the needs of a multitude of underwater applications such as oceanographic data collection, warning systems for natural disasters, military underwater surveillance, assisted navigation, offshore explorations, etc [2,3]. Underwater acoustic channels are generally recognized as one of the most difficult communication media in use today. Sound propagates underwater at a very low speed of approximately 1500 m/s, and propagation occurs over multiple paths. In the upper mixed layers over an extended region of the ocean, sound velocity depends on the temperature, salinity, and pressure, which vary with the depth and location of ocean [4,5]. It means that the distribution of underwater acoustic channels is also influenced by these ocean parameters, which determine the number of propagation paths, propagation distances, and time delays of acoustic communication. Therefore, it is extremely important to investigate the sound velocity profile of the upper-ocean mixed layers.
There are two types of main approaches to obtain the sound velocity in ocean. One is to calculate the sound velocity with the empirical equation by obtaining the temperature, salinity and pressure of seawater using the conductivity-temperature-depth (CTD) instruments [6,7], which is classified as indirect measurement. The other is to calculate the value of the sound velocity by obtaining physical quantities related to the sound velocity, which is classified into the direct measurement, such as standing wave interferometry, resonance acoustic spectroscopy, phase comparison method, time difference method and so on [8–11]. However, these two types of ways are time-consuming, labor-intensive, and low-resolution and do not allow the rapid, accurate, and real-time range-resolved detection. Therefore, a cost efficiency, flexibility and real-time remote sensing technique for sound velocity is highly urgent.
Brillouin LiDAR is a promising tool for such remote sensing of the sound velocity. Brillouin LiDAR involves Brillouin scattering, LiDAR, and remote sensing technology, it was proposed by Guagliardo et al. in 1980 [12]. Several studies have demonstrated the feasibility of Brillouin scattering for measuring the sound velocity and temperature in water [13–18]. Compared with the other methods, Brillouin LiDAR has the advantages of real-time, high accuracy, and non-contact. And more importantly, Brillouin LiDAR holds the potential ability to obtain the depth-resolved temperature and sound velocity profiles in the upper ocean mixed layers over an extended region of the ocean [19–21]. At present, a great deal of works have demonstrated the potential of Brillouin LiDAR for detecting the temperature, sound velocity, and underwater objects [22–30].
In this paper, the sound velocity profiles of the upper-ocean mixed layers are retrieved theoretically and experimentally. Theoretically, the temperature and salinity data of the South China Sea are selected from the World Ocean Atlas 2018 (WOA18) [31,32] as an example for retrieving the sound velocity profile from 0 to 400 m. Experimentally, a special ocean simulation system is designed to measure the Brillouin frequency shift for retrieving the sound velocity profile by using SBS LiDAR technique. The corresponding acoustic impedances in different temperatures, salinities, and pressures are also presented based on the retrieved sound velocity results. The results provide the significant support for remote sensing the sound velocity profiles of the upper-ocean mixed layers by using Brillouin LiDAR technique.
The structure of this article is as follows. The general principle for retrieving the sound velocity is introduced in Section 2. The theoretical simulation results of sound velocity distribution profile in the upper-ocean mixed layer of South China Sea are presented in Section 3. Experimental Setup and measurement are described in detail in Section 4. Experimental results and discussions are described in Section 5. Section 6 summarizes the theory, experiment, and data analysis.
2. General principle
2.1 Del Grosso algorithm
There are three empirical expressions for calculating the sound velocity in seawater that Del Grosso algorithm [33,34], Wilson algorithm [35,36] and Chen-Millero-Li algorithm [37,38]. The three algorithms present different applicable ranges and errors for calculating the sound velocity of seawater. After analyzing the results of sound velocity, the standard errors of Del Grosso algorithm, Wilson algorithm and Chen-Millero-Li algorithm are 0.05, 0.30, and 0.19 m/s, respectively. Therefore, the Del Grosso algorithm is employed for the theoretical calculation of sound velocity in our work.
The sound velocity in seawater is related to the temperature, salinity, and pressure of seawater. The Del Grosso algorithm for the sound velocity in seawater has been developed with validity not only for realistic combinations of the temperature, salinity, and pressure, but with extension to pure water as well. The equation of Del Grosso algorithm for sound velocity can be expressed as [34]:
where the ${c_0}$ is a constant, ${c_T}$, ${c_S}$, ${c_P}$ and ${c_{TSP}}$ are related to the temperature (T), salinity (S), and pressure (P) of seawater, respectively. T is in °C, S is in ‰, and P is in kg/cm2. Therefore, the sound velocity can be obtained by combining the temperature, salinity, and pressure of seawater that are obtained from historical oceanographic data.2.2 Fundamentals of Brillouin scattering
Brillouin scattering is one of the light scattering phenomena, which is a typical inelastic scattering effect generated by the interaction between the incident light and the elastic acoustic wave field in mediums. The acoustic waves are derived from the thermal density fluctuations of mediums. The acoustic waves move stochastically in all propagation directions with the sound velocity. Due to the optical Doppler effect, the scattered light exhibits a symmetric frequency shift with respect to the initially incident light at the wavelength $\lambda$. The frequency shift of Brillouin scattering can be expressed as [18]:
There are two alternative techniques for constructing Brillouin LiDAR: spontaneous Brillouin scattering and stimulated Brillouin scattering (SBS) [39–41]. Compared with spontaneous-Brillouin LiDAR, SBS LiDAR has the advantages of optical phase conjugation (OPC) and high signal-to-noise ratio (SNR) [42,43]. Owing to the OPC effect of SBS, the scattering angle θ is equal to 180°, so the frequency shift of SBS can be expressed as:
For a given incident laser wavelength $\lambda$, the sound velocity can be retrieved by using the frequency shift of Brillouin scattering:
The refractive index $n({S,T,\lambda ,P} )$ is depended on the wavelength, temperature, salinity, and pressure, and can be calculated by using the equation as reported by Seaver [44]:
3. Theoretical simulation
Based on the theory mentioned above, the upper-ocean mixed layer of the partial regions in South China Sea is selected as an example for retrieving the sound velocity distribution profile from 0 to 400 m. The data of temperature and salinity at different depths in South China Sea can be obtained from the World Ocean Atlas 2018 (WOA18). In this work, we selected the annual average data of temperature and salinity at latitude 5.5°∼19.5°N, longitude 109.5°∼119.5°E and depth 0∼400 m (corresponding to pressure 0∼4 MPa) in South China Sea. Figure 1(a) and 1(b) show the temperature and salinity profiles of the upper-ocean mixed layer of the partial regions in South China Sea, respectively. It can be seen that the temperature varies from 9.38 to 29.96 °C when the depth varies from 0 to 400 m. The temperature decreases layer by layer with the increase of depth, and drops by about 4 °C when the depth increases by 100 m. At the same depth layer, the temperature distribution is relatively uniform. In Fig. 1(b), the salinity varies from 32.14 to 34.58 ‰, and the extremum of salinity is about 2.44 ‰ within the depth of 0∼400 m. The salinity increases layer by layer with the increase of depth and then tends to be stable. The salinity distribution near the surface is not homogeneously, the maximum salinity layer distributes in the depth of about 200 m.
Fig. 1. The temperature and salinity profiles in the partial region of South China Sea. (a) Temperature; (b) Salinity.
Based on the temperature and salinity distributions, the sound velocity can be calculated by using Eq. (1). The sound velocity distribution profile is shown in Fig. 2. The sound velocity varies from 1493.24 to 1541.94 m/s within the depth of 0∼400 m. We can see that the sound velocity distribution is basically consistent with the distribution of temperature in the corresponding regions. In the upper-ocean mixed layer, the temperature decreases with the increase of depth, while the changes of salinity and pressure (depth) are not enough to offset the effect of temperature on the sound speed, the sound velocity thus decreases with the increase of depth. The region of upper-ocean mixed layer is called the main thermocline.
To show more visually the relationship between the sound velocity and the ocean depth, Fig. 3 gives the two-dimensional distributions of sound velocity at the latitude 12.5°N and longitude 114.5°E, respectively. It can be seen that the sound velocity distribution in South China Sea is higher at low latitude and high longitude due to the distinct thermocline at the depth of 0∼200 m. After the depth of 200 m, the sound velocity distribution is almost uniform and presents slightly different. The relationship between the sound velocity and the ocean depth can also be seen from the variation curves as shown in Fig. 4. Figure 4 presents the changes of sound velocity versus the change of depth at three different geographical locations (12.5°N, 114.5°E), (19.5°N, 119.5°), and (5.5°N, 113.5°E). Within the depth of 0∼200 m, the sound velocity decreases by about 30 m/s, while decreases by about 10 m/s within the depth of 200∼400 m.
The acoustic impedance is also an important parameter that reflects the transmission of acoustic waves in medium. The acoustic impedance can be expressed by combining the sound velocity and the density as [45]:
where Z is the acoustic impedance, ${\upsilon _s}$ is the sound velocity, and $\textrm{v}$ is the specific volume(reciprocal of density [46]). The specific volume can be expressed as a function of temperature, salinity, and pressure [45]:
The unit of specific volume is cubic centimeter per gram (cm3/g). Figure 5 shows the calculated results of the acoustic impedance, it varies from 1.536×105 to 1.575×105 g/cm2·s. Since the variation range of specific volume is very small from 0.969 to 0.980 cm3/g, the distribution of acoustic impedance is similar to that of the sound velocity.
Based on the above simulation results, we can see that the temperature, salinity, and pressure (depth) of seawater in the upper-ocean mixed layer have different effects on the sound velocity. Compared with the salinity and pressure, the temperature is the most important factor for the sound velocity and acoustic impedance in the upper-ocean mixed layer. Therefore, the distribution profiles of sound velocity and acoustic impedance are similar to that of the temperature. To verify the theoretical simulation results, we have designed a special ocean simulation system to measure the sound velocity in seawater with different temperatures, salinities, and pressures through measuring the frequency shift of SBS, the experiment and results are as follows.
4. Experimental measurement
The configuration of the Brillouin LiDAR system during the measurement of the Brillouin frequency shift is illustrated in Fig. 6. The light source is an injection-seeded and Q-switched Nd: YAG pulse laser operating at 532 nm. Its repetition frequency is 10 Hz, pulse duration is 8 ns, beam diameter is 17 mm, divergence angle is 0.45 mrad. The linewidth of single-longitudinal mode is about 90 MHz. The maximum pulse energy is ∼4 J/pulse, which is higher than the threshold of SBS in seawater. Therefore, the laser power is enough for actual Brillouin frequency measurement. An ocean simulation system consisted of a pressure chamber with one meter length and four hydraulic pumps was employed to simulate the static sea parameters of upper-ocean mixed layer, such as temperature, salinity, and pressure (depth). Since the seawater pressure increases linearly with the increase of the ocean depth [26,47], the ocean depth can be simulated by varying the pressure in the pressure chamber. The maximum pressure of ocean simulation system is 10 MPa (The corresponding depth is about 1000 meters), the water temperature can be stabilized to values between 4 and 40 °C. The pressure sensor and thermocouple are installed to measure the pressure and temperature in the chamber.
Fig. 6. Configuration of the Brillouin LiDAR system for measuring the Brillouin frequency shift. λ/2: half-wave plate, λ/4: quarter-wave plate, PBS: polarization beam splitter, PM: power meter, P: pinhole filter.
The output laser beams from the laser source with the vertical polarization pass through λ/2, PBS and λ/4 in turn and then were focused by achromatic lens into the chamber of ocean simulation system, where the pressure and temperature can be controlled. The SBS signals were excited in the chamber and collected into the spectrometer system consisted of F-P etalon and ICCD camera. The free spectral range (FSR) of the F-P etalon is 20.1 GHz. The timing relationship of the entire system was precisely controlled by the pulse delay generator. The output laser energy was monitored by using the power meter.
Based on the annual average data of temperature and salinity of the upper-ocean mixed layer of the partial regions in South China Sea used in theoretical simulation, the seawater with the salinities of 30, 32, 34, and 35 ‰ were prepared, respectively, by dissolving sea salt (Sigma-Aldrich) in distilled water, the water temperature was stabilized to values between 10 and 30 °C, and the pressure was set at the range of between 0 and 4 MPa.
Figure 7 shows the measured SBS spectrum of seawater when the temperature is 25 °C, salinity is 34 ‰, and pressure is 0 MPa. Figure 7(a) is the original two-dimensional spectrum obtained by using F-P etalon and ICCD camera, in which each order of the fringe includes two rings: the Rayleigh scattering ring and Stokes Brillouin scattering ring. The Brillouin frequency shift can be obtained through image preprocessing, data fusing, spectrum denoising, and spectrum deconvoluting in turn from the original two-dimensional spectrum. Figure 7(b) is the one-dimensional spectrum extracted from Fig. 7(a). rj and rj-1 represent the center position of two neighboring Rayleigh peaks, bj represents the peak position of j-order Brillouin scattering, bj,left and bj,right represent the half-maximum positions, ${\nu _B}$ is the Brillouin frequency shift corresponding to the distance between the Brillouin peak and the Rayleigh peak in the same order, and ${\Gamma _B}$ is the full width at half maximum (FWHM) of Brillouin peak. FSR is the free spectral range of the F–P etalon. The Brillouin frequency shift can be calculated by the following relation [30,48]:
Fig. 7. Backscattered SBS spectrum collected by using F-P etalon and ICCD camera. (a) Original two-dimensional spectrum; (b) one-dimensional spectrum extracted from original spectrum, the abscissa axis represents the pixel points of ICCD.
5. Experimental results and discussions
Figure 8 shows the theoretical and experimental frequency shifts of Brillouin scattering under different temperatures and pressures when the salinity is 0 ‰. It can be seen that the Brillouin frequency shift increases with the increase of temperature at the same pressure and increases with the increase of pressure at the same temperature. To show more visually the relationship between the Brillouin frequency shift and the seawater parameters, Fig. 9 gives a three-dimensional (3D) plot of the experimental data. The experimental results show that the frequency shift varies from 7.48 to 7.83 GHz when the seawater was controlled at the temperature of 10∼30 °C, salinity of 30∼35 ‰ and the pressure of 0∼4 MPa. The frequency shift increases with the increases of temperature, salinity, and pressure. Under the same salinity and pressure, the frequency shift increases rapidly with the increase of the temperature. The results have been proved that the influence of temperature on the frequency shift is more obvious than that of salinity and pressure in the upper-ocean mixed layer.
Fig. 8. Frequency shifts of Brillouin scattering under different conditions. (a) Theoretical simulation; (b) experimental measurement.
Fig. 9. The experimental frequency shift distribution at different temperatures, salinities and pressures.
Based on the measured frequency shift values, the corresponding sound velocity values can be obtained by using Eq. (4). Figure 10 shows the 3D plot of sound velocity distributions corresponding to the results shown in Fig. 9. The sound velocity varies from 1486 to 1554 m/s. The sound velocity is positively correlated with the frequency shift, and increases with the increases of temperature, salinity, and pressure. By performing the polynomial fitting on the sound velocity data obtained from the above experiment, the following fitting equation can be obtained:
The dependence of sound velocity on the temperature, salinity, and pressure can be obtained by solving the partial derivative of Eq. (9). As an example, we selected the temperature of 20 °C, salinity of 33 ‰ and pressure of 2 MPa to analyze the dependence of sound velocity on the temperature, salinity, and pressure. The typical values for the changes in ${\upsilon _s}$ that depend on the changes in T, S, and P are:
It can be seen that the sound velocity changes 2.80, 1.14, and 1.64 m/s when the temperature changes 1 °C, the salinity changes 1 ‰, the pressure changes 1 MPa, respectively.
Substituting the data of temperature, salinity, and pressure at the depth of 0∼400 m in the partial regions of South China Sea into the fitting Eq. (9), the corresponding sound velocities can be retrieved, as shown in Fig. 11(a). The sound velocity varies from 1494.96 to 1543.66 m/s within the depth of 0∼400 m in South China Sea. The results shown in Fig. 11(a) are basically coincided with the theoretical results shown in Fig. 2, the difference between them is approximately 1∼2 m/s. According to the sound velocity profile shown in Fig. 11(a), the acoustic impedance can also be obtained by using Eq. (6), as shown in Fig. 11(b). The acoustic impedance varies from 1.537×105 to 1.577×105 g/cm2·s and is slightly larger than the results shown in Fig. 5.
Fig. 11. The distributions. (a) Sound velocity retrieved by SBS fitting equation; (b) Acoustic impedance obtained by the retrieved sound velocity.
Finally, we have analyzed the differences between the theoretical simulation and experimental measurement in frequency shift, sound velocity, and acoustic impedance at different temperatures, salinities, and pressures of seawater, the results are shown in Fig. 12. The measurement error of the frequency shift of SBS in experiment is the main factor of influence on that of the sound velocity and acoustic impedance. The error of frequency shift varies from 5 to 15 MHz, which resulting in the error of sound velocity varies from 0.9 to 2.6 m/s, and the error of acoustic impedance varies from 0.001 to 0.003 ×105 g/cm2·s. Under the error, the propagation loss of acoustic communication in the sound channel will change less than 4 dB. In this work, the frequency shift was obtained by applying the spectrum processing method, so the further improve on the spectrum processing method will be applicable to increase the measurement accuracies of sound velocity and acoustic impedance.
Fig. 12. Differences between the theoretical simulation and experimental measurement in frequency shift, sound velocity, and acoustic impedance at different temperatures, salinities, and pressures of seawater. (a) Frequency shift; (b) Sound velocity; (c) Acoustic impedance.
6. Conclusion
In this paper, the sound velocity distribution profile in the upper-ocean mixed layer of South China Sea were retrieved theoretically and experimentally. Theoretically, the sound velocity distribution profile of the upper-ocean mixed layer of South China Sea was simulated by using the Del Grosso algorithm and the annual average data of temperature and salinity at latitude 5.5°∼19.5°N, longitude 109.5°∼119.5°E selected from the World Ocean Atlas 2018 (WOA18). In the theoretical simulation, the sound velocity varies from 1493.24 to 1541.94 m/s within the depth of 0∼400 m. Experimentally, a special ocean simulation system was designed to measure the sound velocity in seawater with different temperatures, salinities, and pressures through measuring the frequency shift of SBS. In the experimental measurement, the sound velocity varies from 1494.96 to 1543.66 m/s within the pressure of 0∼4 MPa. Based on the measured sound velocities, a polynomial fitting equation was given for retrieving the sound velocity. The retrieved sound velocity profile by using the polynomial fitting equation is basically coincided with the theoretical simulation. In addition, the acoustic impedance profile of the upper-ocean mixed layer of South China Sea was presented theoretically and experimentally by using the obtained sound velocity profile. Also, the differences between the theoretical simulation and experimental measurement in frequency shift, sound velocity, and acoustic impedance at different temperatures, salinities, and pressures of seawater were given. We find that the temperature of seawater has greater effect on frequency shift, sound velocity, and acoustic impedance than that of salinity and pressure in the upper-ocean mixed layers. The results in this paper are of great significance to the research on remote sensing the profiles of temperature and sound velocity in the upper-ocean mixed layers.
Funding
National Natural Science Foundation of China (41776111); Defense Industrial Technology Development Program (JCKY2019401D002).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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