Water Temperature and Salinity Measurement Using Frequency Comb

Water temperature and salinity are key parameters in many fields such as industry, forestry and agriculture. In this paper, we, theoretically and experimentally, demonstrate a method which is capable of water temperature and salinity measurement based on a laser frequency comb at 518 nm. We have developed a simple Michelson interferometer system. By scanning a mirror on a precision displacement platform, a pair of cross-correlation patterns can be obtained. The real-time optical distance information from these cross-correlation patterns can be used to calculate the optical distance difference changes. Temperature and salinity can be measured via these changes, aided by the empirical formulas. Compared with the reference values, our results show the differences of below 0.12 ◦C for temperature measurements, and 0.06% for salinity measurements. The obtained results indicate that our method can offer a powerful scheme for future temperature and salinity measurement.


Introduction
Water temperature and salinity are essential to many aspects, such as industry, agriculture, aquaculture, forestry, potable usage, sailing, entertainment, and scientific research. In aquaculture, water temperature and salinity are significant parameters for fish growth, survival, reproduction and disease resistance [1,2]. In nuclear power plants, the water temperature should be well and precisely controlled during the nuclear reaction [3]. Besides, the spent nuclear fuel which is full of dissolved ammonium salt with radioactivity should be seriously monitored to prevent severe environmental pollution. For chemical research, some bio-colonies are usually cultivated in a solution. On this occasion, a suitable amount of salinity and a proper temperature are the premise of the experiment. These two physical parameters also mean a lot to oceanography, ocean dynamics, ocean-atmosphere interactions, and underwater communication [4]. The specific phenomenon, such as the internal wave, which can not only improve energy and nutrient exchange, but also affect marine facilities, is related to water temperature and salinity. In a word, the temperature and salinity measurements are imperative and worthwhile.
On account of many aspects mentioned above, the temperature and salinity measurement have received increasing interest in recent years. Scientists and engineers all over the world have come up with multiple methods to measure these two physical quantities. The current methods can be mainly regarded as two groups, direct measurement and indirect measurement. In the perspective of direct measurement, the initial temperature sensor, which is still used in marine surveys nowadays, is the reversing thermometer [5], whose measurement principle is similar to the mercury thermometer. The accuracy can be up to 0.02 • C; nevertheless, its disadvantage lies in long response time and non-continuous measurement. In addition, the other direct temperature measurement sensors are In recent years, since the frequency combs were invented, scientists all over the world have been searching for its application field. The underwater application is a brand-new area for frequency combs, which has rarely been reported on before. Recently, our group has realized underwater distance measurement by frequency comb in both time domain and frequency domain [31]. The experiment results show a difference of 100 µm in the range of 8 m. In this paper, we adopt the frequency comb to realize the detection of water temperature and salinity. The experiments are carried out in a water tank. We adopt a simple Michelson interferometer, in which two measurement arms are designed. A pair of cross-correlation patterns can be obtained to detect the distance between the water arm and air arm, which can be converted to the temperature and salinity by empirical formulas. In particular, our configuration can eliminate the effects of water tank thermal expansion. Meanwhile, a salinity sensor and temperature sensor are involved, whose results can be used to evaluate our measurement results. The experimental results show that our method can precisely measure temperature and salinity.

Temperature Measurement Setup
As shown in Figure 1, the experiment setup is presented. Above all, the whole experiment configuration can be considered as two sections. One section is used for sensing the optical distance variations caused by temperature; the laser source we employ in this section is frequency comb FC (Menlo system orange, FC1000, 518 nm, 100 MHz, 500 mW), links to the frequency reference, Rb clock (Microsemi 8040). In the picture above, the frequency comb sends out a laser beam, which is split from the Beam splitter 1 BS1 (Thorlabs, BSW10R) into two parts. One is reflected by mirror 1 M1 (Thorlabs, PF10-03-P01) fixed in a precision displacement PDP (PI, M521.DD1), which serves as Reference arm RA. The other is divided by BS2. The transmission beam is traversing part of a quartz glass water tank full of water, and reflected by M2, leading into a measurement arm 1 (MA1). The reflection beam is going through the empty part of water tank, and reflected by M4, which introduces the measurement arm 2 (MA2). Three arms meet at the output of BS1, and detected by PD1 (Thorlabs, PDA36A-EC), and waveforms can be observed from the Oscilloscope Scope (LeCroy, WaveRunner9000-MS). The second section is led by a Cw laser (Spectra-Physics, Excelsior-532-300-CDRH, 532 nm), which is used to get a precise position of the scanning mirror M6 by counting the quantity of fringes. This whole section works as a Cw laser interferometer. Please note that M1 and M6 are connected and scanned together. In addition, in this configuration, temperature is measured as a reference by temperature sensor TS (Seabird, SBE56 Temperature Logger) in real time. Besides, the water tank is divided into two partitions: one is full of water, the other is empty. Lastly, the laser beam should be perpendicular to the glass wall to minimize measurement uncertainty, and the distance L 1 in Figure 1 are set very close to make sure the glass temperature of the empty part is almost the same with the water part.
note that M1 and M6 are connected and scanned together. In addition, in this configuration, temperature is measured as a reference by temperature sensor TS (Seabird, SBE56 Temperature Logger) in real time. Besides, the water tank is divided into two partitions: one is full of water, the other is empty. Lastly, the laser beam should be perpendicular to the glass wall to minimize measurement uncertainty, and the distance L1 in Figure 1 are set very close to make sure the glass temperature of the empty part is almost the same with the water part.

Salinity Measurement Setup
The salinity measurement setup is arranged as in Figure 1, which is the same with the temperature system. Please note that the salinity sensor (Mellter Toledo, Seven2go Pro) is used here to measure salinity as a reference, which will be compared with the measurement results. Meanwhile, the temperature sensor serves as a temperature monitor. The water used here is also distilled water in order to get a larger salinity measurement range. Considering the temperature also contributes to the refractive index, the environment should be constant. The experiment photograph is shown in Figure 2.

Salinity Measurement Setup
The salinity measurement setup is arranged as in Figure 1, which is the same with the temperature system. Please note that the salinity sensor (Mellter Toledo, Seven2go Pro) is used here to measure salinity as a reference, which will be compared with the measurement results. Meanwhile, the temperature sensor serves as a temperature monitor. The water used here is also distilled water in order to get a larger salinity measurement range. Considering the temperature also contributes to the refractive index, the environment should be constant. The experiment photograph is shown in Figure 2.

Materials and Methods
Theoretically, the optical path length of MA1 Lw and MA2 La can be expressed as: Among these Equations, ng is the group refractive index of glass. nw stands for the group refractive index of the water. na represents the group refractive index of air. Please note that the MA1

Materials and Methods
Theoretically, the optical path length of MA1 L w and MA2 L a can be expressed as: Appl. Sci. 2019, 9, 5043 5 of 14 Among these Equations, n g is the group refractive index of glass. n w stands for the group refractive index of the water. n a represents the group refractive index of air. Please note that the MA1 optical path distance L w is slightly longer than MA2 L a . Therefore, the optical path difference (OPD) between MA1 and MA2 can be calculated as: When water temperature or salinity changes respectively, the variation of water group refractive from n w to n w1 will change the optical length of MA1 from L w to L w1 , which results in OPD changing into OPD1.

Temperature Measurement Principle
There are various formulas that exclaim the relations of temperature and salinity. In this presented work, we adopt the Quan-Fry formula [32]: In this empirical Equation, S is the salinity in % , T is the temperature in degrees Celsius and λ is the wavelength in nanometers. Here are the coefficient values: With this formula, the phase refractive index n can be obtained. The relation between the group refractive index n w1 and phase refractive index n is: By Equations (8) and (9), the group refractive index n w1 can be indicated as: Hence, the temperature T can be expressed as: In order to avoid the cross-sensitivity influence, we only focus on the situation of distilled water, whose salinity can be considered as 0. Therefore, Equation (11) can be rewritten as: With Equations (7) and (12), we can convert group refractive index n w1 into the temperature T.

Salinity Measurement Principle
Based on the Quan-Fry formula mentioned above, with the Equation (11), the salinity can be expressed as: When the water temperature is relatively constant, with the Equations (7) and (13), the group refractive index n w1 and salinity value S can be converted to each other.

Geometry Distance of the Water
Based on the theoretical analysis carried out above, the measurement of water geometric distance is indispensable. In order to obtain this value, two steps are required.
To the beginning, half part of the water container is full of water, and the other is empty. Thus, a distance value OPD can be acquired. This distance value introduces the optical path difference between MA1 and MA2.
Afterwards, both sides of the container should be empty, and the optical distance of MA1 will be changed to L w2 . Therefore, a new distance value OPD2 will be obtained, which stands for the optical distance between new MA1 and MA2. Please note that when one side of the water tank is full of water, L w is slightly longer than L a , which has been mentioned above. Hence, when both sides of the water tank are empty, L a will be longer than L w2 . Consequently, the water geometry distance can be calculated by the following Equations: The group refractive index n w and n a can be calculated via the empirical formulas. After the values OPD and OPD2 are acquired, D can be calculated.

The Initial Refractive Index
In order to get n w1 , it is also necessary to get the value of n w0 , that is, the initial water group refractive index.
Based on the analysis above, n w0 can be calculated as: The air group refractive index n a can be acquired via the Ciddor formula [33]. Please note that abbreviations we use above are well explained in Appendix A.

Measurement of Water Geometry Distance
In this section, we describe the measurement of the water geometry distance. The environment parameters are: temperature 23.2 • C, pressure 1007.06 hPa, and humidity 16.67%. The group refractive index of air n a can be calculated as 1.00026325 by Ciddor formula.
Firstly, half part of the water tank is full of water. As is shown in Figure 3a, by scanning the moving stage at the speed of 3.5 mm/s, a pair of cross-correlation patterns can be obtained, which is consistent with the position of M2 and M4. Due to the strong dispersion of water, the cross-correlation pattern of MA1 compared with the MA2 is distinctively broadened to about 330 µm (1.1ps). The water temperature is 22.76 • C and the salinity is 0, so the water group refractive index n w can be calculated as 1.35829166 by Equation (10). We do a Hilbert transform to the patterns in Figure 3a, and the results are shown in Figure 3b. Peak positions are marked in the picture, which are used to acquire the corresponding quantities of fringes in the Cw laser interferometer. Hence, the OPD can be measured as 2.424 mm. Secondly, the water tank is empty. By scanning the moving stage at the speed of 30 mm/s, a new pair of cross-correlation patterns is shown in Figure 4a, where the inset is the detailed observation of the patterns. The corresponding Hilbert transform is performed, and the result is indicated in Figure  4b, where the inset is the expansion of the curve. Peak positions are used to acquire the corresponding quantities of fringes. Consequently, the OPD can be measured as 76.716 mm.
Hence, the geometry of the distance D can be calculated as:

Measurement of Water Temperature
We undertook 10-h-long experiments twice from 10:00 p.m. to 8:00 a.m. and from 9:00 p.m. to 7:00 a.m.; during this period, the indoor environments are relatively constant. In the experiment, the water temperature is naturally cooled to environment temperature, which is a very slow procedure. We can regard the water as uniform, and the temperature changes relatively evenly. During the experiment, we use the temperature sensor to detect the neighbor temperature of the water optical beam, which serves as a temperature reference. Please note that in this experiment, distilled water is used and the initial salinity is 0. The scanning speed for PDP is 3 mm/s. Figure 5 shows the cross-correlation patterns in 25.33 °C and 24.50 °C. Figure 6 shows the corresponding Hilbert transform, and the measured OPD change from 0.389 mm to 0.406 mm. As is shown in Figures 5 and 6, we can find that the OPD has enlarged due to the temperature decreasing. Secondly, the water tank is empty. By scanning the moving stage at the speed of 30 mm/s, a new pair of cross-correlation patterns is shown in Figure 4a, where the inset is the detailed observation of the patterns. The corresponding Hilbert transform is performed, and the result is indicated in Figure 4b, where the inset is the expansion of the curve. Peak positions are used to acquire the corresponding quantities of fringes. Consequently, the OPD can be measured as 76.716 mm. Secondly, the water tank is empty. By scanning the moving stage at the speed of 30 mm/s, a new pair of cross-correlation patterns is shown in Figure 4a, where the inset is the detailed observation of the patterns. The corresponding Hilbert transform is performed, and the result is indicated in Figure  4b, where the inset is the expansion of the curve. Peak positions are used to acquire the corresponding quantities of fringes. Consequently, the OPD can be measured as 76.716 mm.
Hence, the geometry of the distance D can be calculated as:

Measurement of Water Temperature
We undertook 10-h-long experiments twice from 10:00 p.m. to 8:00 a.m. and from 9:00 p.m. to 7:00 a.m.; during this period, the indoor environments are relatively constant. In the experiment, the water temperature is naturally cooled to environment temperature, which is a very slow procedure. We can regard the water as uniform, and the temperature changes relatively evenly. During the experiment, we use the temperature sensor to detect the neighbor temperature of the water optical beam, which serves as a temperature reference. Please note that in this experiment, distilled water is used and the initial salinity is 0. The scanning speed for PDP is 3 mm/s. Figure 5 shows the cross-correlation patterns in 25.33 °C and 24.50 °C. Figure 6 shows the corresponding Hilbert transform, and the measured OPD change from 0.389 mm to 0.406 mm. As is shown in Figures 5 and 6, we can find that the OPD has enlarged due to the temperature decreasing.

Measurement of Water Temperature
We undertook 10-h-long experiments twice from 10:00 p.m. to 8:00 a.m. and from 9:00 p.m. to 7:00 a.m.; during this period, the indoor environments are relatively constant. In the experiment, the water temperature is naturally cooled to environment temperature, which is a very slow procedure. We can regard the water as uniform, and the temperature changes relatively evenly. During the experiment, we use the temperature sensor to detect the neighbor temperature of the water optical beam, which Appl. Sci. 2019, 9, 5043 8 of 14 serves as a temperature reference. Please note that in this experiment, distilled water is used and the initial salinity is 0. The scanning speed for PDP is 3 mm/s. Figure 5 shows the cross-correlation patterns in 25.33 • C and 24.50 • C. Figure 6 shows the corresponding Hilbert transform, and the measured OPD change from 0.389 mm to 0.406 mm. As is shown in Figures 5 and 6, we can find that the OPD has enlarged due to the temperature decreasing.  We conducted 10-h-long measurements from 10:00 p.m. to 8:00 a.m. and from 9:00 p.m. to 7:00 a.m., and the results are shown in Figures 7a and 8a. Please note that the data are stored in a short time interval in the former experiment, and the latter in a lager time interval. In Figures 7a and 8a, the red solid circle stands for our experiment results, and the black solid line is indicated as the reference results obtained by the temperature sensor. The corresponding deviations between our method and the reference are shown in Figures 7b and 8b. Compared with the reference values, our results show differences of below 0.12 °C for temperature measurements.   We conducted 10-h-long measurements from 10:00 p.m. to 8:00 a.m. and from 9:00 p.m. to 7:00 a.m., and the results are shown in Figures 7a and 8a. Please note that the data are stored in a short time interval in the former experiment, and the latter in a lager time interval. In Figures 7a and 8a, the red solid circle stands for our experiment results, and the black solid line is indicated as the reference results obtained by the temperature sensor. The corresponding deviations between our method and the reference are shown in Figures 7b and 8b. Compared with the reference values, our results show differences of below 0.12 °C for temperature measurements.  We conducted 10-h-long measurements from 10:00 p.m. to 8:00 a.m. and from 9:00 p.m. to 7:00 a.m., and the results are shown in Figures 7a and 8a. Please note that the data are stored in a short time interval in the former experiment, and the latter in a lager time interval. In Figures 7a and 8a, the red solid circle stands for our experiment results, and the black solid line is indicated as the reference results obtained by the temperature sensor. The corresponding deviations between our method and the reference are shown in Figures 7b and 8b. Compared with the reference values, our results show differences of below 0.12 • C for temperature measurements.
time interval in the former experiment, and the latter in a lager time interval. In Figures 7a and 8a, the red solid circle stands for our experiment results, and the black solid line is indicated as the reference results obtained by the temperature sensor. The corresponding deviations between our method and the reference are shown in Figures 7b and 8b. Compared with the reference values, our results show differences of below 0.12 °C for temperature measurements.

Measurement of Salinity
In the experiment, the ambient environment is constant, and the water temperature is constant at 24.5 °C. A multifunctional salinity sensor is adopted to measure the real-time salinity and temperature. During the experiment, we use an analytical balance to add the sodium chloride 10.00 g each time, and wait for 2 h until the sodium chloride is completely dissolved. Please note that in order to get a large measurement range, distilled water is also used in this experiment, and the initial salinity is 0. The scanning speed for PDP is 3 mm/s. Figure 9 shows the cross-correlation patterns in 2.15‰, 4.31‰, 6.49‰ and 8.68‰. The corresponding Hilbert transforms are shown in Figure 10, and the measured OPD are marked in the figure. We can see the results from Figures 9 and 10. When the salinity increases, the refractive index increases, which results in the optical distance difference enlarging.

Measurement of Salinity
In the experiment, the ambient environment is constant, and the water temperature is constant at 24.5 • C. A multifunctional salinity sensor is adopted to measure the real-time salinity and temperature. During the experiment, we use an analytical balance to add the sodium chloride 10.00 g each time, and wait for 2 h until the sodium chloride is completely dissolved. Please note that in order to get a large measurement range, distilled water is also used in this experiment, and the initial salinity is 0. The scanning speed for PDP is 3 mm/s. Figure 9 shows the cross-correlation patterns in 2.15% , 4.31% , 6.49% and 8.68% . The corresponding Hilbert transforms are shown in Figure 10, and the measured OPD are marked in the figure. We can see the results from Figures 9 and 10. When the salinity increases, the refractive index increases, which results in the optical distance difference enlarging.
order to get a large measurement range, distilled water is also used in this experiment, and the initial salinity is 0. The scanning speed for PDP is 3 mm/s. Figure 9 shows the cross-correlation patterns in 2.15‰, 4.31‰, 6.49‰ and 8.68‰. The corresponding Hilbert transforms are shown in Figure 10, and the measured OPD are marked in the figure. We can see the results from Figures 9 and 10. When the salinity increases, the refractive index increases, which results in the optical distance difference enlarging.  We conducted a measurement from 0 to 15.80‰, and the results are shown in Figure 11a. In Figure 11a, the blue solid circle stands for our experiment results and the dashed line is indicated as the reference results obtained by the salinity sensor. The corresponding deviations between our method and the reference are shown in Figure 11b. We can see that our results show differences below 0.06‰ for salinity measurements, compared with the reference values. We conducted a measurement from 0 to 15.80% , and the results are shown in Figure 11a. In Figure 11a, the blue solid circle stands for our experiment results and the dashed line is indicated as the reference results obtained by the salinity sensor. The corresponding deviations between our method and the reference are shown in Figure 11b. We can see that our results show differences below 0.06% for salinity measurements, compared with the reference values. We conducted a measurement from 0 to 15.80‰, and the results are shown in Figure 11a. In Figure 11a, the blue solid circle stands for our experiment results and the dashed line is indicated as the reference results obtained by the salinity sensor. The corresponding deviations between our method and the reference are shown in Figure 11b. We can see that our results show differences below 0.06‰ for salinity measurements, compared with the reference values.  Based on the results in Figures 7, 8 and 11, it is clear that the two parameters, temperature and salinity, can be precisely measured by our method. The comparisons with the reference values show a difference of within 0.12 • C for temperature measurements, and within 0.06% for salinity measurements, respectively. The deviations can be attributed to the measurement accuracy of the corresponding OPD, and the accuracy of the empirical formula (i.e., Quan-Fry formula). We consider that several factors can make contributions to the measurement accuracy of OPD, including the accuracy of the precision displacement platform, the program of the data process, thermal expansion of the water tank, optical beam alignment, and water inhomogeneity. Additionally and alternatively, other empirical formulas (e.g., Harvey formula [34], Millard [35], McNeil [36]) can be used to calculate the temperature and salinity.

Conclusions
In this work, a frequency comb, for the first time, is applied to measure water temperature and salinity. We achieved the target of temperature and salinity measurement, respectively. By a simple Michelson interferometer, based on the optical distance difference change between two arms, the refractive index change can be obtained, which empirical formulas can convert into temperature and salinity. Compared with the reference values, our results show differences of below 0.12 • C for temperature measurements, and 0.06% for salinity measurements. Owing to the limitation of our experimental equipment, we performed the experiment in a limited range. However, our method can be applied to a larger range, which provides a powerful scheme for future temperature and salinity measurements.  Salinity Sensor L 0 , L 1 , L 2 , L 3 , L 4 geometric distance of the optical path in Figure 1  D geometric distance of water d thickness of the glass tank L w , L w1 , L w2 optical path length of AM1 L a optical path length of AM2 OPD, OPD1, OPD2 optical path difference between AM1 and AM2 n g group refractive index of glass n w , n w1 group refractive index of water n w0 initial water group refractive index n a group refractive index of air n phase refractive index of water n (S, T, λ) phase refractive index in Quan-Fry formula n 0 , n 1 , n 2 , n 3 , n 4 , n 5 , n 6 , n 7 , n 8 , n 9 coefficient values in Quan-Fry formula S salinity in % T water temperature in • C λ optical wavelength in nanometers