# Water Temperature and Salinity Measurement Using Frequency Comb
## 4 Results and Discussion
### Measurement of Salinity  
In the experiment, the ambient environment is constant, and the water temperature is constant at 24.5 \({}^{\circ}\)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.  
Figure 8: Long-term measurement of water temperature 9:00 p.m. to 7:00 a.m. (**a**) Results obtained using temperature sensor and our method. Red solid circle: our method results, black solid line: the temperature sensor results; (**b**) the difference between our method and the temperature sensor.  
Figure 7: Long-term measurement of water temperature from 10:00 p.m. to 8:00 a.m. (**a**) Results obtained using temperature sensor and our method. Red solid circle: our method results, black solid line: the temperature sensor results; (**b**) the difference between our method and the temperature sensor.  
Figure 10: (**a**) Results of the Hilbert transform in 2.15%; (**b**) results of the Hilbert transform in 4.31%; (**c**) results of the Hilbert transform in 6.49%; (**d**) results of the Hilbert transform in 8.68%.  
Figure 9: (**a**) Cross-correlation patterns in 2.15%; (**b**) cross-correlation patterns in 4.31%; (**c**) Cross-correlation patterns in 6.49%; (**d**) cross-correlation patterns in 8.68%.  
We conducted a measurement from 0 to 15.80%, and the results are shown in Figure 11. In Figure 11, 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 11. 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 \({}^{\circ}\)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., [PERSON] formula [34], [PERSON] [35], [PERSON] [36]) can be used to calculate the temperature and salinity.