# An Optical Differential Method for Underwater Wireless Communication in Turbid Environments
## 4 Results  
Figure 3 shows optical transmission tests at different light propagating distances in the water (a, b) and Formazin solution (c, d). The error bars stem from three measurements under the same conditions for each case. Figure 3a shows the signal reliability decays in the natural water using only the 6000 K-CCT LED. The measured optical signals include the intensity (luminous flux) and color (chromaticity coordinates). As can be seen, the light intensity decays much faster than the color. The chromaticity coordinate, \(x\), shows a negligible decay in the given propagating distance. The stable propagating distance is defined by the distance \(l\) at which the signal reliability decays to a level of 90%. The  
Figure 2: Experimental setup and light source modulation method. (**a**) Experimental setup. The insets show the details of a home-built light source with precise manipulations of chromaticity and luminosity. (**b**) Images of light spots at two positions on the optical path. (**c**) Experimental demonstration of precise color manipulations of the light source using a digital color-coding method. stable propagating distances for the chromaticity coordinates, \(x\) and \(y\), are 643.14 cm and 306.03 cm, respectively, which are 16 and 7.6 times longer than that of light intensity. If the light is switched to the 3000 K-CCT LED, the chromaticity coordinates, \(x\) and \(y\), show almost the same decay tendency, as shown in Figure 3b. The stable propagating distance for the chromaticity coordinates is 18.9 times longer than that of light intensity. In order to simulate a turbid water environment, 3 NTU Formazin solution is prepared for the light transmission tests. The diameter of Formazin particles ranges follows almost a normal distribution, and the diameter at the center of the distribution is approximately 2.7 \(\upmu\)m. If the 6000 K-CCT LED is used, the chromaticity coordinates, \(x\) and \(y\), show almost the same decay tendency, as shown in Figure 3c. The stable propagating distance for chromaticity coordinates becomes 44.1 cm, which decreases by 93% in comparison with the case in the natural water. However, the stable propagating distance for chromaticity coordinates is 5.5 times longer than that of light intensity. If the 3000 K-CCT LED is used in 3 NTU Formazin solution, the chromaticity coordinates, \(x\) and \(y\), show almost the same decay tendency, as shown in Figure 3d. The stable propagating distance for the chromaticity coordinates becomes 342.48 cm, which is 42 times longer than that of light intensity. The underwater optical communications using ODCM are further demonstrated. For guiding eyes, digital data from a binary image are encoded at the transmitting side and  
Figure 3: Spatial optical transmissions in the water and Formazin solution by using lights with different colors. (**a**) The signal reliability decays as the light of the 6000 K LED propagates in the natural water. (**b**) The signal reliability decays as the light of the 3000 K LED propagates in the natural water. (**c**) The signal reliability decays as the light of the 6000 K LED propagates in the 3 NTU Formazin solution. (**d**) The signal reliability decays as the light of the 3000 K LED propagates in the 3 NTU Formazin solution. The error bars result from three measurements under the same conditions for each case. decoded at the receiving side after passing by a water channel. As shown in Figure 4, the binary image depicting a two-way road sign contains 61 \(\times\) 65 pixels. Each pixel represents a binary bit. In accordance with the theory of digital color-coding method, the intensity and the chromaticity of visible light could be separately manipulated at will by modulating duty cycles of driving pulses [24; 25]. The definitions of logic \"on\" and \"off\", as well as the noise level, in optical communication are listed in Table 1. \(D_{\text{c}}\) and \(D_{\text{w}}\) represent the duty cycles of the 6000 K-CCT and 3000 K-CCT LEDs, respectively.