## 3 Results and Discussion
the detectors through a range of angles, the polar plot showing the angular dependence of the scattering cross-section intensity (such as the scattering patterns in Figure 1) can be obtained. The scattering pattern that is collected using MISTS-LIDAR will then be scanned against the scattering intensity patterns in the database to identify the particles present in the scattering center. In practice, multiple scattering centers emitting the same pollutant particle could be present within the vicinity, for instance within a 10-100 km radius. To collect and identify the correct scattering pattern that originated from the scattering center being monitored, a time gate will be used. Using a time gate requires that the laser source is pulsed. The principle behind this time gate is illustrated in Figure 3. If \(l_{0}\) is the known distance from the laser to the scattering particle source \(S_{0}\), and \(l_{i}\) is the distance from the scattering particle to the \(i\)th detector, then the time it takes to reach detector \(Di\) will be  
\[t_{i}=\frac{l_{0}+l_{i}}{c} \tag{17}\]  
where \(c\) is the speed of light. Owing to the pulsed emission of the incident laser source, scattering from surrounding sources will arrive at the detector at different time intervals. For instance, if a pulsed laser light with a 10-ns pulse duration is scattered by the pollutant particles from a scattering center, then the estimated spatial resolution of the time gate is around 3 m. Meaning, the minimum distance between the scattering centers should be 3 m for MISTS-LIDAR to correctly assign the collected scattering patterns to the correct scattering center. The spatial resolution can be improved to 1.5 m if the laser that is used has a pulse duration of 5 ns. Since the telescope detectors in Figure 2 collect the Mie backscattering and recreate the back-scattered intensity profile, the back-scattering intensities are further analyzed by plotting the intensities as a function of the size of the scatterer for different incident laser wavelengths. The backscattering intensities for pure water, contaminated water, and black carbon are shown in Figure 4a-c, respectively. The results show that the backscattering intensities are unique  
Figure 3: Principle of the proposed time gate to identify the pollutant particles from the correct scattering center. Due to the pulsed emission of the incident laser source, scattering from different scattering centers will arrive at the detector at different time intervals \(t_{i}=\frac{l_{i}+l_{i}}{c}\) where \(l_{0}\) is the known distance from the laser to the scattering particle source and \(l_{i}\) is the distance from the scattering particle to the \(i\)th detector. for each of the scattering particles regardless of particle size and laser wavelength. For pure water, backscattering is more efficient for larger droplets with radii from about 0.5 \(\upmu\)m and as the size increases, longer wavelength laser light would also be better. Light having 355 nm wavelength would be appropriate for droplet sizes that are at least 0.6 \(\upmu\)m. On the hand, a laser operating at 532 nm wavelength would be an appropriate light source for droplet sizes that are at least 0.8 \(\upmu\)m. A laser operating at 1064 nm can be used for bigger droplet sizes as well, but the results in Figure 4a show that in this instance 532 nm wavelength would be a better choice. For contaminated water, a laser operating at 355 nm wavelength will be appropriate for droplet sizes smaller than about 0.5 \(\upmu\)m. As Figure 4b shows, higher backscattering efficiency is achieved with 355 nm wavelength for these small droplet sizes. On the other hand, more efficient backscattering can be observed from droplet sizes between 0.5 \(\upmu\)m and 1.0 \(\upmu\)m when the wavelength of the illuminating light is 532 nm. For bigger droplet sizes whose radii are more than 1.0 \(\upmu\)m, 1064 nm will yield the highest backscattering intensity. For black carbon, the smaller the particle size is, the higher the backscattering intensity.