# Elastic Scattering Time–Gated Multi–Static Lidar Scheme for Mapping and Identifying Contaminated Atmospheric Droplets

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{7}

^{8}

^{9}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Simulation Method

_{n}and b

_{n}as described by Equations (1) and (2).

_{4}. Such laser systems are typically used in conventional lidar monitoring stations and were, therefore, chosen for our simulations. The complex refractive indices of pure water, contaminated water and black carbon at the chosen excitation wavelengths are summarized in Table 1. The contaminated water considered in this case contains a mixture of ammonium sulfate and carbon. The radii of the scattering particles that we considered in our calculations, along with the corresponding size parameters obtained from Equation (5) are summarized in Table 2. The radii 0.1 μm, 0.5 μm and 1.25 μm were chosen since these are approximately the average sizes (diameter) of particulate matter, for example, black carbon (0.085 μm to 0.5 μm) and PM2.5 (≤2.5 μm) [31]. MIe scattering is also the more appropriate model compared to Rayleigh scattering when the particle size is larger than around 10% of the wavelength of the incident radiation. Accordingly, the minimum particle radius for MIe scattering to be valid is around 0.1 μm given the longest laser wavelength considered in our work, which is 1.064 μm [32].

_{max}= x + 4x

^{1/3}+ 2 terms as proposed by Bohren and Huffman [24]. The x in n

_{max}also refers to the size parameter given in Equation (3).

_{S}. The scattered far field in spherical coordinates (E

_{Sθ}, E

_{Sϕ}) is given by

## 3. Results and Discussion

_{10}scale to emphasize the salient features of the scattering patterns. For all three particles, the scattering intensity is nearly uniform with a slight preference for forward scattering when the size of the particle is within 20% of the incident laser’s wavelength, for example (a) $x$ = 0.59, (b) $x$ = 1.18, and (c) $x$ = 1.77 where the particle size is 0.1 μm and the wavelength is (a) 1.064 μm and (b) 0.532 μm. The cross-sectional scattering intensity patterns for pure water, contaminated water, and black carbon also appear to be similar, especially when $x$= 0.59 (Figure 1a) where it appears to be indistinguishable. As the size parameter increases because of the particle becoming bigger and the laser wavelength becoming shorter, forward scattering is favored with the forward scattering intensity becoming confined within a narrower polar distribution. The scattering patterns from pure water, contaminated water, and black carbon start to exhibit distinguishable features, especially from the back-scattered light when $x$= 1.77. The patterns then become increasingly unique as the value of $x$ increases. These results show that for small particle sizes, shorter laser lidar wavelengths should be used to distinguish between the particles. As the size of the particle increases, there is more flexibility in using longer laser lidar wavelengths to distinguish between the particles. Interestingly, when the particle size is 1.25 μm, a laser lidar wavelength of 0.532 μm (Figure 1h) gives a similar scattering intensity pattern as a laser lidar wavelength of 0.355 μm (Figure 1i). Using either laser lidar wavelength gives clearly distinguishable scattering intensity patterns that can differentiate between pure water, contaminated water, and black carbon. This result is important economically since it is cheaper and easier to use the second harmonics (0.532 μm wavelength) instead of the third harmonics (0.355 μm wavelength) of Nd-based laser systems. The second harmonic also has a higher light intensity compared to the third harmonic. The unique scattering patterns demonstrated by different particulate matter could serve as fingerprints that can be used to identify the scattering particle. Calculation of the cross-sectional scattering intensity patterns could be extended to other types of pollutants as well. By doing so, a database of atmospheric pollutants and their corresponding scattering patterns can be created.

_{4}laser. The importance of the laser being pulsed will be discussed later. The laser emission can be sequentially tuned to its fundamental (1.064 μm), second (0.532 μm), or third (0.355 μm) harmonic wavelengths. The laser light source is located at a distance l

_{0}from the scattering center. Furthermore, the laser is at a lower elevation compared to the scattering center such that the laser beam is directed upward toward the scattering center. The backscattered laser light is then collected by a set of multiple telescope detectors (D

_{0}to D

_{n}). The collected light then creates the MIe scattering intensity profiles, which will then be compared against the database to identify the type of scattering particle present in the scattering center that is being observed. The number of telescope detectors is correlated to the angular scattering cross-section. For example, for x = 0.59 or 1.18 (Figure 1a,b), at least four telescope detectors will be needed to recreate the cross-sectional scattering intensity patterns. The number of telescope detectors increases as the size parameter also increases. This is because as the size parameter increases, the scattering intensity patterns also become more complex, as shown in Figure 1. The telescope detectors are placed at known distances around the scattering center. Each detector can rotate through a telescopic angle 0 < θ

_{i}< π so that the detector (Di) that is tilted at an angle θ

_{i}has a distance l

_{i}from the scattering center. By scanning 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 ith detector, then the time it takes to reach detector Di will be

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Available online: https://www.c2es.org/content/short-lived-climate-pollutants/ (accessed on 19 December 2022).
- Durdina, L.; Brem, B.T.; Schönenberger, D.; Siegerist, F.; Anet, J.G.; Rindlisbacher, T. Nonvolatile Particulate Matter Emissions of a Business Jet Measured at Ground Level and Estimated for Cruising Altitudes. Environ. Sci. Technol.
**2019**, 53, 12865–12872. [Google Scholar] [CrossRef] [PubMed] - Panahifar, H.; Moradhaseli, R.; Khalesifard, H.R. Monitoring atmospheric particulate matters using vertically resolved measurements of a polarization lidar, in-situ recordings and satellite data over Tehran. Iran. Sci. Rep.
**2020**, 10, 20052. [Google Scholar] [CrossRef] [PubMed] - Liu, Z.; Sun, Y.; Zeng, Y.; Guan, Y.; Huang, Y.; Chen, Y.; Li, D.; Mo, L.; Chen, S.; Mai, B. Semi-volatile organic compounds in fine particulate matter on a tropical island in the South China Sea. J. Hazard. Mater.
**2021**, 426, 128071. [Google Scholar] [CrossRef] [PubMed] - Wilson, W. Semi-Volatile Species In PM 2.5: Development And Validation Of Integrated And Continuous Samplers For PM 2.5 Research Or Exposure Monitoring. In Proceedings of the AWMA Specialty Conference, PM 2000, Charleston, SC, USA, 24–28 January 2000. [Google Scholar]
- Hallett, F.R. Particle size analysis by dynamic light scattering. Food Res. Int.
**1994**, 27, 195–198. [Google Scholar] [CrossRef] - Koestner, D.; Stramski, D.; Reynolds, R.A. Polarized light scattering measurements as a means to characterize particle size and composition of natural assemblages of marine particles. Appl. Opt.
**2020**, 59, 8314. [Google Scholar] [CrossRef] [PubMed] - Siebert, K.J. Relationship of Particle Size to Light Scattering. J. Am. Soc. Brew. Chem.
**2000**, 58, 97–100. [Google Scholar] [CrossRef] - Lockwood, D.J. Rayleigh and MIe Scattering. In Encyclopedia of Color Science and Technology; Lou, M.R., Ed.; Springer: New York, NY, USA, 2016. [Google Scholar]
- Wyatt, P.J. Differential light scattering and the measurement of molecules and nanoparticles: A review. Anal. Chim. Acta X
**2021**, 7, 100070. [Google Scholar] [CrossRef] - Zimm, B.H. Apparatus and Methods for Measurement and Interpretation of the Angular Variation of Light Scattering; Preliminary Results on Polystyrene Solutions. J. Chem. Phys.
**1948**, 16, 1099–1116. [Google Scholar] [CrossRef] - Salzman, G.C.; Crowell, J.M.; Goad, C.A.; Hansen, K.M.; Hiebert, R.D.; LaBauve, P.M.; Martin, J.C.; Ingram, M.L.; Mullaney, P.F. A flow-system multiangle light-scattering instrument for cell characterization. Clin. Chem.
**1975**, 21, 1297–1304. [Google Scholar] [CrossRef] - Macke, A.; Mishchenko, M.I. Applicability of regular particle shapes in light scattering calculations for atmospheric ice particles. Appl. Opt.
**1996**, 35, 4291. [Google Scholar] [CrossRef] - Mishchenko, M.I.; Hovenier, J.W.; Travis, L.D. Light Scattering by non Spherical Particles; Academic Press: San Diego, CA, USA, 2000. [Google Scholar]
- Mishchenko, M.I.; Dlugach, J.M.; Liu, L. Applicability of the effective-medium approximation to heterogeneous aerosol particles. J. Quant. Spectrosc. Radiat. Transf.
**2016**, 178, 284–294. [Google Scholar] [CrossRef] [Green Version] - Onofri, F.R.A.; Barbosa, S.; Touré, O.; Woźniak, M.; Grisolia, C. Sizing highly-ordered buckyball-shaped aggregates of colloidal nanoparticles by light extinction spectroscopy. J. Quant. Spectrosc. Radiat. Transf.
**2013**, 126, 160–168. [Google Scholar] [CrossRef] - Barbosa, S.; Onofri, F.R.A.; Couëdel, L.; Wozniak, M.; Montet, C.; Pelcé, C.; Arnas, C.; Boufendi, L.; Kovacevic, E.; Berndt, J.; et al. An introduction to light extinction spectrometry as a diagnostic for dust particle characterization in dusty plasmas. J. Plasma Phys.
**2016**, 82, 15820403. [Google Scholar] [CrossRef] [Green Version] - Yurkin, M.A.; Hoekstra, A.G. The discrete-dipole-approximation code ADDA: Capabilities and known limitations. J. Quant. Spectrosc. Radiat. Transf.
**2011**, 112, 2234–2247. [Google Scholar] [CrossRef] - Draine, B.T.; Flatau, P.J. Discrete-Dipole Approximation For Scattering Calculations. J. Opt. Soc. Am. A
**1994**, 11, 1491–1499. [Google Scholar] [CrossRef] [Green Version] - Bi, L.; Yang, P.; Kattawar, G.W.; Hu, Y.; Baum, B.A. Scattering and absorption of light by ice particles: Solution by a new physical-geometric optics hybrid method. J. Quant. Spectrosc. Radiat. Transf.
**2011**, 112, 1492–1508. [Google Scholar] [CrossRef] - Sun, B.; Yang, P.; Kattawar, G.W.; Zhang, X. Physical-geometric optics method for large size faceted particles. Opt. Express
**2017**, 25, 24044–24060. [Google Scholar] [CrossRef] [Green Version] - Hassan, P.A.; Rana, S.; Verma, G. Making Sense of Brownian Motion: Colloid Characterization by Dynamic Light Scattering. Langmuir
**2014**, 31, 3–12. [Google Scholar] [CrossRef] - Abramowitz, M.; Stegun, I.A. (Eds.) Handbook of Mathematical Functions; Dover Publication: New York, NY, USA, 1965; pp. 355–435. [Google Scholar]
- Bohren, C.F.; Huffman, D.R. Absorption and Scattering of Light by Small Particles; John Wiley: New York, NY, USA, 1998; pp. 82–129. [Google Scholar]
- Deirmendjian, D. Electromagnetic Scattering on Spherical Polydispersions; American Elsevier: New York, NY, USA, 1969; pp. 12–46. [Google Scholar]
- Ishimaru, A. Wave Propagation and Scattering in Random Media; Academic Press: Orlando, FL, USA, 1978; Volume 1, pp. 9–40. [Google Scholar]
- Meador, W.E.; Weaver, W.R. Two-Stream Approximations to Radiative Transfer in Planetary Atmospheres: A Unified Description of Existing Methods and a New Improvement. J. Atmospheric Sci.
**1980**, 37, 630–643. [Google Scholar] [CrossRef] - van de Hulst, H.C. Light Scattering by Small Particles. Q. J. R. Meteorol. Soc.
**1957**, 84, 91–204. [Google Scholar] [CrossRef] - Zhang, X.; Chen, X.; Wang, J. A number-based inventory of size-resolved black carbon particle emissions by global civil aviation. Nat. Commun.
**2019**, 10, 534. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Frisvad, J.R. Phase function of a spherical particle when scattering an inhomogeneous electromagnetic plane wave. J. Opt. Soc. Am. A
**2018**, 35, 669–680. [Google Scholar] [CrossRef] [PubMed] - Long, C.M.; Nascarella, M.A.; Valberg, P.A. Carbon black vs. black carbon and other airborne materials containing elemental carbon: Physical and chemical distinctions. Environ. Pollut.
**2013**, 181, 271–286. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Eremin, Y.A. SCATTERING|Scattering Theory. In Encyclopedia of Modern Optics; Elsevier: Amsterdam, The Netherlands, 2005; pp. 326–330. [Google Scholar]
- Jurányi, Z.; Burtscher, H.; Loepfe, M.; Nenkov, M.; Weingartner, E. Dual-wavelength light-scattering technique for selective detection of volcanic ash particles in the presence of water droplets. Atmospheric Meas. Tech.
**2015**, 8, 5213–5222. [Google Scholar] [CrossRef] [Green Version] - Dozier, J.; Painter, T.H. MULTISPECTRAL AND HYPERSPECTRAL REMOTE SENSING OF ALPINE SNOW PROPERTIES. Annu. Rev. Earth Planet. Sci.
**2004**, 32, 465–494. [Google Scholar] [CrossRef] [Green Version] - Jennings, S.G.; Pinnick, R.G.; Auvermann, H.J. Effects of particulate complex refractive index and particle size distribution variations on atmospheric extinction and absorption for visible through middle ir wavelengths. Appl. Opt.
**1978**, 17, 3922–3929. [Google Scholar] [CrossRef] [PubMed] - Liu, F.; Yon, J.; Fuentes, A.; Lobo, P.; Smallwood, G.; Corbin, J.C. Review of recent literature on the light absorption properties of black carbon: Refractive index, mass absorption cross section, and absorption function. Aerosol Sci. Technol.
**2020**, 54, 33–51. [Google Scholar] [CrossRef] - Aden, A.L.; Kerker, M. Scattering of Electromagnetic Waves from Two Concentric Spheres. J. Appl. Phys.
**1951**, 22, 1242–1246. [Google Scholar] [CrossRef] - Toon, O.B.; Ackerman, T.P. Algorithms for the calculation of scattering by stratified spheres. Appl. Opt.
**1981**, 20, 3657–3660. [Google Scholar] [CrossRef] - Reagan, J.A.; Byrne, D.M.; Herman, B.M. Bistatic LIDAR: A Tool for Characterizing Atmospheric Particulates: Part I—The Remote Sensing Problem. IEEE Trans. Geosci. Remote Sens.
**1982**, GE-20, 229–235. [Google Scholar] [CrossRef] - McManamon, P. Monostatic versus Bistatic Lidar. In Book Chapter in, Field Guide to Lidar; SPIE Digital Library: Washington, DC, USA, 2015; pp. 12–13. [Google Scholar]
- Acharya, R. Chapter 3—Interaction of waves with medium. In Satellite Signal Propagation, Impairments and Mitigation; Acharya, R., Ed.; Academic Press: Cambridge, MA, USA, 2017; pp. 57–86. [Google Scholar]

**Figure 1.**Mie angular scattering intensity patterns from pure water for each of the size parameters in Table 2: particle size of a = 0.1 μm for (

**a**) λ = 1.064 μm, (

**b**) λ = 0.532 μm, and (

**c**) λ = 0.355 μm; a particle size of a = 0.5 μm for (

**d**) λ = 1.064 μm, (

**e**) λ = 0.532 μm, and (

**f**) λ = 0.355 μm and a particle size of a = 1.25 μm for (

**g**) λ = 1.064 μm, (

**h**) λ = 0.532 μm, and (

**i**) λ = 0.355 μm.

**Figure 2.**Schematic diagram of the proposed MIe Scattering Time–gated laSer LIDAR (MISTS–LIDAR) experimental set-up for obtaining the MIe scattering angular cross sections as a function of the wavelength of the incident laser light, complex refractive index of the scatterer, and size of the scatter. E (red rectangle)—laser source, D (green rectangles) —telescope detector, l

_{i}–distance between the scattering center and Di that is tilted at an angle θ

_{i}, l

_{0}—distance between the scattering center and the laser source.

**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 ${t}_{i}=\frac{{l}_{0}+{l}_{i}}{c}$ 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 ith detector.

**Figure 4.**Back scattering intensity from (

**a**) pure water, (

**b**) contaminated water and (

**c**) black carbon as a function of the size of the scatterer for different incident laser wavelengths.

**Figure 5.**Back scattering intensity from (

**a**) pure water, (

**b**) contaminated water and (

**c**) black carbon as a function of the wavelength of the incident laser for various particle radii a = 0.1 μm, 0.5 μm, and 1.25 μm.

**Table 1.**Complex refractive index of contaminated water and black carbon at the 1.064, 0.532, and 0.355 μm wavelengths of the incident radiation.

Scatterer | Wavelength of Incident Radiation (μm) | ||
---|---|---|---|

1.064 | 0.532 | 0.355 | |

Pure Water [33,34] | 1.327 + i2.89 × 10^{−6} | 1.334 + i1.32 × 10^{−9} | 1.343 + i6.5 × 10^{−9} |

Contaminated Water [35] | 1.54 + i0.015 | 1.54 + i0.015 | 1.54 + i0.015 |

Black Carbon [36] | 1.95 + i0.79 | 1.77 + i0.63 | 1.70 + i0.64 |

λ (μm) | 1.064 | 0.532 | 0.355 |
---|---|---|---|

a (μm) | |||

0.1 | 0.59 | 1.18 | 1.77 |

0.5 | 2.95 | 5.91 | 8.85 |

1.25 | 7.38 | 14.76 | 22.12 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Mui, L.V.; Hung, T.N.; Shinohara, K.; Yamanoi, K.; Shimizu, T.; Sarukura, N.; Shimadera, H.; Kondo, A.; Sumimura, Y.; Hai, B.V.;
et al. Elastic Scattering Time–Gated Multi–Static Lidar Scheme for Mapping and Identifying Contaminated Atmospheric Droplets. *Appl. Sci.* **2023**, *13*, 172.
https://doi.org/10.3390/app13010172

**AMA Style**

Mui LV, Hung TN, Shinohara K, Yamanoi K, Shimizu T, Sarukura N, Shimadera H, Kondo A, Sumimura Y, Hai BV,
et al. Elastic Scattering Time–Gated Multi–Static Lidar Scheme for Mapping and Identifying Contaminated Atmospheric Droplets. *Applied Sciences*. 2023; 13(1):172.
https://doi.org/10.3390/app13010172

**Chicago/Turabian Style**

Mui, Luong Viet, Tran Ngoc Hung, Keito Shinohara, Kohei Yamanoi, Toshihiko Shimizu, Nobuhiko Sarukura, Hikari Shimadera, Akira Kondo, Yoshinori Sumimura, Bui Van Hai,
and et al. 2023. "Elastic Scattering Time–Gated Multi–Static Lidar Scheme for Mapping and Identifying Contaminated Atmospheric Droplets" *Applied Sciences* 13, no. 1: 172.
https://doi.org/10.3390/app13010172