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1.Rayleigh and Mie Scattering 2.Phase Functions 3.Extinction 4 Aerosol and Clouds WS2014 5 November 2014 Outline 1.Rayleigh and Mie scattering 2.Phase functions 3.Extinction 4.Single and multiple scattering Luca Lelli [email protected] Room U2080 Phone 0421.218.62097 Aerosol and Clouds WS2014 Scattering fundamentals •Scattering can be broadly defined as the redirection of radiation out of the original direction of propagation, usually due to interactions with molecules and particles •Reflection, refraction, diffraction etc. are actually all just forms of scattering •Matter is composed of discrete electrical charges (atoms and molecules – dipoles) •Light is an oscillating EM field – excites charges, which radiate EM waves •These radiated EM waves are scattered waves, excited by a source external to the scatterer •The superposition of incident and scattered EM waves is what is observed Aerosol and Clouds WS2014 Scattering geometry Aerosol and Clouds WS2014 Scattering geometry Backward Forward scattering scattering ✓ = ⇡(= 180◦) ✓ =0◦ ✓ Aerosol and Clouds WS2014 Types of scattering 1. Elastic scattering the wavelength (frequency) of the scattered light is the same as the incident light (Rayleigh and Mie scattering) 2. Inelastic scattering the emitted radiation has a wavelength different from that of the incident radiation (Raman scattering, fluorescence) 3. Quasi-elastic scattering the wavelength (frequency) of the scattered light shifts (e.g., in moving matter due to Doppler effects) Aerosol and Clouds WS2014 Rayleigh and Mie scattering Aerosol and Clouds WS2014 Rayleigh and Mie scattering example Brighter beam Laser beam Enhanced forward Wavelength 532 nm scattering (Mie) in the direction of observation Shallower beam Beam splitter Side scattering (Rayleigh) Aerosol and Clouds WS2014 More types of scattering 1) Single scattering •Photons scattered only once •Prevails in optically thin media (τ << 1), since photons have a high probability of exiting the medium (e.g., a thin cloud) before being scattered again •Also favored in strongly absorbing media (ω << 1) 2) Multiple scattering a) 1 photon b) 3 photons g=0 g = 0.85 !=0 •Prevails in optically thick, strongly scattering and non-absorbing media •Photons may be scattered hundreds of times before emerging !"=10 Aerosol and Clouds WS2014 Parameters governing scattering (1) The wavelength (λ) of the incident radiation (2) The size of the scattering particle, usually expressed as the non-dimensional size parameter, x: 2⇡r x = λ r is the radius of a spherical particle, λ is wavelength (3) The particle optical properties relative to the surrounding medium: the complex refractive index Scattering regimes: x << 1 : Rayleigh scattering x ~ 1 : Mie scattering x >>1 : Geometric scattering Aerosol and Clouds WS2014 Atmospheric particles Type Size Number concentration Gas molecule ~10-4 µm < 3×1019 cm-3 Aerosol, Aitken < 0.1µm ~104 cm-3 Aerosol, Large 0.1-1 µm ~102 cm-3 Aerosol, Giant > 1 µm ~10-1 cm-3 Cloud droplet 5-50 µm 102-103 cm-3 Drizzle drop ~100 µm ~103 m-3 Ice crystal 10-102 µm 103-105 m-3 Rain drop 0.1-3 mm 10-103 m-3 Graupel 0.1-3 mm 1-102 m-3 Hailstone ~1 cm 10-2-1 m-3 Insect ~1 cm <1 m-3 Bird ~10 cm <10-4 m-3 Airplane ~10-100 m <1 km-3 Aerosol and Clouds WS2014 Some refractive indices Substance nr ni (n = nr+ i ni) Water 1.333 0 Water (ice) 1.309 0 NaCl (salt) 1.544 0 H2SO4 1.426 0 (NH4)2SO4 1.521 0 SiO2 1.55 0 (λ = 550 nm) Carbon 1.95 -0.79 (λ = 550 nm) Mineral dust 1.56 -0.006 (λ = 550 nm) The most significant absorbing component of atmospheric particles is elemental carbon (soot); reflected in the large value of the imaginary part of the refractive index. Other common atmospheric particles are purely scattering. Aerosol and Clouds WS2014 Scattering regimes Only single scattering Only spheres UV Visible Near IR IR Thermal Microwave 1 cm Hail 1 mm 000 Raindrops Geometricx=2 Optics 100 µm Drizzle 10 µm Mie Scattering Cloud droplets Dust, 1 µm x=0.2 Smoke, Particle Radius Haze 0.1 µm } Rayleigh x=0.002Scattering Aitken Nuclei 10 nm 1 nm Negligible Scattering Air Molecules 0.1 µm 1 µm 10 µm 100 µm 1 mm 1 cm 10 cm Wavelength Aerosol and Clouds WS2014 Scattering phase function Forward scattering x=10 x=3 Scattering lobes derived from Mie x=1 theory for homogeneous spheres x=0.1 The scattering phase function, or phase function, gives the angular distribution of light intensity scattered by a particle at a given wavelength Aerosol and Clouds WS2014 Rayleigh scattering phase function E Atmospheric composition: N2 (78%), O2 (21%), Ar (1%) Size of N2 molecule: 0.31 nm Size of O2 molecule: 0.29 nm Size of Ar molecule: 0.3 nm ! Visible wavelengths ~400-700 nm Vertically polarized => Size parameter << 1 ! E Horizontally polarized ✓ ! Unpolarized 10 Light Scattering Theory Aerosol and Clouds WS2014 Rayleigh and Mie scattering Figure 1.2: Normalized angular distribution of the scatterd light for 4 di↵erent size parameters. (a) Rayleigh limit (b) x =0.01 (c) x =0.1 (d) x = 10. The green curve is the parallel incident polarization. The red is the perpendicular one and the blue one for unpolarized light. Rayleigh coefficients, due to the molecular part of the atmosphere8 8⇡r m2 1 QRayleigh = Im( − ) abs λ m2 +2 64⇡4r4 m2 1 2 QRayleigh = − (1.16) sca λ4 m2 +2 128⇡4r4 m2 1 2 QRayleigh = − ⇡ λ4 m2 +2 4 The strong wavelength dependence of the scattering (λ− ) means that blue light is scattered much more than red light. In the atmosphere, this results in blue wavelength being scattered to a greater extent than red wavelengths, and this explains the blue light of the sky. Conversely, at sunsets and sunrises, the colour of the sun appears more red due to the longer propagation path of light through the atmosphere. 3 Starting from a radius of about 0.1 µm (which is about x = 10− at 72 Aerosol and Clouds WS2014 CLOUD OPTICS Mie scattering phase function 0.532µm Cloud of poly-dispersed water 1000 1.064µm droplets of mean radius 6 micron 1.64µm 2.13µm 100 10 ✓ phase function 1 0.1 0.01 20 40 60 80 100 120 140 160 180 scattering angle, degrees Fig. 2.5. The phase function of water clouds at wavelengths 0.532, 1.064, 1.64, and 2.13 µm for the cloud C1 PSD. visible. There is a large asymmetry in forward—backward scattering. Interestingly, the phase function around 30◦ is almost insensitive to the wavelength. The value of the phase function is close to 2 at this angle. The peak in the forward direction is more pronounced in the visible. One can find even more differences in the degree of light polarization presented in Fig. 2.6 at several wavelengths for solar light illumination conditions. We see that the degree of polarization generally decreases with the wavelength. The largest polarization is in the region of the rainbow.The degree of polarization is low at small scattering angles. But it is quite large at θ π, where the degree of polarization ≈ changes its sign in the vicinity of backward scattering. The normalized scattering matrix elements p34 and p44 are shown in Figs. 2.7 and 2.8. The element p34 coincides with the degree of circular polarization for lin- early polarized light illumination conditions (with the azimuth –45◦). We see that Chapter 1 Light Scattering Theory The main purpose of this work is the characterization of the atmospheric particle sizes. For this objective a laser light source is used and a lidar (Light Detection and Ranging) experimental technique is employed. The lidar working principle relies on the amount of scattered light in the backward direction by certain con- stituents in the atmosphere. Therefore, it is necessary to apply a proper theoret- ical model describing the interaction between a monochromatic electromagnetic wave (a laser is typically used in lidars) and a particle. Such a model is known as Mie scattering theory. In Mie theory the amount of scattered light is dependent on the diameter of the particle, on its size compared to the wavelength and on its refractive index. The main features of the Mie theory summarized in this chapter follow the treatises of Bohren and Hu↵man6, Van der Hulst7, and Kerker8. 1.1 Introduction In its most general description6,7, the problem of light scattering with a particle involves the resolution of the Maxwell equations where the electric and magnetic susceptibility " and µ are continuous, that is inside and outside the particle. The discontinuity on the interface forces us to fix boundary conditions for the electric and magnetic field, in order to ensure the energy conservation onto theAerosol interface: and Clouds WS2014 Rayleigh and Mie scattering Maxwell equations + boundary (!E int !E ext) d!S = !0 − ⇥ conditions at(1.1) particle surface 8 (!H !H ) d!S = !0 < int − ext ⇥ It is possible to find the: general solutions for the Maxwell equations and boundary constraints (1.1) as linear combination from known solutions. The Chapter 1 Light Scattering Theory The main purpose of this work is the characterization of the atmospheric particle sizes. For this objective a laser light source is used and a lidar (Light Detection and Ranging) experimental technique is employed. The lidar working principle relies on the amount of scattered light in the backward direction by certain con- stituents in the atmosphere. Therefore, it is necessary to apply a proper theoret- ical model describing the interaction between a monochromatic electromagnetic wave (a laser is typically used in lidars) and a particle.
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