Lecture 6 Introduction to Scattering

Transcription

1 Lecture 6 Introduction to Scattering Collin Roesler 12 July 2017

2 Scattering Theory B = scatterance b= scattering coefficient (m -1 ) B = F b /F o F b F a b = B/Dx F o F t b (m -1 ) = (-1/x) ln(f t /F o ) Dx How is this measurement difference from beam c, a?

3 Geometry of scattering

4 Volume Scattering Function (VSF) b(q, f) = power per unit steradian emanating from a volume illuminated by irradiance b(q,f) = 1 df F o dr dw b = 4p b(q,f) dw What is dw? b = 2p o pb(q,f) sinq dq df

5 Calculate Scattering, b, from the volume scattering function b = 4p b(q,f) dw If there is azimuthal symmetry p b = 2p b(q,f) sinq dq 0 b f = 2p b f = 2p p/2 0 p p/2 b(q,f) sinq dq b(q,f) sinq dq Phase function: b(q,f) ~ = b(q,f)/b These are spectral!

6 Particle parameters that influence scattering Concentration Diameter : wavelength refractive index relative to surrounding medium absorption of radiation through particle Particle shape

7 Electromagnetic Radiation Oscillating magnetic and electric fields Perpendicular to direction of propagation May be polarized

8 Interactions between EM radiation and particles Consider the relationship between particle size and EMR wavelength

9 Interaction of light with small particles: d<<l Rayleigh scatterers Energy from propagating EM wave sets up oscillating dipole in particle

10 Small Particles: Rayleigh scatterers d<<l Propagating EM wave sets up oscillating dipole in particle Oscillating dipole induces EM radiation from particle (scattered radiation)

11 Small Particles: Rayleigh scatterers Angular distribution of radiation is called the volume scattering function (VSF or b(q)) Equal in forward and backward directions

12 Interaction of light with large particles d>> l EMR induces multiple dipole oscillations Some EMR penetrates particle

13 Large particle scattering Diffraction Refraction Reflection Dera, Marine Physics

14 Large Particle Scattering Three effects: refraction, reflection and diffraction

15 Fresnel s Law Quantifies reflection and transmission of EM radiation across an interface between two media with different refractive indices EMR Incident = EMR transmitted + EMR reflected Function of relative indices of refraction and incidence angle

16 Snell s Law: refractive index impact on wave propagation, describes angle of transmission

17 Refraction As EMR crosses an interface (say from water to a particle) it will change celerity If it slows down, the wavelength shortens up Thus it will bend (refract) Once it exits the particle, it will return to its original celerity and wavelength, but likely at a different angle and or phase than original

18 Refraction Change in angle Change in phase

19 Optical cross section Optical cross section for scattering? If every photon incident on the particle scatters geometric cross section Optical/geometric cross section =1 What about for absorbing particle?

20 Diffraction

21 Optical cross section Optical cross section for scattering if you include diffraction? Diffraction can occur 2 radii away Optical/geometric crossection = 2 What about for absorbing particle?

22 Effect of non-sphericity on diffraction (forward scattering pattern) Rectangles/ cylinders Circles/ spheres

23 Basis for design of LISST

24 What influences a particle s refractive index? Variations in particle composition: Stramski et al

25 What influences a particle s refractive index? Highly refractive particles Weakly refractive particles Variations in bulk composition: Twardowski et al

26 Effect of absorption Parameterized by n, the imaginary refractive index relative to surrounding medium Describes attenuation of EM radiation as it passes through particle Reduces scattered radiation

27 Draw absorption

28 Effect of Absorption in the extreme Only diffraction

29 What are the constituent properties that we need to consider Particle size Particle composition Index of refraction (real part) Index of refraction (imaginary part) Particle shape Internal structures

30 What are the particles in the ocean that are responsible for light scattering Water molecules Dissolved matter Inorganic salts Organic matter (CDOM, colloids) Particles Organic Cells and organisms (viruses, bacteria, phytoplankton, to ) Detrital aggregates Inorganic Sediments Minerals Air bubbles

31 Size matters Applicable scattering theory Particle Size Range

32 Particle size in the ocean Stramski and Kiefer 1991

33 Scattering in the ocean: Rayleigh Scattering water molecules

34 Small Particle Scattering follows Rayleigh Theory b( q) b(l) Example for water ~ l -4 VSF q Wavelength (nm)

35 Scattering in the ocean: water Clusters formed from hydrogen bonds between the polar water molecule (Frank-Wen flickering cluster model) A function of temperature (kinetic energy)

36 Scattering in the ocean: dissolved salts Increased b relative to pure water 30% Model of salt dissociation Zhang et al 2009 OptExp

37 Scattering in the ocean: marine viruses Balch et al. 1999

38 Scattering in the ocean: submicron particles (~colloids) Yamasaki et al 1998 Stramski and Wozniak 2005

39 Scattering by CDOM: From Emmanuel Boss Scattering by molecules whose D<<l. Rayleigh scattering: ( ) 4 l l 2 b b( q ) 1 cos ( q ) ( ) No evidence in the literature that scattering is significant (the only place I have ever found significant dissolved scattering (c g >a g ) was in pore water).

40 Scattering in the ocean: phytoplankton Stramski et al. 2001

41 Scattering in the ocean: inorganic minerals Terrestrial dust sources Stramski et al. 2007

42 Void fraction Contribution to bb # bubbles/m 3 /mm Scattering in the ocean: air bubbles Terrill et al Acoustics Size distribution Modeled b Radius (mm) Wind speed (m/s) Terrill et al Radius (mm) Void fraction

43 Scattering in the ocean: air bubbles

44 Mie Theory describes the interaction between EM and particles Homogeneous spheres Size index r ~ d / l Real refractive index relative to surrounding medium (n = m p /m w ) Slows wave propagation Imaginary refractive index relative to surrounding medium (n = m p /m w ) Attenuation of wave propagation

45 VSF of 5 mm particle as a function of refractive index

46 VSF of particles with refractive index 1.05

47 b(q) response to particle size distribution First let s talk about particle size distributions r -3 r -5 Stramski and Kiefer 1989

48 b(q) and response to particle size distribution b(q) / V p Roesler and Boss, 2008

49 b(q) response to index of refraction b(q) / V p Roesler and Boss, 2008

50 Scattering in the ocean: which particles contribute Boss et al., 2004, TOS

51 Consider what information scattering can provide and what do you want to measure b b f b b b(q)

52 Scattering closure Reductionist view (Stramski and Mobley 1997; Mobley and Stramski 1997) Particle-specific volume scattering Particle concentration Add them up

53 Importance of scattering in the ocean Competing forces of absorption and scattering on the downward propagation of light in the ocean

54 Importance of scattering in the ocean Competing forces of absorption and scattering on the downward propagation of light in the ocean Backscattering and the upward propagation of light from the ocean Normalized water-leaving radiance in the Mediterranean Sea (Sept 2003) 412 nm 490 nm