Transcript Light Scattering - www.gps.caltech.edu

Light Scattering
Rayleigh Scattering & Mie
Scattering
What is Scattering?
• Process by which particles suspended in a medium of a different index
of refraction diffuse a portion of the incident radiation in all directions
• No energy transformation results, only a change in the spatial
distribution of the radiation
• Function of ratio of particle diameter to wavelength of incident
radiation
Scattering Plane
• Defined by the two rays involved, the source-particle ray and the
particle-observer ray
• Determined by observation, not fixed in space. For example, if the
observer moves, the scattering plane will move with the observer.
Rayleigh Scattering
• Particles much smaller than wavelength of radiation
• Proportional to 1/ λ4
• Shorter wavelengths scattered much more than longer wavelengths
• Air molecules (N2 and O2) just the right size to very effectively scatter
the shorter wavelengths (blue light) of incident solar radiation => blue
sky
Mie Scattering
• Scattering by a isotropic, homogeneous sphere
• Particle dimension comparable to wavelength of radiation (aerosols,
water vapour)
• Longer wavelengths scattered more than shorter wavelengths
• More forward scattering
• Scattering properties depend on wavelength, size, real and imaginary
parts of refractive index, and size distribution
Angle-Dependent Phase Function
Phase Function Moments
Discrete Ordinate
Radiative Transfer
Code: DISORT
Theory
• Fundamental Equation of RT
dI ( ,  ,  )


 I ( ,  ,  ) 
d
4
2 1
  P( ,  ,;  ' , ' ) I ( ,  ' , ' ) d ' d '
0 1
• Phase Function Expansion
P( , cos) 
2 M 1
 (2l  1) g ( ) P (cos)
l 0
l
l
• Can use addition theorem for spherical harmonics to expand P in
Fourier cosine series over azimuthal angle
Theory (Contd…)
• Expand I in Fourier cosine series
• RT equation transformed into 2M independent integro-differential
equations

dI m ( ,  )
 I m ( ,  )  S m ( ,  )
d
• Integration performed by Gaussian quadrature (2N ‘streams’)
• Reference:
http://www.gps.caltech.edu/~vijay/Papers/RT_Models/DISORT%20
Report.pdf