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/ λ 4 Shorter wavelengths scattered much more than longer wavelengths Air molecules (N 2 and O 2 ) 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 Phase Function Expansion 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 Integration performed by Gaussian quadrature (2N ‘streams’) Reference: Report.pdf