Rayleigh and Mie Scattering Remote Sensing ERAU Dr. Darrel Smith September 30, 2008

Rayleigh & Mie Scattering

Rayleigh Scattering

Rayleigh Scattering Light scattering off of air molecules (N2, O2) Can be extended to scattering from particles up to ~ 1/10 . Rayleigh scattering off the molecules of the air gives rise to a “blue” sky. Lord Rayleigh calculated the scattered intensity from dipole scatterers much smaller than the wavelength to be:

Rayleigh Scattering

Rayleigh Scattering from Particles When scattering from a particle of size d with light of wavelength , the Rayleigh scattering is found to be: where R is the distance to the particle, n is the index of refraction, and  is the scattering angle.

Cross Section The cross-section of a particle is determined by the following equation where: is the differential cross section. Another way of representing this is by:

Problem Find the Rayleigh scattering cross-section for scattering from a small particle of size d using a wavelength  if the scattered intensity is: where R is the distance to the particle, n is the index of refraction, and  is the scattering angle. Answer:

Scattering from molecules A 5 mW green laser pointer is visible at night due to Rayleigh scattering and airborne dust.  = 532 nm

Homework Problem #1 If the Rayleigh cross-section for an N2 molecule is 5.1 x 10-31 m2 at a wavelength of 532 nm (green light), what would be the characteristic size of an N2 molecule? Assume that the index of refraction of air is: nair = 1.000293

Problem What is the number density nbeam for a 5 mW green laser pointer whose wavelength is 532 nm and whose cross-sectional beam size is 2 mm?

Homework Problem #2 What fraction of the light from a 532 nm pen laser gets scattered every meter?

Degree of Polarization In general, Rayleigh scattering is for randomly polarized incident flux and the scattered flux will be polarized. The degree of polarization induced by scattering from a small particle exposed to randomly polarized flux is: Bohren and Huffman (1998)

Homework Problem #3 Plot the “degree of polarization” as a function of scattering angle . At what angle is the scattered light completely polarized? How might you observe this?