Biophotonics_Concepts_to_Applications

450 cm^1



x¼ln 0: 368 ¼ 0 : 9997

which yields x = 2.22× 10 −^3 cm = 0.022 mm.

6.3.2 Rayleigh Scattering

Rayleigh scatteringis a category of elastic scattering. In this particular process the
scattering particles are smaller than the wavelength of the light impinging on the
tissue [ 3 , 5 , 16 , 27 ]. If the incoming light is unpolarized, a superposition of
lightwaves with all possible polarizations yields the following intensity distribution
due to Rayleigh scattering

Is¼I 0

8 p^2 a^2

r^2 k^4

1 þcos^2 h



ð 6 : 14 Þ

Here r is the distance from an observation point to the scattering molecule,θis the
scattering angle measured relative to the original propagation direction of the
photon, andαis themolecular polarizability, which is proportional to the dipole
moment induced in the molecule by the electricfield of the light (see Sect.2.7). The
molecular polarizability of a sphere with radiusais given by [ 16 ]

a¼

n^2 rel 1

n^2 relþ 2

a^3 ð 6 : 15 Þ

where nrel=ns/nbis the relative refractive index of the sphere of index nsembedded
in a background material of index nb. The Rayleigh scattering cross section is given
by

rs¼

8 pk^4 a^2

3

ð 6 : 16 Þ

where k = 2πnb/λis the propagation constant.

Example 6.6Consider Eq. (6.14) for Rayleigh scattering. Show the effect

that theλ−^4 behavior has on the relative intensity Is/I 0 in the range 300–

800 nm.

Solution: Because only theλ−^4 behavior is of interest in this question, let the

parameter defined by

6.3 Scattering 165