Biophotonics_Concepts_to_Applications

A

8 p^2 a^2

r^2

1 þcos^2 h



be afixed quantity. Then the relative intensity Is/I 0 is shown in Fig.6.14as a

function of λ. The plot is given in normalized units such that A/

(300 nm)^4 = 100. Note that even in the range of the visible spectrum, the

Rayleigh scattering effect is significantly smaller in the red region (around

680 nm) compared to the blue region (around 450 nm).

Example 6.7Consider a spherical particle that has a radiusa= 10 nm and a

refractive index ns= 1.57. (a) If the sphere is in a background material of

refractive index nb= 1.33, what is the scattering cross section at a wavelength

λ= 400 nm? (b) How does this compare to the geometric cross section of the

sphere?

Solution: (a) First from Eq. (6.15)withnrel=ns/nb= 1.57/1.33 = 1.18 and

with k = 2πnb/λ, it follows from Eq. (6.16) that the scattering cross section is

rs¼

8 pk^4 a^2

3

¼ 2 : 15  10 ^20 m^2

(b) The geometric cross section of the sphere isπa^2 = 3.14× 10 −^18 m^2

Thescattering efficiencyQsis another parameter used in describing scattering.
This parameter is defined as [ 16 ]

Qs¼

8x^4

3

n^2 rel 1

n^2 relþ 1

 2

ð 6 : 17 Þ

Ultra- Visible Infrared

violet

Rayleigh scattering

(^300400500600700800)
400
100
200
300
0
Wavelength (nm)
Scattered intensity (normalized units)
Fig. 6.14 Comparison of
Rayleigh scattering in the UV,
visible, and IR regions
166 6 Light-Tissue Interactions