Biophotonics_Concepts_to_Applications

can be modeled fairly well by Mie theory applied to spheres of comparable size and
refractive index. The Mie theory is somewhat mathematically involved and will not
be addressed here. However, Mie scattering is of importance when examining
scattering from blood cells, which have sizes ranging from about 2.5 to 20μm
depending on the blood cell type. If the size of the tissue particle is much smaller
than the wavelength of the incident light (i.e., less than about 100 nm), the simpler
Rayleigh scattering theory can be used.
Scattering is quantified by a parameter called thescattering cross sectionσs.
This parameter indicates the scattering strength of an object and gives the pro-
portionality between the intensity I 0 =P 0 /A of a light beam of power P 0 incident on
the object of geometrical cross-sectional area A and the amount of power Ps
scattered from it. That is, the scattering cross section is defined by

rs¼

Ps

I 0

ð 6 : 10 Þ

which has units of area. As depicted in Fig.6.12, basically the scattering cross
section describes the area that a scattering object removes from the cross section of
an incident light beam during the process of diverting the amount of scattered
power Psfrom the beam. It is important to note that the scattering cross section is
not the projected geometric area of an object, because different identically sized
objects can have different scattering cross sections.
Similar to absorption, the non-scattered intensity component Isremaining after
light has traveled a distance x in a medium can be described by a Beer-Lambert law as

IsðxÞ¼I 0 expðlsxÞð 6 : 11 Þ

Hereμsis thescattering coefficientof the material. The scattering coefficient is
defined as the probability per unit path length that a photon is scattered in a particular
material and is measured in units of cm−^1 or mm−^1. In a tissue that has a uniform
distribution of identical scatters with a number densityρ, the scattering coefficient is

ls¼qrs ð 6 : 12 Þ

Incident light beam

of cross-sectional

area A

Outgoing light beam

of cross-sectional

area (A -σs)

Scattering particle

of cross-sectional

area σs

Input power

Pin= I 0 A

Scattered power

Ps= I 0 σs

Output power

Pout= I 0 (A -σs)

Fig. 6.12 Concept of the scattering cross section

6.3 Scattering 163