Biophotonics_Concepts_to_Applications

falling on the object of cross-sectional area A and the amount of power Pabs
absorbed from the incident beam. That is, the absorption cross section has units of
area and is defined by

ra¼

Pabs

I 0

¼

Pabs

P 0 =A

ð 6 : 1 Þ

The absorption cross section further defines a parameterμa, which is theabsorption
coefficientof the material. In a tissue that has a uniform distribution of identical
absorbers with a number densityρ, the absorption coefficient is

la¼qra ð 6 : 2 Þ

The absorption coefficient is defined as the probability per unit path length that a
photon is absorbed in a particular material. It is measured in units of inverse length,
such as cm−^1 or mm−^1.
As noted in Sect.5.1in relation to photon absorption in semiconductor photo-
diodes, in biological tissues there is an analogous behavior of photon absorption as
a function of the distance x that the light penetrates into a tissue. This behavior
states that in a tissue layer the intensity of a collimated light beam is attenuated due
to absorption in accordance with the exponentialBeer-Lambert Law

IðxÞ¼ðÞ 1 RI 0 expðlaxÞð 6 : 3 Þ

where I(x) is the intensity at a distance x into the tissue, I 0 is the intensity of the
incident light,μais the absorption coefficient of the material, and R is the coefficient
of Fresnel reflection at the tissue surface at a normal beam incidence, as given in
Eq. (2.35). The absorption-induced intensity decreases as a light beam travels
through tissue is shown in Fig.6.7assuming there is no surface reflection. For
example, Fig.6.7shows the remaining intensity I(d) after the light has traveled to a

Energy (arbitrary units)

2

3

4

5

1

dj,min

Internuclear separation (arbitrary units)

ν= 0

ν= 1

ν= 2

ν= 3

ν= 4

Allowed vibrational

energy levels Dissociation energy

D 0 De

re (^1234)
ν= j dj,max
Morse
potential
curve
Fig. 6.6 Illustration of
molecular vibrational energy
levels described by a Morse
potential
6.2 Absorption 155