Biophotonics_Concepts_to_Applications

depth d into the tissue. Note that the Beer-Lambert Law sometimes is called the
Lambert-Beer Law, Lambert’s Law, or Beer’s Law.
In most cases the absorption coefficient is wavelength dependent, particularly
when the absorption coefficient is expressed explicitly in terms of the material
properties. That is, suppose there are N different types of absorbing molecules in a
medium. Let the concentration of the nth molecule type be cn(measured in
moles/liter) and let itsmolar absorption coefficient(also known as themolar
extinction coefficient)beεn(λ), which is measured in M−^1 cm−^1 where M is given in
moles/liter. Then the absorption coefficient is given by

la¼

XN

n¼ 1

cnenðkÞð 6 : 4 Þ

This is the sum of the molar concentration of various absorbers cnpresent in the
material multiplied by the molar absorption coefficient of each absorberεn, which
typically is wavelength dependent and is a measure of how strongly the nth
molecule type absorbs light.
A parameter used in relation to absorption is theoptical densityD(λ), which also
is known asabsorbance. For absorption over a distance d, using Eqs. (6.3) and
(6.4), this parameter is defined as

DðkÞ¼ln

I 0

Ia



¼

XN

n¼ 1

cnenðkÞd ð 6 : 5 Þ

For a larger optical density, more optical power gets attenuated as a beam propa-
gates through a medium.
The inverse of the absorption coefficient is called thepenetration depthor the
absorption lengthLa. Thus

La¼ 1 =la ð 6 : 6 Þ

The absorption length is the light penetration distance x into the tissue for which the
intensity has dropped to 1/e of its initial value, that is, when x = La=1/μa.

Depth in the tissue x

I 0

I(d)

Relative intensity

d

Intensity at the tissue surface

Intensity remaining at a depth d

I 0 - I(d) = Intensity decrease in a depth d

0

Fig. 6.7 Photon absorption as a function of the distance x that the light penetrates into a tissue

156 6 Light-Tissue Interactions