RADIOMETER ABL800 FLEX, Reference Manual

Page: 64 / 206

3. Optical measuring principles ABL800 FLEX Reference Manual
Optical system,
Continued
Lambert-Beer’s
law Absorption spectroscopy is based on Lambert-Beer's law which states that the
measured absorbance for a single compound is directly proportional to the
concentration of the compound and the length of the light path through the sample
[
1
]
:
A c
y y
λ λ ε = × ×
y
l
where:
A
y
λ
=
absorbance of compound y at wavelength
λ
ε λ
y
=
extinction coefficient of compound y at wavelength
λ
(a constant,
characteristic of the compound)
c
y
= concentration of compound y in sample
l
= length of the light path
Absorbance The absorbance (A) of a compound is defined as the logarithm of the ratio of the
light intensity before and after transmission through the compound.
In practice it is the logarithm of the ratio of the light intensity transmitted through
water to the light intensity transmitted through the compound.
A
I
I
= log
0
where:
I
0
=
intensity of light transmitted through water ( I
0
is measured as the
intensity of light transmitted through the Cal 1 or Cal 2 solutions)
I = intensity of light transmitted through the compound
Total
absorbance For samples containing more than one optically active compound, the total
absorbance (A
total
) is the sum of the individual compounds’ absorbance, since
absorbance is an additive quantity.
For example, if a sample contains 6 compounds y
1
, y
2
, ….y
6
, the total absorbance
measured for that sample at wavelength
λ
1
is:
A A A A A A A
total y y y y y y
1 2 3 4 5
λ λ λ λ λ λ
1 1 1 1 1 1
1
= + + + + +
6
λ
( )
= + + + + +
l c c c c c c
y y y y y y y y y y y y
1 1 2 2 3 3 4 5 5 6 6
ε ε ε ε ε ε
λ λ λ λ λ λ
1 1 1 1
4
1 1
If there are Y compounds and measurements are taken at n wavelengths, a general
expression can be written for A
total
at the wavelength
λ
n
:
A c
n n
total y y
y
Y
λ λ
ε
= ×
=
∑
1
l
×
where:
λ
n
= the individual wavelengths.
Continued on next page
3-4