
3
Copyright 2000 by ASME
From equation (1), it is evident that fluorescence intensity
is dependent on:
(1) the amount of exciting light available to produce
molecular transitions to higher, excited levels,
(2) molar absorpsivity, which determines how much of the
incident light per molecule produces actual molecular
transitions,
(3) dye concentration, which is a measure of the number
of molecules present,
(4) quantum efficiency, which is the ratio of the energy
emitted by the energy absorbed, and is a measure of
how much of the energy stored in the higher electronic
states is emitted as fluorescence light, when the
molecules return to their ground state, and,
(5) the volume of the element, which is the control volume
over which excitation and fluorescence takes place.
Dividing equation (1) by the area
A
, the fluorescence
intensity normal to the area
A
is obtained,
x
C
)
I
I
laser
e
If the area
A
is assumed to be the projected area of a single
pixel, it is apparent that pixel intensity is proportional to the
excitation intensity, dye characteristics, concentration, and
thickness of the fluid element. For very thin film thickness, this
representation is accurate. If the excitation intensity is known,
dye characteristics, and concentration are constants, the fluid
film thickness can be directly inferred from the fluorescence. A
more accurate representation of the fluorescence phenomena
can be obtained by from Lambert’s Law of Absorption (Poll, G.,
et. al., 1992), which takes into account the absorption of the
exciting light by the finite fluid through which it travels;
f
=
)
[
]
x
C
)
I
(x)
I
laser
o
e
=
exp
)
Consider the differential element shown in figure 3 within a
region of finite film thickness. The fluorescence intensity
collected by the CCD from this fluid element is
dx
C
)
I
dI
laser
e
Thus, from equation (4):
f
=
)
.
[
]
dx
C
)
x
C
)
I
dI
laser
laser
o
f
=
exp
)
For a given fluid thickness,
t
, the total intensity collected
by the CCD is
[
]
∫
=
∫
t
laser
laser
o
t
f
f
dx
C
)
x
C
)
I
dI
(t)
I
0
0
exp
)
such that
[
]
{
1
}
t
C
)
I
(t)
I
laser
o
f
=
exp
)
For small values of
t
(thin films), equation (7) can be
approximated as:
t
C
)
I
(t)
I
laser
o
f
≈
This is identical to equation (2) and is the basis for the
concepts of optically thin and optically thick systems. The
fluorescence dependence on film thickness is linear for optically
thin systems, while it is exponential for optically thick systems.
What is considered a thin or thick film thickness depends on the
product
ε
(
λ
laser
)C
.
)
emission
excitation
dx
x
t
X
Y
differential
element
camera
fluid film
Figure 3: Fluorescence through a thick fluid film
Reabsorption
Emission reabsorption is often encountered in fluorescence
techniques and is generally problematic. Fluorescent dyes have
different absorption spectrums and emission spectrums (Fig. 4).
When the emission spectrum of one dye overlaps the absorption
spectrum of another or with its own absorption spectrum,
reabsorption of the dye fluorescence occurs (Fig. 5). This has
two effects: (1) it increases the fluorescence emission of the
second dye as, in addition to the external light source excitation,
it is being excited by the fluorescence of the first dye. More
importantly, (2) the fluorescence emission of the first dye is
reduced since it is being reabsorbed by the second dye. In LIF,
the external illumination intensity is generally much greater
than dye fluorescence. Consequently, the increase in
fluorescence emission due to excitation by the fluorescence of