
6
Copyright 2000 by ASME
and/or
=
7
)
21
(
The problem of separating the temperature information
from the exciting light intensity contained in the fluorescence
still exists. This is further complicated by the film thickness
information that is also imbedded in the fluorescence. The
same two-dye fluorescence ratiometric approach used to
separate the film thickness information from the exciting light
intensity information can be used for temperature measurement.
However, the optical conditions for proper temperature
measurement are quite different from that of film thickness
measurement. Reabsorption of one dye fluorescence by the
other must be avoided as it adds film thickness information to
the fluorescence making it difficult to separate the temperature
information contained in the fluorescence. In addition, the
system must be optically thin. There are two reasons for this:
(1) even if there is reabsorption (it is hard to control whether a
system will have reabsorption or not, and in most practical
situations reabsorption is present) an optically thin system will
ensure that the reabsorption effects are minimal as the
fluorescence is approximately linear with film thickness. More
importantly, (2) it is easier to deal with temperature variations
in the direction of observation (i.e.,
x
direction in figure 3). Let
us explore the last point in more detail. The goal in using
fluorescence for temperature measurement is to obtain a two-
dimensional map of temperature, that is, temperature variations
in the plane of observation. It, however, is very likely that the
temperature field also varies in the direction of observation. If
this is the case and, if in particular, equation (20) holds, one can
rewrite equation (6) as
[
∫
=
∫
o
f
f
I
dI
T)
(t,
I
0
0
exp
dx
C
×
However, since
T
=
T(x)
, equation (22) cannot be
integrated unless the temperature field as a function of
x
is
known. This implies that, in order to correlate fluorescence to
temperature, an
a priori
knowledge of the temperature field in
the direction of observation is needed defeating the purpose of
the technique. Thus, the two-dimensional temperature map
cannot be easily inferred from the fluorescence for optically
thick films if the fluorescence temperature dependence is
contained in the molar absorption (or extinction) coefficient. In
general, it is difficult to correlate fluorescence with temperature
if there are temperature variations in the direction of
observation. However, if the temperature dependence is
contained in the quantum efficiency coefficient and/or the
system is optically thin, the effects of temperature variation in
]
t
laser
laser
t
T)
,
x
C
T)
,
)
22
(
the direction of observation on the fluorescence are not as
substantial and a more accurate two-dimensional map of the
temperature can be obtained. In the limit of optically thin
systems, the fluorescence will correlate to the temperature at the
boundary of the film, that is at location
x = 0
for figure 3.
For optically thin systems with no reabsorption, one can
use the ratiometric approach to obtain a fluorescence ratio that
will correlate to temperature. Using equation (8) to calculate
the fluorescence of optically thin systems, one has:
I
)
,
R(T,
f,
2
2
)
)
(
C
)
(
)
(
C
T)
,
(
I
filter
(
laser
filter
laser
f,
filter
filter
2
2
2
2
1
1
1
1
1
1
2
1
=
=
23
and/or
)
(
C
)
(
)
(
(T)
1
C
)
(
I
I
)
,
R(T,
filter
24
(
laser
filter
laser
f,
f,
filter
filter
2
2
2
2
2
1
1
1
1
2
1
2
1
=
=
)
The dependence of fluorescence on excitation light
intensity and film thickness cancels when the ratio of the two
fluorescences is used. By using this ratiometric approach on
optically thin systems, temperature variations in the direction of
observation are averaged over the film thickness and the
fluorescence ratio can be correlated to an average temperature
in the direction of observation (see figure 7).
Figure 7: Temperature ratio