Appendix A. Calibrating KH20
A.1 Basic Measurement Theory
The KH20 uses an empirical relationship between the absorption of the light
and the material through which the light travels. This relationship is known as
the Beer’s law, the Beer-Lambert law, or the Lambert-Beer law. According to
the Beer’s law, the log of the transmissivity is anti-proportional to the product
of the absorption coefficient of the material,
k
, the distance the light travels,
x
,
and the density of the absorbing material,
ρ
. The KH20 sensor uses the UV
light emitted by the krypton lamp: major line at 123.58 nm and the minor line
at 116.49. As the light travels through the air, both the major line and the
minor line are absorbed by the water vapor present in the light path. This
relationship can be rewritten as follows, where
k
w
is the absorption coefficient
for water vapor,
x
is the path length for the KH20 sensor, and
ρ
w
is the water
vapor density.
w
w
x
k
e
T
ρ
−
=
A-1
If we express the transmissivity,
T
, in terms of the light intensity before and
after passing through the material as measured by the KH20 sensor,
V
and
V
0
,
respectively, we obtain the following equation.
w
w
x
k
e
V
V
ρ
−
=
0
A-2
Taking the natural log of both sides, and solving for the density,
ρ
w
, yields the
following equation.
)
ln
(ln
1
0
V
V
x
k
w
w
−
−
=
ρ
A-3
If the path length,
x
, and the absorption coefficient for water,
k
w
are known, it
becomes possible to measure the water vapor density
ρ
w
, by measuring the
signal output,
V
, from KH20.
A.2 Calibration of KH20
The KH20 calibration process is to find the absorption coefficient of water
vapor,
k
w
. To do this, we rewrite the equation A-3, and solve for ln(V).
0
ln
ln
V
x
k
V
w
w
+
−
=
ρ
A-4
It now becomes obvious from the equation A-4 that there is a linear
relationship between the natural log of the KH20 measurement output, ln
V
, and
the water vapor density,
ρ
w
. Figure A-1 shows the plot of the equation A-4
after we ran a KH20 over a full calibration vapor range.
A-1
Summary of Contents for KH20
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