A-1
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 vapour present in the light path. This relationship can be rewritten as
follows, where
k
w
is the absorption coefficient for water vapour,
x
is the path
length for the KH20 sensor, and
ρ
w
is the water vapour 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 vapour 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 vapour,
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
vapour density,
ρ
w
. Figure A-1 shows the plot of the equation A-4 after we ran a
KH20 over a full calibration vapour range.
