Wet Labs ac-s, User Manual

Page: 20 / 43

12 ac-s User’s Guide (ac-s) Revision F 9 Feb. 2006
Tr = e-
c
x (1)
where Tr is the transmittance, c is the attenuation coefficient, and x is the pathlength of
the water volume being measured. The following treatment applies to the absorption case
if
c
is replaced by
a
. The pathlength of the ac-s is fixed at 25 cm. In the case of the ac-s
the transmittance is computed by taking the ratio of the signal value to the reference
value:
Tr= (C
sig
/C
ref
) / N (2)
Substituting equation (2) into equation (1) we get,
(C
sig
/C
ref
) / N = e-
c
x,
(3)
where Csig and Cref are the signal and reference count values from the instrument and N
is an instrument specific calibration constant obtained in the laboratory using clean water.
For more information about how N is derived, see Section 4, Calibration and
Characterization.
We therefore can solve for
c
(or
a
) by,
c
= - 1/x [ln (C
sig
/C
ref
) - ln (N)] (4)
or
c
= - 1/x (ln(C
sig
/C
ref
)) - (- 1/x (ln(N)) (5)
or
c
= [(ln(N)/x) - (ln(C
sig
/C
ref
)/x)] (6)
Since the ac-s pathlength is a fixed constant at 25 cm, we only require the determination
of (ln(N)/x) in order to accurately measure
c
. This value is derived for each channel and
is supplied with each instrument’s calibration data sheet as the “Water Offset” value and
is referred to as C
off
in equation (7).
The temperature correction is applied using the temperature from the reference line and
the channels correction table from the configuration file. The approximate correction
value is linearly interpolated from the table. First, the correct temperature bin is
determined by finding the two bin temperatures,
T
0
and
T
1
, that bracket the current
temperature. Then, using the values,
∆
Tn
and
∆
Tn+1
, from the table, we obtain
( )
( ) (
)
Tn Tn Tn T
T T
T T
∆ − ∆
−
−
+ ∆ = ∆
+
1
0 1
0 * (7)
where,
∆
T
= compensation constant
T
= current temperature