Page 236 - Photodetection and Measurement - Maximizing Performance in Optical Systems

Measurand Modulation

Measurand Modulation 229

values will be constant. Also, the longer we go on making measurements, the
better we will define this mean. This just isn’t how drift and temperature errors
seem to work! For example, the precision of measurement of a shot-noise limited
100mA photocurrent is typically far worse than the noise calculation would
suggest. Experience seems to say that the potential error depends in some way
on the time-scale, for example on the time since last calibration. The longer we
wait, the greater is the likely error. This is, after all, the basis of industry’s
reliance on periodic calibration. In order to understand the errors, we must esti-
mate the measurement noise frequencies and related timescales, which depend
on the type of measurement we are making.
The first is an absolute measurement, where we are given an unknown
sample, and asked to measure the absorption. We just insert the sample and
press “read.” The instrument was calibrated three months ago, so the impor-
tant characteristic is the variation that is likely to have taken place since then.
This is given by the noise spectral density at the corresponding frequency, some-
thing like 0.33 month . An alternative and much easier measurement is where
-1
we have a chance to zero the equipment with a blank. Much of laboratory spec-
troscopy is carried out in this way. First we measure a cuvette of deionized water
and call the transmission unity. Then the real sample’s transmission is mea-
sured, and the intensity ratio is computed. In this case the pertinent fre-
quency is 1/(time between the blank and sample measurements) or perhaps
-1
1 minute . In the case of gas absorption modulation in the organ pipe of Fig.
10.6 the frequency could be ªkHz.
For some instruments such as electrochemical sensors used to measure chlo-
rine disinfectants in drinking water the noise-and-drift is quite different. Here
the dominant problem is fouling, and the sensitivity of the electrochemical
process essentially just degrades with time. If the sensor is used as input to a
closed loop dosing control system the true concentration will be automatically
adjusted upward to compensate for the reducing sensor sensitivity, until the
electrodes are cleaned and the instrument recalibrated. The resultant “saw-
tooth” drift function is clearly quite unlike Gaussian white noise, and the cal-
culation of the mean signal and standard deviation depends on the time-scale
evaluated. Similar problems arise with optical transmission systems which do
not include compensation for window fouling. They become gradually dirtier.
White noise just doesn’t describe these processes.
As another possibility, what if the noise-and-drift spectrum really has a
1/f character, as sketched in the upper part of Fig. 10.16. After all, we know
that this is prevalent in active electronic components and many natural
processes. Then the noise power density for frequencies corresponding to a year
since calibration (1/year) would be much greater than those for blank and
sample measurements separated by a minute. The longer we wait, the greater
the likelihood of measuring with a larger error, and the longer we go on meas-
uring, the greater becomes the standard deviation of the distribution. This
seems to corresponds much better to practice. The time-series of the lower part
of Fig. 10.16 was calculated by setting up a frequency distribution of random

Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com)
Copyright © 2004 The McGraw-Hill Companies. All rights reserved.
Any use is subject to the Terms of Use as given at the website.