Page 222 - Photodetection and Measurement - Maximizing Performance in Optical Systems

Measurand Modulation

Measurand Modulation 215

For example, if the source intensity drops by 10 percent, this just gives a 10
percent reduction in LOD.
Figure 10.1b shows a quite different situation in which a weak, slowly chang-
ing optical absorption is being measured in transmission, and the available path
length and absorption strength are such that the relative reduction in trans-
mitted power d through absorption is very small. Examples of such systems
include trace chemical detection at the limit of an instrument’s performance,
monitoring the growth of bacterial colonies by absorption, and long-term envi-
ronmental monitoring. These situations, with small and slow absorption
changes, represent some of the most difficult examples of conventional optical
measurement.
As before, a high power modulated optical source is available, almost all the
power is transmitted to the detector, and the LOD is determined by the small-
est change in relative power transmission d that can be detected. For best per-
formance, at commissioning the displayed reading is set up as 100 percent of
full scale, and repeated measurements are shown to be distributed randomly
about 100 percent. The next day V m has decreased by a small amount DV to just
below full-scale, so we ask whether the absorption has actually increased. What
determines the smallest change in V m that we can confidently say is due to
absorption? As in Fig. 10.1a the standard deviation of high frequency meas-
urement noise will limit the LOD, but this noise is likely to be small because of
the high levels of received power and hence ease of achieving shot-noise limited
performance. We will still be affected by baseline drift errors, but these will be
minimized using source modulation and synchronous detection. Unlike the case
of Fig. 10.1a, however, the LOD is additionally limited by gain changes in the
measurement channel. If the gain changes by 10 percent, then (1 - d) and V m
also change by 10 percent of full-scale, and this is the smallest change that can
be confidently detected. This will usually limit the LOD to a value far greater
than that defined by the S/N. As we are already operating with a full-scale
signal, we do not have the opportunity to improve LOD by increasing the gain
and reducing the bandwidth. Similarly, increasing source power and resetting
the detector for full-scale doesn’t help the LOD. Limitations on LOD due to
errors caused by gain instability are likely to be many orders of magnitude
greater than limits due to measurement noise. This is a fundamental problem
of such a bright field measurement. If in Fig. 10.1a the relative signal due to d,
DV = 1 percent and there is a 10 percent gain decrease, then DV changes by 10
percent to 0.9 percent of full-scale, a 10 percent error. If in Fig. 10.1b DV = 1
percent and there is a 10 percent gain decrease, DV becomes 10x larger in value,
a 1000 percent error.

10.2 Path-length Modulation
Let’s suppose we want to detect a 0.01 percent change in transmission of a
liquid sample. This would require a temperature stability of the order of
4ppm/°C if a 25°C instrument temperature change is foreseen. If the source is

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