Page 250 - Photodetection and Measurement - Maximizing Performance in Optical Systems

Multiple Channel Detection

Multiple Channel Detection 243

There are many ways to generate the Walsh functions. Where only eight
channels are needed, it is simple to hard-code the 8-bit bytes into a micro-
controller, and to read them out sequentially. The spectra of Fig. 5.4 were
obtained in this way with sequential readout of memory locations in a Basic
Stamp computer, which contains a PIC microprocessor. Henning Harmuth
(1964) has given detailed theory of the numerical generation of Walsh functions,
while Beslich (1973) has described solutions for Walsh generators using digital
logic.

11.7 Time Multiplexing

11.7.1 Source-polling
One of the simplest multichannel techniques for a few or a few dozen channels,
as long as a microcontroller is available in the measurement setup, is to time
multiplex. The sources are illuminated in turn, and a common photo-receiver
determines the intensity in that channel. If the multiplexing is performed
thousands of times per second, this is equivalent to shifting the measurement
to higher frequencies. The repetitive short-time samples give a periodic comb
of passbands in the frequency domain. By spreading the information over a
wide range, interference from specific, unfortunately-placed signals can be
suppressed. Hence performance can be better than that of a narrow-band
modulation/demodulation system.

11.7.2 Weighing designs
The problem with time division into a large number of time-slots is the poor
use of the source’s energy. As we have seen, the signal to noise ratio (S/N) is
determined by the number of photons detected during a measurement, so
arranging for each source to be off for most of the time is not the way to
optimize performance. We need to have sources on for as much of the time as
possible. Improvements can be made by illuminating combinations of sources
together, and detecting the now larger composite signals. This is equivalent to
the classic “weighing problem” of statistical analysis, and treated by Yates
(1935). A short treatment is given in App. D. For now we limit ourselves to a
brief description of the technique, and work through a tiny example. Assume
that we want to measure the light intensities from three weak sources, arranged
here as a vector,

È 10 6. ˘
Í
I true = 11 3. ˙
Í ˙
Î Í13 7. ˚ ˙
and the S/N is not good because of the receiver noise, which is normally dis-
tributed. The detection variance, combined with the weak received intensities,
gives a large relative error for each of the three measurements. Now let us

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