Page 251 - Photodetection and Measurement - Maximizing Performance in Optical Systems

Multiple Channel Detection

244 Chapter Eleven

perform a different set of three measurements, by first illuminating LEDs 1 and
3, then 2 and 3, then 1 and 2. The choice of on/off LEDs at each stage is given
by subsequent rows of the so-called S-matrix:

È 10 1 ˘
Í
S = 01 1 ˙
Í ˙
Î Í11 0 ˚ ˙

We can conveniently use a microcontroller to sequentially illuminate the three
LED groups. With each combination we digitize the integrated intensity as
usual. The resulting measurements are:

È 24 3 . ˘
Í
M = 25 0 . ˙
Í ˙
Î Í21 9 . ˚ ˙
Each combination provides one intensity value. Because the aggregate inten-
sity of the three signals in each measurement is larger (about twice as large)
than that of a single source, the relative error of the second set (M) will be
reduced by comparison with set (I true). To recover the individual channel inten-
sities we multiply the vector M by the correct inverse S-matrix:

.
È 05 . -05 05 . ˘È 24 3 . ˘ È 10 6 . ˘
Í
Í
I est = SM = -05 05 . 05 . ˙Í 25 0 . ˙ = 11 3 . ˙
-1
.
Í ˙Í ˙ Í ˙
Î Í05 . 05 . -05 . ˚ ˙ Î Í21 9 . ˚ ˙ Î Í13 7 . ˚ ˙
The improvement in S/N which is possible with only a few channels is rather
modest. With N = 3 the gain of 1.22 is not impressive, but becomes interesting
for larger N.
In particular, this technique has been put to very effective use in infrared
spectroscopy. When dispersive spectroscopy is performed with narrow input
and output slits, most of the source power is lost for most of the time. If
instead the usual single slits are replaced by coding masks in the form of one-
dimensional S-vectors, the improvement in light throughput can be large (about
N/2 for one mask). Either input-only, output-only or both slits may be so
replaced. Light passing through illuminates a single detector. To record the
spectrum the mask is scanned just as in the recording of a direct spectrum.
After recording, the true spectrum is recovered through a software matrix
product. At a time when only single detectors were available, resolution and
S/N of these so called Hadamard spectrometers were much superior to classic
instruments. Harwit and Sloane (1979) provide a beautiful description of their
design and operation.
With the development of large area detector arrays, which can detect photons
in all spectral channels simultaneously for the full time of the measurement,

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