Instrumentation & Measurement Magazine 24-5 - 59

Fig. 3. Calculation of errors comparing the OSA data with the curve fitting of various spectral functions. (a) The wavelength corresponding to the minimum
amplitude of the attenuation band; (b) The minimum amplitude of the attenuation band. This test was done for multiple LPFG spectra, represented by their number
in the x-axis.
Although the spectral reconstruction does not match the original
data in the regions farther from the center of the attenuation
band, it provides a good fit in this region, allowing for a good determination
of the parameters of interest. In the case presented,
the errors of the central wavelength of the attenuation band and
the amplitude where 0.01% and 1.34%, respectively. Nevertheless,
there are some aspects that should be noted:
◗ For the case of very narrow (few nanometers) or very
wide (~20 nm) attenuation bands, the error increases
considerably, especially in the amplitude parameter. For
these limiting cases, errors up to 5% in the amplitude
parameter have been observed.
◗ For a good quality spectral reconstruction, the attenuation
band should fall within the range of central wavelengths
of the DFBs used (in this case between 1530 and 1570 nm).
Ideally, three sets of points should be acquired: one in
each side of the attenuation band and one in the continuum
(as seen in Fig. 4).
◗ More elaborated methods for parameter estimation (and
uncertainty) could be used by employing Markov-Chain
Monte Carlo methods. This would also allow for the
inclusion of prior information (such as expected behavior
and laboratory information) that could be used to
increase the quality of the fitting procedure. This feature
will be developed in the future and tested, both to
measure its performance and the response from the Raspberry
Pi module to the more intensive computation.
Bayesian Model Comparison for LPFG
Sensing
Fig. 4. Simulation of the low-cost platform spectral reconstruction, using data in 4 nm intervals around 1530, 1550 and
1570 nm.
August 2021
IEEE Instrumentation & Measurement Magazine
Another objective regarding the development of the lowcost
LPFG sensing platform is the monitoring of specific
processes such as corrosion
or changes in pH and
humidity over long periods.
The development of a
platform to automatically
calculate the evidence for
a specific process the user
wants to study would allow
it to display a warning
message when this process
is detected. In this case, a
framework for the calculation
of the process evidence
based on the collected data
is required, thus justifying
the usage of Bayesian
model comparison. Here, a
brief overview of the model
comparison method following
[6] and [7] is presented.
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