System and method for monitoring Fabry-Pérot cavity displacements
A system and method for monitoring Fabry-Perot cavity (“FPC”) displacement implementing a predictor-corrector scheme. The system includes an optical interrogator apparatus and a data processing apparatus. The optical interrogator apparatus interrogates the FPC, obtains a spectral interference pattern and outputs a corresponding signal including data associated with a plurality of peaks. The data processing apparatus processes the output signal to produce a prediction for a peak location based on the data associated with the plurality of peaks, and then uses the prediction to identify as correct one of the plurality of peaks. The data processing apparatus then determines and outputs a plurality of FPC length variations. In one embodiment, the data processing system implements a period tracking algorithm to produce the prediction based on the data associated with the plurality of peaks, and uses a phase tracking algorithm to determine an FPC length variation using the identified peak.
1 . A system for measuring variations in time of a length of a Fabry-Perot cavity (FPC), the system comprising:
an optical interrogator apparatus configured to
interrogate the FPC with light,
produce a periodic spectral interference pattern from the light that interrogated the FPC, wherein the periodic spectral interference pattern spans over an operational spectral range {λ min , λ max }, and wherein locations of peaks of the periodic spectral interference pattern vary in time in accordance with the variations of the FPC length, and
output a signal of the peak locations; and
a data processing apparatus communicatively coupled with the optical interrogator apparatus and configured to
receive, from the optical interrogator apparatus, the signal of the peak locations,
determine a reference length of the FPC as an average of FPC lengths corresponding to a reference instance of the signal of the peak locations,
for each instance of the signal of the peak locations following the reference instance,
determine a current length of the FPC as an average of FPC lengths corresponding to a current instance of the signal of the peak locations,
predict peak locations corresponding to the current instance of the signal of the peak locations based on the current length, the reference length, and the reference instance of the signal of the peak locations,
identify as corrected peak locations the corresponding ones from among the peak locations of the current instance of the signal within the operational spectral range that are nearest to the predicted peak locations,
estimate a current FPC length variation as a median of FPC length variations corresponding to the corrected peak locations, the reference instance of the signal of the peak locations, and the reference length, and
determine the current FPC length variation as a median of previously estimated FPC length variations over a moving time window of predetermined duration, and
output a signal of the determined FPC length variations.
2 . The system of claim 1 , wherein a sampling frequency of the signal of the peak locations is about 1 kHz, and
the predetermined duration of the moving time window is in a range of >10 samples.
3 . The system of claim 2 , wherein the data processing apparatus is implemented as one of a microprocessor, an FPGA, or an ASIC.
4 . The system of claim 2 , wherein the data processing apparatus is implemented as a software module to be integrated in a software system configured to control the optical interrogator apparatus.
5 . The system of claim 1 , wherein the average used by the data processing apparatus to determine a particular length of the FPC comprises a truncated average of the FPC lengths corresponding to the particular instance of the signal of the peak locations.
6 . The system of claim 1 , wherein
the maximum variation of the FPC length Δl(t) corresponds to
λ
max
-
λ
min
λ
C
l
(
t
0
)
,
where
(
λ
max
-
λ
min
)
is the operational range, and λ C is the central wavelength of the light used to interrogate the FPC, and
the data processing apparatus is configured to reset the determined reference length of the FPC from l(t 0 ) to a larger value l(t>t 0 )>l(t 0 ) to enhance the system's dynamic range for measuring variations of the FPC length.
7 . The system of claim 1 further including the FPC.
8 . The system of claim 7 , wherein the FPC includes an optical fiber disposed in spaced relation to a flexible diaphragm, the flexible diaphragm configured to change shape in response to variations in at least one of pressure and corrosion, the flexible diaphragm having a reflective surface facing the optical fiber.
9 . The system of claim 8 wherein the optical interrogator includes a tunable laser source, a first photodetector, a second photodetector and a plurality of optical fibers operatively joining the tunable laser, the first photodetector and the second photodetector with the FPC.
10 . A sensor for measuring corrosion in nuclear reactors, the sensor comprising:
an FPC; and
the system of claim 1 .
11 . A sensor for measuring pressure, the sensor comprising:
an FPC; and
the system of claim 1 .
12 . A system for measuring variations in time of a length of a Fabry-Perot cavity (FPC), the system comprising:
an optical interrogator apparatus configured to
interrogate the FPC with light,
produce a periodic spectral interference pattern from the light that interrogated the FPC, wherein the periodic spectral interference pattern spans over an operational spectral range {λ min , λ max }, and wherein locations of peaks of the periodic spectral interference pattern vary in time in accordance with the variations of the FPC length, and
output a signal of the peak locations; and
a data processing apparatus communicatively coupled with the optical interrogator apparatus and configured to
receive, from the optical interrogator apparatus, the signal of the peak locations,
determine a reference length of the FPC as a function of at least one FPC length corresponding to a reference instance of the signal of the peak locations,
for each instance of the signal of the peak locations following the reference instance,
determine a current length of the FPC as a statistical analysis of FPC lengths corresponding to a current instance of the signal of the peak locations,
predict peak locations corresponding to the current instance of the signal of the peak locations based on the current length, the reference length, and the reference instance of the signal of the peak locations,
identify as corrected peak locations the corresponding ones from among the peak locations of the current instance of the signal within the operational spectral range that are nearest to the predicted peak locations, and
estimate a current FPC length variation as a statistical analysis of FPC length variations corresponding to the corrected peak locations, the reference instance of the signal of the peak locations, and the reference length, and
output a signal of the FPC length variations.
13 . The system of claim 12 wherein the statistical analysis used by the data processing apparatus to determine a current length of the FPC is further defined as an average of FPC lengths corresponding to a current instance of the signal of the peak locations.
14 . The system of claim 12 wherein the statistical analysis used by the data processing apparatus to estimate a current FPC length variation is further defined as a median of FPC length variations corresponding to the corrected peak locations, the reference instance of the signal of the peak locations, and the reference length.
15 . The system of claim 12 wherein the statistical analysis used by the data processing apparatus to determine a current length of the FPC is further defined as an average of FPC lengths corresponding to a current instance of the signal of the peak locations;
wherein the statistical analysis used by the data processing apparatus to estimate a current FPC length variation is further defined as a median of FPC length variations corresponding to the corrected peak locations, the reference instance of the signal of the peak locations, and the reference length;
wherein the data processing apparatus is configured to determine the current FPC length variation as a median of previously estimated FPC length variations over a moving time window of predetermined duration; and
wherein the output signal is further defined as a signal of the determined FPC length variations.
16 . The system of claim 12 wherein the optical interrogator includes a tunable laser source, a first photodetector, a second photodetector and a plurality of optical fibers operatively joining the tunable laser, the first photodetector and the second photodetector with the FPC.
17 . A method for monitoring Fabry-Perot cavity (FPC) displacement, comprising the steps of:
interrogating the FPC with light by a light source emitting light over an operational spectral range {λ min , λ max };
obtaining a spectral interference pattern representative of light returning from the FPC, the returning light being reflected from at least two different reflective surfaces, wherein locations of peaks of the periodic spectral interference pattern vary in time in accordance with the variations of the FPC length;
producing a signal including data associated with a plurality of peaks in the spectral interference pattern;
determining a reference length of the FPC as a function of FPC lengths corresponding to a reference instance of the signal of the peak locations
for each instance of the signal of the peak locations following the reference instance,
processing the signal using a period tracking algorithm to produce a prediction for a peak location based on the data associated with the plurality of peaks;
identifying as correct one of the plurality of peaks, the correct peak being selected as one of the plurality of peaks closest to the predicted peak location;
estimating a plurality of FPC length variations using a phase tracking algorithm;
determining the current FPC length variation as a median of previously estimated FPC length variations over a moving time window of predetermined duration; and
output a signal of the determined FPC length variations.
18 . The method of claim 17 wherein the step of determining a reference length of the FPC is further defined as determining a reference length of the FPC as an average of FPC lengths corresponding to a reference instance of the signal of the peak locations.
19 . The method of claim 18 , wherein the maximum variation of the FPC length Δl(t) corresponds to
λ
max
-
λ
min
λ
C
l
(
t
0
)
,
where
(
λ
max
-
λ
min
)
is the operational range, and λ C is the central wavelength of the light used to interrogate the FPC.
20 . The method of claim 18 wherein the step of processing the signal using a period tracking algorithm is further defined as processing the signal using a period tracking algorithm to produce a prediction for a peak location based on the data associated with the plurality of peaks as a function of a current length, a reference length and a reference instance of the signal of the peak locations.