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Fiber Bragg Gratings and Two Wave Mixing Spectral Demodulator System
for Impact Detection and Localization
Goutham KIRIKERA, Oluwoseyi BALOGUN, Sridhar KRISHNASWAMY
Center for Quality Engineering and Failure Prevention,
Northwestern University, Evanston, IL 60208, USA.
ABSTRACT
Multiplexed fiber Bragg grating (FBG) sensors capable of dynamically measuring high
frequency (>200KHz) ultrasonic waves using a two wave mixing spectral demodulator has been
reported by us previously. The two-wave mixing spectral demodulator enables multiplexing of
several FBG sensors and also acts as a high pass filter eliminating low frequency thermal drift
and vibrational noise without the need for stabilization as required by other interferometric
demodulation schemes. We have demonstrated that this system is capable of monitoring and
locating of impact events if several FBG sensors are used. In this paper, we present recent results
that have extended our original architecture to take into account the directional dependence of
FBG sensor sensitivity to propagating ultrasonic waves. Since the FBG is highly directionally
dependent at high frequencies, a simple rosette FBG pattern is implemented enabling effective
detection of impact from any location.
Keywords: structural health monitoring, fiber sensors
1. INTRODUCTION
Fiber Bragg grating (FBG) sensors have been developed for a variety of applications including
optical remote sensing of strain, temperature, and pressure. These sensors offer special
advantages: they are light-weight, resistant to corrosion, immune to electromagnetic interference,
and can be multiplexed thus allowing for the simultaneous measurement of strain, temperature
and pressure at multiple locations. Several applications of FBG sensors in health monitoring of
structures have been reported in the literature1-8.
In this paper, we describe a recently-developed two-wave mixing spectral demodulator9-
11 that is used in conjunction with a network of FBG sensors to monitor high frequency dynamic
strains (>10KHz). Unlike existing demodulation methods, the TWM demodulator enables
monitoring high-frequency dynamic strains simultaneously from several FBG sensors.
Moreover, the system is immune to quasistatic drift caused by temperature or quasistatic strains.
As such the system is ideally suited for monitoring stress waves caused by impact or acoustic
emissions.
In the following sections, the principle of a high-power TWM spectral demodulation is
briefly described, followed by a description of the system performance in terms of frequency
response etc. An application to impact monitoring is then described. Finally, preliminary results
from a low-power TWM spectral demodulator with significantly lower system cost is described.
2 HIGH-POWER TWO-WAVE MIXING SPECTRAL DEMODULATOR:
The system diagram for a TWM interferometer used as a wavelength demodulator for the FBG
sensor is shown in Figure 1. The FBG sensor is illuminated by a broadband amplified
spontaneous emission (ASE) source in the C-band, and the reflected light is coupled by a
circulator into an Erbium doped fiber amplifier (EDFA) with output power 500mW (hence
called high-power system). The amplified light is split into pump and signal beams that travel
unbalanced optical paths to the PRC. The light reflected from the FBG sensor will undergo
spectral shift due to strain-induced changes in the Bragg-reflectivity. The sensors by themselves
are sensitive to both quasi-static and dynamic strains, and are also subject to thermal drift.
17th World Conference on Nondestructive Testing, 25-28 Oct 2008, Shanghai, China
However, since the TWM demodulator is adaptive, the system will only track dynamic strains,
and will automatically compensate for quasistatic drifts.
λ/2 λ/2PBS
PRC
DC 6KV/cm
InP:F
e
EDFA
ASE Broadband
Source
FBG Sensor
Circulator
Photodetector
λ/2
Figure.1 System diagram of TWM fiber Bragg-grating sensor demodulator.
For TWM to work as a wavelength demodulator of dynamic FBG spectral shifts, the basic idea is
similar to that of the Mach-Zehnder Interferometer (MZI) or other path unbalanced
interferometric demodulation schemes. In these schemes, the wavelength shift is tracked as a
phase-shift that results from the same input beam traveling two different optical path lengths.
The main point is that the signal and pump beams in the TWM are both obtained from the same
FBG sensor and therefore are both subject to the same wavelength shift. However, the two
beams are made to travel unbalanced paths prior to mixing in the PRC. Therefore the spectral
shift is effectively converted to an optical phase difference which is given by:
)(
2
)( 2t
d
t
λ
λ
π
ϕ
Δ−= , (1)
where d is the optical path difference (OPD), λ is the nominal center wavelength of the light
from the Bragg-grating sensor; Δλ is the time-varying shift in the wavelength caused by the
measurand.
In order to demonstrate wavelength demodulation, we applied a 10 kHz, 10 µε strain onto
the FBG sensor and measured the wavelength
demodulated signal amplitude at different values
of the optical path difference. As shown in
Figure 2, an intermittent DC field is applied from
1ms to 6ms with respect to a reference trigger,
and the photorefractive grating initially builds
up. The dynamic strain is applied as a toneburst
starting from 2ms to 6ms.When the OPD equals
to zero, although the TWM energy gain12 is at its
maximum, there is no detected wavelength
demodulated signal because there is no OPD to
convert the wavelength shift into phase shift. As
the OPD increases, the wavelength demodulated
signal starts to appear. The signal reaches
maximum when OPD equals 8mm and beyond
that further increasing of the OPD causes the
signal to drop.
Figure 2 Wavelength demodulated signal at
different values of OPD. An intermittent DC
field is applied to the PRC starting from 1ms to
6ms and a 10 kHz 10 µε strain is applied to the
FBG from 2ms to 6ms
2.1 Adaptivity to low-frequency drift:
One of the advantages of using the two-wave mixing interferometer as a wavelength
demodulator is its adaptivity to low frequency drift. As
mentioned earlier, the two-wave mixing interferometer
is automatically adaptive to low frequency strain or
temperature drift of the FBG sensor. In order to show
adaptivity to quasistatic strain, we applied a frequency
sweep signal from 10Hz to 1.2 kHz with a constant
magnitude of 10µε. Figure 3 shows the response of the
wavelength demodulator to this frequency sweep signal.
The demodulator ignores the low frequency strain
applied in the beginning and starts to respond to
frequencies above 600Hz.
Figure 4 demonstrates the adaptivity to
quasistatic strain more clearly in the frequency domain.
Figure 4 (a) is the Fourier spectrum of the applied
sweep signal, Figure 4 (b) is the spectrum of the
system response to the sweep signal, and Figure 4 (c)
is the system transfer function (modulus) calculated by
dividing the system response spectrum by the sweep
signal spectrum. From Figure 4, it is clear that the
TWM wavelength demodulator is adaptive to low
frequency strains and acts like a high pass filter with a
cut-off frequency of 600 Hz. The cut-off frequency of
the system is directly related to the response time of
the InP:Fe PRC.
2.2 Multiplexing of FBG sensors:
In addition to adaptivity to low frequency drift,
another major advantage of using TWM as wavelength
demodulator for FBG sensors is that it can be
multiplexed without significant increase in cost. This
is because all the channels (wavelengths) share the
same PRC and there is no expensive feedback
electronics involved.
We now demonstrate a four-channel TWM wavelength demodulator together with quasi-
static drifts monitoring. The experimental configuration is shown in Figure 5. Four 0.15nm line-
width FBG sensors are connected in series and are centered at 1536nm, 1540nm, 1544nm and
1548nm respectively. The experimental configuration is similar to that of the single channel
configuration shown in Figure 1 except that after the PRC, there is a free space to fiber coupler
to couple the free space light into a set of four band drop filters, and also there is an optical
spectrum analyzer monitoring the transmitted light through the FBG sensors.
In order to show that four FBG sensors can be monitored simultaneously, we applied 10
kHz 5 µε strain on FBG sensor 1 (1536nm), 5 kHz 5 µε on FBG sensor 2 (1540nm), 2 kHz 5 µε
on FBG sensor 3 (1544nm) and 20 kHz 5 µε on FBG sensor 4 (1548nm) simultaneously. Figure
6 shows that the dynamic strain from four channels can be demodulated simultaneously.
0.0 0.2 0.4
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0.02
Signal Amplitude(v)
Time(s)
Zoom in
0.1 0.3 0.5
Figure 3 TWM wavelength demodulator
response to a frequency sweep signal
from 10 Hz to 1.2 kHz.
0 200 400 600 800 1000 1200
(c)
Frequenc y(Hz )
Trans fer function
cut-off frequency :
600Hz
Response spectrum
(a)
Sweep spctrum
(b)
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1.0
Figure 4 (a) Fourier spectrum of the
applied frequency sweep signal from 10
Hz to 1.2 kHz. (b) Fourier spectrum of the
response of the TWM wavelength
demodulator. (c) Transfer function of the
TWM wavelength demodulator. The cut-
off frequency is seen to be around 600 Hz
for this configuration
2.3 Source Location:
The signals from multiple FBG sensors can be used to locate the source of an acoustic event.
The FBG sensor is surface mounted on a large
aluminum plate of 1mm thickness as shown in Fig. 7.
The acoustic emission event is simulated by dropping a
7.9mm steel ball at location 1, 2 and 3 from a controlled
height of 1 meter. The FBG sensor is located at position
(25cm, 21cm) with respect to the lower left corner of
the plate. Figure 8 shows the detected acoustic emission
signals at location 1, 2 and 3. From the results, we can
clearly see a dispersive plate wave is detected by the
FBG sensor.
The captured time traces then are analyzed using
wavelets to determine the location of the ball
impact. A Gabor wavelet (mother wavelet) is used
to perform the analysis. The experimentally
generated dispersion curves are backtracked to
identify the location of the impact as follows. The
arrival time at each frequency corresponds to the
group velocity of the propagating wave. Also the
wavelet coefficients obtained at each frequency is
strongly dependent on the size of the window and
influences the calculated location of the source.
To obtain an accurate result, averaging of the
localization results obtained with various window
sizes is performed to identify the impact location.
Circulator
ASE
Broadband Optical Amplifier
1 by 2
Coupler
Collimato r
Collimator
PRC
DC field 6kV/cm
InP:Fe
λ/2
λ/2
Free
space to
fiber
coupler
Photod etector
Photod etector
1548nm
1552nm
Band drop fil ters
Photod etector
Photod etector
1560nm
1556nm
1536nm 1540nm 1544nm 1548nm
Optical Analyzer
Figure 5 Experimental configuration for the four-channel TWM
demodulator for both dynamic and static strain measurement.
0.0050 0.0055 0.0060 0.0065 0.0070 0.0075
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1.05
1.10
Time (s)
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1.10
0.90
0.95
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1.05
1.10
0.90
0.95
1.00
1.05
1.10
Signal Amplitude (a.u .)
Ch 1
Ch 2
Ch 3
Ch 4
Figure 6 Simultaneous demodulation of the
signals from four-FBG sensors using a 4-
channel TWM wavelength demodulator.
x
y
FBG Sensor
12
3
Aluminum Plate
Figure 7: Experimental setup for acoustic
emission event detection and source
location determination.
0 0.2 0.4 0.6 0.8 1.0
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0.03
Amp lit u de
Time (ms)
0 0.2 0.4 0.6 0.8 1.0
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Amplitude
Time (ms)
0 0.2 0.4 0.6 0.8 1.0
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0.01
0.02
0.03
Amplitude
Time (ms)
Location 1
Location 2
Location 3
Figure 8 FBG sensor signals detected for the three
impact locations
One sensor is used in this analysis to show that the proposed algorithm is suitable for impact
location. This enables identification of the source
to within a circle. Precise location information
through the process of triangulation can be
achieved by adding more FBG sensors and
applying the same algorithms on the time trace
obtained from each sensor.
Figures 9 shows the time-frequency
analysis13 for one of the impact signals. The
experimentally generated dispersion curves can be
seen in the wavelet transformation showing the
fundamental lower order asymmetric mode of the plate wave. For source location identification,
a search algorithm is implemented that identifies the minimum of the difference between
locations at two different frequencies for an assumed time. In other words, to start with, the
algorithm assumes a vector of time ranging from 0 to 100 microseconds with a small step size. A
vector ( KHz
Location80 ) consisting of the location information at 80 KHz using the group velocity
(KHz
Cg80 ) and the assumed time vector (Time ) is generated using:
TimeCgLocation KHzKHz *
8080 = (2)
Similarly, the location information is found for 70KHz using:
)(* 707070 KHzKHzKHz tTimeCgLocation
Δ
+
= (3)
where KHzKHzKHz TimeTimet 708070 −=Δ . KHz
Time80 and KHz
Time70 are the arrival times determined
from Figure 9.
The minimum of the difference between
Eqns (2) and (3) indicates the time at
which the impact was initiated. The same
procedure is repeated for multiple
frequencies. Thus at each frequency a
value for the likely impact source location
is obtained. The predicted locations are
shown in Figure 10. A single sensor can
predict the location of the impact within
the diameter of the circle. Multiple
sensors need to be used for more accurate
source localization. It is seen that this
algorithm provides the impact location
quite accurately.
3. LOW-POWER TWM SPECTRAL DEMODULATOR:
We next present preliminary experimental results on the detection of impact signals using a
low power (1 mW) TWM demodulation system. Low power operation, while offering significant
cost-reduction of the demodulator system, is typically undesirable in TWM interferometers
because the intensity of the interacting optical beams in the PRC may not be high enough to
achieve fast photorefractive grating formation12. This can limit the ability of the interferometer to
selectively monitor dynamic wavelength shifts in the presence of low frequency temperature
drifts. To overcome this, the interacting beams are focused into the PRC in order to facilitate fast
photorefractive grating formation. Furthermore, the TWM gain is optimized through resonant
Figure 9. Impact location 1 (a) Response of sensor (b)
wavelet transformation of the experimentally generated
signal.
Figure 10. Actual impact location (x) and the predicted impact
location
(
circles
)
.
enhancement of the space charge electric field formed in the PRC by the photorefractive effect
using temperature-intensity resonance14,15.
3.1 Enhancing the TWM Gain using temperature-intensity resonance:
First, the formation of the photorefractive grating in the PRC and beam diffraction was
established. An intermittent DC electric field of amplitude 6 KV/cm was applied to the PRC for
10 ms at a repetition rate of 10 Hz. The output of the PRC was measured with the photodetector.
The TWM intensity gain ( Λ) is defined by
the following;
1
2
1A
In
lA
⎛⎞
Λ= ⎜⎟
⎝⎠
(1)
where A1 is the intensity of the transmitted
signal beam and the diffracted pump beam, A2
is the intensity of the transmitted signal
beam, l is the length of the PRC, and In is the
natural logarithm function. It is seen that
Λ
is
greater than zero when the DC field is applied
to the PRC and negligible otherwise. The
application of the DC field enhances the
space charge electric field and the
photorefractive grating formed in the PRC.
The TWM gain was measured to be
approximately 0.12 cm-1 , about four times smaller than the value obtained with the high-power
TWM system using the 500 mW source as described earlier. Furthermore, the rise time of the
gain plot is less than 2 ms, which gives an estimate of the response time of the PRC. Based on
the estimated PRC response time, the expected cut-off frequency of the TWM wavelength
demodulation system is close to 500 Hz, which is sufficient to selectively monitor dynamic FBG
wavelength shift in the presence of low frequency temperature drifts.
In order to further optimize Λ for efficient wavelength demodulation, the temperature of the
PRC was tuned leading to a resonant enhancement of the space charge electric field, a
phenomenon referred to as the intensity-temperature resonance14,15. The intensity-temperature
resonance occurs in InP PRCs operated in the drift mode. In these PRCs, the photorefractive
effect involves the thermal- and photo- excitation of both electrons and holes. Typically, thermal
excitation of electrons and photo-excitation of holes is dominant in InP, and a resonance
condition is obtained when these dominating effects are exactly balanced. As such, for a fixed
optical intensity delivered to the PRC, the average temperature in the PRC can be controlled to
resonantly enhance the TWM gain. Figure 11 shows the measured TWM gain plots obtained at a
few PRC temperatures. The temperature of the PRC is controlled with the thermoelectric cooler.
It is seen that the TWM gain increases steadily as the PRC is cooled indicating that resonance
occurs at a low temperature for the 1 mW source. The thermoelectric cooler was not stable below
10 oC, as such, the actual resonance temperature was not ascertained in these experiments. It is
noteworthy that the response time of the PRC increases as the resonant temperature is
approached, which is due to large charge accumulation in the PRC. Therefore, a trade-off has to
be made between TWM gain and PRC response time in choosing the operational temperature.
Preliminary experiments on the demodulation of dynamic strains in a FBG sensor were
carried out using the low power system. The strains were produced by impact loading from a ball
drop on the aluminum plate. For this experiment, the ball drop location was 14 cm away from the
FBG sensor position. The temperature of the PRC was maintained at 12 oC. The response of the
02468101214
0.00
0.05
0.10
0.15
0.20
0.25
0.30
TWM Intensity Gain (cm-1)
Time (ms)
10 oC
12 oC
15 oC
20 oC
Crystal Temperature
Figure 11. Transient plot of two-wave mixing intensity gain at
various values of the PRC temperature
FBG sensor was compared to the response of a
PZT piezoelectric sensor mounted close to the
FBG sensor on the plate. A first order low pass
filter at 150 KHz was applied to the FBG
response to reduce the broadband noise in the
signal. The same filter was applied to the PZT
response. The FBG and PZT sensor responses are
shown in Fig. 12.
Note that the data were taken in single shot
mode on the oscilloscope, which was pre-
triggered with the PZT response. The transient
responses are in good qualitative agreement. The
signal to noise ratio (SNR) of the FBG response is
low, which is expected because the SNR of the
TWM interferometer is proportional to the square
root of the optical power in the shot noise limited case. Consequently, the lower the optical
power, the lower the SNR. Nevertheless, these experimental results are encouraging in that they
indicate that a low power TWM demodulation system can be feasibly implemented, thus
allowing for a substantial reduction in the system cost. We are currently exploring the use of
high DC fields to improve the SNR of the system.
CONCLUSIONS
A TWM spectral demodulator is described that can be used for dynamic demodulation of FBG
sensors. Multiple FBG’s are used to identify the actual location of the impact based on wavelet
analysis. Ultrasonic frequencies exceeding 200 KHz were detected by the adaptive FBG
demodulator system. The location of the impact was determined with good accuracy. A low-
power TWM demodulator is currently being developed to bring the system cost down.
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