Dynamic two-axis curvature measurement using
multicore fibre Bragg gratings
A Fenderi, W N MacPhersoni, A J Moorei, J S Bartoni, J D C Jonesi, S
McCullochii, B J S Jonesii, D Zhaoiii and L Zhangiii
(i) Applied Optics and Photonics, Heriot-Watt University, Edinburgh, EH14
4AS, UK;
(ii) AWE Plc, Aldermaston, Reading, RG7 4PR, UK.
(iii) Photonics Research Group, Electronic Engineering and Computer Science
Division, Aston University, Birmingham B4 7ET, UK
A.Fender@hw.ac.uk
Abstract. We present high speed, two-axis curvature measurement using fibre Bragg
gratings (FBG) written into the cores of a four-core optical fibre. This configuration
allows the local curvature of the fibre to be obtained by measuring the strain gradient
across the fibre due to the applied bend. Using differential measurements between
pairs of gratings intrinsically compensates for common mode temperature effects. In
addition, this approach to shape measurement eliminates strain transfer issues,
provided the fibre accurately takes the shape of the component under test. Two-axis
measurement is facilitated by the square matrix formation of the cores. To satisfy a
requirement for high bandwidth monitoring, each grating in the multicore fibre is
interrogated by a separate arrayed waveguide grating. These act as a series of
narrowband transmission filters and allow the FBGs to be interrogated at speeds of up
to tens of kHz. For dynamic measurement of a cantilever vibrating at 28 Hz, with an
interrogation speed of 1125Hz, both horizontal and vertical axes showed a curvature
resolution of 0.09 m -1. Applications of this technique include high bandwidth shape
and vibration sensing and multi-axis acceleration measurement.
1. Introduction
The shape of an object may be monitored by measuring changes in the local curvature at
discrete locations on the surface of the object. Local curvature may be measured with optical
fibre techniques provided the sensing region is offset from the neutral axis of the fibre. This
method has been demonstrated using FBGs [1], LPGs in D-shaped [2] or eccentric core fibre
[3] and a 3-fibre sensing head [4].
Writing FBGs into the cores of a multicore fibre (MCF) provides a means of measuring
strain at several off-axis points within the cladding of the fibre [5,6]. Bending the multicore
fibre introduces differential strains between cores, from which the curvature of the fibre may
be inferred. By multiplexing MCF gratings at several points along the length of the fibre [7],
the shape of a test object may be recovered from the local curvature measurements. Using a
four-core fibre, with cores arranged in a square formation, allows curvature to be measured
in two dimensions by measuring two orthogonal strain differences. Using differential
measurements between pairs of gratings intrinsically compensates for common mode
temperature effects. In addition, this approach to shape measurement, compared with direct
measurement of surface strain, eliminates potential errors introduced by slippage or creep
between the test surface and a strain sensing fibre. It is relatively easy to ensure that the
fibre accurately follows the shape of the component under test, since only small transverse
bending forces need be applied to the fibre.
In the references above, the FBG reflection spectra were obtained with an optical
spectrum analyser (OSA); this approach was appropriate because the curvatures or loadings
were slowly varying. However, if we wish to monitor structural curvature dynamically the
required measurement bandwidth may exceed that available from detection by an OSA, a
scanning Fabry-Perot filter or a tunable laser, therefore FBG interrogation based on
wavelength-to-intensity conversion is appropriate. Here we present dynamic curvature
measurements using arrayed waveguide gratings (AWGs) for ratiometric detection of
wavelength shifts of FBGs in MCF to track the free vibration of a cantilever in two
dimensions.
2. Interrogation of multicore FBGs by arrayed waveguide gratings
The AWG is a commercially available wavelength division multiplexing component which
acts as a series of narrowband transmission filters. Two channels of an AWG may be used to
interrogate a FBG spectrum which lies between them (figure 1). Following Sano and Yoshino
[8], the ratio  of power in these channels may be used to determine the wavelength of the
FBG,
I
(1)
 B   log i 1
Ii
where Ii is the intensity signal from the ith AWG channel and B is the FBG centre wavelength.
In the ideal case of identical AWG and FBG spectral profiles and for small FBG
wavelength shifts, the logarithmic ratio  linearises the conversion to wavelength. This is
compared with the response for real AWG and FBG spectra in figure 2, which departs from
linearity for shifts exceeding ~0.3 nm. Provided this curve is repeatable, it is possible to
compensate for any systematic non-linearities, by polynomial or spline fitting for example.
-6
5
log (AWG channel power ratio)
x 10
Intensity (a.u)
2.5
2
1.5
1
0.5
0
1542.5
1543
1543.5
1544
1544.5
wavelength (nm)
Figure 1: FBG interrogation by two
channels of an AWG
(---) real spectra,
() Gaussian approximation.
4
3
2
1
0
-1
-2
-3
1543.2
1543.4
1543.6
1543.8
1544
1544.2
FBG wavelength (nm)
Figure 2: Theoretical plot of FBG wavelength
vs. AWG channel power ratio
(---) real spectra,
() Gaussian approximation.
The MCF (figure 3) has four cores located at the vertices of a 50 m square. This fibre
was fabricated by inserting four Ge-doped silica rods into holes drilled into a silica preform
before the fibre was drawn. Each core is singlemode at 1550 nm. The cladding diameter of
the fibre is 125 m with a 250 m diameter buffer coating, designed to match that of standard
singlemode fibre. Light may be coupled into or out of the MCF using a specially fabricated
fan-out [6].
50 m
Reflected intensity (a.u)
4
Core
2
core 2
FBG
FBG
3
2
1
Core 1
FBG
Core 3
FBG
core 3
FBG
1543
1543.5
1544
1544.5
1545
wavelength (nm)
Figure 3: Cross section of multicore fibre
(MCF).
Figure 4: Reflection spectra of FBGs in MCF.
Gratings were written into three of the MCF cores at the same position along the length of
the fibre using a phase-mask scanning technique with a frequency doubled Ar laser at 244
nm. The MCF gratings used in these tests had reflection spectra of width ~0.25 nm (FWHM)
and centre wavelengths in the region 1543.5 nm-1545 nm, as shown in figure 4. The gratings
were ~1 cm in length.
For the purpose of two-axis curvature measurement using FBGs in MCF, several AWGs
may be used to each interrogate a particular core of the MCF. The fibre curvature may then
be obtained from the strains 1 and 2 in two cores of the MCF as shown in figure 5. The
radius of curvature R in the plane of the cores is simply related to the strain difference
between gratings in cores 1 and 2 by
d
R
(2)
1   2
where d is the spacing between the cores and n is the strain in the nth core. By using two
orthogonal pairs of cores it is possible to obtain curvature in two dimensions.
3. Dynamic two-axis curvature measurement
To demonstrate high bandwidth curvature measurement, the MCF containing the FBGs was
placed inside a close fitting stainless steel tube (inside diameter 279 m), which was
clamped at one end to form a cantilever. The fibre was positioned such that the gratings
were located close to the clamp, where the curvature is greatest. Figure 6 illustrates the
experimental setup. To remove any constant offset in the AWG channel intensities, arising
from unwanted reflections for example, background values were measured by attenuating
the signal via small loops in the MCF between the fan-out and the cantilever.
An x-y stage was used to deflect the cantilever through a set of displacements equivalent
to a 6 mm × 6 mm grid at 1 mm intervals. The orientation of the fibre axes relative to the xand y-directions was arbitrary. At each grid position (x,y), the orthogonal strain pair values,
calculated from the output voltages of the sensing AWGs, were recorded. This allowed a
matrix to be calculated to allow the x and y deflections of the cantilever to be calculated from
the two strain values of the sensor.
core 1
core 2
source

2
d
R
Multicore fiber
inside cantilever tube
circulator
fan-out
1
FBGs
AWG
x-y
stage
Detectors A/D
Figure 5: Differential
Figure 6: AWG interrogation of MCF FBGs embedded in a
curvature measurement cantilever. The FBG is located close to the cantilever support. For
using two cores of MCF. simplicity, the interrogation scheme is only shown for one of the
four cores.
The x-y stage was then removed and a high-speed camera (Kodak 4540) was used to
image the end of the cantilever as it vibrated freely in two dimensions after an initial
deflection. This enabled direct comparison between the cantilever displacement (measured
using the camera) and that predicted by the FBG curvature measurement.
The camera frame rate was 1125 frames per second, whilst FBG strain data were
recorded at 11250 Hz. The FBG data were downsampled using 10-point averaging to give an
effective sampling rate of 1125 Hz, equivalent to the camera frame rate.
x deflection (mm)
10
5
5
0
-5
2.80
2.82
-5
-10
-10
2.84
2.86
2.88
Time (s)
0
-5
0
x deflection
5
10
y deflection (mm)
y deflection
10
5
0
-5
-10
2.80
2.82
2.84
2.86
2.88
Time (s)
Figure 7a: Sequence of images from high Figure 7b: (upper): x deflection measured by
speed camera at 4 ms intervals. Circles MCF (—) and camera (×); (lower): y deflection
show corresponding position predicted by
measured by MCF (—) and camera ().
FBG sensor.
Selected images from the camera, at 4 ms intervals, are shown in figure 7a, along with the
corresponding displacement measurement from the sensor. The same results are plotted in
figure 7b with displacement from camera and sensor plotted on the same axes. The standard
deviation of the difference between the camera and sensor displacements was 0.9 mm for
both x and y. This indicates a curvature resolution of 0.09 m-1, or a maximum detectable
bend radius of 11 m at 1125 Hz.
4. Conclusions
We have shown that the differential strain between orthogonal pairs of Bragg gratings in
multicore fibre can resolve fibre curvature to 0.09 m-1 in two axes simultaneously. The
multicore fibre grating technique enables curvature to be measured by a sensing element no
larger than a conventional silica fibre, and therefore applicable in circumstances in which
limited access prevents the use of full-field or imaging methods. Arrayed waveguide gratings
can be used to convert Bragg wavelength shifts to intensity changes, permitting curvature to
be measured dynamically at kHz frequencies. The technique has been demonstrated by
tracking an arbitrary two-dimensional cantilever oscillation at 28 Hz.
Applications for dynamic curvature measurement include measurement of the response of
flexible structures to rapid deformation, structural vibration and as a dual-axis accelerometer
comprising a multicore fibre cantilever mass-loaded at its end.
Acknowledgements: The authors acknowledge the UK Engineering and Physical Sciences
Research Council (EPSRC) and AWE plc for supporting this work, and Gary Fleming, NASA
Langley for helpful discussions and provision of the multicore fibre. W. MacPherson
acknowledges the EPSRC for funding via the Advanced Fellowship Scheme.
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