Demonstrating the style for the Journal of Physics

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Photonic guided path tomography
Samuel Joshua1, Yee Man Keung2, Patricia Scully2, Krikor B.Ozanyan1
1
School of Electrical and Electronic Engineering, 2School of Chemical
Engineering and Analytical Science, The University of Manchester, PO Box 88,
Manchester, M60 1QD UK.
[email protected]
Abstract. The basic concepts of the recently introduced Guided-Path
Tomography (GPT) are reviewed, with emphasis on the possibility to measure
the spatial distribution of various fields on non-planar surfaces. As opposed to
a previous demonstration of GPT with low-frequency EM fields (down to DC)
for temperature imaging, we show that guided paths can be achieved by optical
fibres, which can be sensitise, in this case, to bending.
We demonstrate Photonic GPT for imaging of deformation on a quasi-planar
surface utilising specially developed and manufactured Plastic Optical Fibre
(POF) curvature sensors. The performance of the individual sensors are
studied in a low-curvature regime by validation with a strain-gauge and highcurvature regime, where significant bends on the POF element were
introduced. A full set of the forward-transformed data from 16 line integrals and
4 projections at 45o was obtained with a phantom object by carefully planned
measurements on a single POF element. Image reconstruction was performed
with a simple ART algorithm.
1. Introduction
Strain measurement systems are needed and widely deployed in the field of health
monitoring of structures in a range of engineering industries including the aerospace,
civil, automotive, and marine sectors. Optical fibre sensing systems have attracted
considerable attention and have been widely demonstrated as highly promising
technology for strain measurement systems. Fibre optic sensors offer many
advantages over conventional strain sensors; these include their insensitivity to
electromagnetic fields, light weight and minimal intrusiveness. Plastic Optical Fibres
(POF), with their inherent fracture toughness and flexibility, as well as simplicity of
handling, makes them much more desirable in field applications than their glassbased counterparts. Various POF sensors have been demonstrated, sensitive to a
number of chemical and mechanical parameters of interest in the industrial and other
sectors.
Guided path tomography (GPT) is a new concept in tomography and has been
introduced as a method for imaging on non planar surfaces by measurements at their
periphery [1]. The principal motivation is the possibility to obtain the spatial
distribution of a given quantity F(x,y,z) on real or virtual non-planar surfaces, by
employing a flexible sensor, which assumes the shape of that surface. Combining the
concepts of GPT and POF sensing, it becomes possible to build a GPT system for
mapping deformation in a non planar surface.
Tomography is based on taking measurements from the periphery of an object and
solving the inverse problem to reconstruct the object. The measurements are in the
form of line integrals of the imaged parameter. In Computer Tomography (CT,
typically with X-rays), the line integrals are along straight lines, as is the beam
propagation (eq.1).
L
Φ  Φ 0  μ ( x )dx
(1)
0
Here μ(x) is the imaged parameter varying in space, Φ is the photon flux and the
integration is along the straight line L. In the theory of CT, this approach is suitable
only for cross-sections of flat objects (2D imaging). However, there no requirement for
the line integrals to be along straight lines, and if that common perception is
abandoned, it is possible to use a huge arsenal of reconstruction methods on
measurements resulting from line integrals along curved lines. A demonstrated
example is the “temperature mat”, where integrals of resistivity are taken along wires,
which can be bent to assume the shape of curved surfaces (2.5D imaging) [1].
L
1
R   ρ(T( x ))dx
A0
(2)
Here ρ(T(x)) is the temperature dependent wire resistivity, A and R are the sensor
wire cross-sectional area and total resistance respectively and the integral is along
the wire (straight or not). Eqs (1) and (2) show clearly the similarity between the two
line integrals, but they offer different functionality in the two cases.
It is clear from the above, that guided paths can be achieved in ways other than just
confine current within wires. We have applied this concept to guiding a much higher
frequency EM field (visible light) by means of optical fibres, incorporating sensor
sections to yield the required line integrals.
2. Optical fibre sensors
Optical fibre sensors were fabricated from 1 mm diameter polymethyl methacrylate
optical fibre by cutting transverse grooves into the fibre along its length, This method,
compared to tapering by extrusion or chemically etching, preserves better the fibre
integrity and is easier to implement in large numbers along the length of a single
stretch of fibre. Both hot or cold scalpel techniques were applied and the latter was
found to be more reliable (fig 1a), as substantial material displacement takes place at
higher temperatures of the cutting edge (fig 1b).
a)
b)
Figure 1: Images of grooves fabricated by cold (a) and hot (b) scalpel technology
The grooves sensitise the fibre to stretching and bending, as shown in fig 2. It is
notable that sensitivity is observed in both directions of deviation from the zero
deformation: the overall light throughput decreases when the sensor is stretched or
bent in direction opposite to the grooves (fig. 2b) and increases when the sensor is
compressed or bent in the direction of the grooves (not shown). A quantitative
description of the light losses as a function of the groove geometry has been given
previously [2] by introducing a light de-coupling factor as a function of the groove
opening angle. A similar description is possible for the case of bending and will be
given in future work.
a) zero deformation
b) stretch and bend
Figure 2: Compared to the case of no deformation (a), the loss of light propagating
through the sensitised fibre is greater when the fibre is stretched or bent (b).
The transversal groove method has previously been used to form a fibre strain sensor
with a drag element as a flow sensor [3] for wind, but has not yet been evaluated as a
distributed sensor with uniform sensitivity along its length. Such uniformity is required
in order to ensure that a line integral of the type shown in eq.(1) describes the
measurements reasonably well.. This is generally achievable if the losses at each
groove are kept low, and can be understood in the light of a linear approximation of
the exponential light attenuation along the fibre (Beer-Lambert law) in the small-signal
regime.
Systematic tests were carried out on 1m POF elements with up to 100 groves and
varying groove depth. The issue of uniform sensitivity was examined along the fibre
by placing a cylindrical object with radius 60mm and mass 5.37kg on the fibre, which
was fixed to a thick underlay of deformable foam. The typical signal-to-noise ratio
observed in these experiments was SNR > 1000.
depth of
modulation
0.1mm groove, 75 grooves
1.02
0.02
1.01
0.01
1
0
0.99
-0.01
Series3
0
20
40
60
80
100
0.98
-0.02
distance(cms)
Figure 3: Relative sensitivity to placing a 5.37 kg object on a 1 m fibre sensor as a
function of the distance along the fibre.
Fig 3 shows the spread in the individual measurements in the case of 75 grooves,
each of depth 0.1 mm, over the middle 60 cm section of the POF element. Here, the
signal (induced change in the transmitted intensity) at all positions between 22 and 60
cm is taken as reference and the deviation in the rest of the measurements are
indicated relative to that signal. The spread is within 1.5%, indicating a good linear
approximation leading to uniform sensitivity. This is also visualised in fig.4, where the
intensity of the light lost from each of the grooves appears to be similar along the
whole length of the POF element.
Figure 4. Visualisation of the losses at the individual grooves.
3. Application to Tomography
To demonstrate the suitability of the POF sensor for tomography imaging, a phantom
object (fig 5a) has been simulated by measurements taken with a single POF element
for 62 line integrals in 4 projections separated by 45o. This corresponds to a typically
low spatial sampling situation, but is indicative of realistic scenarios where the available
resources, as well as practicalities, limit the measurements. The observed standard
deviation for a single channel measurement is 0.7%. The recorded data from the 62
measurements was used for standard image reconstruction by a simple Algebraic
Reconstruction Technique, which is also popular for under-sampled Computed
Tomography, where iterative methods have to be used. The results from a single
iteration are shown in the reconstructed image of the phantom (fig 5b). The
reconstruction grid is 16x16 pixels, each pixel corresponding to 5x5cm.The
reconstruction quality is unaffected by addition of up to 6% noise. The artefacts in the
reconstructed image are a cumulative effect of the measurement errors and errors from
the mathematical procedure.
a
b
Figure 5: (a) phantom object; (b) reconstructed image of the phantom object
4. Conclusion
Photonic GPT imaging of deformation on a quasi-planar surface has been successfully
demonstrated, utilising grooved POF strain sensors. The latter have been optimised for
transmitted intensity and sensitivity with groove number. Linear attenuation was
achieved along 1m fibre sensors, resulting in the identical response at identical
pressure on different sections of the sensor. A full set of forward-transformed data was
obtained from measurements on a single POF element and inverse-transformed by a
simple ART algorithm. The implications of these results can be discussed and taken
further along the lines of the design and manufacture of inexpensive embedded and/or
disposable non-planar deformation imagers, e.g. of strain in structures, respiratory
changes for health monitoring and others.
References
[1] K B Ozanyan, S Garcia Castillo and F J Parra Ortiz, “Guided-path tomography
sensors for non-planar mapping”, IEEE Sensors J. 5 (2005) 167-17.
[2] Rekha Rebecca Philip- Chandy, “Fluid flow measurement using electrical and
optical fibre strain gauges”, PhD Thesis, Liverpool John Moores University,1997.
[3] R Philip-Chandy, P J Scully and R Morgan,“The design, development and
performance characteristics of a fibre optic drag-force flow sensor”. Measurement
Science and Technology 11 (2000) N31- N35
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