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Remotely addressed optical fibre curvature sensor using multicore photonic crystal fibre
15 June 2001
Optics Communications 193 (2001) 97±104
www.elsevier.com/locate/optcom
Remotely addressed optical ®bre curvature sensor using multicore photonic crystal ®bre W.N. MacPherson a, M.J. Gander a,*, R. McBride a, J.D.C. Jones a, P.M. Blanchard b, J.G. Burnett b, A.H. Greenaway b, B. Mangan c, T.A. Birks c, J.C. Knight c, P.St.J. Russell c b
a Department of Physics, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, UK Defence Evaluation and Research Agency, Electronics Sector, St. Andrews Road, Malvern, Worcs WR14 3PS, UK c Optoelectronics Group, School of Physics, University of Bath, Claverton Down, Bath BA2 7AY, UK
Received 31 January 2001; received in revised form 18 April 2001; accepted 19 April 2001
Abstract We demonstrate an all-®bre curvature sensor that uses two-core photonic crystal ®bre (PCF) as the sensing element. The PCF acts as a two-beam interferometer in which phase dierence is a function of curvature in the plane containing the cores. A broadband source illuminates both cores, and the spectrum at a single point in the far-®eld interferogram is recorded. Applying a three-wavelength phase recovery algorithm to the data provides an unambiguous measurement of the interferometer phase, and hence curvature. Ó 2001 Published by Elsevier Science B.V. Keywords: Multicore; Photonic; Crystal; Fibre interferometer; Sensor
1. Introduction Optical ®bre strain sensors have been demonstrated as a promising technology for monitoring complex structures, for example in aerospace, marine and civil engineering; designs based on ®bre Fabry±Perot interferometers [1] and on in-®bre gratings [2] have proved particularly successful. For many applications, it is the ease with which the optical sensors can be multiplexed that is the compelling advantage [3], substantially reducing the number of connections required to the test
*
Corresponding author. Fax: +44-131-451-3136. E-mail address: [email protected] (M.J. Gander).
object. In other situations, the all-dielectric construction is the most important feature [4]. An enduring problem with interferometric and grating strain sensors is their unwanted temperature sensitivity. For dierential strain measurement, the unwanted sensitivity can be compensated by common mode rejection. For example, to measure bending in a cantilever, strain gauges can be deployed on opposite sides of the test specimen and suciently close together that in some circumstances they can be considered to be isothermal [5]. A sensor structure in which common mode rejection is advantageously achieved is one in which the individual sensing elements each form part of dierent cores in a multicore ®bre. We have
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W.N. MacPherson et al. / Optics Communications 193 (2001) 97±104
demonstrated the idea of dierential strain sensing in multicore ®bre where the sensing element has been a ®bre Mach±Zehnder interferometer [6] or Bragg gratings [7]. The multicore ®bres had singlemode doped silica cores in a silica cladding, formed by milling four standard preforms and drawing them together [8]. Such sensors have promise for structural monitoring, of which an important example is the case of measuring the shape of ¯exible structures by means of embedded ®bres, via a set of measurements of curvature by dierential strain sensing. Practical requirements exist in the monitoring of the shape of e.g. towed hydrophone arrays and ¯exible antennae. These applications require ®bre sensing elements with ¯exibility in design in the disposition of the cores within the cladding of the ®bre, to control sensitivity and directional capabilities. In order to be practical, and particularly to allow embedding, it is necessary to be able to operate the sensing element remotely via a ®bre downlead. In this paper we describe a sensor for bending based on a multicore sensing element formed from photonic crystal ®bre (PCF), where the sensing element is addressed via a downlead of conventional single-mode ®bre. PCF is manufactured by stacking identical hollow silica capillaries in a hexagonal array around a single silica rod, then drawing the bundle down into a ®bre. The capillaries fuse together to form an eective low-index cladding, with light propagation in the eective high-index region associated with the solid core. A multicore PCF can be fabricated by including additional silica rods in the preform. The unusual structure of PCF leads to novel waveguiding properties, in particular a single guided mode over a very broad range of wavelengths [9], and has seen much development and characterisation [10]. Bend sensitivity of core-to-core coupling has been demonstrated previously [11], and the concept of using PCF for interferometric bend measurement has been reported [12], however this paper describes a quantative bend sensor based on an interferometer fabricated from ®bre in which the core-to-core coupling is deliberately minimised. The ease of de®ning additional cores
Fig. 1. Micrograph of the cleaved end face of a two-core PCF.
with low cross-coupling [13] makes the design of multicore PCF for this application feasible. Fig. 1 shows the end face of a two-core PCF in which two solid cores, separated by 16 lm, are surrounded by a silica±air cladding. The outer coating of solid silica increases the mechanical strength of the ®bre and increases the overall diameter to 108 lm, oering a robust multicore ®bre for sensing applications. 2. Bend theory Consider a two-core ®bre that bends in the plane containing the two cores, as shown in Fig. 2,
Fig. 2. Independent optical strain gauges in multicore ®bre.
W.N. MacPherson et al. / Optics Communications 193 (2001) 97±104
where each core supports a single guided mode. In this case the outer core experiences an increase in length DL1 while the inner core undergoes a reduction in length DL2 , where the change in length depends upon the bend radius. A simple bend sensor can be made using these two cores as the two arms of a Mach±Zehnder interferometer: light from a source is divided into two mutually-coherent beams that propagate along each core, and are then brought together to form an interferogram. The two cores can be considered as independent ®bre strain gauges of unstrained length L (the length of the ®bre), separated by a ®xed distance d (the separation between cores), as in Fig. 2. Bending the ®bre into a circular arc with radius of curvature R in the plane of the cores produces a dierence in strain between the cores of De d=R d=LDh, where h L=R is the angle through which the ®bre is bent. Bending changes the phase dierence between the cores by 2pL dn 2pL D/ n K De 1 De k de k where n is the eective refractive index of the core and the constant K n dn=de is typically around 1.159 for germanosilicate ®bre [14] at wavelength k 633 nm. D/
2pd K Dh k
2
When the radius of curvature is not constant, Eq. (2) remains valid as can be demonstrated by integrating d/ corresponding to an arbitrary planar deformation over incremental changes dh, hence the phase shift of the interferogram depends only on the core separation and the overall angle through which the ®bre bends. When the plane of bending makes an angle of w with the plane containing the two cores, D/ is reduced by the factor cos w. 3. Measurement of d/=dl The guiding mechanism of PCF is such that light propagation is con®ned almost entirely within undoped fused silica [15]. It would therefore seem
99
Fig. 3. Experimental con®guration for the measurement of D/=DL for PCF ®bre; BS, beamsplitter; HeNe, helium neon; M, mirror; PCF, photonic crystal ®bre.
reasonable to expect the eective strain-optic coecients, and hence K, to be similar to that of bulk silica; we tested this assumption by experiment. Previous measurements of D/=DL for standard single-mode fused silica ®bre at 633 nm [12] indicate that D/=DL 11:50 0:02 106 rad m 1 . For comparison we measured D/=DL for the PCF at this wavelength. This was accomplished by con®guring a known length of PCF as a Fizeau interferometer, and monitoring the phase change D/ as a function of the applied extension DL. The experimental arrangement is illustrated in Fig. 3. Light from a 633 nm HeNe laser is launched into a 50:50 directional coupler made from conventional single-mode ®bre, with one arm butt coupled to a single core of the PCF. The PCF acts as a Fizeau interferometer de®ned by the Fresnel re¯ections from both front and rear faces. Care was taken to ensure that light from the singlemode addressing ®bre was coupled into only one core of the PCF. This was monitored by viewing the near- and far-®eld transmission output from the PCF and adjusting the alignment to optimise coupling until only one core is observed to emit light in the near-®eld output, and no far-®eld interference fringes are observed. We strained the PCF using a stepper-driven translation stage, generating monochromatic Fizeau fringes, detected in re¯ection via the coupler. A bulk optic Michelson interferometer simultaneously provided accurate measurement of translation as shown in Fig. 3. We used a simple fringe
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counting technique to measure movement providing a resolution of 160 nm, hence an error of less than 0.5% for a 30 lm extension. Similarly the phase resolution for the PCF interferogram was better than p over 200p rad, introducing a further 0.5% error. By this technique, we measured D/=DL to be 11:40 0:08 106 rad m 1 , giving K 1:148 0:008. This result, within experimental error, falls between the value calculated for bulk silica 11:3 106 rad m 1 [12] and that measured for doped fused silica ®bre. We therefore considered D/=DL for PCF to be approximately identical to that for solid core ®bre. Using this value for K, Eq. (2) becomes D/ 2:296
pd Dh k
3
Then for a core separation of d 16 lm and k 860 nm, Eq. (3) simpli®es to D/ 134:2 Dh
4
4. Photonic crystal ®bre bend sensor If monochromatic light is coupled from a single-mode ®bre into both cores of a two-core PCF, the two emerging beams will be mutually coherent, and will form an interferogram in the far-®eld. If at some ®xed point in the interferogram, light is coupled into a second ®bre, the phase dierence between recombining beams is given by / a1 / 1 c 1
a2 /2 c2
5
where the phases a, /, and c are designated in Fig. 4 which illustrates our design, in which standard single-mode ®bres are used to form a downlead and uplead to address a remote section of PCF which forms the sensing element. The input and output couplings are rigid, thus ®xing ai and ci ,
whilst allowing the PCF to bend, so that any changes in / depend only on /1 and /2 . The phase / is a function of source wavelength k via /i k
2pnLi k
6
and the interferogram describing the power coupled into the collecting ®bre is also wavelength dependent: I k k kI0 k 1 V k cos / k
7
where I k is the detected intensity, I0 k is the incident intensity, V k is the fringe visibility, and k k is a constant that incorporates system losses. Thus, if a polychromatic source is used and the collected light fed into a spectrometer, the resulting spectrum will be modulated according to the path length imbalance between the two cores. A number of techniques can be used to recover path dierence from such a channelled spectrum; delay recovery via the Hilbert transform [16] gives accurate phase measurements but leads to an interrogation system that is both expensive and slow. Exploiting the known phase dierences between measurements at a set of ®xed wavelengths, however, e.g. using multiple wavelengths generated by a single source, is potentially much faster and cheaper; we therefore adopted such a `phase stepping' system, based on the data obtained from the spectrometer.
5. Bend measurement: experimental con®guration We constructed a bend sensor as follows. We supported the ends of the solid core, single-mode, downlead ®bre and the PCF in a silica capillary of 125 lm internal diameter. Their separation was adjusted to optimise coupling between the ®bres,
Fig. 4. PCF as a Mach±Zehnder interferometer.
W.N. MacPherson et al. / Optics Communications 193 (2001) 97±104
and then the ®bres were bonded to the capillary using UV-curing cement. It was thus possible to couple light into both cores of the PCF simultaneously. Similarly, a second solid core, singlemode uplead ®bre was attached to the output of the PCF. The portion of the far-®eld interferogram captured by the uplead ®bre is a function of both the uplead core diameter and its separation from the PCF. It is important that only a small fraction of the interferogram is captured, in order to maximise fringe visibility. A 315 mm length of the PCF was held in a plastic tube of 2 mm inside diameter, mounted as a cantilever beam with the ®bre rotated to provide maximum sensitivity in the plane of bending. Since the PCF was unbuered, we used index-matching gel to strip out cladding modes. To simplify the signal processing, we generated an additional, ®xed path imbalance between the two cores by introducing an additional bend in the PCF outwith the cantilever. The end-displacement of the cantilever was controlled by a motor-driven stage that oered positioning accuracy better than 1 lm over a 5000 lm range. The broadband source was a superluminescent diode source (SLED, centre wavelength 860 nm, FWHM 20 nm, output power 1 mW). The sensor output, typically a few lW, was detected using a grating spectrometer (S2000 spectrometer, Ocean Optics Inc.), which incorporates a linear CCD array and gives a wavelength resolution of 0.3 nm over a wavelength range of 600±900 nm. The downlead and uplead ®bres were chosen for singlemode operation for all wavelengths of interest and with a cut-o wavelength below 780 nm. The sensor transmission losses are predominantly due to coupling light into, and out o, the PCF. In particular the air-gaps between the PCF and the addressing ®bres add signi®cant losses due to divergence, but are necessary to ensure light is coupled into, and out of, both cores in the PCF. The ®nal con®guration is shown in Fig. 5. 6. Bend measurement: signal processing The path length imbalance (670 rad path length imbalance) generated by introducing an
101
Fig. 5. Bend measurement experimental con®guration.
Fig. 6. Measured spectrum (solid line), and envelope (broken line).
additional bend to the PCF ensured that phase varied rapidly with wavelength, introducing a periodic modulation into the output spectrum, as shown in Fig. 6. As a result, phase-stepped intensity signals could be obtained by sampling points from the spectrum at a number of ®xed wavelengths. To normalise the fringes to account for the source intensity spectrum and ®bre transmission characteristics, we require the maximum and minimum envelope of the measured spectrum. The envelopes are obtained as follows: the sensor phase is cycled through 2p rad by bending the sensor, therefore for every wavelength channel there is a range of values of which the maximum and minimum are extracted. These form the basis for the maximum and minimum envelope at that wavelength. The resulting envelopes are shown by the broken lines in Fig. 6, with the normalised unitvisibility channelled spectrum shown in Fig. 7.
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Fig. 7. Normalised signal intensity.
7. Bend measurement: signal processing Phase recovery from interferograms has been extensively reported [17], with single and multiple phase techniques developed. We chose to recover the phase using a three-wavelength phase recovery algorithm since it yields a single valued result (unlike the one or two-wavelength algorithms) with only phase unwrapping to resolve the 2p phase ambiguity required. Typically a multiplestep phase recovery algorithm requires pre-de®ned phase steps, for example p=2, 2p=3, etc. However, our experimental con®guration does not allow the wavelengths to be tuned between pixels on the spectrometer linear CCD array, therefore it is not possible to obtain accurate pre-de®ned phase steps. Hence we chose to use a variant of the simple three step algorithm that allows arbitrary step sizes [18]. We then measured the phase sensitivity to bending by displacing the cantilever end using the motor-driven stage, and measuring the spectrum for each displacement step. The phase change was calculated using the three-wavelength phase recovery technique, centred about 860 nm, with 2.5 nm wavelength step size, corresponding to a phase step size of 2=3p. The displacement of the cantilever can be related to a bend angle, h, by applying simple mechanical beam bending theory [19], thus
Fig. 8. Experimental bend measurement.
h
3h 2L
8
where h is the displacement of the end of the cantilever beam, and L is the length of the beam. The experimental relationship between bend angle and phase for our cantilever beam is shown in Fig. 8. The gradient of a linear least-squares ®t applied to the data gave a bend sensitivity of d/=dh 127 rad/rad. By considering the RMS value of the residual error between the experimental data and the linear ®t, it is possible to estimate the phase measurement resolution. From this the bend measurement resolution may be established. A phase resolution of 22 mrad was achieved which yields a bend resolution of 170 lrad. The spectrometer used in this system was also capable of time resolved measurements. For an adequate signal to noise level, up to 25 spectra per second could be acquired. This allowed us to measure the natural oscillation of the cantilever as shown in Fig. 9.
8. Discussion The experimental bend sensitivity of 127 rad/ rad is in good agreement with the theoretical value of 134.2 rad/rad predicted in Section 2, and a minimum resolvable bend angle of 170 lrad was
W.N. MacPherson et al. / Optics Communications 193 (2001) 97±104
103
multicore PCF was successfully incorporated into a sensing scheme using conventional ®bre and components. The channelled spectrum was used as a basis for a three-step algorithm to recover phase. The bend sensitivity of the sensor was found to be 127 rad/rad, within 5% of that predicted by theory. An angular resolution better than 170 lrad was obtained at 25 Hz, with continuous unambiguous operation over several radians.
Acknowledgements Fig. 9. Time resolved bend angle measurement.
demonstrated with no apparent hysteresis. The slightly reduced sensitivity in comparison with theory may be due to misalignment between the plane of bending and the cores, or twist along the PCF in the cantilever. The range of bend measurement was not tested past the results presented in Fig. 8, however it is expected to be limited by the mechanical performance of the PCF, which is not signi®cantly dierent from conventional unbuered ®bre. The temporal response of this spectrometerbased interrogation system is currently limited to 25 samples per second. The spectrometer provided the most ¯exible means of investigating this type of sensor, but would be too slow for many practical applications. Using a single polychromatic source and wavelength division at the detector end, threewavelength phase stepped phase measurements could easily be made in real time at tens of kilohertz, fast enough to detect most mechanical vibrations. Such schemes have been demonstrated to be capable of mrad phase resolution [18], which in this application corresponds to a bend resolution in the tens of lrad; for example a phase resolution of 5 mrad would result in a bend resolution of 40 lrad. 9. Conclusion We have demonstrated an all-®bre bend sensor based on a two-core PCF sensing element. The
This work was supported by funding from the MoD under their Corporate Research Programme, Technology Group 04 (Materials and Structures). Their support is gratefully acknowledged.
References [1] S.F. Masri, M.S. Agbabian, A.M. Abdelghaar, M. Higazy, R.O. Claus, M.J. Devries, J. Eng. Mech.-ASCE 120 (1994) 1696±1717. [2] D.R. Hjelme, L. Bjerkan, S. Neegard, J.S. Rambech, J.V. Aarsnes, Appl. Opt. 36 (1997) 328±336. [3] A.D. Kersey, T.A. Berko, W.W. Morey, Opt. Lett. 18 (1993) 1370±1372. [4] P. Nash, IEE Proc. Radar, Sonar Navig. 143 (1996) 204± 209. [5] M.G. Xu, J.-L. Archamblault, L. Reekie, J.P. Dakin, Int. J. Optoelectron. 9 (1994) 281±283. [6] M.J. Gander, D. Macrae, E.A. Galliot, R. McBride, J.D.C. Jones, P. Blanchard, J.G. Burnett, A.H. Greenaway, M.N. Inci, Eur. Workshop Optical Fibre Sensors Proc. SPIE 3483 (1998) 64±68. [7] M.J. Gander, W.N. MacPherson, R. McBride, J.D.C. Jones, L. Zhang, I. Bennion, P.M. Blanchard, J.G. Burnett, A.H. Greenaway, Electron. Letts. 36 (2000) 120± 121. [8] G. Le Noane, D. Boscher, P. Grosso, J.C. Bizeul, C. Botton, International Wire and Cable Symposium Proceedings, 1994, pp. 203±209. [9] T.A. Birks, J.C. Knight, P.St.J. Russell, Opt. Lett. 22 (1997) 961±963. [10] M.J. Gander, R. McBride, J.D.C. Jones, D. Mogilevtsev, T.A. Birks, J.C. Knight, P.St.J. Russell, Electron. Lett. 35 (1999) 63±64. [11] M.A. van Eijkelenborg, J. Canning, T. Ryan, K. Lyytikainen, Opt. Exp. 7 (2) (2000) 88±94. [12] P.M. Blanchard, J.G. Burnett, G.R.G. Erry, A.H. Greenaway, P. Harrison, B. Mangan, J.C. Knight, P.S. Russell,
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M.J. Gander, R. McBride, J.D.C. Jones, Smart Mat. Struc. 9 (2) (2000) 132±140. [13] B.J. Mangan, J.C. Knight, T.A. Birks, P.St.J. Russell, A.H. Greenaway, Electron. Lett. 36 (2000) 1358±1359. [14] A. Bertholds, R. D andliker, J. Light. Technol. 6 (1988) 17± 20. [15] J.C. Knight, T.A. Birks, P.St.J. Russell, D.M. Atkin, Opt. Lett. 21 (1996) 1547±1549.
[16] J.W. Goodman, Statistical Optics, Wiley, New York, 1985. [17] D.W. Robinson, G.T. Reid, Interferogram analysis ± Digital fringe pattern measurement techniques, IOP Publishing, Bristol, 1993. [18] W.N. MacPherson, S.R. Kidd, J.S. Barton, J.D.C. Jones, IEE Proc. ± Optoelectron. 144 (1997) 130±133. [19] P.P. Benham, R.J. Crawford, C.G. Armstrong, Mechanics of Engineering Materials, Longman, 1996.
Optics Communications 193 (2001) 97±104
www.elsevier.com/locate/optcom
Remotely addressed optical ®bre curvature sensor using multicore photonic crystal ®bre W.N. MacPherson a, M.J. Gander a,*, R. McBride a, J.D.C. Jones a, P.M. Blanchard b, J.G. Burnett b, A.H. Greenaway b, B. Mangan c, T.A. Birks c, J.C. Knight c, P.St.J. Russell c b
a Department of Physics, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, UK Defence Evaluation and Research Agency, Electronics Sector, St. Andrews Road, Malvern, Worcs WR14 3PS, UK c Optoelectronics Group, School of Physics, University of Bath, Claverton Down, Bath BA2 7AY, UK
Received 31 January 2001; received in revised form 18 April 2001; accepted 19 April 2001
Abstract We demonstrate an all-®bre curvature sensor that uses two-core photonic crystal ®bre (PCF) as the sensing element. The PCF acts as a two-beam interferometer in which phase dierence is a function of curvature in the plane containing the cores. A broadband source illuminates both cores, and the spectrum at a single point in the far-®eld interferogram is recorded. Applying a three-wavelength phase recovery algorithm to the data provides an unambiguous measurement of the interferometer phase, and hence curvature. Ó 2001 Published by Elsevier Science B.V. Keywords: Multicore; Photonic; Crystal; Fibre interferometer; Sensor
1. Introduction Optical ®bre strain sensors have been demonstrated as a promising technology for monitoring complex structures, for example in aerospace, marine and civil engineering; designs based on ®bre Fabry±Perot interferometers [1] and on in-®bre gratings [2] have proved particularly successful. For many applications, it is the ease with which the optical sensors can be multiplexed that is the compelling advantage [3], substantially reducing the number of connections required to the test
*
Corresponding author. Fax: +44-131-451-3136. E-mail address: [email protected] (M.J. Gander).
object. In other situations, the all-dielectric construction is the most important feature [4]. An enduring problem with interferometric and grating strain sensors is their unwanted temperature sensitivity. For dierential strain measurement, the unwanted sensitivity can be compensated by common mode rejection. For example, to measure bending in a cantilever, strain gauges can be deployed on opposite sides of the test specimen and suciently close together that in some circumstances they can be considered to be isothermal [5]. A sensor structure in which common mode rejection is advantageously achieved is one in which the individual sensing elements each form part of dierent cores in a multicore ®bre. We have
0030-4018/01/$ - see front matter Ó 2001 Published by Elsevier Science B.V. PII: S 0 0 3 0 - 4 0 1 8 ( 0 1 ) 0 1 2 6 0 - 3
98
W.N. MacPherson et al. / Optics Communications 193 (2001) 97±104
demonstrated the idea of dierential strain sensing in multicore ®bre where the sensing element has been a ®bre Mach±Zehnder interferometer [6] or Bragg gratings [7]. The multicore ®bres had singlemode doped silica cores in a silica cladding, formed by milling four standard preforms and drawing them together [8]. Such sensors have promise for structural monitoring, of which an important example is the case of measuring the shape of ¯exible structures by means of embedded ®bres, via a set of measurements of curvature by dierential strain sensing. Practical requirements exist in the monitoring of the shape of e.g. towed hydrophone arrays and ¯exible antennae. These applications require ®bre sensing elements with ¯exibility in design in the disposition of the cores within the cladding of the ®bre, to control sensitivity and directional capabilities. In order to be practical, and particularly to allow embedding, it is necessary to be able to operate the sensing element remotely via a ®bre downlead. In this paper we describe a sensor for bending based on a multicore sensing element formed from photonic crystal ®bre (PCF), where the sensing element is addressed via a downlead of conventional single-mode ®bre. PCF is manufactured by stacking identical hollow silica capillaries in a hexagonal array around a single silica rod, then drawing the bundle down into a ®bre. The capillaries fuse together to form an eective low-index cladding, with light propagation in the eective high-index region associated with the solid core. A multicore PCF can be fabricated by including additional silica rods in the preform. The unusual structure of PCF leads to novel waveguiding properties, in particular a single guided mode over a very broad range of wavelengths [9], and has seen much development and characterisation [10]. Bend sensitivity of core-to-core coupling has been demonstrated previously [11], and the concept of using PCF for interferometric bend measurement has been reported [12], however this paper describes a quantative bend sensor based on an interferometer fabricated from ®bre in which the core-to-core coupling is deliberately minimised. The ease of de®ning additional cores
Fig. 1. Micrograph of the cleaved end face of a two-core PCF.
with low cross-coupling [13] makes the design of multicore PCF for this application feasible. Fig. 1 shows the end face of a two-core PCF in which two solid cores, separated by 16 lm, are surrounded by a silica±air cladding. The outer coating of solid silica increases the mechanical strength of the ®bre and increases the overall diameter to 108 lm, oering a robust multicore ®bre for sensing applications. 2. Bend theory Consider a two-core ®bre that bends in the plane containing the two cores, as shown in Fig. 2,
Fig. 2. Independent optical strain gauges in multicore ®bre.
W.N. MacPherson et al. / Optics Communications 193 (2001) 97±104
where each core supports a single guided mode. In this case the outer core experiences an increase in length DL1 while the inner core undergoes a reduction in length DL2 , where the change in length depends upon the bend radius. A simple bend sensor can be made using these two cores as the two arms of a Mach±Zehnder interferometer: light from a source is divided into two mutually-coherent beams that propagate along each core, and are then brought together to form an interferogram. The two cores can be considered as independent ®bre strain gauges of unstrained length L (the length of the ®bre), separated by a ®xed distance d (the separation between cores), as in Fig. 2. Bending the ®bre into a circular arc with radius of curvature R in the plane of the cores produces a dierence in strain between the cores of De d=R d=LDh, where h L=R is the angle through which the ®bre is bent. Bending changes the phase dierence between the cores by 2pL dn 2pL D/ n K De 1 De k de k where n is the eective refractive index of the core and the constant K n dn=de is typically around 1.159 for germanosilicate ®bre [14] at wavelength k 633 nm. D/
2pd K Dh k
2
When the radius of curvature is not constant, Eq. (2) remains valid as can be demonstrated by integrating d/ corresponding to an arbitrary planar deformation over incremental changes dh, hence the phase shift of the interferogram depends only on the core separation and the overall angle through which the ®bre bends. When the plane of bending makes an angle of w with the plane containing the two cores, D/ is reduced by the factor cos w. 3. Measurement of d/=dl The guiding mechanism of PCF is such that light propagation is con®ned almost entirely within undoped fused silica [15]. It would therefore seem
99
Fig. 3. Experimental con®guration for the measurement of D/=DL for PCF ®bre; BS, beamsplitter; HeNe, helium neon; M, mirror; PCF, photonic crystal ®bre.
reasonable to expect the eective strain-optic coecients, and hence K, to be similar to that of bulk silica; we tested this assumption by experiment. Previous measurements of D/=DL for standard single-mode fused silica ®bre at 633 nm [12] indicate that D/=DL 11:50 0:02 106 rad m 1 . For comparison we measured D/=DL for the PCF at this wavelength. This was accomplished by con®guring a known length of PCF as a Fizeau interferometer, and monitoring the phase change D/ as a function of the applied extension DL. The experimental arrangement is illustrated in Fig. 3. Light from a 633 nm HeNe laser is launched into a 50:50 directional coupler made from conventional single-mode ®bre, with one arm butt coupled to a single core of the PCF. The PCF acts as a Fizeau interferometer de®ned by the Fresnel re¯ections from both front and rear faces. Care was taken to ensure that light from the singlemode addressing ®bre was coupled into only one core of the PCF. This was monitored by viewing the near- and far-®eld transmission output from the PCF and adjusting the alignment to optimise coupling until only one core is observed to emit light in the near-®eld output, and no far-®eld interference fringes are observed. We strained the PCF using a stepper-driven translation stage, generating monochromatic Fizeau fringes, detected in re¯ection via the coupler. A bulk optic Michelson interferometer simultaneously provided accurate measurement of translation as shown in Fig. 3. We used a simple fringe
100
W.N. MacPherson et al. / Optics Communications 193 (2001) 97±104
counting technique to measure movement providing a resolution of 160 nm, hence an error of less than 0.5% for a 30 lm extension. Similarly the phase resolution for the PCF interferogram was better than p over 200p rad, introducing a further 0.5% error. By this technique, we measured D/=DL to be 11:40 0:08 106 rad m 1 , giving K 1:148 0:008. This result, within experimental error, falls between the value calculated for bulk silica 11:3 106 rad m 1 [12] and that measured for doped fused silica ®bre. We therefore considered D/=DL for PCF to be approximately identical to that for solid core ®bre. Using this value for K, Eq. (2) becomes D/ 2:296
pd Dh k
3
Then for a core separation of d 16 lm and k 860 nm, Eq. (3) simpli®es to D/ 134:2 Dh
4
4. Photonic crystal ®bre bend sensor If monochromatic light is coupled from a single-mode ®bre into both cores of a two-core PCF, the two emerging beams will be mutually coherent, and will form an interferogram in the far-®eld. If at some ®xed point in the interferogram, light is coupled into a second ®bre, the phase dierence between recombining beams is given by / a1 / 1 c 1
a2 /2 c2
5
where the phases a, /, and c are designated in Fig. 4 which illustrates our design, in which standard single-mode ®bres are used to form a downlead and uplead to address a remote section of PCF which forms the sensing element. The input and output couplings are rigid, thus ®xing ai and ci ,
whilst allowing the PCF to bend, so that any changes in / depend only on /1 and /2 . The phase / is a function of source wavelength k via /i k
2pnLi k
6
and the interferogram describing the power coupled into the collecting ®bre is also wavelength dependent: I k k kI0 k 1 V k cos / k
7
where I k is the detected intensity, I0 k is the incident intensity, V k is the fringe visibility, and k k is a constant that incorporates system losses. Thus, if a polychromatic source is used and the collected light fed into a spectrometer, the resulting spectrum will be modulated according to the path length imbalance between the two cores. A number of techniques can be used to recover path dierence from such a channelled spectrum; delay recovery via the Hilbert transform [16] gives accurate phase measurements but leads to an interrogation system that is both expensive and slow. Exploiting the known phase dierences between measurements at a set of ®xed wavelengths, however, e.g. using multiple wavelengths generated by a single source, is potentially much faster and cheaper; we therefore adopted such a `phase stepping' system, based on the data obtained from the spectrometer.
5. Bend measurement: experimental con®guration We constructed a bend sensor as follows. We supported the ends of the solid core, single-mode, downlead ®bre and the PCF in a silica capillary of 125 lm internal diameter. Their separation was adjusted to optimise coupling between the ®bres,
Fig. 4. PCF as a Mach±Zehnder interferometer.
W.N. MacPherson et al. / Optics Communications 193 (2001) 97±104
and then the ®bres were bonded to the capillary using UV-curing cement. It was thus possible to couple light into both cores of the PCF simultaneously. Similarly, a second solid core, singlemode uplead ®bre was attached to the output of the PCF. The portion of the far-®eld interferogram captured by the uplead ®bre is a function of both the uplead core diameter and its separation from the PCF. It is important that only a small fraction of the interferogram is captured, in order to maximise fringe visibility. A 315 mm length of the PCF was held in a plastic tube of 2 mm inside diameter, mounted as a cantilever beam with the ®bre rotated to provide maximum sensitivity in the plane of bending. Since the PCF was unbuered, we used index-matching gel to strip out cladding modes. To simplify the signal processing, we generated an additional, ®xed path imbalance between the two cores by introducing an additional bend in the PCF outwith the cantilever. The end-displacement of the cantilever was controlled by a motor-driven stage that oered positioning accuracy better than 1 lm over a 5000 lm range. The broadband source was a superluminescent diode source (SLED, centre wavelength 860 nm, FWHM 20 nm, output power 1 mW). The sensor output, typically a few lW, was detected using a grating spectrometer (S2000 spectrometer, Ocean Optics Inc.), which incorporates a linear CCD array and gives a wavelength resolution of 0.3 nm over a wavelength range of 600±900 nm. The downlead and uplead ®bres were chosen for singlemode operation for all wavelengths of interest and with a cut-o wavelength below 780 nm. The sensor transmission losses are predominantly due to coupling light into, and out o, the PCF. In particular the air-gaps between the PCF and the addressing ®bres add signi®cant losses due to divergence, but are necessary to ensure light is coupled into, and out of, both cores in the PCF. The ®nal con®guration is shown in Fig. 5. 6. Bend measurement: signal processing The path length imbalance (670 rad path length imbalance) generated by introducing an
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Fig. 5. Bend measurement experimental con®guration.
Fig. 6. Measured spectrum (solid line), and envelope (broken line).
additional bend to the PCF ensured that phase varied rapidly with wavelength, introducing a periodic modulation into the output spectrum, as shown in Fig. 6. As a result, phase-stepped intensity signals could be obtained by sampling points from the spectrum at a number of ®xed wavelengths. To normalise the fringes to account for the source intensity spectrum and ®bre transmission characteristics, we require the maximum and minimum envelope of the measured spectrum. The envelopes are obtained as follows: the sensor phase is cycled through 2p rad by bending the sensor, therefore for every wavelength channel there is a range of values of which the maximum and minimum are extracted. These form the basis for the maximum and minimum envelope at that wavelength. The resulting envelopes are shown by the broken lines in Fig. 6, with the normalised unitvisibility channelled spectrum shown in Fig. 7.
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Fig. 7. Normalised signal intensity.
7. Bend measurement: signal processing Phase recovery from interferograms has been extensively reported [17], with single and multiple phase techniques developed. We chose to recover the phase using a three-wavelength phase recovery algorithm since it yields a single valued result (unlike the one or two-wavelength algorithms) with only phase unwrapping to resolve the 2p phase ambiguity required. Typically a multiplestep phase recovery algorithm requires pre-de®ned phase steps, for example p=2, 2p=3, etc. However, our experimental con®guration does not allow the wavelengths to be tuned between pixels on the spectrometer linear CCD array, therefore it is not possible to obtain accurate pre-de®ned phase steps. Hence we chose to use a variant of the simple three step algorithm that allows arbitrary step sizes [18]. We then measured the phase sensitivity to bending by displacing the cantilever end using the motor-driven stage, and measuring the spectrum for each displacement step. The phase change was calculated using the three-wavelength phase recovery technique, centred about 860 nm, with 2.5 nm wavelength step size, corresponding to a phase step size of 2=3p. The displacement of the cantilever can be related to a bend angle, h, by applying simple mechanical beam bending theory [19], thus
Fig. 8. Experimental bend measurement.
h
3h 2L
8
where h is the displacement of the end of the cantilever beam, and L is the length of the beam. The experimental relationship between bend angle and phase for our cantilever beam is shown in Fig. 8. The gradient of a linear least-squares ®t applied to the data gave a bend sensitivity of d/=dh 127 rad/rad. By considering the RMS value of the residual error between the experimental data and the linear ®t, it is possible to estimate the phase measurement resolution. From this the bend measurement resolution may be established. A phase resolution of 22 mrad was achieved which yields a bend resolution of 170 lrad. The spectrometer used in this system was also capable of time resolved measurements. For an adequate signal to noise level, up to 25 spectra per second could be acquired. This allowed us to measure the natural oscillation of the cantilever as shown in Fig. 9.
8. Discussion The experimental bend sensitivity of 127 rad/ rad is in good agreement with the theoretical value of 134.2 rad/rad predicted in Section 2, and a minimum resolvable bend angle of 170 lrad was
W.N. MacPherson et al. / Optics Communications 193 (2001) 97±104
103
multicore PCF was successfully incorporated into a sensing scheme using conventional ®bre and components. The channelled spectrum was used as a basis for a three-step algorithm to recover phase. The bend sensitivity of the sensor was found to be 127 rad/rad, within 5% of that predicted by theory. An angular resolution better than 170 lrad was obtained at 25 Hz, with continuous unambiguous operation over several radians.
Acknowledgements Fig. 9. Time resolved bend angle measurement.
demonstrated with no apparent hysteresis. The slightly reduced sensitivity in comparison with theory may be due to misalignment between the plane of bending and the cores, or twist along the PCF in the cantilever. The range of bend measurement was not tested past the results presented in Fig. 8, however it is expected to be limited by the mechanical performance of the PCF, which is not signi®cantly dierent from conventional unbuered ®bre. The temporal response of this spectrometerbased interrogation system is currently limited to 25 samples per second. The spectrometer provided the most ¯exible means of investigating this type of sensor, but would be too slow for many practical applications. Using a single polychromatic source and wavelength division at the detector end, threewavelength phase stepped phase measurements could easily be made in real time at tens of kilohertz, fast enough to detect most mechanical vibrations. Such schemes have been demonstrated to be capable of mrad phase resolution [18], which in this application corresponds to a bend resolution in the tens of lrad; for example a phase resolution of 5 mrad would result in a bend resolution of 40 lrad. 9. Conclusion We have demonstrated an all-®bre bend sensor based on a two-core PCF sensing element. The
This work was supported by funding from the MoD under their Corporate Research Programme, Technology Group 04 (Materials and Structures). Their support is gratefully acknowledged.
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