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Prospects for non-linear forward-scatter distributed optical-fibre sensing
Optics and Lasers in Engineering 16 (1992)179—192
Prospects for Non-linear Forward-Scatter Distributed Optical-Fibre Sensing A. J. Rogers Department of Electronic and Electrical Engineering, King’s College London, Strand, London WC2R 2LS, UK (Received 7 January 1991; revised version received and accepted 18 May 1991)
ABSTRACT Opticalfibres offer special advantages for fully-distributed sensing. They comprise an essentially one-dimensional measurement medium which can be used to provide the spatial distribution of a variety of measurands within large structures. To date, most fully-distributed optical-fibre sensor systems have relied on backscatter, OTDR, techniques. This paper proposes an alternative, forward-scatter approach; it utilises non-linear interactions between counter-propagating beams in optical fibres. This latter approach offers possibilities for a significant improvement in performance for such sensors. Some possible systems based on this approach are described and preliminary experimental results are presented.
1 INTRODUCTION The advantages offered by optical fibres in the measurement function are well known: they provide an insulating, passive, flexible, dielectric medium whose optical propagation properties are influenced by a large variety of external physical parameters. It is therefore possible to install measurement devices and systems, based on these features, easily into industrial plant or into diagnostic structures, with minimum disturbance to the environment and in a safe, reliable way. The one-dimensional nature of this measurement medium allows it to be used in two novel ways: for line integration, and for line differentiation. In the former usage it becomes possible to measure 179
Optics and Lasers in Engineering O143-8166/92/$O5~OO© 1992 Elsevier Science Publishers Ltd, England. Printed in Northern Ireland
180
A. J. Rogers
electric currents via ioop integration of the surrounding magnetic field. or voltages via the line integration of electric field, or simply to derive a configured path average for a measurand. In the latter usage, that of line differentiation, it becomes possible to determine the spatial distribution of a measurand, along a chosen path. simultaneously with its temporal variation. Such an arrangement is known as a distributed optical-fibre sensor (DOFS). Distributed optical-fibre measurement offers many advantages for industrial use. The ability to obtain simultaneously both spatial and temporal information on a measurand field (e.g. pressure. strain, temperature, magnetic field, electric field) provides at once a convenient monitor on the performance of large-structures. and a more detailed understanding of their behaviour, with implications for unproved design. Applications which come easily to mind are strain distribution in critical structures such as dams, bridges, pressure vessels, aircraft and spacecraft; temperature distributions in power transformers, boilers, electrical generators, high voltage cables and aerofoils: electric/magnetic field distributions in electric power transmission lines and telecommunications cables; highly directional antennas are also possible.’ A distinction must be made between two types of distributed optical-fibre sensor (DOFS), in order to avoid confusion. In the first of these it is necessary to make measurements only at discrete, predetermined points (or along specific, limited lengths) on the fibre. The measurement system then takes on the character of a series-distributed array of discrete transducers. This we call a quasi-distributed system; in the literature it sometimes has been called a multiplexed system. In the second type the measurement may be made continuously as a function of position at any point along the fibre; this, clearly, is a much more powerful and flexible arrangement. This we call a fully-distributed, or. more often, simply a distributed sensor. Systems which have been studied to date have been described in several reviews.’3 The vast majority of these use optical—time domain reflectometry (OTDR) methods45 to provide the spatial information. These rely on time resolution of the light backscattered from an optical pulse propagating in the fibre. Backscattered light levels in amorphous silica are relatively low and impose limitations on the sensitivity and spatial resolution which can be achieved in DOFS. If the spatial and temporal measurand information could be obtained in forward scatter, significant improvement in performance could result. This paper considers three novel, but related, forward scatter systems for DOFS. They represent ideas which presently are being actively researched, and which hold considerable promise for development into practical systems of value, in aerospace applications and elsewhere.
Non-linear forward-scatter distributed optical-fibre sensing
181
Their promise lies in their ability to make measurements with high sensitivity (—1%) and good spatial resolution (—0.1 m) in short time scales (—~is).These features are attractive for aerospace use since they would allow effective continuous monitoring of, for example, strain and temperature, over a complete airframe or space frame, in a way which would permit effective response, either manually or automatically. Self-adjusting geometries also become possible when in possession of the offered information.
2 BACKSCATTER VERSUS FORWARD-SCATTER DOFS Backscatter DOFS systems rely on the Optical Time Domain Reflectometry (OTDR) principle. A generalised schematic for backscatter DOFS is shown in Fig. 1. A pulse of light is launched into an optical fibre and the Rayleigh backscattered light is monitored and time resolved at the launch end. The measurand field through which the fibre threads modifies the optical properties of the fibre in a deterministic way, leading to a modulation of the backscattered light. This modulation is decoded by a demodulation analyser at the detector end, which, together with the time-differentiation, yields the spatial distribution of the measurand field. For an optical pulse of energy E0 launched into a fibre the received 5 backscattered power after a time t is given by p(t)
=
(c/2)E
0o~Sexp (—crct) Beam splitter
__________
Pulsed laser
(1)
J’t —
—
*
_______
—
—
—
-~
..-
Fibre
_______
~
Measurand MCI)
ar
___
U
Demodulation analyzer function
resolution element
I
+
detector~
~
~~MCI) Display
Fig. 1
182
A. J. Rogers
where c is the velocity of light in the fibre, a~is the attenuation coefficient, and
S is the hackscatter capture fraction. Since the attenuation normally is due to Rayleigh scattering, there exists an optimum value of a~for a given length of system: too large a value over-attenuates the light; too small a value provides insufficient backscatter. This value of & clearly is given by ~=
l/ct= IlL say.
Hence the minimum value of p in a hackscatter system is given by =
cE0S/2Le
(e = exp(l))
Now for a spatial resolution of 61 the energy received from L by the detector in the resolution time interval 261/c is given by 6E =p~,.26//c
For an accuracy of measurement, that
=
(2)
E0S/e. 6/IL
i~, we
require, in the shot noise limit, 2
6E/hv> l/i~ (where h is Planck’s constant and v is the optical frequency). Or, using
eqn (2) 6!> (eLhv/E 0S).
(3)
l/~
which provides the relationship between resolution and accuracy for backscatter DOFS, in the shot noise limit. Consider now the forward-scatter arrangement shown in Fig. 2. In this arrangement a continuous wave (CW) source is launched, at one end (F) of the fibre, into one of two possible modes T and R. say. These might be two propagation modes, two polarization modes, or even two separate cores within the same cladding. The important conditions which must obtain are that the two modes must be separately identifiable at the output from the fibre, and that light coupling between them must both be possible and dependent, in some 4 T Channel FlSource CW-~ C~ 4
—
K0 ~ ~
1
CR
M(U
Fig. 2
R’Channel
B Detector PD
Non-linearforward-scatter distributed optical-fibre sensing
183
way, on the external field to be measured (measurand). The mode into which the CW is launched will be labelled the ‘filled’ (in this case T) mode whilst the other is the ‘free’ (in this case R) mode. An optical pulse is now launched into the other end (B) of the fibre in such a way as to allow it, whilst propagating in the opposite direction to the CW, to couple the latter from the ‘filled’ to the ‘free’ mode. If, as was required above, the coupling mechanism is modulated by the measurand in a deterministic way, then, by time-resolving the CW power level emerging from end B in the ‘free’ mode, one obtains the spatial distribution of the measurand field. The important advantage which this method offers over the backscatter technique is that of increased received power level. There is no longer an optimum attenuation coefficient for a given fibre length, since one is not relying on backscatter (although the mode-coupling requirement might impose other limitations on the minimum attenuation allowable). After a length L the CW power will, in this case, be given by Po exp (—ct’L)
p(L)
Suppose that a fraction q of this light power is coupled from the filled to the free mode, by the passage of the counterpropagating pulse, in the absence of a measurand field. For a resolution length 61, at distance L from the CW launch end, the coupled energy will be 6E
=
qp02ôLIc
(since a~can now be very small). As before, if we require an accuracy of ij,
in the shot noise limit we may write 1/~
(ôE/hv)
and thus, analogously to eqn (3), we have (chv/2qp ~) 1/~
61
Comparing eqns (3) and (4) we may write: 2)backscatter/(61
(61.
(4)
.
.
~7~)~orwar,js~atter
=
2eLqp 0/cE0S
?J
If now we assume that both arrangements use the same source, but in a pulsed mode for backscatter and in a CW mode for forward scatter, we find Po
=
E0 c/2L .
since the pulse repetition frequency must be c/2L as an optimum for the backscatter system (i.e. all backscattered light from one pulse must be received before another can be sent).
184
A. J. Rogers
Hence s~attCr= eq/S (5) (61 ~2)hack..c~~t~r/( 61 ~l2)f,,rwar~I A typical value for S in monomode fibre is 5 x ~ A typical value for q might be 0~1.For these values we find .
.
eq/S
50
This is thus the improvement in forward scatter relative to backscatter under these conditions. For a given accuracy (for example) the spatial resolution will be better, by this factor, for forward scatter compared with backscatter. The improvement in accuracy for a given resolution will, however, according to eqns (3) and (4), vary as the square root of this factor. Clearly, forward-scatter systems merit close investigation. Some forward-scatter systems have already been studied and have been reported in the literaturei~ Three new systems which are presently under investigation will now he described. Each of these systems will require access to both ends of the fibre.
3 BRILLOUIN-WAVE RESONANT COUPLING DOFS The arrangement for the first of these systems is shown in Fig. 3. A high-birefringence (hi-bi) fibre with intrinsic linear hirefringence f~ (i.e. the difference between propagation constants for the two linearlypolarised eigenmodes) is exposed to the measurand field, which acts to Beam splitter
Measurand field
Display
‘Hi-Bifibre
1
~ Pulse dump
Fig. 3
lser
Non-linearforward-scatter distributed optical-fibre sensing
185
modify /3. The birefringence now becomes a function of fibre position, /3(z) say, and thus the variation of /3 maps the measurand field along the path of the fibre. Suppose CW light is launched from one end of the fibre exclusively into one of the two eigenmodes. If the birefringence is large (beat length —1 mm, say) the fibre will have good polarisation-holding properties, and the light will be held quite strongly in its launch eigenmode. Substantial coupling to the other mode can take place only when a coupling influence acts with a spatial period close to the fibre beat length, for then the individual coupling points reinforce coherently, and the coupling becomes ‘resonant’. (Capricious environmental influences with periods as small as this are rare, which is why the polarisation holding is good.) The present method seeks to provide such an influence by optical means. This is to be done by propagating a light pulse, counter to the CW, with an optical frequency chosen so as to interfere (optically, in the fibre) with the CW, and giving rise to an interference pattern with spacing between maxima equal to the (measurand-unperturbed) birefringence beat length. With this ‘resonant’ interference pattern, coupling of light from the ‘filled’ to the ‘free’ eigenmode might occur via one or more of several possible mechanisms. Clearly some coupling will occur via direct (resonant) Rayleigh scattering, but a more powerful mechanism probably will result from the acoustic (Brillouin) wave9 set up by the interference pattern. This wave will act locally to rotate the birefringence axes, and thus couple between the eigenmodes as the pulse propagates. The action is as follows: at the maxima of the interference pattern (in one of the two eigenmodes) the transverse electric field of the optical waves will generate a shear acoustic wave (with the same polarisation and wavelength as the pattern) via electrostriction (the mechanical strain induced by the action of an electric field on a medium). This shear wave is evanescent, but will couple to a propagating longitudinal wave, via Poisson’s ratio; this, in turn, will couple (again via Poisson’s ratio) to the orthogonal polarisation shear acoustic wave. The two shear waves are of unequal amplitude (the second being much the smaller) and they will combine vectorially to give a resultant shear wave linearly polarised at a small angle to the original eigenmode axis. The result of this is a small rotation of the eigenmode axes, which varies at the acoustic frequency, since the refractive index of the medium will vary in sympathy with the acoustic wave amplitude, via the strain—optic effect. Hence, provided that the interference pattern has a spatial period equal to the beat length, resonant coupling (into the originally-empty
186
A. J. Rogers
eigenmode) can occur. Clearly, for this coupling mechanism to act, each of the two waves must possess a coherence length at least as great as the resolution length, say 0~lm: this implies source spectral widths of order 2 GHz (or less). This mechanism almost certainly will dominate over resonant Rayleigh scattering since the latter will rely on local anisotropy in the scattering centres to provide a component in the orthogonal polarisation state, via the non-zero off-diagonal components of the susceptibility tensor. For an amorphous material this will be third order compared with the exciting wave, whereas the Brillouin coupling will be second order. If the birefringence is a constant, independent of fibre position, the result is a constant power level for the CW emerging from the ~free’ eigenmode output end. Any measurand-induced perturbation of the birefringence will modify the coupling coefficient, and will impress itself on the emergent light as a time-varying function whose analysis will yield the spatial distribution of the measurand. This is a particularly simple scheme in regard to signal processing, since all that is required is a normalisation of the ~free’ mode’s emergent power level to provide the required information. Furthermore, the coupled. emergent light will be frequency-shifted by the Brillouin wave to allow ready noise discrimination. Some orders of magnitude for the relevant numbers will now be provided to establish feasibility. For a 1 mm beat length, the two optical waves should differ by about 200 GHz (—05 nm) to provide a corresponding interference pattern. We require the interference pattern to have good ~visibility’ (i.e. minima which are close to zero). This necessitates close-to-equal powers for the two counterpropagations. In order to estimate the magnitude of the coupling coefficient it is necessary to estimate first the value of the coefficient of electrostriction in silica. The electrostrictive coefficient y in an isotropic medium is defined by” a = yE2 where a is the strain induced by the electric field, modulus El. The refractive index change, An, is related to a via An ~
n3 U
where Pe is the photo-elastic constant for silica. The value of An can be estimated from the Brillouin gain coefficient in silica,” and this then permits an estimate of the coupling coefficient, between eigenmodes.
Non-linearforward-scatter distributed optical-fibre sensing
187
If we assume a ‘coupling’ length of 0~1m (also, of course, the resolution length) then there will be 100 acoustic wavelengths within it (i.e. 100 X 1 mm beat lengths). We find that the fraction of coupled amplitude over 01 m is given by q 5 x 10’~ El2. For 10% amplitude coupling (1% power coupling) in a typical single mode hi-bi fibre, this expression implies a power level requirement, for each of the two beams, of —20mW, giving an easily-measurable coupled power of —-0-2 mW. As a further check on feasibility it is interesting to note that the above numbers imply a refractive index change, by the acoustic wave, of —10~. This is of the same order as the difference between eigenmode refractive indices for hi-bi fibre of 1 mm beat length. Clearly, the above system could also work in a pulse/pulse mode, with the measurand mapping occurring as a result of an increasing delay inserted between successive pulse pairs. Inevitably, the latter arrangement would possess a system bandwidth two or three orders smaller than for a pulse/CW system; however, it would assist considerably in meeting the requirement for equal powers in the counter-propagations. Work on this idea has proceeded to the point where coupling has been observed between two counterpropagating pulses derived from a YAG-pumped dye laser, suitably modified to provide a variable frequency difference between the pulses.12 Detailed results will be published in a later paper. -—
4 FREQUENCY-DERIVED BRILLOUIN-WAVE RESONANT COUPLING A variation on the method just described in Section 3 could be used when the coupling coefficient can be made large, and when high sensitivity is required. Suppose that the propagating pulse can couple approximately half of the CW light from the ‘filled’ to the ‘free’ mode, and consider the coupling which occurs at distance s from the end at which the CW emerges. If the velocities in the two modes are given, respectively, by c 1(s) and c2(s), then the phase delay acquired by light, in each of the two modes, between coupling and emergence is given by
4i(s)=wj-~ 42(s)—wI
i~ c2(s)
(6)
A. J. Rogers
188 Beam splitter
Measurand field
L~’~ ___________
~
splitter
beam
~~controlIers
-
~f~ence~7m
~~Mirrors ~~~~Photodetectors
~“LIIII1
/
‘Hi-Bi’ fibre
~‘er
~
Pulse dump
Integrator
Frequency meter
Display
Fig. 4
where w is the optical angular frequency. The difference between c and c2 will be small for available hi-hi fibre, hence we may write c,(s)
=
~.
—
v(s)/2
c7(s)=c+v(s)/2
with v(s)<
Thus from eqns (6) we have 2w f~
A~(s)=~1(s)—~2(s)=-—--I v(s)ds C—
(7)
Jo
Suppose now that we allow the two emergent modes to interfere optically, (with suitable polarisation manipulation), on the surface of a detector photodiode (Fig. 4). Then the two waves will give rise to a term which can be written as E,E2cosA4
(8)
where E, and E2 are the two interfering optical-electric field amplitudes. (This term is a maximum for E1 = E2 under the constraint that E~+ E~is constant; hence the desirability of 50% coupling.) As the pulse propagates, the time dependence of s will generate a time dependence of AØ, and the term given in eqn (8) will become time variable, with an ‘instantaneous’ frequency given by =
d(A~1)/dt= d(A4)/ds. ds/dt = wv(s)/c
(since s
=
ct/2)
Non-linear forward-scatter distributed optical-fibre sensing
189
This gives fD(t)
WD(t)/2Jr
=
f/c. u(s)
and the frequency f0(t) thus maps the velocity u(s), and hence also the birefringence as a function of position along the fibre. However, in order to measure frequency to, say, 1%, —100 cycles are required per resolution length. If this length is to be —0~1m the implication is for a mean value offD 100 GHz. Clearly, the accurate measurement of such a high frequency is not a trivial matter, and this must be considered a disadvantage. However, ideas for circumventing this difficulty are under active investigation, and some promising results have recently been reported. —~
5 ACOUSTIC-PULSE-INDUCED RESONANT COUPLING A logical development of the method described in Section 4 is to effect the optical coupling via an externally generated pulse of acoustic waves which propagates along the optical fibre. The fibre is now used 4asThe an acoustic waveguide in addition to its use for optical guiding.’ advantages of this method are, firstly, a more direct control over the coupling process, since it is possible quite readily to vary the amplitude, frequency and polarisation of the externally generated acoustic waves and, secondly, a relaxation on the speed required in the signal processing, since the acoustic wave travels —10~times slower than optical waves in the fibre. Acoustic waves already have been used successfully to couple light between eigenmodes and between spatial modes in hi-bi fibres, primarily in pursuit of the fabrication of fibre phase modulators and frequency shifters.’5”6 The scheme is illustrated in Fig. 5. Thus we launch CW light into one of the two eigenmodes of a hi-bi fibre, as before. A counterpropagating, transverse-polarisation acoustic pulse is launched on to the fibre from the other end. The acoustic carrier wavelength is chosen to be equal to the fibre beat length, again as before. Shear waves in silica travel at a velocity of —3-8 x 10~ms’, and thus a 1 mm wavelength is achieved with an acoustic frequency of —-4 MHz. The acoustic pulse, again, resonantly couples light from the ‘filled’ to the ‘free’ mode as it propagates, the efficiency of the coupling being dependent upon the correspondence between the beat length and the acoustic wavelength. A significant disadvantage of this method is likely to be the difficulty of launching acoustic waves on to the fibre at this frequency, and maintaining the required amplitude and polarisation over large dis-
A. J. Rogers
190
M II)
_______
~w ~ser
~
-
J
— -—
Hi-Bj’fjbre /
Acoustic P~1P~oto-
----~~
v
detector System
Acoustic driver
Frequency meter
L ~j
M(L) Display
Fig. 5
tances (—lOOm). The fact that the acoustic wavelength is an order larger than a typical fibre diameter implies that most of the acoustic energy propagates in the evanescent field, in the medium surrounding the fibre; this makes the acoustic propagation highly dependent on conditions in that medium, and thus on the support and configuration of the fibre. One solution to the problem might be to construct an acoustic waveguide with an optical fibre embedded within a largerdiameter acoustic guiding structure. The further difficulty here however, is that the acoustic structure will act to shield the fibre from the measurand, and its composition must he chosen with that in mind, in addition to the acoustic requirements, and those of installation flexibility within the measurement environment. These requirements are very restrictive however, and experimental results obtained so far have not been encouraging. If this method is used in the ‘frequency-derived’ mode described in Section 4, above, there is advantage in the fact that the frequency to be measured is now reduced to —2 MHz. Furthermore, it is easier to arrange for the 50% coupling which is ideally required, when using external acoustic coupling. Whether these advantages can outweigh the disadvantages mentioned, however, is a question which cannot be resolved without further experimentation.
Non-linearforward-scatter distributed optical-fibre sensing
191
6 CONCLUSIONS The advantages of forward-scatter distributed optical-fibre sensors which use non-linear interactions between counterpropagating light beams have been stressed. These are, primarily: much larger received light power than backscatter (OTDR) techniques, leading to improved sensitivity and spatial resolution; and markedly simpler signal processing. Several possible arrangements for implementing such sensors have been described. Advantages and disadvantages of each have been emphasised. The arrangements presently are under experimental investigation and the results will be reported fully elsewhere. It is clear that there is much work yet to be done before such methods can be shown to be viable for operational measurement. In particular, it is clear that great reliance will, of necessity, be placed upon the fabrication of special fibres for enhancement and control of the non-linear optical interactions, and for optimised interfacing with the measurand field. The potential pay-offs in terms of a generic range of fully-distributed optical-fibre sensors capable of providing for the majority of requirements in industrial measurement (in addition to allowing access to an extra level of information) are deemed such as to make the research investment conspicuously worthwhile.
REFERENCES 1. Rogers, A. J., Distributed optical-fibre sensors. J. Phys. D, 19 (1986) 2237—55.
2. Culshaw, B., Distributed and multiplexed fibre-optic sensor systems. Proc. NATO Adv. Study Inst., Erice, Sicily, 1986. Nijhoff, The Hague, 1987. 3. Kist, R., Fibre-optic sensors for networks. In Proc. mt. Conf. on Optical-Fibre Sensors, OFS ‘86, Tokyo. IECEJ (Japan), 1986, pp. 209—25. 4. Barnoski, M. K. & Jensen, S. M., Fibre waveguides: a novel technique for investigating attenuation characteristics. App!. Opt., 15(9) (1976) 2112— 15. 5. Rogers, A.
J., Polarization-optical time domain reflectometry: a technique for the measurement of field distributions. Appl. Opt., 20 (1981) 1060—74. 6. Farries, M. C. & Rogers, A. J., Distributed sensing using stimulated Raman interaction in a monomode optical fibre. Proceedings 2nd mt. Conf. on Optical-Fibre Sensors, OFS ‘84, Stuttgart. VDE—Verlag GmbH, Berlin 1984. Paper 45, pp. 121—32. 7. Dakin, J. P., Pratt, D. J., Edge, C., Goodwin, M. J. & Bennion, I., Distributed fibre temperature sensor using the optical Kerr effect. Proc. SPIE, 798 (Fibre-Optic Sensors II) (1987), 149—56.
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8. Valis, T., Turner, R. D. & Measures, R. M., Fibre optic sensing based on counter-propagating waves. SPIE Meeting, Optical Engineering and Industrial Sensing for Advanced Manufacturing Technologies, Dearborn. USA, 26—30 June 1988.
9. Thomas, P. J., Rowell, N. L., Van Driel, H. M. & Stegeman, G. 1.. Normal, acoustic modes and Brillouin scattering in optical fibres. Phys. Rev. B, 19 (1979) 4986. 10. Nye, J. p. 257.
F., Physical Properties of Crystals. Oxford University Press. 1976.
11. Cotter, D., Stimulated Brillouin scattering in monomode optical fibre. J. Opt. Comm., 4(1) (1983) 86—95.
12. Handerek, V. A., Ahmed, U. & Rogers, A. J., Modification of dye-laser cavity for simultaneous
oscillation
at two laser frequencies.
IREE
(Australia). (To be published in Review of Scientific Instruments.) 13. Parvaneh, F., Handerek, V. A. & Rogers, A. J., Frequency-derived distributed optical-fibre sensing: a heterodyned version. Proc. OFS7. Paper WEO 4.2, 1990. 14. Rogers, A. J., Distributed optical-fibre sensors for the measurement of pressure, strain and temperature. Physics Reports, 169(2) (1988) 99—143. 15. Risk, W. P., Kino, G. S., Shaw, H. J. & Youngquist, R. C.. Acoustic fibre-optic modulators. IEEE Symposium on Sonics and Ultrasonics.
Atlanta, 1984, paper AO-5. 16. Pannell, C. N., Tatam, R. P., Jones, J. D. C. & Jackson. D. A., Optical
frequency shifter using linearly birefringent monomode fibre. Elect. Let!.. 23 (1987) 847.
Prospects for Non-linear Forward-Scatter Distributed Optical-Fibre Sensing A. J. Rogers Department of Electronic and Electrical Engineering, King’s College London, Strand, London WC2R 2LS, UK (Received 7 January 1991; revised version received and accepted 18 May 1991)
ABSTRACT Opticalfibres offer special advantages for fully-distributed sensing. They comprise an essentially one-dimensional measurement medium which can be used to provide the spatial distribution of a variety of measurands within large structures. To date, most fully-distributed optical-fibre sensor systems have relied on backscatter, OTDR, techniques. This paper proposes an alternative, forward-scatter approach; it utilises non-linear interactions between counter-propagating beams in optical fibres. This latter approach offers possibilities for a significant improvement in performance for such sensors. Some possible systems based on this approach are described and preliminary experimental results are presented.
1 INTRODUCTION The advantages offered by optical fibres in the measurement function are well known: they provide an insulating, passive, flexible, dielectric medium whose optical propagation properties are influenced by a large variety of external physical parameters. It is therefore possible to install measurement devices and systems, based on these features, easily into industrial plant or into diagnostic structures, with minimum disturbance to the environment and in a safe, reliable way. The one-dimensional nature of this measurement medium allows it to be used in two novel ways: for line integration, and for line differentiation. In the former usage it becomes possible to measure 179
Optics and Lasers in Engineering O143-8166/92/$O5~OO© 1992 Elsevier Science Publishers Ltd, England. Printed in Northern Ireland
180
A. J. Rogers
electric currents via ioop integration of the surrounding magnetic field. or voltages via the line integration of electric field, or simply to derive a configured path average for a measurand. In the latter usage, that of line differentiation, it becomes possible to determine the spatial distribution of a measurand, along a chosen path. simultaneously with its temporal variation. Such an arrangement is known as a distributed optical-fibre sensor (DOFS). Distributed optical-fibre measurement offers many advantages for industrial use. The ability to obtain simultaneously both spatial and temporal information on a measurand field (e.g. pressure. strain, temperature, magnetic field, electric field) provides at once a convenient monitor on the performance of large-structures. and a more detailed understanding of their behaviour, with implications for unproved design. Applications which come easily to mind are strain distribution in critical structures such as dams, bridges, pressure vessels, aircraft and spacecraft; temperature distributions in power transformers, boilers, electrical generators, high voltage cables and aerofoils: electric/magnetic field distributions in electric power transmission lines and telecommunications cables; highly directional antennas are also possible.’ A distinction must be made between two types of distributed optical-fibre sensor (DOFS), in order to avoid confusion. In the first of these it is necessary to make measurements only at discrete, predetermined points (or along specific, limited lengths) on the fibre. The measurement system then takes on the character of a series-distributed array of discrete transducers. This we call a quasi-distributed system; in the literature it sometimes has been called a multiplexed system. In the second type the measurement may be made continuously as a function of position at any point along the fibre; this, clearly, is a much more powerful and flexible arrangement. This we call a fully-distributed, or. more often, simply a distributed sensor. Systems which have been studied to date have been described in several reviews.’3 The vast majority of these use optical—time domain reflectometry (OTDR) methods45 to provide the spatial information. These rely on time resolution of the light backscattered from an optical pulse propagating in the fibre. Backscattered light levels in amorphous silica are relatively low and impose limitations on the sensitivity and spatial resolution which can be achieved in DOFS. If the spatial and temporal measurand information could be obtained in forward scatter, significant improvement in performance could result. This paper considers three novel, but related, forward scatter systems for DOFS. They represent ideas which presently are being actively researched, and which hold considerable promise for development into practical systems of value, in aerospace applications and elsewhere.
Non-linear forward-scatter distributed optical-fibre sensing
181
Their promise lies in their ability to make measurements with high sensitivity (—1%) and good spatial resolution (—0.1 m) in short time scales (—~is).These features are attractive for aerospace use since they would allow effective continuous monitoring of, for example, strain and temperature, over a complete airframe or space frame, in a way which would permit effective response, either manually or automatically. Self-adjusting geometries also become possible when in possession of the offered information.
2 BACKSCATTER VERSUS FORWARD-SCATTER DOFS Backscatter DOFS systems rely on the Optical Time Domain Reflectometry (OTDR) principle. A generalised schematic for backscatter DOFS is shown in Fig. 1. A pulse of light is launched into an optical fibre and the Rayleigh backscattered light is monitored and time resolved at the launch end. The measurand field through which the fibre threads modifies the optical properties of the fibre in a deterministic way, leading to a modulation of the backscattered light. This modulation is decoded by a demodulation analyser at the detector end, which, together with the time-differentiation, yields the spatial distribution of the measurand field. For an optical pulse of energy E0 launched into a fibre the received 5 backscattered power after a time t is given by p(t)
=
(c/2)E
0o~Sexp (—crct) Beam splitter
__________
Pulsed laser
(1)
J’t —
—
*
_______
—
—
—
-~
..-
Fibre
_______
~
Measurand MCI)
ar
___
U
Demodulation analyzer function
resolution element
I
+
detector~
~
~~MCI) Display
Fig. 1
182
A. J. Rogers
where c is the velocity of light in the fibre, a~is the attenuation coefficient, and
S is the hackscatter capture fraction. Since the attenuation normally is due to Rayleigh scattering, there exists an optimum value of a~for a given length of system: too large a value over-attenuates the light; too small a value provides insufficient backscatter. This value of & clearly is given by ~=
l/ct= IlL say.
Hence the minimum value of p in a hackscatter system is given by =
cE0S/2Le
(e = exp(l))
Now for a spatial resolution of 61 the energy received from L by the detector in the resolution time interval 261/c is given by 6E =p~,.26//c
For an accuracy of measurement, that
=
(2)
E0S/e. 6/IL
i~, we
require, in the shot noise limit, 2
6E/hv> l/i~ (where h is Planck’s constant and v is the optical frequency). Or, using
eqn (2) 6!> (eLhv/E 0S).
(3)
l/~
which provides the relationship between resolution and accuracy for backscatter DOFS, in the shot noise limit. Consider now the forward-scatter arrangement shown in Fig. 2. In this arrangement a continuous wave (CW) source is launched, at one end (F) of the fibre, into one of two possible modes T and R. say. These might be two propagation modes, two polarization modes, or even two separate cores within the same cladding. The important conditions which must obtain are that the two modes must be separately identifiable at the output from the fibre, and that light coupling between them must both be possible and dependent, in some 4 T Channel FlSource CW-~ C~ 4
—
K0 ~ ~
1
CR
M(U
Fig. 2
R’Channel
B Detector PD
Non-linearforward-scatter distributed optical-fibre sensing
183
way, on the external field to be measured (measurand). The mode into which the CW is launched will be labelled the ‘filled’ (in this case T) mode whilst the other is the ‘free’ (in this case R) mode. An optical pulse is now launched into the other end (B) of the fibre in such a way as to allow it, whilst propagating in the opposite direction to the CW, to couple the latter from the ‘filled’ to the ‘free’ mode. If, as was required above, the coupling mechanism is modulated by the measurand in a deterministic way, then, by time-resolving the CW power level emerging from end B in the ‘free’ mode, one obtains the spatial distribution of the measurand field. The important advantage which this method offers over the backscatter technique is that of increased received power level. There is no longer an optimum attenuation coefficient for a given fibre length, since one is not relying on backscatter (although the mode-coupling requirement might impose other limitations on the minimum attenuation allowable). After a length L the CW power will, in this case, be given by Po exp (—ct’L)
p(L)
Suppose that a fraction q of this light power is coupled from the filled to the free mode, by the passage of the counterpropagating pulse, in the absence of a measurand field. For a resolution length 61, at distance L from the CW launch end, the coupled energy will be 6E
=
qp02ôLIc
(since a~can now be very small). As before, if we require an accuracy of ij,
in the shot noise limit we may write 1/~
(ôE/hv)
and thus, analogously to eqn (3), we have (chv/2qp ~) 1/~
61
Comparing eqns (3) and (4) we may write: 2)backscatter/(61
(61.
(4)
.
.
~7~)~orwar,js~atter
=
2eLqp 0/cE0S
?J
If now we assume that both arrangements use the same source, but in a pulsed mode for backscatter and in a CW mode for forward scatter, we find Po
=
E0 c/2L .
since the pulse repetition frequency must be c/2L as an optimum for the backscatter system (i.e. all backscattered light from one pulse must be received before another can be sent).
184
A. J. Rogers
Hence s~attCr= eq/S (5) (61 ~2)hack..c~~t~r/( 61 ~l2)f,,rwar~I A typical value for S in monomode fibre is 5 x ~ A typical value for q might be 0~1.For these values we find .
.
eq/S
50
This is thus the improvement in forward scatter relative to backscatter under these conditions. For a given accuracy (for example) the spatial resolution will be better, by this factor, for forward scatter compared with backscatter. The improvement in accuracy for a given resolution will, however, according to eqns (3) and (4), vary as the square root of this factor. Clearly, forward-scatter systems merit close investigation. Some forward-scatter systems have already been studied and have been reported in the literaturei~ Three new systems which are presently under investigation will now he described. Each of these systems will require access to both ends of the fibre.
3 BRILLOUIN-WAVE RESONANT COUPLING DOFS The arrangement for the first of these systems is shown in Fig. 3. A high-birefringence (hi-bi) fibre with intrinsic linear hirefringence f~ (i.e. the difference between propagation constants for the two linearlypolarised eigenmodes) is exposed to the measurand field, which acts to Beam splitter
Measurand field
Display
‘Hi-Bifibre
1
~ Pulse dump
Fig. 3
lser
Non-linearforward-scatter distributed optical-fibre sensing
185
modify /3. The birefringence now becomes a function of fibre position, /3(z) say, and thus the variation of /3 maps the measurand field along the path of the fibre. Suppose CW light is launched from one end of the fibre exclusively into one of the two eigenmodes. If the birefringence is large (beat length —1 mm, say) the fibre will have good polarisation-holding properties, and the light will be held quite strongly in its launch eigenmode. Substantial coupling to the other mode can take place only when a coupling influence acts with a spatial period close to the fibre beat length, for then the individual coupling points reinforce coherently, and the coupling becomes ‘resonant’. (Capricious environmental influences with periods as small as this are rare, which is why the polarisation holding is good.) The present method seeks to provide such an influence by optical means. This is to be done by propagating a light pulse, counter to the CW, with an optical frequency chosen so as to interfere (optically, in the fibre) with the CW, and giving rise to an interference pattern with spacing between maxima equal to the (measurand-unperturbed) birefringence beat length. With this ‘resonant’ interference pattern, coupling of light from the ‘filled’ to the ‘free’ eigenmode might occur via one or more of several possible mechanisms. Clearly some coupling will occur via direct (resonant) Rayleigh scattering, but a more powerful mechanism probably will result from the acoustic (Brillouin) wave9 set up by the interference pattern. This wave will act locally to rotate the birefringence axes, and thus couple between the eigenmodes as the pulse propagates. The action is as follows: at the maxima of the interference pattern (in one of the two eigenmodes) the transverse electric field of the optical waves will generate a shear acoustic wave (with the same polarisation and wavelength as the pattern) via electrostriction (the mechanical strain induced by the action of an electric field on a medium). This shear wave is evanescent, but will couple to a propagating longitudinal wave, via Poisson’s ratio; this, in turn, will couple (again via Poisson’s ratio) to the orthogonal polarisation shear acoustic wave. The two shear waves are of unequal amplitude (the second being much the smaller) and they will combine vectorially to give a resultant shear wave linearly polarised at a small angle to the original eigenmode axis. The result of this is a small rotation of the eigenmode axes, which varies at the acoustic frequency, since the refractive index of the medium will vary in sympathy with the acoustic wave amplitude, via the strain—optic effect. Hence, provided that the interference pattern has a spatial period equal to the beat length, resonant coupling (into the originally-empty
186
A. J. Rogers
eigenmode) can occur. Clearly, for this coupling mechanism to act, each of the two waves must possess a coherence length at least as great as the resolution length, say 0~lm: this implies source spectral widths of order 2 GHz (or less). This mechanism almost certainly will dominate over resonant Rayleigh scattering since the latter will rely on local anisotropy in the scattering centres to provide a component in the orthogonal polarisation state, via the non-zero off-diagonal components of the susceptibility tensor. For an amorphous material this will be third order compared with the exciting wave, whereas the Brillouin coupling will be second order. If the birefringence is a constant, independent of fibre position, the result is a constant power level for the CW emerging from the ~free’ eigenmode output end. Any measurand-induced perturbation of the birefringence will modify the coupling coefficient, and will impress itself on the emergent light as a time-varying function whose analysis will yield the spatial distribution of the measurand. This is a particularly simple scheme in regard to signal processing, since all that is required is a normalisation of the ~free’ mode’s emergent power level to provide the required information. Furthermore, the coupled. emergent light will be frequency-shifted by the Brillouin wave to allow ready noise discrimination. Some orders of magnitude for the relevant numbers will now be provided to establish feasibility. For a 1 mm beat length, the two optical waves should differ by about 200 GHz (—05 nm) to provide a corresponding interference pattern. We require the interference pattern to have good ~visibility’ (i.e. minima which are close to zero). This necessitates close-to-equal powers for the two counterpropagations. In order to estimate the magnitude of the coupling coefficient it is necessary to estimate first the value of the coefficient of electrostriction in silica. The electrostrictive coefficient y in an isotropic medium is defined by” a = yE2 where a is the strain induced by the electric field, modulus El. The refractive index change, An, is related to a via An ~
n3 U
where Pe is the photo-elastic constant for silica. The value of An can be estimated from the Brillouin gain coefficient in silica,” and this then permits an estimate of the coupling coefficient, between eigenmodes.
Non-linearforward-scatter distributed optical-fibre sensing
187
If we assume a ‘coupling’ length of 0~1m (also, of course, the resolution length) then there will be 100 acoustic wavelengths within it (i.e. 100 X 1 mm beat lengths). We find that the fraction of coupled amplitude over 01 m is given by q 5 x 10’~ El2. For 10% amplitude coupling (1% power coupling) in a typical single mode hi-bi fibre, this expression implies a power level requirement, for each of the two beams, of —20mW, giving an easily-measurable coupled power of —-0-2 mW. As a further check on feasibility it is interesting to note that the above numbers imply a refractive index change, by the acoustic wave, of —10~. This is of the same order as the difference between eigenmode refractive indices for hi-bi fibre of 1 mm beat length. Clearly, the above system could also work in a pulse/pulse mode, with the measurand mapping occurring as a result of an increasing delay inserted between successive pulse pairs. Inevitably, the latter arrangement would possess a system bandwidth two or three orders smaller than for a pulse/CW system; however, it would assist considerably in meeting the requirement for equal powers in the counter-propagations. Work on this idea has proceeded to the point where coupling has been observed between two counterpropagating pulses derived from a YAG-pumped dye laser, suitably modified to provide a variable frequency difference between the pulses.12 Detailed results will be published in a later paper. -—
4 FREQUENCY-DERIVED BRILLOUIN-WAVE RESONANT COUPLING A variation on the method just described in Section 3 could be used when the coupling coefficient can be made large, and when high sensitivity is required. Suppose that the propagating pulse can couple approximately half of the CW light from the ‘filled’ to the ‘free’ mode, and consider the coupling which occurs at distance s from the end at which the CW emerges. If the velocities in the two modes are given, respectively, by c 1(s) and c2(s), then the phase delay acquired by light, in each of the two modes, between coupling and emergence is given by
4i(s)=wj-~ 42(s)—wI
i~ c2(s)
(6)
A. J. Rogers
188 Beam splitter
Measurand field
L~’~ ___________
~
splitter
beam
~~controlIers
-
~f~ence~7m
~~Mirrors ~~~~Photodetectors
~“LIIII1
/
‘Hi-Bi’ fibre
~‘er
~
Pulse dump
Integrator
Frequency meter
Display
Fig. 4
where w is the optical angular frequency. The difference between c and c2 will be small for available hi-hi fibre, hence we may write c,(s)
=
~.
—
v(s)/2
c7(s)=c+v(s)/2
with v(s)<
Thus from eqns (6) we have 2w f~
A~(s)=~1(s)—~2(s)=-—--I v(s)ds C—
(7)
Jo
Suppose now that we allow the two emergent modes to interfere optically, (with suitable polarisation manipulation), on the surface of a detector photodiode (Fig. 4). Then the two waves will give rise to a term which can be written as E,E2cosA4
(8)
where E, and E2 are the two interfering optical-electric field amplitudes. (This term is a maximum for E1 = E2 under the constraint that E~+ E~is constant; hence the desirability of 50% coupling.) As the pulse propagates, the time dependence of s will generate a time dependence of AØ, and the term given in eqn (8) will become time variable, with an ‘instantaneous’ frequency given by =
d(A~1)/dt= d(A4)/ds. ds/dt = wv(s)/c
(since s
=
ct/2)
Non-linear forward-scatter distributed optical-fibre sensing
189
This gives fD(t)
WD(t)/2Jr
=
f/c. u(s)
and the frequency f0(t) thus maps the velocity u(s), and hence also the birefringence as a function of position along the fibre. However, in order to measure frequency to, say, 1%, —100 cycles are required per resolution length. If this length is to be —0~1m the implication is for a mean value offD 100 GHz. Clearly, the accurate measurement of such a high frequency is not a trivial matter, and this must be considered a disadvantage. However, ideas for circumventing this difficulty are under active investigation, and some promising results have recently been reported. —~
5 ACOUSTIC-PULSE-INDUCED RESONANT COUPLING A logical development of the method described in Section 4 is to effect the optical coupling via an externally generated pulse of acoustic waves which propagates along the optical fibre. The fibre is now used 4asThe an acoustic waveguide in addition to its use for optical guiding.’ advantages of this method are, firstly, a more direct control over the coupling process, since it is possible quite readily to vary the amplitude, frequency and polarisation of the externally generated acoustic waves and, secondly, a relaxation on the speed required in the signal processing, since the acoustic wave travels —10~times slower than optical waves in the fibre. Acoustic waves already have been used successfully to couple light between eigenmodes and between spatial modes in hi-bi fibres, primarily in pursuit of the fabrication of fibre phase modulators and frequency shifters.’5”6 The scheme is illustrated in Fig. 5. Thus we launch CW light into one of the two eigenmodes of a hi-bi fibre, as before. A counterpropagating, transverse-polarisation acoustic pulse is launched on to the fibre from the other end. The acoustic carrier wavelength is chosen to be equal to the fibre beat length, again as before. Shear waves in silica travel at a velocity of —3-8 x 10~ms’, and thus a 1 mm wavelength is achieved with an acoustic frequency of —-4 MHz. The acoustic pulse, again, resonantly couples light from the ‘filled’ to the ‘free’ mode as it propagates, the efficiency of the coupling being dependent upon the correspondence between the beat length and the acoustic wavelength. A significant disadvantage of this method is likely to be the difficulty of launching acoustic waves on to the fibre at this frequency, and maintaining the required amplitude and polarisation over large dis-
A. J. Rogers
190
M II)
_______
~w ~ser
~
-
J
— -—
Hi-Bj’fjbre /
Acoustic P~1P~oto-
----~~
v
detector System
Acoustic driver
Frequency meter
L ~j
M(L) Display
Fig. 5
tances (—lOOm). The fact that the acoustic wavelength is an order larger than a typical fibre diameter implies that most of the acoustic energy propagates in the evanescent field, in the medium surrounding the fibre; this makes the acoustic propagation highly dependent on conditions in that medium, and thus on the support and configuration of the fibre. One solution to the problem might be to construct an acoustic waveguide with an optical fibre embedded within a largerdiameter acoustic guiding structure. The further difficulty here however, is that the acoustic structure will act to shield the fibre from the measurand, and its composition must he chosen with that in mind, in addition to the acoustic requirements, and those of installation flexibility within the measurement environment. These requirements are very restrictive however, and experimental results obtained so far have not been encouraging. If this method is used in the ‘frequency-derived’ mode described in Section 4, above, there is advantage in the fact that the frequency to be measured is now reduced to —2 MHz. Furthermore, it is easier to arrange for the 50% coupling which is ideally required, when using external acoustic coupling. Whether these advantages can outweigh the disadvantages mentioned, however, is a question which cannot be resolved without further experimentation.
Non-linearforward-scatter distributed optical-fibre sensing
191
6 CONCLUSIONS The advantages of forward-scatter distributed optical-fibre sensors which use non-linear interactions between counterpropagating light beams have been stressed. These are, primarily: much larger received light power than backscatter (OTDR) techniques, leading to improved sensitivity and spatial resolution; and markedly simpler signal processing. Several possible arrangements for implementing such sensors have been described. Advantages and disadvantages of each have been emphasised. The arrangements presently are under experimental investigation and the results will be reported fully elsewhere. It is clear that there is much work yet to be done before such methods can be shown to be viable for operational measurement. In particular, it is clear that great reliance will, of necessity, be placed upon the fabrication of special fibres for enhancement and control of the non-linear optical interactions, and for optimised interfacing with the measurand field. The potential pay-offs in terms of a generic range of fully-distributed optical-fibre sensors capable of providing for the majority of requirements in industrial measurement (in addition to allowing access to an extra level of information) are deemed such as to make the research investment conspicuously worthwhile.
REFERENCES 1. Rogers, A. J., Distributed optical-fibre sensors. J. Phys. D, 19 (1986) 2237—55.
2. Culshaw, B., Distributed and multiplexed fibre-optic sensor systems. Proc. NATO Adv. Study Inst., Erice, Sicily, 1986. Nijhoff, The Hague, 1987. 3. Kist, R., Fibre-optic sensors for networks. In Proc. mt. Conf. on Optical-Fibre Sensors, OFS ‘86, Tokyo. IECEJ (Japan), 1986, pp. 209—25. 4. Barnoski, M. K. & Jensen, S. M., Fibre waveguides: a novel technique for investigating attenuation characteristics. App!. Opt., 15(9) (1976) 2112— 15. 5. Rogers, A.
J., Polarization-optical time domain reflectometry: a technique for the measurement of field distributions. Appl. Opt., 20 (1981) 1060—74. 6. Farries, M. C. & Rogers, A. J., Distributed sensing using stimulated Raman interaction in a monomode optical fibre. Proceedings 2nd mt. Conf. on Optical-Fibre Sensors, OFS ‘84, Stuttgart. VDE—Verlag GmbH, Berlin 1984. Paper 45, pp. 121—32. 7. Dakin, J. P., Pratt, D. J., Edge, C., Goodwin, M. J. & Bennion, I., Distributed fibre temperature sensor using the optical Kerr effect. Proc. SPIE, 798 (Fibre-Optic Sensors II) (1987), 149—56.
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8. Valis, T., Turner, R. D. & Measures, R. M., Fibre optic sensing based on counter-propagating waves. SPIE Meeting, Optical Engineering and Industrial Sensing for Advanced Manufacturing Technologies, Dearborn. USA, 26—30 June 1988.
9. Thomas, P. J., Rowell, N. L., Van Driel, H. M. & Stegeman, G. 1.. Normal, acoustic modes and Brillouin scattering in optical fibres. Phys. Rev. B, 19 (1979) 4986. 10. Nye, J. p. 257.
F., Physical Properties of Crystals. Oxford University Press. 1976.
11. Cotter, D., Stimulated Brillouin scattering in monomode optical fibre. J. Opt. Comm., 4(1) (1983) 86—95.
12. Handerek, V. A., Ahmed, U. & Rogers, A. J., Modification of dye-laser cavity for simultaneous
oscillation
at two laser frequencies.
IREE
(Australia). (To be published in Review of Scientific Instruments.) 13. Parvaneh, F., Handerek, V. A. & Rogers, A. J., Frequency-derived distributed optical-fibre sensing: a heterodyned version. Proc. OFS7. Paper WEO 4.2, 1990. 14. Rogers, A. J., Distributed optical-fibre sensors for the measurement of pressure, strain and temperature. Physics Reports, 169(2) (1988) 99—143. 15. Risk, W. P., Kino, G. S., Shaw, H. J. & Youngquist, R. C.. Acoustic fibre-optic modulators. IEEE Symposium on Sonics and Ultrasonics.
Atlanta, 1984, paper AO-5. 16. Pannell, C. N., Tatam, R. P., Jones, J. D. C. & Jackson. D. A., Optical
frequency shifter using linearly birefringent monomode fibre. Elect. Let!.. 23 (1987) 847.