Velociuteters This invention relates to veloclmeters and, 1n particular, to differential laser Doppler veloclmeters based on the use of a modified fibre optic Sagnac Interferometer. A feature of the Invention 1s that the Interferometer phase 1s dependent not on the target displacement, but on Its velocity. Unlike Interferometers used to measure a Doppler frequency shift directly, the practical use of the Sagnac 1s not restricted to very high velocities. It finds particular advantage In the measurement of high frequency oscillatory velocities, where the direct response to velocity effectively discriminates against unwanted low frequency components. To optimise the sensitivity of the Interferometer, we have Introduced a ιr/2 phase bias between the two beams, using a passive technique based on control of the birefringence of the fibre loop.

Fibre optic techniques In laser velodmetry are known (Jackson, D.A., Jones, J.D.C. 1986 Fibre Optic Sensors. Optlca Acta 33, 1469, Jackson, D.A., Jones, J.D.C. 1986 Extrinsic fibre optic sensors for remote measurement : parts one and two. Opt. and Laser Tech. 18, 243, 299). Many commercial Instruments are now available which use fibres to form flexible waveguides between a source/detector module and a remote probe. It is thus appropriate to consider further applications of fibre optics in which their properties are exploited to facilitate optical signal processing of the Doppler signal. In particular, the use of fibres and fibre components allows the implementation of Interferometer configurations which are impractical using conventional optics. In the present work, we have considered interferometer arrangements in which the detected optical phase 1s a function of target velocity, rather than the more usual situation in which an optical Intensity is amplitude modulated with a frequency proportional to target velocity. We have thus sought

to transfer the signal processing step of frequency discrimination from the electronic to the optical domain.

Direct measurement of velocity is of particular value in measurements on oscillatory targets or flows. For example, consider the use of a conventional reference beam laser velocimeter (such one having the configuration of a Michelson

Interferometer, in which the target is effectively one mirror of the Interferometer) used to measure out of plane vibration. The phase of the interferometer is dependent on the displacement of the target surface, and hence for a given velocity the amplitude of the phase modulation declines as the oscillation frequency 1s increased. Hence the measurement of high frequency oscillations

1s difficult, and 1t is generally necessary to use active phase modulation techniques to recover the high frequency signal in the presence of unwanted larger amplitude low frequency ambient vibrations.

According to the present Invention there 1s provided a velocimeter comprising an interferometer including a loop of fibre optic radiation guide, means for launching optical signals in opposite directions around said loop, probe means located within said loop and adapted to launch said optical signals from said radiation guide towards a oveable target, to receive said signals after reflection from said target and to re-direct said signals into said radiation guide. Embodiments of the invention will now be described by way of example with reference to the accompanying drawings in which:-

Figure 1 shows a fibre optic Sagnac interferometer used in one embodiment of the invention, Figure 2 shows an experimental layout, Figure 3 illustrates various probe configurations,

Figure 4 is a graphical representation of measurements of signal amplitude, Figure 5 is a display of a network analyser trace, and Figure 6 is an oscilloscope trace.

Referring now to Figure 2 of the drawings, this shows a new approach based on the fibre Sagnac interferometer. Classical Interferometers have been used to measure optical frequencies, and hence Doppler shifts, directly. For example, both Mlchelson and Fabry-Perot interferometers have been employed in this way as frequency discriminators for the measurement of Doppler shifts. However, such a technique is appropriate only for the measurement of very high velocities. Otherwise, very long optical paths are required to give the necessary frequency resolution, or Impractically high finesse 1s demanded from a Fabry-Perot. In principle it Is possible to make very long path Imbalance fibre interferometers. However, such an Instrument requires use of a laser source with a very long coherence length, and the measured Doppler shift 1s indistinguishable from laser frequency noise.

A schematic of a fibre optic Sagnac Interferometer 1s shown 1n Figure 1. Light is guided from a source S and launch lens L by a monomode fibre 1 and is amplitude divided at a directional coupler Cl . Divided light then follows clockwise and anticlockwise paths around a loop 2, recombining at the coupler. The Intensities I _α , I ₂ returned by the coupler arms are measured using photodetectors PD1 , PD2. For an Interferometer with an Ideal, lossless coupler Cl , any phase difference φ between recombining beams modulates the output intensities by the two beam interferometer transfer function.

I _1>2 = I ₀₁ , ₀₂ (l ± V ₁ , ₂ cos _φ ) (2.1)

where I ₀₁ , ₀₂ are constant intensities and V _χ , ₂ are the fringe visibilities. In a static, non-birefringent loop the optical path lengths for the counter-propagating waves are identical, hence φ _* 0. Thus the loop acts as a reflector with reflectance dependent on visibility V , itself in turn dependent on the directional coupler's coupling ratio K.

In practice, phase shifts between counter-propagating beams can be caused by birefringence (including gyrotropic effects), rotation of the loop (fibre gyroscope) and non-uniform, dynamic path length changes in the loop, can thus be written,

φ = φ _β + φ _D (2.2)

where _B is due to birefringence and φ _D to dynamic effects. Recovery of phase φ from output intensity has previously been obtained by a variety of schemes, including phase modulation within the loop with subsequent signal processing polarisation analysis of the output and the use of 3x3 directional couplers.

We have taken the novel approach of using a polarisation controller in the loop .to maintain phase quadrature, that is

φ _B -= (2N - l)ιr/2 (2.3)

N is an integer so (2.1) becomes

These complementary outputs may be subtracted, using appropriate weighting, to yield:

- ⁽ V, SInφ _D 2.5

^• ' ^■ 01 ^• ' ^■ 02

Phase modulation is achieved by interrupting the fibre loop near the directional coupler with a probe which reflects the beams from a moving target.

Consider two wavefronts recombining at the directional coupler at time t. These will have encountered the target at different times t-x _x , t-τ ₂ , due to the asymmetrical positioning of the probe within the loop, resulting in a phase difference of

φ _D = Φ ₂ - _χ - 2k [χ(t-τ ₁ ) - x(t-τ ₂ ) ] (2.6)

where x is the normal surface displacement, k = 2ιr/λ where λ is source wavelength, ^ι _z ^are the absolute phases of counter-propagating waves. <PQ can be written

t-τ

= 2k vΔτ 2.8 where Δτ = τ ₂ -τ _x v(t) = dχ(t) dt

and v ^• = average target velocity between t-τ ₂ and t-τ _χ

The phase shift is thus due to a time average of the target velocity; the averaging time Δτ is determined by the length of the fibre loop:

where L = L ₂ -L ₁ (where L _χ , L ₂ are fibre lengths from Cl to probe) n «= effective Index of fibre c = speed of light 1n vacuo

The frequency response of phase due to velocity 1s now obtained by considering a surface vibrating with frequency fs = ω _s /2 , so that

x = x ₀ sinω _s t 2.10

hence the normal velocity is

v = v ₀ sinω _s t 2.11

where v ₀ = x ₀ ω _s . Then

^< ?ϋ = 2kx ₀ [sin ω _c (t-τ ^u i,)- - sin ω _c (t-τ ₂ „).3 2.12

4kx ₀ si COSω _s (t-τ _Q ) 2.13 where ( ₁ + τ ₂ )/2 and Δτ = τ ₂ - τ,

l .e. tψQ = 2kv _Q Δτ s1nc(7o _s Δτ) COS ω _s (t-τ ₀ ) (2.14) A roll-off in response occurs at about fs = l/2Δτ and nulls at fs •= 1/Δτ, thus determining a maximum loop delay Δτ for a required system bandwidth.

The output intensity of a Sagnac interferometer may be modulated by loop birefringence due to the introduction of phase bias and polarisation offset between counter-propagating beams.

Further it may be shown that with the ability to produce an arbitrary birefringence in the loop, any arbitrary incident polarisation state can have any arbitrary phase difference imposed upon the counter-propagating waves: this is seen by referring to Figure 1. Monochromatic light of Jones vector E enters loop via directional coupler C _x and is amplitude divided into fields E _x , and is amplitude divided into fields E ₃ and M. propagating around the loop in opposite directions, and recombining as E ₃ ' , E ₄ ' . Let the birefringence of the loop in the clockwise direction be given by Jones Matrix J _A . Then, due to the co-ordinate change on return,

E ₃ ' = J _{.A .B} E ₃ (2.15)

where J_ _B = -j 0] L 0 jj

representing co-ordinate reversal by the loop.

Assuming the loop is lossless, then E ₄ ' is given by

^■ T

-°-B -°-A ^E 4 - ^B ^J A E = JA E, 2.16

as J. _β is symmetric, and where J. _A '« _i _A J _B The loop actually has attenuation e ^"" "-- which is considered identical for all polarisation states, giving the modified forms

E ₃ = e -« ^L J _A E ₃

E ₄ = e -* J _A ^T E ₄ 2.17

where E ₃ = (1 - γ)V(l- )E ₁

E ₄ - (1 - γ ⁾ ^ E ₁ 2.18

where K is the coupling ratio, γ is the excess loss, and the coupler is assumed non-birefringent. Therefore,

(E ₄ tE ₃ ) = e-J ^ιr/ ₂ (l-γ)(l- ^% E ₁ tE ₁ 2.19

(where t represents Hermitian conjugate). For a general phase offset of and Identical return polarisation state, we need

so that E+ _A ^T J-AE _I - eJ*E ^E 2.21

1 ^{n n *} - ^* 1 1

₊ T thus E[ ME _χ - e3*E ₁ E ₁ 2.22

^• * ME, = e÷) ^φ E, 2.23

where M = _A ^T)t iA = -°-A ² - ²⁴ This is solved for given Φ, E _x by finding M satisfying (2.23) and then J _A ' satisfying (2.24).

In the Poincare sphere representation any birefringence can be represented as a rotation of angle I" about a given axis. The axis is that corresponding to the two polarisation eigenstates of the birefringence, and the angle r is given by the difference in retardation between fast and slow eigenstates, 1e. r = 2Φ. Thus any Φ, £ ₁ uniquely define M . Writing M in terms of its unit eigenvectors

and their eigenvalues eχp(±jΦ)

M = (E _ιa E _lb ) diag (eJ ^φ ,e-J )(E _ιa E _lb )t 2.25

Substituting for E _ιa E^

A B ^' reJ ^φ +lαl ² e-*3 ^φ 2jα* sinΦ

M = -B* A* α 2jα si nΦ _e -J ^"φ ₊ |α| ² e-J ^φ

2.26 which can be used to solve (2.24) for J _A :

fB* 1-A*1

J _Δ - 2.27

-/[2(l-cosΦ)] L-l+A B J then

as requ re .

It should be noted that the condition E-^ M E _x - 0 is also easily satisfied so that the undesirable condition of 50% reflection without Interference can be generated. A phase modulator must therefore be used in order to monitor phase difference and fringe visibility whilst setting up the

Interferometer.

The fringe visibilities V _{l t 2} are products of three parameters of the light waves returning to the coupler

1. Their relative intensities

V _1nt « 2|E ₃ ||EJ/(|E ₃ | ² ₊ |E ₄ | ²

2. The scalar product of their polarisation states,

V _pol - |E E

3. Their mutual coherence V _coh - |γ ₃₄ |

Thus, assuming fibre losses for counter-propagating beams are identical, the only other effect is due to the coupler:

V _i "as V _1nt ^« 1

V ₂ has V _1nt * 1 (C2K(1-K)]- ¹ - l) ^"1

A polarisation controller consisting of two quarter- and one half-wave plate is capable of synthesising any general birefringence. If the actual loop birefringence is given by J^ then the controller must synthesise J _p - li ^"1 ^. Then, aside from fluctuations in birefringence, we obtain V _po - _| * 1.

Mutual coherence depends on source coherence and path length imbalance. As path length imbalance is simply the delay due to

birefringence, potentially subwavelength, its effect on V would generally be negligible for all but highly broadband sources.

This sensor thus has the advantage of an Inherently high fringe visibility. The phase resolution of the Sagnac depends on the following noise sources:

Detector Photocurrent Noise or Shot Noise

- sets a fundamental system limit. Assuming visibility is close to 1, when the system is close to quadrature, the intensity Incident on PD1 Is

I _χ = I ₀₁ (1 + sin φ _D ), φ _D small 2.29

This produces a detector photocurrent

where q = electronic charge v •= frequency of source light h = Plancks constant n •= quantum efficiency of detector (0.69 for a silicon photodetector used at a wavelength of 633nm)

which, measured over a bandwidth B, has a shot noise of

Ushot -^^cu ⁾ -31

with a resultant phase error of

Ψishot - ¹ ιshot = 2.32 di i ₀₁

If the system has two antiphase outputs which are subtracted so as to reduce Intensity variations, then

φshot - shot

e.g. 2 x TO-* rad HZ ^"% at 633nm with recovered power of ImW per detector. Laser Phase/Frequency Noise

- will be converted Into intensity noise by any optical path length imbalance 1n the interferometer, by

Δφ = Δω/C

However, 1n this Interferometer the path imbalance arises from birefringence effects, due mainly to bend induced birefringence in the fibre coll , and is thus only a few wavelengths. For path length Imbalance ~ Nλ, N an integer,

Nλ Δf

Δφ - 2ιrΔf 2τr N

so even for, say N 5, to achieve Δφ = 10~ ⁵ rad over 1MHz we need

e.g. for 830 n , f = 361THz, so need Δf = 100MHz.

This is well beyond the frequency noise characteristics of, for example, diode lasers. The Sagnac is thus Insensitive to

slowly-varying changes in laser frequency, compared with the loop propagation time, with a residual frequency noise floor arising from dynamic effects. Coherent Rayleigh Noise (CRN)

- due to delayed self-homodyne type mixing of the primary light and Rayleigh backscattering. If primary and backscattered light occupied the same polarisation state, this would lead to a phase error of

where I _ray = Rayleigh backscattered intensity

Idrc = Circulating intensity

B - Bandwidth f = Linewldth of source

Consider a loop of monomode fibre operated at 633nm with an attenuation of lOdB km ^-1 , most of which is Rayleigh scattered.

Backscattered power into fibre will be of the order of

ιr(N.A.) ²

= 10~ ³ of total scattered power n ² .4ιr (assuming isotropic scattering)

where N.A. = fibre numerical aperture n fibre refractive index

So for a 200m coil with a source having

Δf = 60MHz (L _c = 5m), φ _CRN = 5 x 10 ^"7 rad HZ - ^y *

Three main approaches are available which will reduce the level of CRN:

1. Longer wavelength source to reduce Rayleigh scattering (scales 1/λ ⁴ )

2. Broadband source : SLED, superfluorescent fibre or using a laser diode, simulate a low coherence by fast frequency modulation

3. Ensure that the polarisation state of the backscattered beam 1s orthogonal to co-propagat1ng primary beam over as great a fibre length as possible. Other noise 1s due to reflection from any fibre splice or discontinuity at the probe will result in the same type of delayed self-homodyne noise as CRN. Any reflections within a few coherence lengths of each other will also yield output signals varying due to source frequency noise and optical path length fluctuations within the fibre. Further, in a region within a coherence length of half way round the loop backscatter will be coherent with the primary light and will result in noise at the output with a spectrum corresponding to fluctuation of optical path length within the loop. These effects are minimised by avoiding reflections in the system, and following the same precautions as for coherent Rayleigh noise.

Laser amplitude noise will directly modulate any out of quadrature signal when antiphase outputs are subtracted. It would In principle be removed by analogue or digital division of the photodetector output by an Intensity reference. Such devices do not usually have sufficient dynamic range and bandwidth however, so the preferred solution is to use a quiet source. Three basic probe types have been considered for use in this interferometer: (Figure 3) (a),(b). This shows the Ideal case. Beams from both fibres F1.F2 are focussed on to overlapping beam waists. If the target is a smooth surface, efficient coupling between fibres is achieved for minimal back reflection. Disadvantages are complexity and difficulties in alignment.

In a further embodiment Figure 3(c), the probe beam is collimated, so a flat surface must be used. The system is nominally misaligned for d > focal length f but reasonable cross-coupling efficiencies can be achieved for minimal backscatter.

A still further embodiment, Figure 3(d), is the simplest of all three probe types with only the most basic alignment required. The directional coupler DC does waste power, however, and backscattering from target is as large as the cross-coupling. The source coherence time must therefore be much less than the loop propagation time.

We now compare the performance of above embodiments with that of the other velocity interferometers.

Consider the case where light from a source of angular frequency ω ₀ is reflected normally off a target moving with velocity v and then analysed by an unbalanced Michelson interferometer, with arms of optical path length L _lf L ₂ .

After target, ω ₀ is doppler shifted to ω _r » ω ₀ (1 + 2v/c). The phase difference between recombining beams is given by

ω _r ω _r 2 V φ = 2 (L ₂ -L _χ ) = 2 ΔL = - (1 + 2 - ) ω ₀ Δ 2.35 c c c c

so, presuming an adequate phase recovery scheme exists, the following phase dependences will be observed:

θφ 2 V ω.

2 - ω. for V <<c

3Δ _L c c

This system has three clear disadvantages compared to the Sagnac, in the measurement of low velocities:

5 1. It requires a source coherence length > ΔL, limiting the potential velocity sensitivity. 2. It cannot distinguish between frequency noise In the source and doppler shift due to surface vibration, unless a second reference cavity is used. 103. It 1s extremely sensitive to changes in path length imbalance. A change in ΔL of λ/4 results 1n a phase shift of -rr/2, leading to the stringent condition

3(ΔL)/ΔL << λ/4ΔL

15 e.g. for λ - 633nm, ΔL « 150m, λ/4ΔL * 10 ^-9

Path length stability Is a particular problem in fibre optic Interferometers, because of the strong temperature dependence of the fibre refractive index. 0 The Fabry-Perot interferometer has also been used with success to recover velocity Information from frequency shifts and is an obvious extension of the Michelson with the same drawbacks of source coherence, sensitivity to frequency noise and stringent stability requirements. 5 The Sagnac interferometer offers potential as a simple, passive laser doppler analysis (LDA) system which gives the sign as well as the magnitude of the appropriate velocity component of a seed particle. Consider such a system using probe type c:

A particle of velocity v along axis of probe, traversing the 0 beam waist, will produce pulses at the complementary outputs of I-^t), I ₂ (t) where I _χ + I ₂ gives the intensity of backscattered light and (I _χ - -^z^^ _i + I ₂ > gives the velocity, with appropriate sign, of the particle along the beam axis.

If Interference is to take place, it is essential that the 5 time that the particle spends in the beam, τ _p , is longer than

the loop delay Δτ. In order to see when this condition is fulfilled, consider a flow with seed particles of maximum velocity v _maχ . The loop delay can then be set to give a maximum dynamic phase shift of ~τr/4, ensuring linearity, a good signal to noise ratio and avoiding velocity ambiguity.

^2kv max ⁸ - ^{2ιr 1 6v} max vmax λ

The dimensions of the linear region L^ must thus be such that

L λ τ _p - >> Δτ ^• = 2.38 ^v max ^16v max λ 1e L* >> — 2.39

16

a condition which is automatically fulfilled for practical optical systems. The experimental arrangement is shown in Figure 2. It is similar to that described in the previous section with a loop 2 of length (L) of approximately 210m. A number of precautions were taken to reduce potential noise sources. The source laser S was Isolated from the Interferometer using a polariser and quarter-wave plate PQ to prevent returns from the Interferometer reflecting back off the laser output coupling mirror. Interference arising from Fabry-Perot cavities caused by Fresnel reflection at fibre-air interfaces was minimised using index-matching gel and microscope coverslips. Fibre connections were made by fusion splicing to reduce other unwanted reflections. The interferometer was acoustically, vibrationally and thermally shielded by embedding it in foam. The purpose of the second directional coupler C2 was to enable both measurement

of the reflected Sagnac output and monitoring of the power entering the loop.

A response proportional to target velocity, and hence proportional to frequency for harmonically oscillating targets of fixed vibration amplitude was demonstrated 1n "Closed-loop ¹ tests where the experimental arrangement was that of Figure 2 without the probe section. A vibrating surface was simulated by periodically stretching the fibre using a plezo-electric tube ⁽ PZT ⁾ , wound with approximately 50 turns of fibre. The PZT frequency response was measured 1n an ancillary experiment, using a Mlchelson fibre Interferometer. The frequency response was found to be approximately flat and linear from dc up to about 10kHz, above which frequency mechanical resonances were observed accompanied by strong nonlinearities. Interferometer tests were carried out over the linear frequency response range of the PZT. The two optical outputs, at PD1 and PD2, were found to vary in antiphase, 1n accordance with theory. This observation precludes the possibility that the observed output was due to intensity modulation, caused for example by bend losses in the fibre, rather than the predicted phase modulation. (Intensity modulation would cause the outputs to vary 1n phase). The complementarity of the outputs was checked by addition, with Independent gains to compensate for the signal reduction of one output due to 1t traversing the additional coupler. The addition did Indeed produce a line of reasonably constant intensity, with a slight modulation due to the non-ideal nature of the coupler Cl .

The sensitivity of the Interferometer was found to be dependent on the adjustment of the polarisation controller, in accordance with the theoretical prediction, such that it was possible to operate at any point on the transfer function and also vary the visibility of the fringes. The tests were carried out with the interferometer adjusted to Its quadrature point, where it exhibits maximum sensitivity. Because the detected optical phase in the Sagnac is a function of target velocity, we

expect the output photocurrents to be amplitude modulated to a depth proportional to the PZT modulation frequency at constant PZT output voltage. This is illustrated by the results shown in Figure 4 (normalised with respect to the PZT driver's output voltage). The superimposed straight line corresponds to a device sensitivity of 21.2 rad/ms ^-1 .

We developed two alternative techniques to determine the absolute change in optical path distance.

The first of these we term the 'Fringe Amplitude' method. By examination of equation (2.1) we see that the detected intensity at either of the Sagnac outputs at quadrature

(I.e. φ _B -τr/2) for a harmonically vibrating surface

(i.e. p _D = s sin ω _s ^ is given by,

^L qo 1 ± V _g sin (φ sin ω _s t) 3.1

now, assuming φ _D small, the modulation amplitude of the detected signal ; is given by,

^I qm ⁼ -tqoVs ³ ' ²

Due to the high visibility of the Sagnac output fringes, i.e. V _q « 1, the induced phase shift (in radians) is this given by

φS = 3.3

that is, by the ratio of the actual modulated signal amplitude to the fringe amplitude.

The second empirical way of determining the phase shift induced by the PZT is by the "Harmonics" method, whereby we compare the system outputs when the polarisation controller is

adjusted to set the operating point either at quadrature or at a turning point of the transfer function.

If the system 1s operated at a turning point then the extrinsic phase φ _B = ^■ 0 and, on making the small δ _D approximation, the detected signal,

φ _s ² sin ² ω _s t

It - Ito 1 ± V _t 3.4

which is a signal modulated at twice the frequency (and hence termed the Second Harmonic) of the output at quadrature (I.e. the first harmonic).

Therefore, the modulation amplitude,

h o ^v t? ^{s L} tm 3.5

Thus, by comparison with (3.2) and assuming V _t - V _q , 1t follows that the Induced phase shift,

The phase shift <p _s can be predicted using the expected values of dΦ/dV for the phase shifter and loop delay Δτ.

This type of PZT typically gives (52 ± 5)mradV- ¹ turn ^-1 at low frequencies. The 52 turns used here give a predicted dΦ/dV

« (2.70 ± 0.26)radV ^-1 . Total loop length here was estimated at

(210 ± 10)m, resulting in ΔT = (1.02 ± 0.05μs) yielding, for harmonic excitation,

A sample comparison of phase shift values induced in the closed-loop tests calculated by both the fringe amplitude and harmonics techniques shown in Table 1 illustrates that both methods agree with the prediction within experimental error. In practice the former was found more convenient to implement.

It 1s possible to calculate the peak velocity (v ₀ ) of the surface over the propagation time of the loop (Δτ) from the

Induced phase shift. That is, from equation (2.14), the peak induced phase shift amplitude,

r _ωσ Δl

*s = = 2-CkK.vV _Λ OΔ'τ sine 3.8

from which v ₀ may be determined If Δτ is known.

Velocities calculated in this manner for the closed-loop tests are given in Table 2.

Verification of the Sagnac's linear frequency response was confirmed using a Network Analyser to sweep the PZT driver's frequency from 100Hz to 100 kHz. The driver was shown to have constant output voltage up to 10kHz and the Interferometer a corresponding linear response - shown in Figure 5.

To show the device operating in a practical situation on a real moving surface a probe section (design c in Figure 3) was spliced into the loop as per Figure 2. The probe fibres were 3m long and the probe beams set afocal using a xlO microscope objective lens. A reflective element mounted on a small piezo-electric shaker (PZS) driven directly from a function generator was used as a target. The fibre to target distance was arbitrarly chosen to be 16cm and the measurement volume spot radius was approximately 1.6mm.

The probe was aligned to couple the counter-propagating beams back off the target into the opposite fibres and open- ^' .oop static-mirror tests performed at quadrature using the PZT in the loop to provide the phase modulation showed that the system gave

- 21 - the same response proportional to frequency as 1n the closed-loop tests but with an approximate 50% decrease 1n overall signal intensities due to the extra loss Introduced by Incomplete re-coupling back into the probe. Vibrating mirror tests were performed at sample resonant PZS frequencies and the Induced phase shifts calculated using the Fringe Amplitude method. The detected phase shifts ranged from 0.02 to 0.30 radians corresponding to peak target velocities of l.lm s" ^"1 to 15.6mms ^-1 . A typical set of antiphase outputs with vibration frequency 244kHz is shown in Figure 6. One output shows a modulation amplitude of (6.75 ±0.25)mV with a fringe amplitude of (37.5 ±2.5)mV and the other (4.25 ±0.25)mV of modulation with a full fringe of (25 ±5)mV. These correspond to self-consistent phase shifts of (0.18 ±0.01)rad and (0.17 ±0.02)rads respectively, and hence to velocities of (9.5 ±0.7)mms~ ¹ and (8.9 + l.Dmms ^-1 respectively.

The noise floor of the system was measured, in the absence of an external signal, and was found to be equivalent to a target velocity of around 50nms" ¹ Hz"" ^yι r.m.s. in the frequency range above 100kHz.

The Sagnac was found to give a null response at 935kHz thus giving Δτ « 1.07μs corresponding to a loop length L - 220m. We measured modulated signals from surfaces vibrating at frequencies 1n the range 90kHz to 1MHz limited only by the PZT response falling off beyond these frequencies.

The optical fibre Sagnac Interferometer may be adapted to form a passive velocimeter whose output is directly dependent on target velocity. Much lower velocities can be measured using this technique than is achievable using, for example, a Fabry-Perot interferometer, and the technique is much less sensitive to the effects of source frequency noise. We have demonstrated the operation of a practical fibre optic Sagnac velocimeter with a linear response for non-contacting velocity

measurement of vibrating surfaces. Its linearity was verified in tests with a simulated vibration signal up to 10kHz and we have shown it is possible to retrieve the signal from a real vibrating surface via a probe at frequencies at least up to 1MHz. Quadrature operation was maintained by a novel method involving the controlled Introduction of fibre birefringence. We have presented alternative designs which allow the technique to be applied in the measurement of fluid velocities.

Table 1

INDUCED PHASE SHIFT /rad

FREQ. FRINGE HARMONICS PREDICTED /kHz AMPLITUDE METHOD METHOD

Table 2

PEAK SURFACE VELOCITY /cms -1