**5.5 Dual FSI sensor implementation and results**

The second example of an FSI based sensor makes use of the Dual FSI concept. The prototype was designed to measure at a nominal distance of 50 m, within a 10 m interval (Cabral et al., 2010). As mentioned previously, for such a distance, in a traditional FSI implementation (single interferometer mode), the uncertainty is dominated by the two uncertainty components related to the sweep range measurement and, to achieve accuracies below 100 μm it would be necessary to increase significantly the complexity of the FP subsystem. The Dual FSI approach overcomes this limitation without a major increase in the complexity, simply by adding a long reference fibre in the reference arm of a measurement interferometer and using an additional (reference) interferometer to calibrate the fibre.

In order to provide the sensor with assembly flexibility, the prototype implementation comprises three subunits, mechanically decoupled, with an optical connection implemented by fibres:


Fig. 10 shows a picture of the Dual mode FSI sensor breadboard where is possible to identify the Laser & Detection, the FSI Head, the Optical Head unit and the long reference fibre housing.

Fig. 10. Dual FSI sensor breadboard, showing Laser & Detection unit (top left), the FSI Head (top right), the Optical Head (bottom left) and the long reference fibre housing (bottom right).

In the Laser & Detection unit, the laser is the StableWave™ Model TLB-7021 by NewFocus, based on a Littman-Metcalf design (1024 nm). This ECDL is fibre pigtailed, and can achieve a maximum 85 GHz mode-hop-free frequency sweep, resulting in a minimum synthetic wavelength of 3.5 mm. In terms of sweep speed, it is possible to perform the complete sweep range in 50 ms, using a triangular shaped modulation, without noticing any major change in the laser response. The laser has a good stability in the short-term (µs), shorter than 50 kHz, but a poor stability performance at the medium-term (ms), having a direct impact in the sensor performance (disturbances caused by acoustically excited mechanical resonances in the laser cavity).

The FSI Head starts with a Faraday Isolator to prevent any residual back reflection into the laser as the ECDL behaviour is highly sensitive to feedback. Next, the light is split to the interferometers and the FP. As mentioned before, the FP has a critical impact in the system performances. An air spaced confocal etalon was manufactured (by IC Optical Systems Ltd) in Zerodur with a cavity length of 50 mm, corresponding to a FSR of 1.5 GHz. In terms of Finesse, the selected high reflectivity coating produces a very thin resonance peaks, experimentally measured to be, at least, 4700. The measured level of thermal stability (approximately 10 mK) corresponds to a FSR stability of a few tens of Hz, two orders of magnitude lower than the requirement in the uncertainty of the FSR.

Fig. 10. Dual FSI sensor breadboard, showing Laser & Detection unit (top left), the FSI Head (top right), the Optical Head (bottom left) and the long reference fibre housing (bottom

In the Laser & Detection unit, the laser is the StableWave™ Model TLB-7021 by NewFocus, based on a Littman-Metcalf design (1024 nm). This ECDL is fibre pigtailed, and can achieve a maximum 85 GHz mode-hop-free frequency sweep, resulting in a minimum synthetic wavelength of 3.5 mm. In terms of sweep speed, it is possible to perform the complete sweep range in 50 ms, using a triangular shaped modulation, without noticing any major change in the laser response. The laser has a good stability in the short-term (µs), shorter than 50 kHz, but a poor stability performance at the medium-term (ms), having a direct impact in the sensor performance (disturbances caused by acoustically excited mechanical

The FSI Head starts with a Faraday Isolator to prevent any residual back reflection into the laser as the ECDL behaviour is highly sensitive to feedback. Next, the light is split to the interferometers and the FP. As mentioned before, the FP has a critical impact in the system performances. An air spaced confocal etalon was manufactured (by IC Optical Systems Ltd) in Zerodur with a cavity length of 50 mm, corresponding to a FSR of 1.5 GHz. In terms of Finesse, the selected high reflectivity coating produces a very thin resonance peaks, experimentally measured to be, at least, 4700. The measured level of thermal stability (approximately 10 mK) corresponds to a FSR stability of a few tens of Hz, two orders of

magnitude lower than the requirement in the uncertainty of the FSR.

right).

resonances in the laser cavity).

After the beam splitter that directs half the light to the FP, the light is split again towards a small connection fibre and the long reference fibre, both already part of the interferometers arms. Both fibres are PANDA Polarization Maintaining (PM) with FC/APC connectors (low return loss). All the fibres are located in the fibre housing, shown in Fig. 11, to ensure mechanical stability and increase (by inertia) the short term thermal stability.

The length of the long reference fibre, used in the Dual FSI interferometers, must be twice the distance we want to subtract to the measuring range (while the light in the measurement path performs a round trip in the reference fibre it only travels in one direction). A 71 m fibre was selected, allowing an OPL subtraction of approximately 102 m (corresponding to the difference between the reference fibre length and the measurement arm fibre of 1 m multiplied by the refractive index of the fused silica). The setup of the Optical Head is slightly different from the one illustrated in Fig. 2, as in the reference interferometer an additional retro-reflector (RRREF) allows the definition of the point from where the absolute measurement is referenced. Fig. 11 shows the optical setup of the implemented measurement (a) and reference interferometer (b). The position of the BS was chosen in order to make the measured OPD in the reference interferometer equal to the difference between the two fibres (FREF – FMEAS).

Fig. 11. The dual FSI measurement (a) and reference (b) interferometer.

The performances of the sensor result on the added contribution of the uncertainty in the reduced OPD measurement (by the measurement interferometer) and the long reference fibre calibration (by the reference interferometer).

The graph in Fig. 12 shows the results obtained with the contribution of the two mentioned uncertainty components. Each point corresponds to the 2σ dispersion (95% confidence interval) for 300 measurements. As shown, the contribution of the reduced OPD measurement is lower than 10 μm for the first few meters, and smaller than 30 μm for an absolute distance of 10 m.

To evaluate the component related with the calibration of the reference fiber, 2500 sequential measurements were performed, each with a duration of 100 ms. The measurement dispersion at 2σ was 554 μm for a mean value of 101 805 363 μm. The final uncertainty in the calibration of the fiber OPL is a function of the number of measurements that contribute to the calculated average length (and also the contribution of the FP FSR calibration uncertainty). The longer the duration of the calibration, the larger will be the decrease (by √N) of the uncertainty value resulting from the measurement dispersion. With a calibration period of 300 s (during which temperature was stable enough to consider a static OPL in the fibre), the uncertainty for the 101.8 m fibre OPL 31.2 µm (note that the contribution to the measured distance will be half of this value).

Fig.12 shows the uncertainty for the current dual FSI configuration using a 71 m fused silica fiber (101.8 m OPL) that allows a measurement range from 51 m to 61 m with accuracy smaller than 40 µm.

Fig. 12. Uncertainty for the current dual FSI configuration using a 71 m fused silica fibre (101.8 m OPL).

As it can be seen in Fig. 12, the improvements resulting from the Dual FSI concept compared to the expected results in a single FSI implementation are clear. Although the concept is limited by configuration to specific range intervals (determined by the length of the reference fiber), the enhancement in the measurement accuracy is about one order of magnitude.
