**6. Conclusions**

74 Modern Metrology Concerns

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

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

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

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

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

absolute distance of 10 m.

smaller than 40 µm.

(101.8 m OPL).

measured distance will be half of this value).

This chapter showed that FSI is a particularly versatile technique for absolute dimensional metrology, allowing different approaches for different applications with different needs, both in terms of range and accuracy.

The concept has a simple model, experimentally validated, the results of which are presented in this work. There is an excellent match between measurements and computer simulations.. The model proved to be sufficiently robust to allow the setup of the different parameters and implementation concepts for particular applications.

The most critical issue in the FSI technique is sensitivity to drift. Whilst in a laboratory with a controlled environments (temperature, pressure and vibrations) it is possible to achieve conditions where drift can be neglected, the same does not applies to the majority of the applications (like the example of space instrumentation). The case of FSI as a low complexity sensor requires self-sufficiency in terms of drift compensation. A drift compensation method using two consecutive measurements was also presented. In addition to the compensation of the error introduced by drift, the method was also provides an efficient way to measure drift speed, using exclusively the same set of data.

In terms of FSI performance, the accuracy at small distances is determined by the capability to interpolate a synthetic fringe. To improve accuracy we must choose the smallest possible synthetic wavelength, corresponding to the highest possible mode hop free frequency sweep range. The sweep range and the measurement frequency (which defines the sweep duration) determine the required frequency sweep rate. Even in an ECDL (currently the fastest tunable laser), the sweep rate should not exceed a few thousands of GHz/s, otherwise sweep non-linearities will jeopardise sensor performance. Therefore, even if the laser is capable of a larger sweep, the measurement frequency will limit the minimum synthetic wavelength. A smaller synthetic wavelength also decreases the influence of the drift because it decreases the amplification factor.

For large distances, accuracy is determined by the uncertainty in the synthetic wavelength value, as this will be propagated through the large number of synthetic fringes. As the synthetic wavelength is measured by counting the number of FSR in a FP, its uncertainty is determined by the stability of the FSR and also by how accurately the resonance peaks are located. Whenever the range is limited to a region around a large distance, it is possible to achieve high accuracy at large distance using a Dual FSI sensor approach, maintaining the reduced complexity inherent to the FSI technique.

Frequency sweeping interferometry is therefore an essential method for absolute distance metrology, especially when complexity and robustness are critical drivers (a must in space metrology). The flexibility of its parameterisation is an important advantage of the technique, allowing the same device to be used for a wide variety of mission requirements.

### **7. References**

