**5.4 FSI sensor implementation and results**

The first example of an FSI based sensor was designed to measure the OPD between two sub-telescopes of a multiple aperture optical telescope (Cabral & Rebordão, 2007). The implemented setup is sketched in Fig. 7. In the case of an absolute OPD measurement the result may be either positive or negative. The sign of the absolute OPD is thus required and must be measured. To overcome the ambiguity, a calibrated offset distance is created in arm A (A' = A + Offset) of the interferometer (Fig. 7) ensuring that A'-B > 0, always, with the cost of increasing the maximum range (the Offset must be larger than half of the measurement range). The real distance difference is obtained by subtracting the calibrated Offset value.

Fig. 7. Setup of the implemented FSI absolute sensor.

A Faraday isolator (FI) prevents feedback from the interferometer components back to the ECDL laser, and an anamorphic prism pair (AP) circularizes the elliptical cross section of the beam. The beam is then split by the first beam splitter (BS): one part is reflected to the sweep range & power monitoring measurement subsystems and the remainder is transmitted to the interferometer. A second BS splits the reflected beam into the power monitoring detector (D1) (reflected part) and the FP Interferometer that includes D2 (transmitted part). The beam transmitted to the interferometer is filtered by the spatial filter (SF) and collimated by lens (L); before entering the interferometer, it goes through a half have plate (HWP) and a 45º oriented polarizer (P). These two elements enable the original vertical polarized light to be rotated by 45º. After the interferometer beam splitter, two quarter wave plates (QWP) transform the reflected vertical and transmitted horizontal polarized into circular polarized light that, after reflection in the retro-reflectors (RR) and another passage through the QWP, are redirected towards the detector (D3). Before the detector, a 45º polarizer (P) enables interferences.

Fig. 8. FSI prototype implementation of the setup described in Fig. 6.

Fig. 8 shows a picture of the implemented prototype. The tunable laser is an ECDL capable of a mode-hop-free sweep range up to 150 GHz (TBL-7000 from NewFocus in a Littman-Metcalf mounting at 633 nm), corresponding to a synthetic wavelength down to 2 mm. The FP has a free spectral range of 1 GHz (TOPTICA high resolution, temperature stabilized, confocal Fabry-Pérot with a real finesse up to 1000). The FP was calibrated using the sensor hardware by means of two absolute measurements and a relative calibrated distance measurement between the two absolute positions, a kind of self-calibration (Cabral & Rebordão, 2006). This is a simple procedure and thus highly convenient to be implemented in space applications.

The graph in Fig. 9 shows the typical results obtained with this sensor. Each point corresponds to 200 consecutive measurements (with sweep duration of 100 ms) and a 2σ m for distances up to 1 m, increasing with distance as expected. Results confirm model predictions (continuous line) for δ*N* = 1/500, δ*FSR* = 6 kHz, and δ*r* = 1/3000 (consequently δΛ = 14 nm). Measurement uncertainty is well below the 10 μm level.

Similar tests were performed for the dynamic mode that confirmed the efficiency of the compensation model, even in the presence of a non-constant drift speed (Cabral & Rebordão, 2007).

transmitted to the interferometer is filtered by the spatial filter (SF) and collimated by lens (L); before entering the interferometer, it goes through a half have plate (HWP) and a 45º oriented polarizer (P). These two elements enable the original vertical polarized light to be rotated by 45º. After the interferometer beam splitter, two quarter wave plates (QWP) transform the reflected vertical and transmitted horizontal polarized into circular polarized light that, after reflection in the retro-reflectors (RR) and another passage through the QWP, are redirected towards the detector (D3). Before the detector, a 45º polarizer (P) enables

Fig. 8. FSI prototype implementation of the setup described in Fig. 6.

δΛ = 14 nm). Measurement uncertainty is well below the 10 μm level.

Fig. 8 shows a picture of the implemented prototype. The tunable laser is an ECDL capable of a mode-hop-free sweep range up to 150 GHz (TBL-7000 from NewFocus in a Littman-Metcalf mounting at 633 nm), corresponding to a synthetic wavelength down to 2 mm. The FP has a free spectral range of 1 GHz (TOPTICA high resolution, temperature stabilized, confocal Fabry-Pérot with a real finesse up to 1000). The FP was calibrated using the sensor hardware by means of two absolute measurements and a relative calibrated distance measurement between the two absolute positions, a kind of self-calibration (Cabral & Rebordão, 2006). This is a simple procedure and thus highly convenient to be implemented

The graph in Fig. 9 shows the typical results obtained with this sensor. Each point corresponds to 200 consecutive measurements (with sweep duration of 100 ms) and a 2σ m for distances up to 1 m, increasing with distance as expected. Results confirm model predictions (continuous line) for δ*N* = 1/500, δ*FSR* = 6 kHz, and δ*r* = 1/3000 (consequently

Similar tests were performed for the dynamic mode that confirmed the efficiency of the compensation model, even in the presence of a non-constant drift speed (Cabral &

interferences.

in space applications.

Rebordão, 2007).

Fig. 9. FSI experimental measurements 2σ error in static a mode.
