3 Experimental results

In this section, experimental data are presented which demonstrate how a single mode fiber can be used to assess the quality of a beam corrected by Adaptive Optics. We tested the coupling of a single-mode fiber to the 3.6m ESO telescope in La Silla, equipped with the ADONIS adaptive optics system (Beuzit et al. 1997). The aim of these tests was twofold:

To assess the gain provided by adaptive optics for the injection of starlight collected by a large pupil into a single-mode waveguide;
To use the SM fiber, in conjunction with a fast photometer, as a "Strehl meter" to monitor the rapid fluctuations of the corrected image.

The imagery infrared channel is focused underneath the ADONIS bench where the fiber injection setup has been installed. The optical layout is shown in Fig. 4.

$\begin{figure}\resizebox{8.8cm}{!}{\includegraphics{fig4.eps}} \end{figure}$

Figure 4: Optical layout to measure the coupling efficiency of the beam corrected by ADONIS and a single-mode fiber

Description of the test bench

The principle of the test is to extract part of the stellar beam to inject it into a single-mode fiber, and to perform a comparative photometry between the output of the waveguide and the direct image of the star. At the output of ADONIS, the corrected beam is thus amplitude divided on the BS1 beamsplitter:

The transmitted beam is transmitted again through BS2 and focused directly onto the detector (an InSb photometer);
The reflected beam goes through the holed mirror M13, is collimated by the spherical mirror M12 and injected with the off-axis parabola M15 into a small length (3m) of single-mode infrared fiber. A control unit is also present to help register the input fiber head, whose diameter is less than 10 $\mu$ m, and the star image. The output of the fiber is imaged onto the photometer by the lens L1, after a reflexion on BS2.

When the shutter located between BS1 and BS2 is closed, only the flux injected in the fiber is measured by the photometer. Conversely, the flux in the direct imagery channel can be measured by depointing the star from the fiber head. The ratio of the two fluxes provides, after calibration of the beamsplitter and additional losses (Table 1), the injection efficiency $\rho$ .

**Table 1:** Compared transmissions between the direct and the fiber channels
	Direct channel	Fiber channel


Reflexion of BS1 and BS2		$0.694 \times 0.734 = 0.509$
Transmission of BS1 and BS2	$0.306 \times 0.266 = 0.081$
Reflexion mirrors Al		(0.96)⁶ = 0.783
Reflexion mirrors Au		(0.98)² = 0.960
Pellicle beamsplitter transmission		0.92
Injection efficiency into the fiber		$\rho$
Fresnel losses at fiber/head interfaces		(0.96)² = 0.922
Signal attenuation in the fiber (30dB/km)		0.979
Fresnel losses on lens L1		(0.96)² = 0.922
Global transmission	0.081	0.293 $\rho$

The f-ratio of the injected beam depends on the focal lengths of the collimating mirror M12 and the off-axis parabola M15. Measurements were made at f/d=3.

Injection efficiency for an internal (static) source

**Table 2:** Coupling efficiency from a non turbulent point source with a circular core fiber (VF 1078) and a polarisation maintaining fiber (VF (MP) 1492)

Fiber		$\rho_0$


VF 1078	Theoretical efficiency	0.39
VF 1078	Measured efficiency	0.35
	(with static correction of the aberrations)
VF 1078	Measured efficiency	0.29
	(without aberration correction)
VF (MP) 1492	Measured efficiency	0.25
	(with static correction of the aberrations)

The first coupling tests were done with an artificial source, internal to ADONIS, that presents only static aberrations. Measurements made with a circular core fiber (VF 1078, $2a=10\,\mu$ m, $O\!N=0.16$ ) and a polarization preserving fiber (VF (MP) 1492, rectangular core $3 \times 8.5\,\mu$ m) are shown in Table 2. For a 3.60m pupil with a 1.57m central obstruction, and a f/d=3 input beam, the overlap integral (Eq. 1) of the Airy disk with the guided mode profile of the circular core fiber gives a theoretical injection efficiency $\rho_0=0.39$ . The f-ratio of the input beam is not optimal for this fiber: the maximum efficiency $\rho_{\mbox{\scriptsize max}}=0.49$ is obtained for f/d=4.3.

Residual aberrations in the imagery channel of ADONIS reduce the injection efficiency to below its theoretical value; by observing the image of an infrared diode set where starts the imagery channel, before observing the celestial source, one can minimize first order aberrations in this channel by introducing offsets in the interaction matrix; thus the injection efficiency depends mainly on the quality of the servo loop, which in turn depends on how well the interaction matrix between the sub-pupils slopes and the actuators was determined (Beuzit et al. 1997). The efficiency shown in the table ( $\rho_0 = 0.35$ ) is the value obtained with the best interaction matrix obtained by ADONIS. In the worst case we found $\rho_0 = 0.20$ . Finally, we found that the quality of the injection in a polarisation maintaining fiber ( $\rho _0=0.25$ ) is better than what could be feared from the very elongated morphology of the core, which does not fit well an Airy disk.

Injection efficiency for a turbulent stellar source

$\begin{figure}\resizebox{8.8cm}{!}{\includegraphics{fig5.eps}} \end{figure}$

Figure 5: Strehl ratio and injection efficiency for a stellar source (GM Lup) in a circular core fiber (VF 1078), at the 3.60m telescope in La Silla corrected by ADONIS. Note the presence of a modulation with a 0.04s period (25Hz) induced by a vibration of the telescope tube. The seeing was excellent and very slow (r₀ = 65cm and $\tau _0 = 0.4$ s in K). The reference efficiency for this setup was $\rho _0=0.25$ and was calibrated on the internal, artificial point source

$\begin{figure}\resizebox{8.8cm}{!}{\includegraphics{fig6.eps}} \end{figure}$

Figure 6: Another recording of the coupling fluctuations, in identical experimental conditions. The 25Hz modulation of the injected energy is now total

The observation of a stellar source enabled us to measure both the coupling efficiency $\rho$ and the Strehl ratio ${\cal S} = \rho / \rho_0$ (Eq. 11), after calibration of $\rho_0$ on the static internal source ( $\rho_0$ = 0.25 when ADONIS was installed at the telescope).

$\begin{figure}\resizebox{8.8cm}{!}{\includegraphics{fig7.eps}} \end{figure}$

Figure 7: Strehl ratio and injection efficiency for a stellar source (GM Lup) in a circular core fiber (VF 1078), at the uncorrected 3.60m telescope in La Silla

Thus for the first time it was possible to follow the fast fluctuations of the Strehl ratio in an image corrected by adaptive optics (Figs. 5 and 6). The coupled flux was found to be modulated with a period of 0.04s, whose instrumental origin was clearly testified. The intensity of the 25Hz component depended on the pointing direction of the telescope, but the vibration was still present when the AO was turned off (Fig. 7). It was concluded that the whole telescope tube vibrated at a rate too fast to be compensated by the tip-tilt mirror of the AO system. The fact that the modulation can reach 100% (as is the case in Fig. 6) means that the vibration amplitude can be greater than the diameter of an Airy disk in K, i.e. 150mas. When ADONIS is used for long exposure imaging as it is the case usually, the vibration cannot be directly detected, but induces a degradation of the Strehl ratio that can reach 70%. The frequency of 25Hz (or 24.8Hz as was later measured) was connected to a natural resonance frequency of the telescope mount, and following this diagnosis the problem was fixed.

Still, despite this limitation, the use of AO led to a major improvement of the time averaged Strehl ratio: $\left< {\cal S} \right> = 0.22$ (Fig. 5) to 0.70 (Fig. 6), depending on the modulation intensity, compared to an average Strehl ( $\left< {\cal S} \right> = 0.019$ ) without AO. The gain in coupling efficiency provided by the correction can therefore reach a factor 0.70 / 0.019 = 37. In the best cases, more than 20% of the stellar light collected by the 3.6 m telescope mirror was injected into the single-mode fiber, which is more than half the theoretical maximum expected of 39% for that telescope. Extrapolating this experimental result to a vibration-free VLT where the 8m pupils feature a proportionally small (1.2m) central obstruction (hence an expected theoretical maximum of 76%), one can predict that actual injection efficiencies of 40% should be achievable with very large telescopes.

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