5 Tests and results

Since the EMILIE spectrograph is not yet available, these tests cover only the beam-handling of FLAG; no radial velocities have been measured so far.

  

Figure 9: Step response. Perturbation: $\sim$0.8 arcsec on X-channel only

  

Figure 10: XY corrections which reproduce seeing-induced photocenter motions. 2.2 arcsec seeing, total time 5 s, star $\alpha$UMA, elevation $70\hbox{$^\circ$}$. Signals from output 2 in Fig. 8. Recording by computer with 1.5 ms RC time constant, 0.6 ms sampling interval

5.1 Autoguider performance

5.1.1 Laboratory tests

Using the tungsten lamp and a 2 arcsec FWHM Gaussian pattern, we tested each channel by introducing a known step-type perturbation. Figure 9 shows the response of channel X to an 0.8 arsec step function, for one particular PID adjustment. The image is re-centered in $\sim$15 ms and fully stabilized in $\sim$30 ms. The noise of this channel is estimated to 0.03 arcsec RMS. Altogether, FLAG qualifies as a moderately-fast autoguider.

5.1.2 Sky tests

Figure 10 shows the angular corrections in X and Y of the "guiding'' plates during a 5-seconds run on $\alpha$UMA. The average seeing for this night was 2.2 arcsec (measured with a CCD at another telescope). These corrections are almost equal to the before-correction image motions, except for the small residuals discussed below in Fig. 12. The power spectral density (PSD) of image motion along X axis is represented in Fig. 11. The dashed line shows the f^-2/3 power law for Kolmogorov turbulence (Martin 1987). One can see a spike around 8.5 Hz: this is a telescope resonance. Above 60 Hz, the curve drops to the system noise. Our autoguider seems to respond correctly up to 60 Hz.

  

Figure 11: Image motion spectral power density. Same data as Fig. 10. Dashed line shows slope expected for Kolmogorov turbulence

  

Figure 12: XY error signals. Same conditions as Fig. 10 but from Output 1 in Fig. 8. With FLAG correction (full curve filling central "knot''). Without FLAG correction(dashed curve)

In order to show the residual (after-correction) image motion, Fig. 12 gives the error signals in volts for the X- and Y-channel, again for 5 seconds on $\alpha$UMA, with and without FLAG. One minor drawback of our technique is the absence of any straightforward conversion of error signals to angular errors. While the centering point (for which the error signals are nulled) is stable and independent of seeing, the magnitude of these signals is not. However, let us assume the seeing remained stable from Fig. 10 to Fig. 12. Then, the large uncorrected fluctuation of Fig. 12 (with FLAG off) is statistically the same as the FLAG correction in Fig. 10. Identifying the RMS figures, we find that in Fig. 12 a 1 volt error signal corresponded to $\sim\! \!0.17$ arcsec for this particular combination of seeing and oscillation amplitude. From which the RMS residual photocenter motion with FLAG active (Fig. 12 central "knot'') is $\sim\! 0.05$ arcsec, which must include a small photon-noise contribution. On the other hand, a small component of photocenter motion above the system bandpass exists, but does not show on our curves.

The system worked without appreciable degradation up to an F8, M_v = 8.2 star, which is sufficient for our program of radial velocities. This limit actually came from the finder video camera. The limited tilt range of "guiding'' plates ($\pm 4$ arcsec) requires observer intervention 2 or 3 times per hour to cancel telescope drift; but these hand-made corrections produce no perturbation of error signals.

Most regrettably, no Z-error-signal recordings were made. However the Z-servo pulled back the telescope focus to the correct position after any manual step-perturbation. No residual image-size drift appeared on the finder video screen during full-night sequences. As expected from any noisy error signal, positive and negative corrections alternated randomly, the average interval was adjusted to roughly 10 seconds. In brief, the Z-channel mimics a well-behaved but slow autoguider.

5.2 Beam fluctuations at fiber output

The measuring system was the one already used for ELODIE (see Fig. 2) with minor changes due to the different fiber. Figure 13 shows a typical result, on $\alpha$UMA.

The quasi-Gaussian far-field is affected by telescope central obstruction, more so than in Fig. 3, which seems to indicate less FRD. The quasi-flat near field is affected by a narrow axial low-index zone in our 50 $\mu$m fiber (FG 050 GLA from 3M). Rays are rejected from this zone by total reflection, but no loss is induced.

Our original plan had been to compare FLAG performance to that of the common-user AURELIE-spectrograph CCD-guider (similar to the ELODIE one); unfortunately AURELIE had to be taken away before our observing run. Hence we had to rely on a second-best comparison, between FLAG and merely-manual guiding. FLAG was turned ON or OFF for stretches of a few minutes; when OFF, an operator kept the video star image centered through the telescope controls in the usual way, which at least removed telescope drift. The average interval between corrections was in the 5-20 seconds range, i.e. comparable to those of the automatic ELODIE device used for Fig. 5. The main difference with the CCD has not been in speed, but in somewhat-subjective centering. A 2-hour sequence of 91 short exposures (60 s), with 2.2 arcsec average seeing, is shown in Fig. 14, giving the geometrical fluctuations of the near- and far-fields.

  

Figure 13: Output beam cross-section with star (152-cm telescope, 50 $\mu$m fiber). Near-field: left; far-field: right. Two windows ($160\times 160$ pixels each) used for computation are shown. 50 $\mu$m and f/2.55 indicated dimensions are reduced to fiber output

The average intensity is $\sim\! 23\%$ greater with the auto- guider ON. This gain agrees well with the figure given by Hecquet & Coupinet (1985) for $D/r_{\rm o} \sim 33$. The parameter M₁ (first order momentum of the near-field) give some information about the width of the image. One sees in Fig. 14a that M₁ increases during hand-guiding intervals. This means that the star image at the fiber input is degraded and widened by seeing plus tracking errors during an exposure. On the practical side, this 23% gain does no more than compensate roughly for the FLAG losses discussed in Sect. 4.1.

  

Figure 14: a) Near- field geometrical fluctuations. INT1: image intensity in ADU. M1: first order momentum in nm. X1, Y1: photocenter motion in nm. b) Far-field geometrical fluctuations. M2: first order momentum in 100 $\mu$rad units. X2, Y2: photocenter motion in 10-$\mu$rad units. Vertical lines show limits of manual guiding intervals, marked M

Data of Fig. 14 were separated in two sets corresponding to FLAG- and hand-guiding- intervals respectively. The RMS residuals from a 3rd-order polynomial fit were computed and are presented in Table 1. FLAG reduces the RMS fluctuations by factors of 2 to 4.

Of course, from these results, we would like to predict residual RV fluctuations given by some future spectrograph, but this is frankly difficult. Only in the case of the near-field X₁, Y₁ can we make a try. A 10 nm photocenter motion corresponds to 1/5000 of the fiber diameter. With EMILIE, this diameter will be imaged on (roughly) one pixel, which has 1500 m/s velocity width; then our 10 nm will induce 0.3 m/s RV change. Unfortunately, it is impossible to make similar predictions from the remaining parameters M₁, X₂, Y₂, M₂, or from any others (the beam cross sections have been stored for later analysis). As stressed in Sect. 1, this would require an exceedingly accurate model of spectrometer aberrations and adjustment. Furthermore, as any minor change in spectrometer focusing etc. wrecks the prediction, one doubts the effort would be worthwhile. Altogether, it is safe to assume that the RV fluctuations from M₁, etc. may prove distincly larger than those just computed from X₁ and Y₁. We have seen that in the ELODIE case, the near-field fluctuations alone contributed to $\sim\! 4$ m/s RV change, whereas the measured radial velocity fluctuations reached $\sim\! 9$ m/s. On the other hand, addition of a double scrambler should give some further improvement.

 

Table 1: RMS computed from a 3 orders polynomial fit for each the parameters of Figs. 14a and 14b

With the ELODIE 100-$\mu$m fiber, we found (see Sect. 3.3.2) that the RMS fluctuations of the near-field were equal to 1/1800 of the fiber diameter. This figure seems to confirm that the autoguider brings a gain of $\sim\! 3$ in the fluctuations of the stellar beam at the output of the fiber. Since our 50-$\mu$m fiber reduces the star image motion by a factor 100, this means that these motions are about 1 $\mu$m RMS, or 0.05 arcsec, which is the RMS residual photocenter motion with FLAG active.