Autoguider locked on a fiber input for precision stellar radial velocities

Astronomy and Astrophysics Supplement Series, Jul 2018

Measurement of stellar radial velocities (RV) is one acknowledged approach for planetary-search and asteroseismology programs. We study the incomplete scrambling action of a fiber feeding a spectrograph, which leaves RV errors at a level of few m/s. Observations realised with the ELODIE fiber-fed crossed-dispersion spectrograph at the 193-cm telescope of Observatoire de Haute-Provence (OHP) are presented. A fiber-locked autoguider (called FLAG) has been specifically built to reduce the stellar-beam geometrical fluctuations within the spectrograph. With FLAG, the fiber-input plays the role of guiding detector. Automatic focusing is also accomplished by the system. The design and performance characteristics of the instrument tested at the 152-cm telescope of OHP are reviewed here.

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Autoguider locked on a fiber input for precision stellar radial velocities

Astron. Astrophys. Suppl. Ser. Autoguider locked on a velocities? F. Bouchy P. Connes Service d'Aeronomie du CNRS Verrieres-le-Buisson Cedex France e-mail: Measurement of stellar radial velocities (RV) is one acknowledged approach for planetary-search and asteroseismology programs. We study the incomplete scrambling action of a ber feeding a spectrograph, which leaves RV errors at a level of few m/s. Observations realised with the ELODIE ber-fed crossed-dispersion spectrograph at the 193-cm telescope of Observatoire de Haute-Provence (OHP) are presented. A ber-locked autoguider (called FLAG) has been speci cally built to reduce the stellarbeam geometrical fluctuations within the spectrograph. With FLAG, the ber-input plays the role of guiding detector. Automatic focusing is also accomplished by the system. The design and performance characteristics of the instrument tested at the 152-cm telescope of OHP are reviewed here. atmospheric e ects | instrumentation; spectrographs | techniques; radial velocities | stars; oscillations | planetary systems 1. Introduction We consider here planetary-search or asteroseismology programs. With CCD-equipped crossed-dispersion spectrographs, photon noise permits in principle to measure the radial velocity (RV) changes of many stars using relatively small telescopes with a precision of the order of 1 m/s (Connes 1985; Brown 1990) . In order to achieve this precision in practice, steps must be taken to control many sources of instrumental errors. A major one is due to the motions of the star image across the spectrometer input due to telescope-guiding or seeing fluctuations. The slit width in a high-resolution echelle spectrograph, in RV units, is typically a few km s−1. Thus, if the photocenter of the star image su ers a shift equal to 10−3 slit width, errors larger than 1 m/s will occur. Since the slit width projected on the sky is typically a few arcsec, it seems that milli-arcsec guiding precision is required. One very successful method makes use of a molecular absorption cell to impress lines of stable wavelength on the incoming starlight (Butler et al. 1996; Cochran & Hatzes 1994; Walker et al. 1995) . The stellar and reference spectra are then recorded from the same beam, thereby circumventing the problem of the photocenter shift. However this approach increases considerably the photon-noise RV errors, hence requires larger telescopes for a given star. Another method, which avoids this drawback, makes use of a beroptic feed for the starlight, plus a second ber carrying light from a stable wavelength source (Mayor & Queloz 1995; Brown et al. 1994) . One may also use a single ber alternately for both beams, as intended for the \absolute accelerometry" (AAA), proposed by Connes (1985) and developed by Schmitt (1997) . Unfortunately, the scrambling action of a ber reduces but does not cancel the stellar-beam geometrical fluctuations within the spectrograph. The use of a double- ber scrambler is a current partial cure. The present paper is devoted to a study of these e ects, and to the description of another partial cure: a ber-locked auto guider (called FLAG), in which the ber-input plays the role of guiding detector. Several fast-guiding (or so-called \tip-tilt") systems have recently been described (e.g. ISIS, DISCO, HRCam, AOC, FASTTRAC, UH/Ifa1). In all cases, the goal is reduction of stellar image size as recorded over \long" exposures (i.e., seconds or minutes) through elimination of fast photocenter wandering. The overall improvement may be as large as 2, for small values of the FRIED ratio D=ro. An even greater gain is realized from adaptive optics (AO), which eliminate not only photocenter motion, but also instantaneous image blurring from wave- et al. 1999), and the results are discussed in Sect. 5. The front distortion; this is achieved at the cost of many servo system is fully compatible with a double-scrambler, but channels, hence far greater complexity. has not yet been used with one. The goal of FLAG is di erent. Image size reduction by itself will be welcome, as leading to either more photons in the spectrometer, or higher resolution or both. 2. Scrambling properties of ber However, with meter-size telescopes in the visible, the improvement may be small at best: e.g., in our Sect. 5.1.2 A review of bers in astronomy has been given by Heacox tests, D = 152 cm, ro = 6 cm, and Hecquet & Coupinot & Connes (1992). Fiber-fed spectrographs use multi-mode (1985) predict a reduction of 1.25 in image diameter. (MM) step-index bers with core sizes typically in the Furthermore, except for the fainter stars within the RV 50- to 500- m range. One property of bers, discussed by program, the results will not be limited by photon noise Ramsey (1988) and Barden (1995) , is focal ratio degradabut by \scrambler noise". Hence, stabilisation of the ber- tion (FRD). A ber tends to increase the divergence (or ouput beam is our prime goal. Moreover, a planetary- \speed") of the beam it carries. This causes either a loss search program involves a large number of \exposures", of light if the exiting cone of light over lls the spectrostretching over years; hence, it is not for minutes but for graph collimator, or a loss of resolution if the collimator is years that we want to keep our beam stable irrespective of replaced with one matching the faster focal ratio. Largerdrifts in the autoguider, possibly even of guiding-detector core bers do appear to have better FRD characteristics changes. For the same reason, we also want to correct than smaller-core ones. Faster input focal ratios are better focus position. preserved than slower ones. One other signi cant charac A last di erence: image size improvements from the teristic of ber optics is their ability to scramble the inabove tip-tilt devices may be predicted from atmospheric put image. The geometry of cylindrical bers introduces turbulence models, and actual agreement is not too bad. two dimensions of scrambling, azimuthal and radial. Both Here, the situation is far more complex: the beam is fed theory (Heacox 1987) and experiments (Hunter & Ramsey not to a plain imaging camera, but to a camera through a 1992) suggest that step index MM bers provide a high ber rst, and a spectrograph second. There is no practical degree of azimuthal scrambling but an incomplete radial way of modeling the overall optical system with the pre- scrambling. Image scrambling improves with an increase cision required here. Presently, all ber-plus-spectrograph of the ber FRD. If the input focal-ratio is fast enough to stellar-RV programs (including ours) are stuck at an er- give little FRD (and this is the case in ber-fed spectroror level of a few m/s: this state of a airs could not graphs), then the input image will be poorly scrambled, have been predicted from any theoretical calculation, and and the output beam preserves some memory of the input still cannot be accounted for quantitatively. This situation beam shape and position. may change drastically in the future, should AO devices Our laboratory tests on a 50 m step index MM ber, progress enough to give acceptable STREHL ratios down and also tests by Casse (1995) on a 300 m ber, both to 400 nm for a 1 or 2-m telescope. As pointed out in measure the photocenter of the near- eld versus a known Sect. 2, we may then feed the spectrometer with a single- displacement of the input beam. We found independently mode (SM) ber, which acts as a perfect scrambler; the that the motion of the output photocenter may be of the output-beam (easily computable) will then be fully stabi- order of 100 times smaller than that of the input photolized, irrespective of any input-beam fluctuation, and even center, with adequate beam and ber parameters. of residual AO errors. This imperfect scrambling is inadequate when the goal Returning to the present day, the intent and limita- is 1 m/s precision. The near- eld pattern of a ber is detions of FLAG may now be better understood: Unlike the ned as the brightness distribution across the output face builders of the current tip-tilt systems, we cannot put a of the ber. In most cases a spectrograph images this outnumber to the expected improvement; worse, we cannot put face directly onto the detector; then variations in ileven hope to demonstrate a large one within the short lumination introduce small changes in pixels illumination time range of the observations reported here. Like them, which lead to radial velocity shifts. A higher-resolution we are doing the best we can with a simple device, which spectrograph reduces these errors, because given image risks obsolescence from future AO progress. shifts on the pixels induce smaller wavelength shifts than A brief review of the scrambling properties of step- in a lower-resolution spectrograph. index bers and their use in astronomical spectrographs The far- eld pattern is de ned as the cross-section of is given in Sect. 2. In Sect. 3, we present our own mea- the beam far from the output face. Far- eld variations surements of stability of the stellar beam within the are projected onto the spectrograph collimator, and cause ELODIE ber-fed spectrograph, using an available but in- changes in grating illumination. Then, spectrograph aberadequate standard autoguider based on a CCD detector. rations and grating imperfections induce small varying In Sect. 4, we describe our prototype FLAG, built for the RV shifts. To increase scrambling, one may incorporate new spectrograph EMILIE (under construction, Bouchy a double- ber scrambler (Brown 1990) , in which a pair of bers is coupled together using a pair of microlenses, separated by their common focal lengths. The bers then see each other at in nity, causing the near- and far- elds to be interchanged. Brown et al. (1991) found that their doublescrambler eliminated temporal variations in grating illumination that were responsible for roughly 5 m/s RMS velocity noise in their spectrograph and increased the precision of radial-velocity observations by a factor of about 3 over a single ber, to the expected shot-noise-limit. The same double scrambler was laboratory-tested by Hunter & Ramsey (1992) . Their results show that intensity variations across the near- and far- eld patterns due to both angular and positional changes in the input beam were reduced by a factor ranging from 2 to 10. Casse (1995) laboratory-tested a similar double-scrambler and found a scrambling gain of about 5 in the near- eld pattern. The decreased radial-velocity noise provided by these doublescramblers is not without drawbacks: the main problem is low throughput. The transmission estimated both by Hunter & Ramsey (1992) and Casse (1995) is between 20 and 25%; Brown (1994) mentioned 66%. A somewhat different double-scrambler was incorporated in March 1997 at the input of the ber-fed ELODIE spectrograph by D. Kohler. Its throughput is about 75% but the overall gain in radial-velocity precision deduced from our own observations is only about 1.5. According to Mayor and Queloz (private communication) the current long-term precision limit of ELODIE is now not due to the scrambler but related to the thermal and mechanical variations of the instrument. Probably their relative long exposures (greater than 10 minutes) averages the scrambler noise. In our case, with time exposure less or equal to 1 minute, we are not convinced that a double-scrambler is su cient. Another solution (proposed by Connes et al. 1996) , will cancel \scrambler noise" altogether. It makes use of a single-mode (SM) ber which (unlike a MM ber) acts as a perfect SM spatial lter: all cross-sections of the output beam are quasi-Gaussian and preserve no memory of the input beam geometry. Hence a SM ber behaves as an ideal scrambler. It may be matched to the Airy pattern at the focus of a di raction-limited telescope, irrespective of its diameter, with an e ciency of about 80%. On the ground, this solution is limited to a telescope pupil smaller than the \Fried diameter" (roughly 12 cm in the visible for 1 arcsec seeing), or requires AO. Such systems are so far limited to the infrared. Altogether, while the association of an SM ber and AO o ers a de nitive solution of our problem, it cannot be tried presently. 3. Fluctuations of the stellar beam at the output of the ber feeding the ELODIE spectrograph 3.1. ELODIE spectrograph A full description of ELODIE is given by Baranne et al. (1996). This is a ber-fed spectrograph within a stable temperature-controlled environment, located at the 193-cm telescope of Observatoire de Haute-Provence, in France. Using a 102 408 mm echelle and a 1024 1024 CCD, it samples a spectrum between 389 and 681 nm (67 echelle orders) with a spectral resolution of about 42 000. The pixel velocity-width is about 3000 m/s. The 100 mcore ber input accepts 2 arcsec from the sky. The beam aperture is converted to f/5 by transfer optics in order to feed the ber, located at the f/15 Cassegrain focus, and then brought back to f/15 at the spectrograph input. At the focus of the f/3 camera lens, the geometrical spot diameter is 60 m corresponding to a velocity-width of about 7500 m/s. It is feasible to record simultaneously star and reference spectra with two bers, the outputs of which are displaced by few pixels in the direction of cross dispersion, and orders for both spectra alternate over the CCD. For our observations, we introduce the channelled spectrum from a Fabry-Perot (FP) etalon illuminated by a white-light source (Fig. 1). With invar spacers and temperature stabilization within 10−2 K, the FP-induced velocity error is about 3 m/s but appears only as a slow drift during a run. Two kinds of recordings are possible: FP/FP spectra (with the FP beam on both bers) and STAR/FP spectra. We record simultaneously the two spectra, extract the echelle orders, and compute the RV change relative to a reference exposure. In order to get meaningful RMS errors within a few hours, and also to check the suitability of ELODIE for studying stellar oscillations, we used a large number (a few hundreds) of short exposures (60 s) on a given star. A full description of our RV measurements with ELODIE has been given by Connes et al. (1996) . The autoguider is the common-user 193-cm-telescope device, the principle of which is standard: a tilted concave mirror pierced with a hole corresponding to 2 arcsec on the sky allows the ber to be fed and, at same time, the outer part of the image to be reflected onto the VIDICON guiding camera (see Fig. 1). Initial image centering is done manually from the video-screen image; then the autoguider is locked on. An HP1000 computer calculates the coordinates of image centroid and triggers relays which operate the ne-guiding telescope motors (with step unit 0.1 arcsec) in order to return the image to the center position. In general, an average of many video images is used before making a correction, which reduces by integration the guiding-camera noise, smooths out the e ect of seeing, and damps the telescope response. Corrections are performed once every few seconds, which means (in our case) at least 10 corrections per spectrograph exposure. The system does not measure seeing. 3.2. Observations and data reduction In a previous study, Connes et al. (1996) have measured apparent fluctuations in stellar velocities with ELODIE. For bright stars, these were much higher than the photon noise. This e ect did not appear when a spatially stable reference beam was used instead the star. An imperfect scrambling of the stellar beam (\scrambler noise") was obvious. Here, we attempted to quantify the geometrical time-fluctuations of the output beam of the stellar ber. For this experiment, about 30% of the output beam was taken with a beam-splitter located within the spectrograph, and the near- and far- elds of the stellar ber output were re-imaged on the same 381 286 CCD. A sketch of the optics is shown in Fig. 2, and a typical image in Fig. 3. In order to detect unusual problems in time to correct them during the observing run, an on-line data treatment was applied. Images were reduced directly after each exposure, and also saved on a PC disk for future analysis. The program computed for each eld (limited to a speci c window on the CCD) the XY photocenter, the rst order momentum and the intensity average within the window. The di erences between these parameters and those computed from a reference image taken at the beginning of the run were displayed on-line. Fluctuations are presented in nanometers for the near- eld, in microradians for the far- eld; relative changes are also given. We estimate that our system could measure CG motions of about 1/1000 pixel, which means about 1 nm on the output face of the 100 m- ber. Acquisition of each eld pattern was synchronous with spectrograph exposures, in order to compare the di erent image parameters with the RV measurements. 3.3. Results 3.3.1. Fabry-Perot etalon beam Our rst experiment used the white-light source and FP etalon only. Hence, the beam falling on the ber input was geometrically stable during a run. We took simultaneous 62 seconds exposures with the spectrograph 1kx1k-CCD detector and with our Fig. 2 381 286-CCD detector. The lost time from readout plus computation was 40 s, hence the cycle time was 100 s and the sequence took about 5 hours. Figure 4a presents the X, Y near- eld photocenter shifts in nanometers versus time. The slow drift is attributed to mechanical relaxations and temperature drifts mostly within the Fig. 2 optical system, hence is uninteresting. We t our data with a 3rd-order polynomial and nd a fluctuation of 5 nm RMS, roughly explainable by photon noise. Figure 4b presents the di erence between the two spurious-RV curves, obtained with FP light on both bers, relative to a previously exposed reference spectrum and computed from a single echelle order (centered at 571 nm, and covering 6.1 nm). Such a test is of course independent of any FP drift. The slow trend shows that the two- ber setup does not compensate fully spectrograph drift (as already shown by Connes et al. 1996) . The residual may arise from a nanometer-scale relative drift between the two bers outputs; it may also involve data treatment and non-identical sampling of the two spectra by the CCD since the absolute drift (for both bers) was about 100 times larger (see Fig. 3 of Connes et al. 1996) . The best cure should be alternate use of the same ber for both beams. The fast residuals (0.82 m/s RMS) come mostly from photon noise, as shown by the fact that they decrease as expected when the RV from many orders are averaged. 3.3.2. Stellar beam We now have star light on ber F2 and FP light on F1. The star γDRA (Mv = 2:2, K5III) was selected because it could be observed all night. A sequence of 130 similar 62-s exposures with 111-s cycles was recorded. Figure 5a presents near- eld X and Y photocenter shifts, Fig. 5b the radial velocity (from a single order, after subtraction of 2nd order polynomial, as only fast fluctuations are of interest here), Fig. 5c the mean intensity for the same order, plus star elevation. The seeing could not be monitored continuously, but did not seem to depart greatly from the usual OHP gure of 2 to 2.5 arcsec. Two main remarks: 1) Missing data points correspond to electronic failures of the Fig. 1 removable mirror system; they are unrelated to guiding problems. 2) Even with the guider ON, the stellar image was invariably seen to drift relative to ber input on the video screen, which indicates poor stability of something in the guider optics. Whenever this drift seemed excessive (i.e. approaching image size), the guider was stopped for few seconds, and the guiding point recentered, again from the video image. Major peaks (marked by arrows) indicate these operations. These irregular and irreproductible guider incidents contribute a major part of the measured RMS, both for X, Y and for the RV. Here we get 9.26 m/s; in our older tests (Connes et al. 1996) , with similar seeing, we had found 6.2 m/s. Lastly, although a large part of the intensity fluctuations arose from changes in seeing and/or transparency, some peaks are correlated with those in Fig. 5a while the reduction of intensity is minimal. Hence, guiding errors not only decrease the intensity of the stellar beam but also change the geometry of the beam in the spectrograph, and degrade the RV results. If we suppose that the 100- m ber reduces the star image motions by a factor 100 (as in Sect. 2), this means that these motions are about 5 m RMS, which corresponds to 0.1 arcsec; this is the step-size of the ne-guiding telescope motors. 3.3.3. More guiding problems Two other severe drawbacks of the 193-cm telescope au toguider for our program were also noted: First, the autoguider does not check nor correct focusing. The size of the video image is seen to drift, and manual focus corrections produce similar RV breaks. Second, this autoguider fails to work with alternate illumination of ber F1 by the star- and FP-beams; operation of the Fig. 1 removable mirrors is not possible within a sequence such as those of Figs. 4 or 5. We have seen that mere use of the second ber F2 for the reference beam leaves uncorrected errors of a few m/s. As far as a search for stellar oscillations during a given night is involved, these problems are likely to nd simple solutions. For instance, no obnoxious guider drift is mentioned by Brown et al. (1994) , whose RV records also cover a few hours. Our 193-cm telescope has a Pyrex-type mirror; with a ZERODUR one, short-term defocusing might become negligible. However, irrespective of any guider improvements, similar di culties are bound to arise during a long-term planetary search. For instance, the VIDICON will soon be replaced by an intensi ed CCD; this will mean a RV break. So far, within any very-long-term program, stellar image centering and focusing are performed from qualitative eye-only estimates. The AAA technique involves use of a wavelengthsliding reference spectrum, reducing the spectrograph role to the classical one of a null-checking device. It eliminates all internal spectrograph problems; even a CCD replacement at spectrograph output should become irrelevant. However, a geometrically-stable stellar beam, alternating with the reference beam, is still essential at the spectrograph input. In order to guarantee that performance over the long term (several years), a sizeable e ort was clearly required to solve the guiding problem. Altogether, an autoguider making use of the ber input itself as a nullchecker of stellar-image XY Z-position appeared best, as it should solve guiding and focusing di culties simultaneously. Such a system is now to be described. 4. Fiber locked auto guider (FLAG) The goal of FLAG is to cancel at ber output all ef fects arising from stellar-image photocenter XY Z motions. Admittedly nothing is done about instantaneous image blurring, which should then become responsible for any remaining perturbations. 4.1. Principle The ber input itself plays the role of position detector. One introduces two small oscillations of stellar image in two perpendicular directions X and Y , with frequencies Fx and Fy. A small translation of a lens on its axis produces a Z-translation of the image, hence a focusing change with frequency Fz . At the output of the ber, any type of single-pixel intensity detector generates a modulated signal; it uses the NIR through a dichro¨c beamsplitter. Three synchronous demodulators at frequencies Fx, Fy and Fz reconstruct three DC error signals SX, SY and SZ. The rst two are applied to some fast tip-tilt device, while SZ may go either to the Z-lens, or to the telescope secondary-mirror motor. The image oscillations widen the seeing pattern, hence induce some loss at ber input; numerical simulation for a single X or Y parameter is shown by Fig. 6; for Z the curves are similar. When all 3 channels are active together, and at least for amplitudes ber radius (as used in practice), the error signals remain the same, with little crosscoupling, while the overall e ciency is the product of the individual ones. Oscillation amplitude is adjustable at will, and the optimum trade-o depends on stellar color and magnitude. In practice, we have kept constant amplitude, obtained nearly constant performance, up to Mv = 8, and measured a 6% loss by switching all three oscillations on and o . The dichro¨c loses another 15% of the visible beam. There are some possible variants, all untried so far: With minor changes, a photon-counter could be substitued. A single frequency might be used for X and Y , with 90 phase di erence; image trajectory would then become a circle rather than a Lissajous pattern. Instead of a dichro¨c, a weak achromatic beamsplitter might bleedo a small fraction of the visible beam. Finally, a double scrambler might be incorporated without any change of the system. 4.2. Optical system Our design was intended for the Coude focus of the 152-cm OHP telescope (Fig. 7); furthermore, it made use Fig. 7. Autoguider optics: 1) tungsten lamp, 2) circular Gaussian-pattern screen, 3) simulated telescope-pupil stop, 4) commutation mirror, 5) guiding plates (10 10 20 mm), 6) scanning plates (5 5 5 mm), 7) eld lens, 8) translating achromat, 9) dichro¨c, 10) guiding detector, 11) atmospheric dispersion compensator, 12) beamsplitter or removable mirror, 13) nder video. Commutation mirror is removed for star beam of available or inexpensive elements only. The f/27 beam is converted to f/2.55, and the star image is formed on the 50 m- ber entrance which accepts 2.7 arcsec on the sky. The two plane-parallel \scanning" plates (6), close to the Coude focus, introduce two small oscillations of the image ( 0:2 arcsec) in two perpendicular directions X and Y , with frequencies Fx (1 190 Hz) and Fy (955 Hz). The larger \guiding" plates (5) can introduce a tilt up to 4 arcsec. The eld lens (7) (focal length 70 mm) reimages the telescope pupil on the achromat (8) which is mounted on a small loudspeaker (drilled through its axis) and oscillates in Z at frequency Fz (215 Hz). The very short 6-mm focal length makes chromatic aberration negligible, which is important as guiding and focusing are checked in the NIR. At the ber output, the beam is split by a 600-nm cuto dichro¨c plate (9). The NIR part falls on a Si avalanche diode, Peltier-cooled (10). In order to make direct measurements of beam shape and position, the visible part produces images of the near- and far- eld as in Fig. 2. Later on, this same beam will be sent to the EMILIE spectrograph (Bouchy et al. 1999) . An atmospheric-dispersion compensator (11) incorporates a pair of counter-rotating low-dispersion prisms piloted by a PC; it is independent of the guider. A nder (12-13) is used to center the star image on the ber (5 7 mm CCD video camera with a 2 3 arcmin eld of view). The commutation mirror (4) interchanges stellar and reference beams. A set of Gaussian screens (2), illuminated by a tungsten lamp (1), simulates stars under di erent condition of seeing. An aperture stop (3) with a central obstruction, is located in a plane conjugate of the telescope pupil; hence the beam shape GDS intensity, greater than needed for recording spectra matches that from the telescope. in practice. During short but total cloud-induced breaks, recording has to stop, and it does not matter that the error signal 4.3. Electronic control system is no longer available. However, when the star reappears, The system is controlled by purely analog electronics one wants the autoguider at least to pick-up the image (Fig. 8); it was built without outside help, entirely on automatically. A level detector triggers at 1/10 th of the solderless test boards. Let us follow the X-guiding chan- maximum GDS intensity, and commands a sample/hold nel. An harmonic oscillator signal at frequency Fx is ap- ampli er to preserve the power ampli er input signal durplied to the X-actuator. If the image mean position is not ing the break. Thus, the autoguider is able to nd the centered on the ber input, the guiding detector signal image at the point of the eld where it was last seen. GDS is modulated at Fx. For exact centering, the Fx fun- Analog X − Y displays of either the error signals or the damental must be nulled, and only harmonic 2 remains; guiding plate tilts are shown on an oscilloscope screen. hence, a demodulator at Fx provides a DC error signal, This allows the observer to monitor the behavior of the and a proportional-integrator-derivator (PID) optimizes system and to correct telescope pointing when the imthe servo response. The oscillation actuators have 1.5 kHz age drift has exceeded the guider-correction eld. Later resonant frequencies, the guiding ones about 200 Hz. A on, we may automatize the process by sending the very rst version of the system used only 2 plates, both for low-frequency guiding errors directly to the ne-guiding scanning and guiding, with the slower actuators; it oper- telescope motors. ated correctly, but was slower. For the Z-channel, the oscillator signal Fz goes to the Z-lens loudspeaker. The DC correction can be applied 5. Tests and results either to the loudspeaker or to the telescope secondarymirror driving motor. We tried both schemes; with the Since the EMILIE spectrograph is not yet available, these loudspeaker, Z-correction was fast but perturbations ap- tests cover only the beam-handling of FLAG; no radial peared on X- and Y -channels, probably due to poor opti- velocities have been measured so far. cal alignment. Since telescope defocusing is very slow, the second scheme (shown in Fig. 8) gave adequate results. Two V/F converters provide slow pulse trains (one pulse for every few seconds); two monostable multivibrators ad- 5.1. Autoguider performance just the length of the motor-on intervals, hence correction speed. The system is roughly equivalent to the Integrate 5.1.1. Laboratory tests channel of the PID. The rest-point of all three servos is independent of Using the tungsten lamp and a 2 arcsec FWHM Gaussian the mean GDS intensity, but the response time is not, pattern, we tested each channel by introducing a known and they would become sluggish when the beam passes step-type perturbation. Figure 9 shows the response of through weak clouds. Hence an automatic gain-corrector channel X to an 0.8 arsec step function, for one particular is added at preampli er output. An analog divider pro- PID adjustment. The image is re-centered in 15 ms and vides the ratio of AC to DC components; the output is a fully stabilized in 30 ms. The noise of this channel is stabilized-amplitude AC signal, and is fed to the demod- estimated to 0.03 arcsec RMS. Altogether, FLAG quali es ulators. The system works well within a 10/1 range of as a moderately-fast autoguider. Figure 10 shows the angular corrections in X and Y of the \guiding" plates during a 5-seconds run on 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. Fig. 12. XY error signals. Same conditions as Fig. 10 but from Output 1 in Fig. 8. With FLAG correction (full curve lling 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 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 o ) is statistically the same as the FLAG correction in Fig. 10. Identifying the RMS gures, we nd that in Fig. 12 a 1 volt error signal corresponded to 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 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, Mv = 8:2 star, which is su cient for our program of radial velocities. This limit actually came from the nder video camera. The limited tilt range of \guiding" plates ( 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 nder 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 wellbehaved but slow autoguider. Fig. 14. a) Near- eld geometrical fluctuations. INT1: image intensity in ADU. M1: rst order momentum in nm. X1, Y1: photocenter motion in nm. b) Far- eld geometrical fluctuations. M2: rst order momentum in 100 rad units. X2, Y2: photocenter motion in 10- rad units. Vertical lines show limits of manual guiding intervals, marked M 2.2 arcsec average seeing, is shown in Fig. 14, giving the geometrical fluctuations of the near- and far- elds. The average intensity is 23% greater with the autoguider ON. This gain agrees well with the gure given by Hecquet & Coupinet (1985) for D=ro 33. The parameter M1 ( rst order momentum of the near- eld) give some information about the width of the image. One sees in 5.2. Beam fluctuations at ber output Fig. 14a that M1 increases during hand-guiding intervals. This means that the star image at the ber input is deThe measuring system was the one already used for graded and widened by seeing plus tracking errors during ELODIE (see Fig. 2) with minor changes due to the dif- an exposure. On the practical side, this 23% gain does ferent ber. Figure 13 shows a typical result, on UMA. no more than compensate roughly for the FLAG losses The quasi-Gaussian far- eld is a ected by telescope discussed in Sect. 4.1. central obstruction, more so than in Fig. 3, which seems to Data of Fig. 14 were separated in two sets correspondindicate less FRD. The quasi-flat near eld is a ected by ing to FLAG- and hand-guiding- intervals respectively. a narrow axial low-index zone in our 50 m ber (FG 050 The RMS residuals from a 3rd-order polynomial t were GLA from 3M). Rays are rejected from this zone by total computed and are presented in Table 1. FLAG reduces reflection, but no loss is induced. the RMS fluctuations by factors of 2 to 4. Our original plan had been to compare FLAG Of course, from these results, we would like to preperformance to that of the common-user AURELIE- dict residual RV fluctuations given by some future specspectrograph CCD-guider (similar to the ELODIE one); trograph, but this is frankly di cult. Only in the case of unfortunately AURELIE had to be taken away before our the near- eld X1, Y1 can we make a try. A 10 nm photoobserving run. Hence we had to rely on a second-best center motion corresponds to 1/5000 of the ber diameter. comparison, between FLAG and merely-manual guiding. With EMILIE, this diameter will be imaged on (roughly) FLAG was turned ON or OFF for stretches of a few min- one pixel, which has 1500 m/s velocity width; then our utes; when OFF, an operator kept the video star image 10 nm will induce 0.3 m/s RV change. Unfortunately, it is centered through the telescope controls in the usual way, impossible to make similar predictions from the remainwhich at least removed telescope drift. The average inter- ing parameters M1, X2, Y2, M2, or from any others (the val between corrections was in the 5 − 20 seconds range, beam cross sections have been stored for later analysis). As i.e. comparable to those of the automatic ELODIE device stressed in Sect. 1, this would require an exceedingly acused for Fig. 5. The main di erence with the CCD has curate model of spectrometer aberrations and adjustment. not been in speed, but in somewhat-subjective centering. Furthermore, as any minor change in spectrometer focusA 2-hour sequence of 91 short exposures (60 s), with ing etc. wrecks the prediction, one doubts the e ort 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- eld fluctuations alone contributed to 4 m/s RV change, whereas the measured radial velocity fluctuations reached 9 m/s. On the other hand, addition of a double scrambler should give some further improvement. With the ELODIE 100- m ber, we found (see Sect. 3.3.2) that the RMS fluctuations of the near- eld were equal to 1/1800 of the ber diameter. This gure seems to con rm that the autoguider brings a gain of 3 in the fluctuations of the stellar beam at the output of the ber. Since our 50- m ber reduces the star image motion by a factor 100, this means that these motions are about 1 m RMS, or 0.05 arcsec, which is the RMS residual photocenter motion with FLAG active. 6. Conclusion and possible extensions We have con rmed that the incomplete scrambling action of a ber feeding a spectrograph leaves RV errors at a level of few m/s. We have described a ber-locked autoguider speci cally built to reduce the stellar-beam geometrical fluctuations within the spectrograph; these were reduced by a factor of 3 even while instantaneous image blurring was not improved. While fluctuations do not vanish, the gain is appreciable, and the system is fully compatible with a future double scrambler. On the other hand, a mere attempt to make FLAG faster does not seem worthwhile: our 0.05 arcsec RMS residual photocenter-motion under 2.2-arcsec seeing, seems to imply that the corresponding RV errors from any spectrograph will be negligible compared with those arising from changes in image blurring; these might be corrected only by AO. Presently FLAG needs 4 plane-parallel plates and is adapted to a f/27 Coude beam, but we can imagine other con gurations with better e ciency. If many 152-cm telescope users at OHP were interested by a ber link, FLAG could be adapted for the primary focus, which would eliminate 4 mirrors and reduce the telescope central obstruction. Also, the plane-parallel plates might be replaced by a single ellipso¨dal o -axis mirror; this would be supported by a PZT-driven tip-tilt platform and used both for scanning and guiding in X and Y . The eld of acquisition/correction would be small ( 2 arcsec), but one might keep a pierced mirror as nder; very low-frequency guiding errors might be sent to the ne guiding telescope motors. The ber input itself would oscillate in Z. The electronic control would be almost unchanged. A similar FLAG could also be built for the Cassegrain focus of larger telescopes. Altogether, we make no claim to have solved the scrambling problem; we merely hope that our plain FLAG will help, as long as adaptive optics are unavailable. Acknowledgements. We are grateful to the members of the Observatoire de Haute-Provence J.P. Sivan, D. Kohler, G. Adrianzyk, A. Moulet and G. Rau for their help. We thank J. Schmitt, M. Martic, J.C. Lebrun and F. Moulin for their help during ELODIE campaigns. The FLAG project was made possible thanks to the support received from the Institut National des Sciences de l'Univers and from the Programme National de Planetologie. 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F. Bouchy, P. Connes. Autoguider locked on a fiber input for precision stellar radial velocities, Astronomy and Astrophysics Supplement Series, 193-204, DOI: 10.1051/aas:1999206