Julien Woillez

Olivier Lai

Guy Perrin

François Reynaud

Marc Baril

Yue Dong

Pierre Fédou

AGILIS: Agile Guided Interferometer for Longbaseline Imaging Synthesis Demonstration and concepts of reconfigurable optical imaging interferometers

Keywords: instrumentation, interferometers -techniques, interferometric

Context. In comparison to the radio and sub-millimetric domains, imaging with optical interferometry is still in its infancy. Due to the limited number of telescopes in existing arrays, image generation is a demanding process that relies on time-consuming reconfiguration of the interferometer array and super-synthesis. Aims. Using single mode optical fibres for the coherent transport of light from the collecting telescopes to the focal plane, a new generation of interferometers optimized for imaging can be designed. Methods. To support this claim, we report on the successful completion of the 'OHANA Iki project: an end-to-end, on-sky demonstration of a two-telescope interferometer, built around near-infrared single mode fibres, carried out as part of the 'OHANA project. Results. Having demonstrated that coherent transport by single-mode fibres is feasible, we explore the concepts, performances, and limitations of a new imaging facility with single mode fibres at its heart: Agile Guided Interferometer for Longbaseline Imaging Synthesis (AGILIS).

Conclusions. AGILIS has the potential of becoming a next generation facility or a precursor to a much larger project like the Planet Formation Imager (PFI).

Introduction

Optical stellar interferometry has flourished in recent years with the advent of large telescope arrays and imaging arrays, leading to important astrophysical results being achieved (e.g. Tuthill et al. 1999;Monnier et al. 2004;Kraus et al. 2005;Monnier et al. 2007; Kloppenborg et al. 2010). The combination of large aperture and long baselines has improved our understanding of many types of stars and has opened up fields outside of stellar physics (Swain et al. 2003;Jaffe et al. 2004;Tristram et al. 2009). Even though much progress has been made in the field of image synthesis, the vast majority of astrophysics carried out with existing interferometers is still model based. This is not surprising if one considers the large number of apertures, or alternatively, the large amount of time taken using fewer telescopes, that is required to map out the (u, v) plane and produce images of sufficient resolution to reach specific science goals.

In most existing interferometers, the telescopes are set at fixed positions in the ground; this ensures a stable baseline.

However, only a few discrete spatial frequencies can be sampled at any given time, therefore only some portions of the (u, v) plane can be mapped depending on which part of the sky is being observed. Some interferometers such as IOTA or the VLTI's ATs can be repositioned at discrete predetermined positions. Although this improves the (u, v) plane coverage, changing the telescopes positions usually relies on heavy infrastructure, requires very accurate mechanical positioning systems, and still delivers a limited (u, v) coverage that compromises the imaging performance.

In the foreseeable future, imaging with milli-arcsecond resolution in the optical/IR domain will be done most efficiently using sparse or diluted pupil interferometry. Still, restricted (u, v) plane coverage will limit the quality of image reconstruction, and the dynamic range of the optical delays may restrict sky coverage for the longest baselines.

We have recently demonstrated a deployable interferometer that uses single-mode fibres for coherent light transport in the context of the 'OHANA (Optical Hawaiian Array for Nanora-

On-sky demonstration of the reconfigurable optical interferometer 'OHANA Iki

At a time when the development of adaptive optics (AO) on large telescopes was expected to improve the sensitivity of optical interferometers [START_REF] Mariotti | NATO ASIC Proc. 423: Adaptive Optics for Astronomy[END_REF], and the use of single-mode fibres in the beam combiner of an optical interferometer had just been demonstrated with the FLUOR instrument (Coudé du Foresto & Ridgway 1992; Perrin et al. 1998), [START_REF] Mariotti | [END_REF] proposed the 'OHANA (Optical Hawaiian Array for Nano-radian Astronomy) concept: turning the large AO-equipped telescopes on the summit of Mauna Kea into a sensitive optical interferometer using coherent beam transport with single-mode fibres.

Around 2000, with the approval of the Mauna Kea telescopes' governing bodies, the 'OHANA concept moved towards implementation [START_REF] Woillez | [END_REF]. Coupling between AO systems and single-mode fibres in the J, H, and K bands was tested on the Canada-France-Hawaii (CFH) telescope and the Keck II telescope in 2002, and on the Gemini telescope in 2003 [START_REF] Woillez | New Frontiers in Stellar Interferometry[END_REF]). The development and characterisation of a pair of 300 m long, single-mode fluoride glass fibres for the K band (Kotani et al. 2005) made the bypass of the Keck Interferometer (KI, Colavita et al. 2013) beamtrains possible. The first onsky fringes were demonstrated in 2005, with the coherent light transport achieved in single-mode fibres between the two AO Nasmyth foci and the interferometric laboratory (Perrin et al. 2006b).

In parallel to this initial demonstration on the already operational KI, the project embarked on the development of a delay line, a beam combiner, and additional pairs of single-mode fibres for the J and H bands (Vergnole et al. 2004(Vergnole et al. , 2005)), aiming for a second demonstration on the 160 m baseline between the two different telescopes: CFHT and Gemini. In order to test the functionalities of the hardware, before attempting to link two large Mauna Kea telescopes, it was deemed prudent to demonstrate routine interference fringes using small, commercially available telescopes, validating the entire interferometric setup independently. This is how the 'OHANA Iki 1 project came to life.

Instrument description

The 'OHANA Iki instrument is made of two Iki telescopes (section 2.1.1), connected with two pairs of 300 m long J and H band polarisation maintaining fibres to a delay-line (section 2.1.2) and a beam combiner (section 2.1.3). All components, including the capture of detector frames, is controlled through a single graphical user interface, or GUI (section 2.1.4). The layout of the instrument inside the CFHT coudé room and outside the observatory facility is illustrated in Fig. 1.

Iki telescopes

A detailed description of the 'OHANA Iki hardware can be found in [START_REF] Baril | Proc. SPIE[END_REF]. Briefly, it consists of two independent units that can be set up a variable distance apart. Each unit consists of a 203.2 mm Schmidt Cassegrain Telescope (SCT, Celestron CPC 800), injection optics, and a control host computer.

1 Iki means small in the Hawaiian language.

After being folded by a tip-tilt mirror at the Cassegrain focus, the incoming light is separated using a beam-splitter cube. Half of the light is directed to a camera (Prosilica GE 680) used for acquisition in full field or for fast guiding in windowed mode. The other half is refocused onto the fibre using an achromat to match the fibre input F-ratio. The total throughput in J band (1.25 µm) is not ideal; half of the light is lost at the beam splitter (T = 50%), the Schmidt corrector plate is not optimized at near infrared wavelengths (T = 70%), and the telescope central obscuration of 31% in diameter reduces the theoretical coupling into the nominally gaussian, fundamental fibre mode (T = 64.7%). Nonetheless, this 22.6% non-turbulent transmission was deemed sufficient for a proof-of-concept demonstration.

The tip-tilt is a voice-coil driven 25 mm diameter mirror (Optics-in-Motion OIM-101 unit). The camera full-frame covers a rectangular field of view of 8 by 6 . When reading a subwindow, guiding frequencies up to 500 Hz are possible. In this fast-guiding mode, the correction bandwidth (0 dB crossing of the attenuation curve) was measured at about 40 Hz, and is limited by the dynamical properties of the tip-tilt mirror rather than the servo loop rate.

Once the telescope is manually aligned with 2 ∼ 3 bright stars in the viewfinder, any subsequent control can be done remotely. On request, the telescope slews to a target; once tracking, a spiral search is performed until the brightest target is detected in the camera's full frame. The control software then moves the star toward a predefined pixel coordinate that corresponds to the fibre core location; at this point fast guiding is enabled to ensure stable injection of starlight into the fibre. In addition to star acquisition requests, the 'OHANA control software interacts with the host computers to perform raster-scans used to optimize injection efficiency into the fibre (see Fig. 4). The units are monitored remotely via VNC using a real-time GUI to obtain feedback on the image quality and guiding stability.

The telescopes routinely achieve 0.1 to 0.2 rms image stability depending on the seeing and wind; turbulent airflow at the ground affects injection stability. With the focal reducer, the 5 µm fibre subtends 1.5 on the sky, so a stability of 1/10 th core should be achieved.

The telescopes can be carried or rolled outside and set up in about 15 minutes. They are preferably set up on the soft cinder away from the observatory building. The telescopes' relative separation and orientation are then roughly adjusted by using a ruler and taking a bearing on landmarks. We estimate a relative separation accuracy on the order of 1 cm, and an orientation accuracy of the resulting baseline on the order of 5 • . Once each telescope is set-up and stabilized on the target star, the starlight is sent through the fibres to the delay line and beam combiner.

Delay line

The delay line was designed for the 163 m baseline between the CFH and Gemini telescopes. With the CFH Coudé room being the only readily available installation location, its physical extent was limited to 15 m. In order to achieve a reasonable sky coverage, the optical path had to be folded multiple times. As illustrated in Fig. 2, a ±50 m optical path stroke is realized with a mobile carriage on 12.5 m long rails used from both sides (×2) and in quadruple pass (×4). The central carriage can be relocated between two observations in order to adjust the general pointing of the interferometer. While observing, an additional 1 m long translation stage (Aerotech ALS50100) in double pass provides the 2 m continuous delay capability required to track the sidereal fringe motion up to 5 mm s -1 . This ±50 m delay line on a quasi North-South 163 m long CFH Gemini baseline, provides a close-to-transit pointing capability for all targets within a declination span of δ = 19.8 • ±18 • . The sidereal velocity of the fringes, for targets at a zenith angle smaller than 45 • , is smaller than 3 mm s -1 . The resulting continuous sidereal tracking autonomy is therefore always longer than 10 min. In order to minimize the down time between two continuous sidereal tracking intervals, the central carriage motion is automatically controlled using a motorized belt and a linear encoder. The optical coupling with the single-mode fibres is achieved using off-axis parabolas. Dihedral mirrors are used to implement the multiple-pass beam folding. Pitch variations of the central carriage, due to the alignment errors of the rails, are corrected with a pitch actuator on that same carriage, using an empirically determined lookup table. Finally, following a relocation of the central carriage, the final fibre-to-fibre alignment is achieved with fine steering mirrors.

Beam combiner

The multi-coaxial beam combiner originally anticipated for 'OHANA has been presented in Woillez (2004). However, when used in the 'OHANA Iki setup, this beam combiner is simplified to a fibred X coupler, the outputs of which are re-imaged on an infrared detector after their polarizations have been separated using a Wollaston prism. This coupler is located on an optical bench inside the CFH Coudé room next to the delay line, and was used for all the results reported here. Fringe contrast measurements are performed with an OPD scanner integrated into the delay line. Specifically, a flat mirror mounted on a piezo-based translation stage (an exact replica of the ones used in FLUOR or VINCI instruments) replaces one of the flat mirrors of the delay line. Finally, the detector used with this beam combiner is a science grade Nicmos camera with a digital gain of 10 e -/ADU, a read-out noise of 30 e -, and a 45% quantum efficiency.

Control software

The supervisory control software, programmed in LabView, runs on a single desktop computer. This software interfaces with the Iki telescopes' host computers through the ethernet network, to request acquisition of new targets and to optimize the coupling into the fibres by performing raster scans of the detected flux using telescope offsets. The software is also responsible for triggering delay line carriage moves, and re-align automatically the input fibre to output fibre coupling on both sides. Based on an estimation of the deployed baseline vector, a sidereal target (position and velocity at a given time) is computed at 1 Hz, and serves as a setpoint for the control of the continuous delay translation stage operated in velocity mode. At configuration time, the parameters of the multi-window non-destructive readout are sent, through a serial interface, to the drive electronics of the infrared camera. Once in free-run mode, the drive electronics are responsible for generating the detector clocks, pre-conditioning, then digitizing the analog video signal. The digital signals are sent, through a fibre optic link, to a digital acquisition card (National Instrument PCI-DIO-32HS).

Configured in a free-running mode, the detector continuously repeats a pattern of 1 reset followed by N non-destructive reads. Each start of a pattern triggers, on an analog output card (National Instrument PCI-MIO-16E-4), a pre-computed triangular waveform driving the OPD scanner. The result is a scanned fringe detection, whose parameters can be adjusted to match the magnitude of the observed object, and fit within the linearity regime of the detector. A spiral OPD pattern on top of the sidereal target, introduced at the level of the delay line (see 2.1.2), allows searching for zero OPD until fringes appear within the scan length. Once the various flux optimizations described earlier are completed and the fringes found, the supervisory software finally carries out the data collection sequence; taking dark frames (both telescopes offset from the target star), obtaining flux ratios from each telescope (each telescope sequentially offset from the target), and recording the fringes (both telecopes on target) as raw data in the disk archive.

System qualification

This section present the system level performance of the instrument; specifically the piston stability (Section 2.2.1), and the overall sensitivity given the transmission and injection losses present (Section 2.2.2). The model used the determine the baseline is outlined in Section 2.2.3).

Internal fringes performance

Before being used on sky, the J-band fibres, delay line, and beam combiner were tested independently in a Mach-Zender configuration, replacing the two telescopes by an additional J-band 2 × 2 coupler connected to the fibre pair inputs and fed with a thermal source. This setup was not only used to measure the zero group delay position in the absence of sidereal contribution, but also to assess the OPD stability through the fibres and delay line, as installed inside CFHT.

In order to reduce the vibrations detected in the initial setup, the fibres were systematically isolated from the telescope building with tubular foam-rubber pipe insulation. However, the measured vibration level remained high, with RMS amplitudes in the range of two waves in J-band, and frequencies of hundreds of Hertz. As shown in Fig. 3, different internal fringe configurations were used to better identify the origin of the measured vibrations. A series of measurements was taken with the CFH telescope drive and dome drive hydraulic pumps turned off. A comparison was made between the power spectral density (PSD) of the internal fringes obtained using three configurations; a 300 m fibre single-pass Mach-Zehnder, a 10 m fibre single-pass Mach-Zehnder, and the delay line operated in double-pass autocollimation. In each case, the PSD peak occurs at ±200 Hz, which represents the fringe frequency, proper. However, when comparing the quiet environment PSDs, the peak is disproportionately broader and lower for the double-pass auto-collimation setup compared to the single-pass configurations with longer fibre lengths. We conclude from this that the main contributor to the interferometer instability is the delay line.

With the hydraulics pumps powered back on, the PSD peak was further reduced and broadened to a full width of ±400 Hz, illustrating the role of external excitation sources on the delay line vibrations. Various modifications were then applied to the delay line, involving the installation of damping material, and the stiffening of optical elements. This resulted in some additional performance improvement, with the PSD full width being reduced to ±150 Hz with the hydraulics pumps powered on.

Based on these internal performance measurements, the vibrations had a significant impact on the sensitivity of the 'OHANA Iki setup. In order to preserve the fringe contrast despite the high frequency vibrations, the measurement rate had to be kept higher than 500 Hz to 1000 Hz, resulting in a fringe peak frequency of at least 100 Hz to 200 Hz, at a scanning speed of 5 samples per fringe. Even though this is an acceptable limitation for a demonstration, the sensitivity of the instrument could have been improved with the addition of metrology through the fibres and delay lines and/or by significant modification of the delay line structure.

Transmission and injection stability

With the help of raster scan patterns (see Fig. 4), the coupling at each telescope of the star light into the single-mode fibre was optimized. Iterative adjustments of the tip/tilt, telescope focus, and focal reducer F-ratio, ensured optimal coupling of the telescope point spread function with the fibre input mode. A similar optimization was performed between the input and output fibres of the delay line. The stability of the injection into the single-mode fibres and the total number of photons detected at the focus of the interferometer were then measured on sky.

An observation of Antares (J=-2.73) resulted in an average detected flux of 3500 e -/ms per telescope, which corresponds to 283 e -/ms per telescope for a J = 0 target. Compared to the theoretical transmission error budget given in Table 2, there is a measured additional loss of ∼ ×23. There is no fundamental reason to incriminate the fibres: percent level transmissions have already been demonstrated in H/K band on the Keck Interferometer (Perrin et al. 2006b). This transmission is certainly specific to the 'OHANA Iki experiment. A similar transmission discrepancy of ∼ ×20 was also measured with the H-band fibres, confirmed by the frequency conversion experiment of [START_REF] Ceus | [END_REF], using the same H band 'OHANA Iki equipment, except for the delay line and beam combiner. Independent verifications of the delay line and fibres transmission on an internal source did not show any significant discrepancy with the transmission error budget, leaving the Iki telescopes as the most probable source of losses. The quasi-ideal Airy pattern shown in Fig. 4 seems to rule out an image quality issue. The transmission of the telescopes in the near-infrared is a significant concern: designed for visible operation, they are not specified in the near-infrared by the manufacturer. An actual measurement of this near-infrared transmission would have been better than just the characterisation of a Schmidt corrector plate supposed identical to those in the Ikis (see details in [START_REF] Baril | Proc. SPIE[END_REF]. Nevertheless, the impact on sensitivity from these losses did not prevent the pursuit of our interferometric objectives.

Finally, the temporal stability of the injection was verified. We did not note any significant injection fluctuations linked to atmospheric turbulence, as would be expected from a small 20 cm diameter telescope, when the the J-band Fried parameter is r 0,J = 30 cm under average 1 Mauna Kea seeing. The telescopes however were impacted by wind shake when left unprotected. Windscreens were installed to help mitigate this effect.

Baseline models

Due to the lack of accurate metrology on the telescope positions, the interferometer wide angle baseline was only known to the order of a centimeter at the beginning of any observing night. With only a pair of targets observable as a result of the limited sensitivity, a pointing model for the baseline vector could not be measured at the beginning of each night. Therefore, an alternative method had to employed to measure the baseline.

With the internal optical path difference constant and independent of the baseline vector, the error in predicting the position of the zero optical path difference is only dependent on the contribution from the baseline error δB to the external delay s • δB, for the given direction s of the observed object. The baseline error stems from the approximate knowledge of the position of the telescopes in a newly deployed array configuration. Once the fringes are found and tracked, the baseline error can be corrected as follows:

s • δB = δ∆, (1)
(ω × s) • δB = ∂δ∆ ∂t , (2)
[ω × (ω × s)] • δB = ∂ 2 δ∆ ∂t 2 , (3)
using the value, velocity, and acceleration of the offset δ∆, where ω is the earth rotation vector. However, since the amplitude of the earth rotation vector is very small (ω = 7.3 × 10 -5 rad s -1 ), the accuracy of the baseline error projected on the velocity vector is poor, and the projection on the acceleration is even less accurate. For this reason, only offsets for the position and velocity projections were applied in practice.

First contrasts measurements

Given the sensitivity losses from vibrations (section 2.2.1), the low transmission throughput (section 2.2.2), and the difficulty of finding fringes on a roughly known baseline, the demonstration proceeded using a very short baseline. The initial installation of the two telescopes on a ∼1 m north-south baseline was performed outside of CFH, using crude visual sightings between the CFH building itself and the neighboring meteorological tower. Since the telescopes could not be left unattended outside during the day, references were left on the ground in order to repeatably position them at the beginning of each observing night. Illustrated in Fig. 5, the first J-band fringes were obtained on Antares (J = -2.7), in July 2010 [START_REF] Dong | Master's thesis[END_REF]. Following this initial demonstration, the performance of the interferometer was systematically improved by stabilizing and maximizing the coupling between the telescopes and the fibres, mitigating the impact of vibration on the fibres and the delay line, and improving the noise performance of the infrared detector. The state of the sub-systems following this improvement campaign are described in section 2.1. Ultimately, the performance reached a level compatible with the observation of a few bright stars with known diameters: Antares (H = -3.5), Arcturus (H = -2.8), Betelgeuse (H = -3.7), and Scheat (H = -2.1).

In June, 2012, the H-band fringe contrast stability was assessed with observations of Antares and Scheat. The fringe contrast was estimated using a technique similar to the integration of the fringe peak of the interferometric signal power spectral density, used for the FLUOR instrument (Coudé du Foresto et al. 1997). Here however, a single, instead of a triple coupler was used without real-time photometry. Single telescope fluxes were estimated before fringe collection in order to estimate the flux ratio contrast loss. The instantaneous photometric fluctuations were rejected by computing the normalized fringe signals (I 1 -I 2 )/(I 1 + I 2 ), where I 1 and I 2 are the two interferometric outputs of the 50:50 coupler. The power spectral densities of these normalized fringe signals were then corrected for the photon noise (Perrin 2003) and readout noise (Woillez 2004) biases. The square fringe contrast was calculated by integrating the biascorrected mean power spectral density.

Results for the night of June 12, 2012, are shown in Fig. 6. The large ±σ ≈ ±0.08 error bars on the fringe contrast estimates result from the lack of simultaneous photometric measurements. The estimated squared fringe contrast for Antares and Scheat are respectively 0.71 and 0.69. Unfortunately, these observations were performed on a 1 m North-South baseline; too short to detect any differential diameter. The predicted square visibility of Antares (diameter ∼32 m ) and Scheat (diameter ∼17 m ), on the respective ∼0.69 m and ∼0.75 m projected baselines, are V 2 = 0.995 and V 2 = 0.987. A ∼ 4 m baseline would have been better suited to demonstrate visibility cross calibration.

The June 2012 run concluded the 'OHANA Iki experiment, validating the technological readiness of a fibred interferometer link between the large telescopes of Mauna Kea. Out of the three phases outlined in the original project roadmap, most of the objectives of Phases I and II have been met; adaptive optics to fibre interfacing [START_REF] Woillez | Interferometry for Optical Astronomy II[END_REF] in Phase I, and an on-sky interferometric demonstration [START_REF] Perrin | Proc. SPIE[END_REF] in Phase II, albeit not using the originally planned CFH-Gemini interferometric combination. Whereas, Perrin et al. (2006b) successfully demonstrated on-sky, long-distance coherent transport through single-mode fibres using the Keck Interferometer, the present paper moves a step further in reporting on the successful implementation and on-sky operation of an interferometer based entirely on single-mode fibres. These two milestones lead the way for Phase III [START_REF] Lai | Interferometry for Optical Astronomy II[END_REF]: the construction of the full 'OHANA array envisioned by [START_REF] Mariotti | [END_REF]. For now, the realization of this vision remains beyond the resources of our current team supported by the observatories of Mauna Kea. However, a fully operational 'OHANA array is presently a demonstrated possibility, for a wider community to eventually implement.

An AGILIS concept, and new project?

The coherent guiding and high transmissivity properties of single-mode fibres allows a greater separation between the light collection, the light delay, and the light combination functions of an interferometer, while preserving sensitivity. In the original 'OHANA concept [START_REF] Mariotti | [END_REF], this function separation is used to easily convert, with no significant infrastructure modification, the already available telescopes on Mauna Kea into an interferometer.

Similarly, the 'OHANA Iki experiment opens another perspective on this function separation: greater freedom is given to the layout of the light collection and delay functions. In the previous section, this capability was partly illustrated when the Iki telescopes had to be setup outside for an observing night: any kind of baseline could have been chosen, without requiring any baseline-specific change in the delay lines setup. In this section, we explore this idea further under the concept name "Agile Guided Interferometer for Long-baseline Imaging Synthesis" or AGILIS.

Agile (u, v) coverage

The main first-order requirement for an imaging optical interferometer is a dense (u, v) plane coverage, to be achieved in a minimum amount of time for evolving targets or for efficiency reasons (see e.g. Berger et al. 2012). Measurements of the complex visibility from individual observations can be recombined a posteriori in an image reconstruction process similar to that used in radio-interferometry (e.g. Sutton & Wandelt 2006).

An imaging optical interferometer must be cophased. To achieve a good limiting magnitude, the fringe sensor employed to cophase the array must operate on the shortest baselines exclusively, where a high fringe contrast and a reasonable flux per baseline are maintained. As a reminder, and considering a uniform disk object as an example, the maximum V 2 in the second lobe is on the order of ∼ 0.17, corresponding to a sensitivity loss of 4.4 magnitudes, under the assumption that photon noise still dominates. The phasing of the longer baselines can only be achieved, without a significant sensitivity impact, by bootstrapping small baselines where the object is unresolved [START_REF] Roddier | European Southern Observatory Conference and Workshop Proceedings[END_REF]Armstrong et al. 1998;Hajian et al. 1998). In this configuration, the shortest baselines should match the overall size of the observed object, whereas the longest baselines should be adapted to the size of the smallest details desired in the reconstructed image. Meeting all these requirements with a fixed telescope array, for a wide range of objects, is not possible. For this reason, optical interferometers typically use relocatable telescopes to adapt the measured spatial frequencies to the size of the observed object, and sequentially pave the (u, v) plane, as at IOTA, VLTI, or the planned MROI (resp. [START_REF] Carleton | Amplitude and Intensity Spatial Interferometry II[END_REF]von der Lühe et al. 1997;[START_REF] Buscher | [END_REF].

With the proposed AGILIS flexibility, the use of single-mode fibres allows rich aperture synthesis with telescopes that can be moved to any location on a terrain, satisfying the requirements above. A global scaling of the array can match the size of the object; a relative scaling between north and east directions can compensate the projection effects of target declination versus instrument latitude and hour angle. Therefore, the array can be optimized both in sensitivity with its shortest baselines, and in angular resolution with its longest baselines.

Innovative array geometries can be considered without the cost impact of a beam routing infrastructure in bulk optics. The regular Y configuration [START_REF] Buscher | Interferometry in Optical Astronomy[END_REF], where the stations are aligned in each of the three arms in order to simplify beam routing, can now be modified to remove the array redundancy, as done in Ireland & Monnier (2014), increasing the instantaneous (u, v) coverage by +25% for a 10 telescope configuration (see Fig. 8). The non-redundant circular arrays [START_REF] Labeyrie | Proc. SPIE[END_REF][START_REF] Labeyrie | Proc. SPIE[END_REF]) become practical, with fibre links running from the individual telescopes to a central delay and beam combination location. Called hypersynthesis in Vivekanand et al. (1988), continuous (u, v) coverage adaptation, with telescopes moving while observing, could even be considered.

The benefit gained in freeing the telescope layout is most obvious when combining a small number of telescopes. The array can be configured for a dense two-dimensional (u, v) coverage, or it can be dedicated to reaching the longest baseline possible with a regularly spaced linear array (see Fig. 8). This amounts to a trade-off between dense (u, v) coverage for instantaneous low angular resolution with high image quality, and sparse (u, v) coverage for sequential high angular resolution but poor image quality.

Delay compensation

All the fibres connecting the telescopes to the delay lines must have the same length, in order to balance their inherent chromatic dispersion (Vergnole et al. 2004(Vergnole et al. , 2005;;Kotani et al. 2005;[START_REF] Anderson | Proc. SPIE[END_REF]. Doing so, all the telescopes of the array are at the same constant optical path distance from the delay lines. This is an improvement over bulk optic implementations, where the delay lines are often used to compensate for the optical distance of the telescope station, reducing the stroke available for pointing the interferometer. In the fibred implementation, the delay lines do not need to provide any differential OPD for an horizontal array and a target at Zenith. Their stroke is fully dedicated to the compensation of the external delay increasing with the zenith angle. For a 340 m baseline, and a zenith angle of 60 • , a 147 m-long double-pass delay line is sufficient. In the case of a Y aligned configuration (see Fig. 8), with the same maximum baseline of 340 m as for the future MROI array, the delay lines have to be 97 m longer physically, when the beams are directly routed from the telescopes, to the delay lines, through the central point of the array. Installing fibres on such an array would reduce by 47% the delay line stroke requirement.

Requirements on the delay line stroke can still be reduced further. As already noted by Vivekanand et al. (1988) for a fibred array, no optical path delay is needed for telescopes contained in a plane orthogonal to the line of sight. The topography of the terrain combined with the mobility of the telescopes can be used to reduce or eliminate the optical path delay needed to point the array. Movable telescopes could be set on a depression, as shown in Fig. 7, where the source direction is locally perpendicular to the surface. Then, delay lines are only required to compensate for Earth rotation during an exposure. The maximum stroke of the delay lines therefore gives the maximum time during which a configuration can be used before telescopes are relocated to another optimum location. As an illustration, for a kilometric east-west baseline at latitude zero observing an object at zenith (i.e. the worst yet realistic geometric configuration for Eq. 2), the fringe velocity is 7.3 cm s -1 , which corresponds to an autonomy of at least 10 min for a 50 m optical path delay line.

The idea of using terrain to support an interferometer or dish is not new. It has been demonstrated by the Arecibo radio telescope and has been proposed by Labeyrie & Mourard (1990) for the Lunar Optical Very Large Interferometer. More recently [START_REF] Labeyrie | Proc. SPIE[END_REF] have used the topography of the Vallée de l'Ubaye to install an equivalent to the CARLINA hypertelescope, previously demonstrated by [START_REF] Coroller | [END_REF]. However, in all these cases, only a fraction of the primary spherical mirror can be used in a given pointing direction. For the hypertelescope, this is set by the amount of spherical aberration that the Mertz corrector can tolerate. For an AGILIS concept using the terrain topography and movable telescopes, all telescopes are active for a given observation and short delay lines play the role of the Mertz corrector of a hypertelescope.

Modal transport

The coupling loss between the airy pattern at a telescope focus, and the fibre fundamental mode (Coudé du Foresto et al. 2000) can be overcome. An off-axis telescope, without central obscuration, can already increase the coupling efficiency to 78%. Following a technique proposed by Guyon (2003), the entrance pupil of the individual telescopes can even be losslessly modified to match the mode profile of the fibres (Jovanovic et al. 2016). A coupling of 100% can virtually be reached, limited only by the size of the mode matching optics. This mode matching approach removes the small low-flux phase estimation disadvantage of single-mode over multi-mode recombination identified in Tatulli et al. (2010). Once the light is injected into the fibre at the telescope focus, the fundamental mode can virtually be preserved all the way to the cophaser and science instrument. This preservation includes the polarization state, either using silicate polarisation maintaining fibres for J and H bands, or low birefringence fluoride glass fibres with passive polarisation control (Lefevre 1980) for K band.

Ideally, the delay function would be performed with the very same fibres. However, the intrinsic dispersion of those currently available (Kotani et al. 2005;Vergnole et al. 2004Vergnole et al. , 2005) ) prevents the generation of large optical path delays by stretching or adding/removing fibre sections, that would be usable over the typical bandwidth of optical atmospheric windows. Only broad band delays on the order of a few centimeters have been demonstrated in laboratory experiments (Huss et al. 2001), or are being integrated in upcoming instruments (Eisenhauer et al. 2011).

The current alternative is to use free-space delay lines. The fundamental mode of a step-index single-mode fibre is close to having a Gaussian profile (Gloge 1971), which is an invariant of diffraction. The only effect, the curvature resulting from the propagation, can easily be compensated with a defocus of the collimating interfaces with the fibres. A double-pass delay line coupled with single-mode fibres can therefore be designed with virtually no diffraction losses.

Since the objective is to combine a large number of telescopes, the footprint of a transverse section of the delay line must be kept to a minimum. This is achieved with the Gaussian beam waist located at mid-range between the fixed collimation/injection optics and the mobile delay-line cart. This configuration requires the capability to track the waist and cart locations with mobile optics at the level of the collimation, injection, and cart. Such variable pupil relay optics are already in operation in the delay line carts of VLTI (Ferrari 1998). The implementation could however be simplified by locating the waist at the level of the cart itself, requiring tracking optics only at the level of the fixed collimation and injection, leaving the delay cart optics completely passive.

A kilometric baseline at a zenith angle of 45 • requires a delay of 700 m, corresponding to a maximal physical length of 350 m in double-pass. In order to keep the Rayleigh distance z R = πω 2 0 /λ larger than this physical length, the waist radius ω 0 of the Gaussian beam at the delay line cart must be larger than 1.57 cm in K band (λ = 2.2 µm), or 0.82 cm in R band (λ = 0.6 µm). For a transmission of 99% of the beam power, taking into account the beam divergence after one Rayleigh distance propagation, the optics diameter must be larger than 6.75 cm in K band, or 3.5 cm in R band. For an estimation of the required volume, each delay line would fit in a cylinder of 15 cm diameter, the double of the optics diameter including margins, so that one hundred of such delay lines could be hexagonally packed, under vacuum, in a cylinder of 1.6 m diameter.

Finally, a spin-off from the field of femto-second lasers, ultra highly reflective broad-band dielectric mirrors with low group delay dispersion are becoming available (Trubetskov et al. 2010). With these mirrors, fibre-pigtailed, multiple-pass commuted delay lines [START_REF] Lai | Interferometry for Optical Astronomy II[END_REF], could significantly reduce the physical length of the delay line, at the cost of an increased cross-section. By allocating to a given beam only the exact volume required to produce the necessary delay, a bank of commuted delay lines could have an overall volume half the size of a traditional bank of double-pass delay lines.

Co-phasing the array

As already mentioned in section 3.1, in order to preserve sensitivity, the co-phasing of the array can only happen on the shorter baselines where the object is unresolved and the fringe contrast high. On the contrary, the imager has to measure all the baselines as corrected by the short baselines' co-phaser. In this section, we investigate how the performance of the co-phaser on these shorter baselines affects the performance of the imager.

The co-phasing loop is modelled as illustrated in Fig. 9, where only piston perturbations and photon noise are consid-ered. This simplification is not far from reality; recent progress with near-infrared detectors has made photon counting available [START_REF] Finger | Proc. SPIE[END_REF]. It is intuitive to consider a fringe sensor operating in the photon noise regime in order to achieve reasonable performance on the longest imaging baselines. The fringe sensor converts the atmospheric piston residual error e coming from the individual telescopes into differential piston with noise n on each of the short fringe sensing baselines. T2B represents the interaction matrix of the telescope piston phases projected onto short baselines, and depends only on the geometry of the baselines established between the different telescopes. Because all the baselines are measured independently, the reconstructor B2T, pseudo-inverse of T2B, converts the differential pistons back into the individual pistons, with the exception of the global piston. The controller S integrates the reconstructed piston error and generates the piston correction c associated with each telescope. To simplify the control diagram, the time delays introduced by sensors and actuators are included in the controller model S . The imager is modeled with the T2I matrix that generates, from the telescope residual piston error e, the differential piston i on all the imaging baselines.

Based on this model, the residual piston error e can be derived from the atmospheric disturbance d and the noise n as follows:

e ∼ 1 1 + S d - S 1 + S B2T × n. (4)
This expression was obtained by observing that T2B × B2T is the identity, provided that the piston mode is discarded as not observable.

From the above, it becomes clear that the geometry of the fringe sensor does not directly influence the rejection of the atmospheric disturbance. However, it plays a role in the way noise affects the control loop. In order to study the noise propagation further, a few fringe sensing configurations were simulated: Y aligned, circular, and hexagonal. Following the bootstrapping requirement of section 3.1, each configuration is built around the same unit fringe sensing baseline length, where the observed object is unresolved. Consequently, the noise on the differential piston is strictly related to the flux contributing to a given baseline, which can be derived from the fringe tracking geometry and the assumption that all telescopes provide the same amount of light. Considering the flux imbalances to be insignificant, the associated contrast losses are also neglected. In this case, the phase errors δφ I on the imaging baselines are related to the phase errors δφ B on the fringe tracking ones by:

δφ I = T2I • B2T • δφ B (5)
Since the fringe tracking phase errors are uncorrelated and inversely proportional to the number of photons N b measured on the baseline b, the variance of the phase errors σ 2 i on a baseline i is expressed as:

σ 2 i = b (T2I • B2T) 2 ib 1/N b (6)
where N b is the number of photons contributing to the phase measurement on baseline b.

The results of these simulations are shown in Fig. 10, representing the differential piston noise on the imaging baselines. As one might expect, the longest baselines are the most affected because they rely more on bootstrapping. The geometry of the array also has an influence on the noise propagation. The results shown in Fig. 10 can be explained by how the fringe tracker connects the telescopes together. The Y and circular geometries are mainly constructed with each telescope connected to two other telescopes. These arrays are effectively one dimensional. The hexagonal array, where each telescope is connected to three other telescopes, is two-dimensional. The longest baselines are the result of many different bootstrapping paths, whereas there is only one for the Y array. Note that for the circular array there are two paths, clockwise and counter-clockwise, to connect the longest baselines, therefore reducing the noise propagation as shown in Fig. 10.

In section 3.5, the telescopes were adapted to the seeing strength, so as to deliver a Strehl compatible with fringe tracking. It is however interesting to consider the impact of a flux dropout for one of the telescopes within the array. One might expect that the consequences are much less drastic for two-dimensional compared with one-dimensional arrays. The loss of a telescope on a Y array breaks the array into two independently phased groups of telescopes (three if the dropped telescope is the central one). With the slight redundancy of the clockwise and counterclockwise paths, the circular array fares better. The array stays phased but the noise propagation around the dropped telescope increases because the phasing now involves the full chain around the missing telescope. As suggested by [START_REF] Petrov | Interferometry for Optical Astronomy II[END_REF], redundancy can be added to one-dimensional arrays by additional fringe tracking between the second nearest telescopes. To preserve the sensitivity, the longest fringe tracking baseline length cannot increase (see section 3.1). Therefore, the minimum distance between telescopes needs to be shortened by a factor two, increasing the overall telescope density, but without benefiting the image reconstruction. Rather than increasing the telescope density, the flux dropout issue would be more efficiently resolved by increasing the adaptive optics correction order at the telescopes.

Limiting magnitude

As mentioned in section 3.1, the cophaser sets the limiting magnitude of the imaging interferometer, which is related to the amount of coherent flux collected at each telescope. Since, larger telescope diameters make (u, v) coverage agility harder to achieve, only smaller telescopes with correction of the atmospheric tip/tilt are considered in the following sensitivity analysis.

The strength and speed of the atmospheric seeing drive the sensitivity of the interferometer. At Cerro Paranal, 5 m above ground, seeing strength and coherence time have been measured [START_REF] Sarazin | [END_REF]) to 1.0 and 2.5 ms, at a wavelength of 500 nm, in median conditions. With telescopes most probably located closer to the ground, and therefore impacted more strongly by ground layer turbulence, we consider less favorable seeing conditions at 1.5 and 1.5 ms.

The maximum single-mode fibre coupling efficiency for a tip/tilt corrected telescope is reached around D = 4r 0 (Shaklan & Roddier 1988). However, the limiting magnitude of a cophased array is set by the capability to continuously estimate the atmospheric piston. For this, a minimum instantaneous Strehl is required. As shown in Fig. 6 of Tatulli et al. (2010), D = 4r 0 with tip/tilt correction leads to a mean Strehl (or coupling efficiency) of |ρ i | ∼ 25%, and therefore significant flux dropouts. Instead, at D = 2r 0 with tip/tilt correction, the mean Strehl increases to |ρ i | ∼ 65%, and the flux dropouts are significantly reduced, which improves the sensitivity of the array, relative to the telescope size2 . This is the configuration we assume. Following Colavita et al. (1999), the exposure time of the fringe sensor is set to the atmosphere coherence time τ 0 , in order to continuously follow the atmospheric piston without introducing unwrapping errors. A minimum required signal to noise ratio of SNR φ = 3 on the phase estimation (phase variance σ 2 φ = 1/SNR 2 φ = 0.11 rad 2 ) sets the number of coherent photons (NV 2 ) and therefore the limiting magnitude. For each of the J, H, K, and R operating bands, Table 1 converts the atmospheric turbulence (Fried diameter r 0 and coherent time τ 0 ) into the interferometer parameters (respectively, diameter D and fringe sensor frequency f ), which determine the limiting magnitude for a realistic level of transmission assumed at 5%.

Conclusion

The 'Ohana Iki project, initially a pathfinder experiment for the development of the 'Ohana concept on Mauna Kea [START_REF] Mariotti | [END_REF], exemplified the convenience of using singe mode fibres in deploying flexible interferometric arrays. A description of this two-telescope experiment, a proof of technical feasibility, was followed by an outline of the key elements necessary to extend this idea to a larger array of telescopes: the AGILIS concept. The use of single mode fibres to link the light collection, delay, and combining functions of the interferometer illustrated the flexibility of configuring the array, while preserving sensitivity. We deliberately did not settle on one technological approach for all aspects of the interferometer in order to illustrate the concept's flexibility.

We also envisage AGILIS as an array that is intended to grow progressively with time. Starting with a small number of telescopes, it begins by capitalizing on the mobility of the telescopes to efficiently pave the UV plane. As telescopes are added, the imaging capabilities would benefit from a phased array that is non-redundant, similar to the FIRST concept (Perrin et al. 2006a;Lacour et al. 2007). With further expansion, the capability to take snapshot images of complex objects will come within reach. In that case, the imager should be based on a homothetic remapping or a densification of the entrance pupil to directly produce an image at the focal plane.

Lastly, AGILIS would be an excellent platform for technological demonstrations in the context of the future Planet Formation Imager (Monnier et al. 2014;Kraus et al. 2014;Ireland & Monnier 2014), or a possible way of converting the light beamer of breakthrough starshot (Lubin 2016) into a stellar interferometer.

Artist conception of a possible implementation of the early phase of AGILIS, in which a few autonomous (and self-propelled) telescopes could be used to reconfigure themselves to sequentially fill the u-v plane, using the concave (or convex) nature of the terrain to minimize the delay line requirements. 1. Estimation of the limiting magnitude m T in each of the K, H, J, and R bands. The assumptions are a seeing strength of 1.5 , a seeing speed of τ 0 = 1.5 ms. From these, the telescope diameter D and the fringe tracker rate f FT can be deduced at each wavelength. The limiting magnitude m T is given in each band considering a reasonable T = 5% total transmission to the fringe tracker (T = 100% gives an indication of the transmission loss effect). Telescopes are moved to a portion of the depression where the source direction is perpendicular to the surface. The requirement on the delay lines stroke is set by: 1) a static term associated to the departure of the local ground surface from a plane, and 2) a dynamic term associated to the desired pointing autonomy, derived from the observed target sidereal motion. . Photon noise propagation factor σ 2 i (Eq. 6, section 3.4), normalized to the photon count per telescope, as a function of the length of the baseline i, for three array geometries: Y shape (top), circular (middle), and hexagonal (bottom). The fringe tracking baselines are those at unit baseline length. All arrays are inscribed within a circle of radius of 4 (red), 6 (green), or 8 (blue) unit baseline lengths.

Array layout

Fig. 1 .Fig. 2 .Fig. 3 .

 123 Fig. 1. Layout and pictures of the 'OHANA Iki demonstration.

Fig. 4 .Fig. 5 .Fig. 6 .

 456 Fig. 4. Typical raster scan image obtained by exploring the field with telescope offsets, and recording the flux detected at each field position. A prominent first Airy ring, resulting from the significant central obscuration of the Iki telescopes, is visible around the central core.

Fig. 7 .

 7 Fig.7. An AGILIS concept using the terrain to minimize the delay line stroke requirement. The interferometer is set in a spherical-like depression. Telescopes are moved to a portion of the depression where the source direction is perpendicular to the surface. The requirement on the delay lines stroke is set by: 1) a static term associated to the departure of the local ground surface from a plane, and 2) a dynamic term associated to the desired pointing autonomy, derived from the observed target sidereal motion.

Fig. 8 .Fig. 9 .

 89 Fig. 8. The AGILIS concept allows the implementation of many different array configurations, and the adaptation of the array to the size of the observed object. Top: Array configuration. Bottom: Instantaneous (u, v) coverage at zenith. Left to Right: circular, Y rotating, Y aligned, and linear array configurations, ordered in increasing maximum to minimum baseline ratio (B max /B min ). Two optimized array scales are presented for observations at a wavelength of 2 µm: B min = 200 m for a 1 m object (large blue dots), and B min = 40 m for a 5 m object (small green dots).

Table

			K	H	J	R	Unit
	Wavelength	λ	2.22	1.60	1.26	0.64	µm
	Bandwidth	∆λ/λ	0.23	0.23	0.16	0.23
	Zero magnitude flux	m 0	670	1080	1600	3080	Jy
	Fried parameter	r 0	41	28	22	7	cm
	Coherence time	τ 0	8.9	6.1	4.7	1.5	ms
	Telescope diameter (2r 0 )	D	81	56	43	14	cm
	Fringe sensor frequency (1/τ 0 )	f	112.7	165.1	211.8	666.7	Hz
	Photons per exposure	N hν	10.7×10 6 5.5×10 6 2.7×10 6 0.24×10 6	hν
	Limiting magnitude	m 100%	13.3	12.6	11.8	9.2	mag
	(phase SNR of 10)	m 5%	10.1	9.4	8.6	5.9	mag

Table 2 .

 2 'OHANA Iki transmission error budget, compared to measured transmission. See text for a discussion on the discrepancy.

	Quantity	Transmission
	Photon flux at J=0	94 673 hν ms -1
	Telescope transmission	22.6%
	Fiber transmission 0.3 dB km -1 × 300 m	97.9%
	Fiber head Fresnel reflection loss (95.6%) 4	83.5%
	Delay line transmission (98%) 10	81.7%
	Detector quantum efficiency	45.0%
	Total	6.8%
	Expected per telescope	6438 hν ms -1
	Measured per telescope	283 hν ms -1

Article number, page 2 of 16 Julien Woillez et al.: AGILIS: Agile Guided Interferometer for Longbaseline Imaging Synthesis

In presence of Kolmogorov turbulence, the mean phase variance after tip/tilt correction is ∆

= 0.134(D/r 0 ) 5/3(Noll 1976), corresponding to a Strehl ρ = e -∆ 3 of 25% and 65%, at respectively D/r 0 =

and D/r 0 = 2.

Article number, page 10 of 16 Julien Woillez et al.: AGILIS: Agile Guided Interferometer for Longbaseline Imaging Synthesis

Article number, page 12 of 16 Julien Woillez et al.: AGILIS: Agile Guided Interferometer for Longbaseline Imaging Synthesis

Acknowledgements. Much of the work on the 'OHANA Iki demonstration was carried out by students from École Polytechnique, and the authors wish to thank Benjamin Lenoir, Nicolas Clerc and Aurélien Bocquet for their contribution to this project, and Flora Bouchacourt and George Zahariade for their early contribution to the two 'Ohana Iki telescopes. The J and H band silicate fibres were integrated and characterised at XLIM with the help of Laurent Delage and Sébastien Vergnole. Installed in the Coudé room of the CFH Telescope, the 'Ohana delay line was built by the Technical Division of the Institut National des Science de l'Univers (INSU). The 'Ohana Iki demonstration would never have been possible without the unfaltering support of the Canada-France-Hawaii and W. M. Keck Telescopes. We finally thank Poli'hau for the snow she never failed to gift us.


Philip M Hinz

Rachel Bowens-Rubin

Christoph Baranec

Kevin Bundy

Mark Chun

Daren Dillon

Brad Holden

Wouter Jonker

Molly Kosiarek

Renate Kupke

Stefan Kuiper

Olivier Lai

Jessica R Lu

Matthew Maniscalco

Matthew Radovan

Sam Ragland

Stephanie Sallum

Andrew Skemer

Peter Wizinowich

Developing adaptive secondary mirror concepts for the APF and W.M. Keck Observatory based on HVR technology

Keywords: Adaptive Optics, Adaptive Secondary Mirrors, Large Format Deformable Mirrors

établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Adaptive optics (AO) is an important capability of ground-based telescopes that enable higher spatial resolution, more sensitive observations. Integrating the AO into the telescope optics (via an adaptive secondary mirror) can significantly improve sensitivity for both diffraction-limited AO (especially at 2-5 µm), and seeing-limited instruments that employ ground-layer adaptive optics (GLAO). Current generation adaptive secondary mirrors (ASM's) have been implemented at several telescopes, including the MMT, LBT, [START_REF] Riccardi | The adaptive secondary mirror for the Large Binocular Telescope: optical acceptance test and preliminary on-sky commissioning results[END_REF] Magellan, and VLT using voice coil actuators and thin glass shells to replace the standard secondaries (see [START_REF] Biasi | Contactless thin adaptive mirror technology: past, present, and future[END_REF] for an overview). While these devices are in routine operation, several aspects make them non-ideal, tied to the low power efficiency of current actuator designs. TNO (The Netherlands Organization) has developed a technology with efficiencies approximately 40 times that of current actuators. [START_REF] Kuiper | Advances of TNO's electromagnetic deformable mirror development[END_REF] The actuators utilize the efficiency gains of enclosing the magnetic field path that moves the actuator in a ferromagnetic material, thus reducing the current needed to apply a particular force. This larger force allows for building in an internal stiffness to each actuator and rigid connections to the facesheet. The resulting assembly has very high structural resonant frequencies, compared to voice coil designs, allowing a simple control approach. Further, the power required to correct turbulent wavefronts can be dramatically lower, allowing for simpler, passive cooling approaches to the system. Finally, the additional efficiency can be traded against the facesheet thickness to provide a sturdier deformable membrane that reduces fabrication risk Send correspondence to P. Hinz, E-mail: phinz@ucsc.edu and complexity. The resulting system has the potential to be more robust and simpler than currently deployed ASM's.

Development of this technology can be aided by lab and on-sky devices that are used on small and medium aperture telescopes, demonstrating the readiness of the technology for large aperture telescopes and next generation observatories such as the TMT. Below, we review some of the motivations for an ASM-based AO system for large aperture telescopes like W.M Keck Observatory (WMKO) and next generation of extremely large telescopes. We describe concepts for a lab-based ASM prototype, called FLASH, a concept for an ASM on the 2.4 m Automated Planet Finder (APF) telescope, and the current status of a concept study for the Keck telescopes.

MOTIVATION FOR ASM-BASED AO

The value of integrating an ASM into a telescope facility primarily lies in the potential for broader use of AO by any instrument that can benefit from the improved image quality. We review below two areas where an ASM-based AO system can be advantageous.

Improved Thermal Infrared Observations

AO systems that are designed for diffraction-limited operation with post-focal plane optics require additional optical surfaces to form an image of the pupil and provide field rotation compensation. Taking the Keck AO bench as an example, the system introduces 7 reflections after the tertiary mirror for a total of 10 reflections. A dichroic also splits the light between science instrument and wavefront sensor (WFS). We assume the primary mirror and tertiary mirrors are 95% reflective in the infrared (up-facing mirrors tend to not stay as clean as the down-facing mirrors) and the secondary and each post-focal mirror is 97.5% reflective. We further assume the dichroic is 96% transmissive. The resulting throughput of the system is 70%. The emissivity (one minus the throughput) of the system is 30%.

An ASM-based system would only have the telescope optics contributing emissivity at the level of 12%. The throughput would be improved by eliminating four reflections to 78%. The field rotator and dichroic could be cooled to eliminat their contribution to any emissive background.

Similar to the calculations shown in, [START_REF] Lloyd-Hart | Thermal Performance Enhancement of Adaptive Optics by Use of a Deformable Secondary Mirror[END_REF] the background for these two comparable systems can be calculated using blackbody emission of the typical nighttime temperature of the telescope over the passband of interest with the emissivity, em, for each system as calculated above. The resulting background flux in photons/s/m 2 /nm/arcsec 2 is given by

F tel = 2 • c • π 2 (180 • 3600) 2 λ 4 em • 10 -9 e h•c λ•k•T tel -1) (1)
where c, h, and k are the speed of light, Planck's constant, and Boltzmann's constant respectively, and T tel is the temperature of the telescope optics. Figure 1 shows the resulting background at two relevant passbands, K and L. Plotted along with these is an estimate of the sky brightness (F Sky ) from Gemini 5 for Maunakea at an airmass of 1.5 and PWV of 1.6 mm.

One notices that there are regions of the K and L band where the telescope emission dominates over the sky background. For these regions of the spectrum, an ASM-based system can provide the most significant improvement in sensitivity. It is possible to estimate the relative time required to achieve a particular sensitivity, [START_REF] Lloyd-Hart | Thermal Performance Enhancement of Adaptive Optics by Use of a Deformable Secondary Mirror[END_REF] if the noise is dominated by the effects described here (as opposed to, say, read-noise from the camera detector, or photon noise from the source itself).

t postf ocal-AO t ASM -AO = T hpt ASM -AO T hpt postf ocal-AO 2 F tel-postf ocal-AO + T hpt postf ocal-AO • F sky F tel-ASM -AO + T hpt ASM -AO • F sky (2)
where T hpt are the throughput numbers for each system above. The right panel of Figure 1 shows this relative time. Time improvements of factors of 2 to 3 are possible in regions of the K and L photometric bands.

Figure 1: Calculation of the background telescope emission for a post-focal plane AO system, compared to an ASM-based AO system at K and L bands. The modeled sky emission for Maunakea at a PWV of 1.6 mm and airmass 1.5 from Gemini is also included. The right panels show the effect on time to reach a particular SNR when comparing these two systems.

Ground Layer Correction

Studies of many ground-based astronomical sites show that a large fraction of the optical turbulence arises within the first few hundred meters of the ground (including Mt. Graham, [START_REF] Masciadri | optical turbulence vertical distribution with standard and high resolution[END_REF] San Pedro Martir, [START_REF] Avila | Generalized SCIDAR Measurements at San Pedro Mártir. I. Turbulence Profile Statistics[END_REF] Paranal, 8 and Antartica 9 ). AO systems that correct for only the ground layer of turbulence, ground-layer adaptive optics system (GLAO) , take this fact into consideration and provide a partially corrected wavefront over fields of view several arcminutes in size. Facility GLAO systems have been deployed at several telescopes, including the LBT 10 and the VLT. In the case of Maunakea, Hawaii it appears that the ground-layer is dominated by a very thin surface layer with most of the optical turbulence within the first 30 meters 11 , 12 , 13 . GLAO over fields of view of 18 arcmin has been demonstrated on Maunakea. [START_REF] Chun | On-sky results from the wide-field ground-layer adaptive optics demonstrator 'imaka[END_REF] An ASM enables these very wide fields of view since the design/fabrication of the optical relay system needed for a conventional deformable mirror system is difficult. The optical designs are driven to large optics (reducing the physical angles on the elements in the relay) and aspheric surfaces. [START_REF] Chun | Imaka: a one-degree high-resolution imager for the Canada-France-Hawaii Telescope[END_REF] We note that the image quality and pupil quality over the field must meet strict optical requirements. By making the wavefront correction within the telescope optics, we avoid the latter problem and a simple field correction (e.g. a field flattener lens) allow these large corrected fields to be obtained. The Subaru, [START_REF] Rigaut | A conceptual design study for Subaru ULTIMATE GLAO[END_REF] and Keck 17 telescopes on Maunakea are developing or are studying GLAO systems for their telescopes. Performance simulations [START_REF] Lu | Ground layer adaptive optics for the W. M. Keck Observatory: feasibility study[END_REF] have been developed to show that a GLAO system on Keck will improve the FWHM by 1.5x for visible (500 nm) and 2x for NIR (1.5 µm) observations. The Gemini Observatory studied this option in the past [START_REF] Szeto | A proposed implementation of a ground layer adaptive optics system on the Gemini Telescope[END_REF] and are reconsidering these gains given the maturing and developing ASM technologies. An ASM based on the TNO actuators [START_REF] Kuiper | Performance Analysis of an adaptive secondary mirror for the University of Hawaii 2.2-meter Telescope[END_REF] is being developed 20 for UH2.2-meter telescope. [START_REF] Chun | A new adaptive secondary mirror for astronomy on the University of Hawaii 2.2-meter Telescope[END_REF]

TESTING TNO ACTUATOR TECHNOLOGY

TNO has built several mirrors with actuators on an 18 mm spacing that have been used in AO demonstrations and test setups. One such device (dubbed DM3 by TNO) has been characterized in the Lab for Adaptive Optics (LAO) at UCSC. [START_REF] Bowens-Rubin | Performance of Large-Format Deformable Mirrors Constructed with TNO Variable Reluctance Actuators[END_REF] Measurements of the stroke, influence functions, linearity and hysteresis have been carried out, verifying the suitability of these devices for use in large format deformable mirrors.

The first on-sky ASM using this technology will be deployed to, and demonstrated at, the University of Hawaii 2.2-meter telescope (UH88) on Maunakea, HI. [START_REF] Chun | A new adaptive secondary mirror for astronomy on the University of Hawaii 2.2-meter Telescope[END_REF] To support the deployment of this TNO ASM at the UH88, we have worked with TNO to build the First LAO Adaptive Secondary Holophote (FLASH). This is a 19 actuator device with the same actuator spacing and facesheet thickness as the UH88 ASM. The device has an aperture of 160 mm. The facesheet has been manufactured and coated from standard polished borofloat sheets that have been pressed flat. The slumping technique explored for FLASH is anticipated to be the standard technique for generating future facesheets for the APF and Keck ASM. FLASH is due to be delivered in late 2020, and will be characterized in a similar way to the DM3. In addition we anticipate carrying out cold and gravity tests of the device as well as capacitive sensor measurements of both its high speed response and long term stability.

MOTIVATION FOR AN ASM FOR APF

Adaptive optics has the potential to improve both the observational efficiency (by concentrating the point spread function of the telescope) and the instrumental stability (by creating a PSF that is more stable than is possible with a seeing-limited telescope) of APF. The approach of designing an AO system for the APF is to deploy a system capable of improving the image quality, while minimizing the changes to the spectrometer and calibration system. Thus, we have elected to build the AO system into the telescope itself.

Instruments such as the APF/Levy tend to observe bright stars in order to make precise radial velocity (RV) measurements. As such, there are plenty of photons available to measure and correct the wavefront of the light going into the spectrometer. Further, there is no anisoplanatism effect since the "guide star" used for wavefront control is the science object itself. This allows for a straightforward and simple implementation of the adaptive optics system. One requires only an on-axis, natural guide star, wavefront sensor.

For typical observations, the APF uses an image plane slit width of 0.5 arcsec. Seeing on Mt. Hamilton averages 1.5 arcsec. Analysis of guider data for a typical sequence allows us to estimate the slit throughput as 21% with variations of 4% as seen by the guider over 1 second integrations (see Figure 2 left). Some of this throughput is due to atmospheric seeing. However, we see a significant portion of the throughput reduction to be due to slow (<1 Hz) tracking variations.

We can simulate the expected improvement. We have used the python package HCIpy 23 to create an atmosphere with similar seeing to the guiding data and have added in slow tracking variations at 0.3 and 0.05 Hz. The resulting slit efficiency (23%) and variations of 8% are similar to what is seen by the APF guider (Figure 2, right). By carrying out closed loop AO corrections we can increase the efficiency by 2.1 times. An additional benefit is the variation in efficiency is reduced to about 1%. For the 1 arcsec slit width the improvement is similar: without AO correction the efficiency is 45% while after correction it is 72% for a 1.6 improvement factor.

The connection between PSF and RV stability is complex. One example of their correlation is seen in HARPS data (admittedly, a different style spectrograph to APF/Levy) where Lo Curto et al. [START_REF] Lo Curto | Along the path towards extremely precise radial velocity measurements[END_REF] note that a guider variation of 0.1 arcsec results in approximately 0.3 m/s errors. Figure 3 shows the improved stability, compared to current performance an AO system can provide. Offset variations, seen at the APF with a standard deviation of 0.2 arcsec at 1 Hz (Figure 3 left top and right top simulated open loop data) can be reduced to 0.004 arcsec (Figure 3 right simulated closed loop data). Similarly the full width at half maximum (FWHM) estimates for 1 s exposures are reduced from 1.2-1.3 arcsec. to 0.05 arcsec. The variations in the FWHM are reduced from 0.1-0.2 arcsec. to 0.001 arcsec. In other words, the point spread function variations in the resulting spectrum can be reduced by dramatic amounts. While it is not straightforward to translate this image stability improvement into RV stability improvement, this setup will allow us to test what the value is for AO-integrated RV spectrometers.

How can we determine whether the image motion and PSF variations affect the quality of the RV measurements? As a comparison, during the nights of Aug 22 and 23 in 2016, two stars were observed simultaneously with the APF/Levy spectrometer and the Planet Finding Spectrograph 25 (PFS) on the Magellan Clay Telescope. The observations were made so to ensure that both data sets had the same start time for each exposure. Both instruments have an Iodine cell; both are mounted on the telescope at the Nasmyth; both use apertures that depend on the natural seeing; both have the same optical design, and the data were reduced by the same individual, Paul Butler, using the same software.

The main differences between the APF/Levy and Magellan/PFS is that the latter has both a larger aperture and better seeing. For both sets of observations of the same star, an additional source of error, beyond the shot-noise measurement errors, is required to explain the scatter in the data. For the APF/Levy, that additional error is 1.2 m/s, as compared with only a 0.6 m/s additional scatter from PFS, see Figure 4. This additional scatter of 1.2 m/s matches the floor in the measurement error found by Burt et al. [START_REF] Burt | The Lick-Carnegie Exoplanet Survey: Gliese 687 b-A Neptune-mass Planet Orbiting a Nearby Red Dwarf[END_REF] for quiet, bright stars on Since the two instruments have nearly identical optics and reduction software, an additional factor appears to be affecting the APF, resulting in over double the internal scatter (1.3 m/s) compared to the PFS data (0.6m/s). It is plausible that this is due to the worse image motion and seeing for the APF. the timescale of months. Since the main difference between the instruments is the better seeing for the PFS, it is plausible that the typical additional scatter seen at APF is due to image motion on the spectrometer slit.

Even if only the efficiency improvement can be realized, the value of AO for the APF is to increase the cadence of nightly observations. The efficiency improvement suggests that we could be able to observe essentially double the number of stars per night compared to current observations. We expect to provide this improvement on stars as faint as I=11. This dramatic speed up of observations is equivalent to having a second APF available.

AO FOR APF CONCEPT

The Automated Planet Finder (APF) is a 2.4 m telescope with a high spectral resolution iodine cell-referenced spectrometer. [START_REF] Vogt | APF-The Lick Observatory Automated Planet Finder[END_REF] Typical targets are relatively bright stars that can be monitored for small radial velocity variations due to orbiting planets. Because of this targeted mission, the design of an AO system to stabilize the PSF for the APF can be relatively straightforward. We require a wavefront sensor that uses light not employed for science observations. A suitable passband is 700-1000 nm. Since the spectrometer is observing a bright star, the WFS will be fixed on-axis. We set the spatial sampling at 8 subapertures across the telescope diameter. This will set both the deformable mirror actuator geometry and Shack-Hartmann lenslet size. We arrived at this value after exploring different spatial samplings in the AO simulation. While better samplings improved the Strehl, the coarse slit size resulted in little improvement in throughput above this value.

ASM

The deformable mirror will be the 37 cm diameter telescope secondary mirror. The high efficiency HVR actuators will allow for us to deploy a secondary mirror without the need for any active cooling of the assembly. This allows for a very compact and relatively simple assembly as shown in Figure 5, the ASM will replace the fixed secondary mirror, while allowing for reuse of the focus and tip/tilt mechanism built into the APF top-end structure. The notional actuator geometry is shown in Figure 5 (right). The actuator spacing is similar to the UH-88 design and to the FLASH prototype being tested in the Laboratory for Adaptive Optics. To match the existing APF design, the facesheet will be a hyperbola shape with a radius of R=1198 mm and a conic constant of -1.49. The facesheet can be generated using a slumping of borofloat flat polished sheets. Tests are underway in the LAO to validate this fabrication approach.

Figure 5: The APF secondary assembly (left) and layout of the ASM actuators (right). Three parallel screw assemblies provide focus tip and tilt of the secondary assembly. These will be reused for the ASM upgrade.

WFS

Since the wavefront sensor requires good sensitivity in the red, and good noise performance to be able to operate on the faintest stars for an APF observation, electron multiplied CCD (EMCCD) devices are ideal. Alpao has developed a Shack-Hartmann (SH) EMCCD device with low latency and high framerates suitable for our needs. The device has 16x16 sub-apertures and can operate at up to 1004 Hz. Since our needs are to have 8x8 SH, we can operate the device at up to 1838 Hz with a frame latency of 69 µs. The SH wavefront sensor will use the light from 700-1000 nm, as shown in Figure 6. The average quantum efficiency over this region is around 50%. Assuming a 30% (not including the detector) system throughput, and using the specified noise for each subaperture from Alpao we estimate being able to provide usable stabilization down to guide star magnitudes corresponding to an I band magnitude of approximately I=11. Simulations with the HCIpy software package 23 confirm this, indicating 1 kHz operation will be optimal to stars as faint as I=9, 300 Hz should be used for stars with 10-12, and that some improvement is possible using 100 Hz framerate down to I=14 (see Figure 6, right).

The WFS will be fed by a short pass dichroic that has a cut-on wavelength of approximately 700-750 nm (to be determined in collaboration with APF observers). The dichroic will feed a transmissive reimaging optic that images the APF pupil onto the Alpao Shack-Hartmann lenslet array. The fore optics for the Levy spectrometer are shown in Figure 7. They are laid out on an optical breadboard that has suitable space for a dichroic, reimaging lens and Alpao WFS module. The remaining light goes through several stages that allow for optics to be inserted in the beam. We will use the calibration source stage to allow insertion of a short pass dichroic in the beam. The dichroic will reflect long wavelength light to an Alpao SH WFS. A simple reimaging lens is all that is needed to create a pupil image on the SH WFS camera.

APF AO system

Currently the APF operates with a guider camera providing pointing information to the telescope at a 1 Hz rate. This system will be retained and used for an acquisition camera for the system. Once the star is acquired on the WFS, the guiding corrections will be turned off and the AO loop will provide stabilization and, if needed, pointing offsets for the telescope tracking software. The real time computer will be based on the Keck RTC setup developed for the infrared pyramid WFS on Keck. As such, the software implementation involves an adaptation of an existing system, rather than implementation of any new AO software.

Calibration

Once delivered, the ASM will be characterized via a deflectometry test. The system will be setup to be illuminated by a large LCD screen. The ASM will undergo a poke test to measure the influence functions of all the actuators. Once these are measured, we will have an initial interaction matrix to deform the facesheet. Further refinements of the interaction matrix will be achieved by applying modal shapes to the mirror, to map out achieved versus commanded surface deformations. Once the deflectometry tests have been completed under standard laboratory Figure 8: Layout for a deflectometry test for the APF ASM. A large (1.1 m x 2 m) LCD screen will be used to illuminate the ASM with a pattern that will be recorded by a camera. The screen does not completely illuminate the optic as seen by the camera (right), but can be rotated to measure the complete surface. conditions we will carry out the same measurements over a range of elevation angles from zenith to horizon. UCO has a cold chamber that can carry out the same tests at temperatures down to -10 C .

KECK ASM CONCEPT DEVELOPMENT

The lab testing and APF ASM described above, along with the HVR ASM on the UH88 will provide technology platforms to demonstrate the suitability of this technology for use in astronomical facilities. In parallel we are developing a concept for an ASM that can be deployed at Keck observatory. Development of the concept allows us to understand the scope and resources needed to deploy an ASM at WMKO.

Instrument Readiness

An ASM facility promises to have broad application for AO-improved performance. However, integrating such a different AO approach into existing and proposed instrumentation will require careful planning and identifications of issues early on in the project to understand what is possible. The work described here builds on the science case and instrument readiness studies lead by J. Lu and summarized in. [START_REF] Lu | Ground layer adaptive optics for the W. M. Keck Observatory: feasibility study[END_REF] While the work for the current study is still to be done, we summarize below the existing and future instruments likely to be used with an ASM-based AO system.

Existing Instruments

MOSFIRE, an infrared imager and multi-slit spectrograph at the Keck I Cassegrain focus, is perhaps best suited for a GLAO feed, although it lacks an atmospheric dispersion compensator. Differential image refraction separates images by about 0.3 arcsec at 2 airmass between 1 and 2.4 µm, so a lack of an ADC is limiting but GLAO can still be beneficial. A replacement detector with smaller pixels than the current 0.18 arcsec. would be needed to take advantage of the GLAO image quality. This is possible with new generation H2RG devices from Teledyne. There is a feasible design for deploying laser-guide star wave-front sensors in front of MOSFIRE in the tertiary tower in order to measure the wave-front error LRIS and DEIMOS may be able to accept a GLAO feed based on their internal image quality; but, they lack either an atmospheric dispersion compensator (DEIMOS) or flexure compensation (LRIS) to utilize narrower slits matched to the GLAO image quality.

Diffraction-limited instruments such as OSIRIS on Keck I and NIRC2 and NIRSPEC+AO on Keck II make use of the AO bench for wavefront sensing and correction. [START_REF] Wizinowich | Observatory Laser Guide Star Adaptive Optics System: Overview[END_REF] A replacement for the AO bench that selects light for wavefront sensing without additional optics would be needed to realize the improvements described above for an ASM-based AO system. To replicate the AO bench functionality with these existing instruments, such a system would need to accomplish field rotation, and natural guide star and laser guide star wavefront sensing, as well as acquisition and tip-tilt sensing. KCWI, a multi-object optical spectrograph with 0.15 arcsec. pixels and a FOV as large as 20x33 arcsec could potentially benefit from GLAO.

Instruments such as HIRES may benefit from the additional image stability an ASM could supply if a natural guide star wavefront sensor could be added to their guiding capabilities.

Future Instruments

Several planned or proposed instruments could benefit from an ASM.

An upgrade to the LRIS (LRIS2) is being planned that will incorporate a flexure compensation system and allow for reconfiguring the system to give space for a WFS package.

The Santa Cruz Array of Lenslets for Exoplanet Spectroscopy (SCALES) is an infrared integral field spectrograph that works at wavelengths out to 5 µm where the lower background of an ASM would benefit sensitivity as well as AO performance.

The Fiber Optic Broad-band Optical Spectrometer (FOBOS) is a proposed wide field (20' diameter), moderate spectral resolution facility instrument for Keck. GLAO with an adaptive secondary would improve photometric depth achieved on single fiber collectors, enable crowded source targeting and create new scientific opportunities with critically sampled IFUs which spatially resolve galaxies beyond z ∼ 0.5.

The Immersion Grating Near Infrared Spectrograph (IGNIS) is a high spectral resolution infrared spectrometer potentially providing improved performance relative to the existing NIRSPEC instrument on Keck, based on immersion grating spectrometers similar to IGRINS. [START_REF] Park | Design and early performance of IGRINS (Immersion Grating Infrared Spectrometer)[END_REF] Integrating such an instrument with the ASM has the potential to provide improved sensitivity at wavelengths beyond 2 µm.

Keck ASM Study Status

The Keck ASM study is currently underway to develop a concept based on HVR technology with the following goals:

• Develop a concept of an ASM suitable for integration with the Keck telescopes The intention is to develop the concept to the level that the scope of such an implementation can be understood, positioning the WMKO community to determine a suitable funding approach for future implementation. The study began in August 2020, with a plan to complete this stage of the effort in summer 2021.

Actuator Tradeoff

The choice of the number of actuators for the study is driven by the scientific motivation of providing a device that can provide good GLAO and diffraction-limited AO performance for future generations of WMKO instruments. HVR devices have been demonstrated on spacings as small as 18 mm and up to 40 mm. For the Keck secondary diameter (1.4 m) this would result in total actuator counts from about 1000 total actuators up to about 4000 actuators.

In the initial portion of this study, we considered three separate general concepts for this study: 1000, 2000, and 4000 total actuators (see Table 1 for a listing of parameters for each concept). The actuators are assumed to be laid out in a circular grid for each concept with an additional outer ring of actuators for each concept, used to control the edge effects of the shell. The requirement on the interactuator stroke drives the thickness of the shell specified for different actuator count ASM designs. We assume in Table 1 that the interactuator stroke required scales with the actuator spacing. The achievable deflection of an actuator also scales with the thickness of the facesheet cubed. Taking these two effects into account we can estimate the thickness required for different actuator counts starting from the calculation that the 1000 actuator count achieves an interactuator stroke of 4 µm for a projected spacing of 350 mm.

The 1000 actuator concept would already provide improved AO performance compared to the current Keck AO bench (which has a fitting error of 190 nm using the same atmospheric parameters as in Table 1). Still, we expect that instruments such as SCALES that depend on high contrast AO performance for achieving their science goals would be limited by the fitting error introduced by this low number of actuators. Similarly GLAO at shorter wavelength could benefit from a finer actuator pitch. For 4000 actuators there are two effects that may make this design less desirable. First, the smaller separation drives the facesheet to smaller thicknesses, to achieve similar levels of interactuator stroke. This potentially makes the shell more difficult to manufacture and possibly more fragile to handle. In addition, the weight for the full system becomes significantly more for this large actuator count. Because of these competing technical issues we have decided to develop further the concept for 2000 actuators for this study. It is useful to note that these alternative concepts are all viable should the motivations for deploying an ASM at WMKO be different from those considered for this study.

Current TNO Concept

Figure 9 shows the current concept for an HVR ASM at WMKO. The device could be housed in a dedicated, existing, octagonal top-end that allows for the complete assembly to be swapped during daytime operations. The moving mass part of the ASM, is similar in depth to the current, solid secondary mirrors for WMKO (about 200 mm at the center). The envelope of the conceptual design allows for existing infrastructure on the telescope top-end, including the laser beam projector optics.

The assembly is mounted on a large hexapod structure that provides up to 50 mm of piston motion. This focus range, along with the large stroke of the ASM, allows for aberration-free adjustment of the location of the Cassegrain focus by 1-2 m. For example, movement of the Cassegrain focal plane 2 m further from its current location could be accomplished by moving the ASM 25.5 mm closer to the primary and applying a correction on the ASM for the spherical aberration introduced by this movement of about 5 µm peak-to-valley. The hexapod assembly also provides static tip, tilt and centration of the secondary, to sub-micron repeatability.

The bright blue backing structure shown in the figure houses the actuators. The backing structure is silicon carbide, while the facesheet will likely be borofloat glass or similar material. The coefficient of thermal expansion for these materials is quite similar, minimizing the potential distortion introduced by thermal changes. The actuator electronics are located at the back end of the hexapod. A kinematic interface exists between the ASM backing structure and the hexapod top ring to minimize deflections from hexapod movement. These locations also provide possible interface locations for fast tip-tilt actuators, should these be desired, to vibrationally isolate the ASM. An initial finite element analysis of the structure indicates that resonant modes of the structure are at or above 750 Hz. It is worth noting that, the actuators are designed to have resonant frequencies of around 1 kHz. Since the actuators are rigidly connected to the facehseet the deformable shell has similarly high frequencies for its resonant modes. This is different from voice coil-based ASM's with facesheet resonant modes that are much lower due to the lack of intrinsic actuator stiffness. Such a design requires more complex internal control laws and co-located position sensors for high speed response and electronic damping 30 of these low frequency shell vibrational modes.

CONCLUSIONS

ASM's that are simple, robust and high performance are being designed are around the hybrid variable reluctance actuators that have been recently developed by TNO. Validation of this technology is underway through several prototype devices and the UH-88 ASM project. Here, we have presented initial concepts for ASM's that can be deployed on the APF and at WMKO. The devices can be designed to work with and expand upon the current capabilities of these facilities. The deployment of an ASM for the APF can provide improved efficiency and image stability, potentially leading to more efficient and stable radial velocity measurements. An ASM for WMKO can provide both GLAO and diffraction-limited capabilities for a wider suite of instruments. It has the potential to broaden the use of AO at WMKO, making adaptive correction of the wavefront available to any instruments capable of measuring the correction needed. Development of a concept and strategy for leveraging this capability with current and future instruments will be important for defining a path forward for telescope-integrated AO at WMKO.

Figure 2 :

 2 Figure 2: Current APF measured slit efficiency as measured using the guider (left) and simulated efficiency (right) without and with AO correction.

Figure 3 :

 3 Figure 3: Current APF image offset (top left ) and image width (bottom left) compared to simulated image offset (top right) and image width (bottom right) for open and closed loop adaptive optics correction. The AO will both reduce the image offset variations and improve the image width and stability of the PSF variations.

Figure 4 :

 4 Figure 4: Histogram of RV scatter seen by the APF (blue) compared to PFS (orange) for simultaneous observations of HD 3651. The typical measurement uncertainty for each instrument is shown in the upper left.Since the two instruments have nearly identical optics and reduction software, an additional factor appears to be affecting the APF, resulting in over double the internal scatter (1.3 m/s) compared to the PFS data (0.6m/s). It is plausible that this is due to the worse image motion and seeing for the APF.

Figure 6 :

 6 Figure 6: Quantum efficiency of the Alpao WFS (left) from the EMCCD factsheet (see alpao.com) and the simulated Efficiency Improvement vs. Magnitude with AO compared to no correction.

Figure 7 :

 7 Figure7: Model of the APF optics, showing the location for a WFS camera. Light arrives from the bottom and is directed to the guider on the bottom right. The remaining light goes through several stages that allow for optics to be inserted in the beam. We will use the calibration source stage to allow insertion of a short pass dichroic in the beam. The dichroic will reflect long wavelength light to an Alpao SH WFS. A simple reimaging lens is all that is needed to create a pupil image on the SH WFS camera.

•

  Develop a dynamical and thermal model for the design • Define interfaces for integrating the device into the telescope top-end • Develop an optical testing strategy for deploying and maintaining the ASM • Develop a rough cost estimate

Figure 9 :

 9 Figure 9: Concept for an ASM for Keck. The left image shows the device housed in an existing Keck top-end hexagonal structure. The right image shows the device mounted on a hexapod capable for static alignment of the ASM.

Table 1 :

 1 Parameters for a Keck ASM for different total actuator count

	Target Number of Actuators	1000 2000 4000
	Actuator spacing on ASM (mm)	36	26	19
	Projected spacing on Primary (mm)	346	245	173
	Actuators Rings	19	26	37
	Actuators in Clear Aperture	1027 1951 3997
	Total Actuators	1135 1951 4213
	Fitting Error for r 0 = 10 cm (nm)	123	92	69
	Facesheet thickness (mm)	3.3	2.9	2.4
	Moving Mass	432	577	855
	Total Mass	982	1127 1405