<title>LBT adaptive secondary preliminary design</title>

LBT adaptive secondary preliminary design D. Gallieni l a, C. Del Vecchio b, E. Anaclerio a, P. G, Lazzarini a a ADS International S.r.l., c.so Promessi Sposi 23/d, 23900 Lecco, Italy b Osservatorio Astrofisico di Arcetri, L.go E. Fermi 5, 50125 Firenze, Italy ABSTRACT We report on the design of the two Gregorian adaptive secondary mirrors of the Large Binocular Telescope. Each adaptive secondary is a Zerodur shell having an external diameter of 911 mm and a thickness of about 1.5 mm. The deformable mirror is controlled by a pattern of 918 electromagnetic actuators. Its shape is referred to a stable ULE back plate by means of capacitive sensors co-located to the actuators pattern. The preliminary design of the system is addressed with particular attention to the reference plate optimization. Keywords: adaptive optics, adaptive secondary, deformable mirror.

1. INTRODUCTION The Large Binocular Telescope’ (LBT) will implement a first stage of wavefront correction by a pair of deformable secondary mirrors (M2). Each one of the adaptive M2 units will be composed by three subsystems, namely the 918 actuators deformable mirror, the pointing hexapod and the laser projector. The feasibility study of the M2 units is hereafter discussed, with particular emphasis on the adaptive mirror design. The LBT adaptive secondary concept is based on the original design2 conceived for the MMT 6Sm conversion and largely documented by dedicated papers presented in this conference3. The major challenges posed by the LBT application are given by the number of channels (almost three times the MMT case) and by the convex shape of the Gregorian secondary mirror. We report on the overall system design of the M2 adaptive unit and we detail the optimization of the reference plate structure. The analysis of the thin shell is documented in a companion paper4presented in this conference.

2. ADAPTIVE SECONDARY LAYOUT The layout of one LBT M2 unit is shown in figure 2. We hereafter describe from top to bottom the major subsystems, highlighting their most relevant features. Laser Projector 1) The laser beam diameter is 550 mm wide. A preliminary design of the laser reflector is based on a honeycomb mirror 128 mm thick. The mirror support system is composed by three webs 120 deg apart and three piezoelectric actuators to steer the mirror. The entire mirror mount implements a manual coarse adjustment capability to align the reflector within the pointing envelope given by the PZT stroke. Hexapod mechanism 11) The hexapod (HP) controls the adaptive secondary position and alignment with respect to the hub platform. Its range is k 5 mm offset along X, Y and 2 directions plus t 0.25 deg tilt. Each HP leg is a linear actuator based on a recycling roller screw driven by a DC motor and controlled by an incremental encoder. A LVDT absolute position sensor is embedded into each leg as well. The actuators are connected to the HP mobile and fixed platforms by universal joints The nominal length of each actuator is 347 mm. Similar actuators have been built for other telescopes (TNG and MMT), achieving micron level accuracy and a typical stiffness of 40 N/pm. * Correspondence. E-mail: gallienieads-intcom;

Figure 1. The Large Binocular Telescope.

URL: www.ads-intcom; telephone: +39 0341 259231; fax ext.: 235.

Proc. of SPIE Vol. 4007, Adaptive Optical Systems Technology, ed. P. Wizinowich, P. Wizinowich (Apr, 2000) Copyright SPIE 508

III) Adaptive Optics unit The adaptive secondary layout is based on the combination of three plates, namely the deformable mirror, the reference plate and the actuators support disk? The structure that holds these plates also hosts the electronics boxes of the parallel computer that drives the actuators. The rest of this section describes the layout and the functionality of each subsystem.

LASER MIRROR

..::g &$.y ,

SWING ARM

SUPPORT FRAME & ELECTRONIC BOXES

COLD PLATE REFERENCE PLATE

5..A... 22. .A. A.. ‘.:.,/.,.:, ._.....A..

DEFORMABLE MIRROR

Figure 2 - The LBT adaptive secondary as it will appear installed into each one of the two Gregorian secondary hubs of the telescope. The exploded view shows the three subsystems of the M2 (Laser Mirror, Hexapod and Adaptive unit) and the major components of the adaptive mirror itself.

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a>

Deformable mirror The Zerodur deformable mirror outer diameter is equal to 911 mm. The thickness of the shell will be the result of an optimization analysis4 that spans over a range from 1 mm to 2 mm. Therefore, 1.5 mm midrange mirror thickness is hereafter assumed. The mirror has a 56 mm central hole, where a membrane is mounted to restrain its lateral motion. 918 permanent magnets are glued on the convex surface of the mirror. The same surface is aluminum plated to make a common armature for the capacitive sensors co-located with the actuators. When the actuators are switched off, the mirror inner and outer edges rest on four end stops connected to the reference plate. Reference plate b) The reference plate is made of ULE and it is 50 mm thick. A central hole with a diameter of 61 mm hosts the support for the membrane that is attached to the deformable mirror. 9 18 holes with a diameter of 13 mm are drilled into the reference plate co-located with the actuators, all radial from the mirror center of curvature. Given the 911 mm obstruction, the reference plate outer surface is cut parallel to the optical axis. The reference plate outer diameter is reduced to 879 mm for a depth of 30 mm to accommodate the outermost actuators row. Aluminum rings (23 mm outer diameter) are plated on the reference plate concave surface that faces the deformable mirror to make a capacitive sensor co-located with each actuator. The reference plate is connected to the aluminum cold plate by three flexures placed 9.61 deg from the optical axis, 120 deg apart. The flexure rods are mounted aligned to the local tangent to absorb the differential thermal deformation of the aluminum and the ULE plates. A set of six astatic levers supports the reference plate as well, in order to reduce its distortion under gravity. These supports are mounted on the aluminum cold plate. Cold plate C> The cold plate is an aluminum disk 45 mm thick with a diameter of 911 mm. It main scope is to hold the 9 18 actuators and to provide an heat sink to remove the power dissipated by the coils. The cold plate is actually made of two separate disks 22.5 mm thick glued together. Cooling channels are machined into one of the two plates. Beside the actuators, the cold plate provide also the interfaces for a pattern of interferometers that measures the absolute separation of the thin mirror from the reference plate surface. These interferometric sensors provide the calibration signals for the capacitive sensors that are co-located with the actuators. Support frame and electronic boxes 4 The cold plate is supported by a frame that interfaces with the hexapod mobile flange. The support frame is connected to the cold plate by mean of six legs that make a sort of passive hexapod mount. A double flexure joint is placed at both ends of each leg to avoid introducing bending moments into the aluminum plate. The support frame embeds three electronic boxes that contain the electronic cards of the parallel computer that controls the actuators. These crates are cooled by pipes that are connected to the cold plate channels.

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Actuators Each actuator is made of a coil that faces the permanent magnet glued on the back of the deformable mirror. The coil has an outer diameter of 11 mm and it is 2.8 mm thick. The radial magnet is 11 mm wide as well and it is 3.6 mm thick. The actuator aluminum cold finger that supports the coil from the cold plate also embeds a PCB for the capacitive sensor signal conditioning. The 102 actuators of the outermost row are tailored to fulfil the space constraint given by the 911 mm obstruction limitation and the concave shape of the mirror. The preliminary mass budget for the M2 unit is resumed in table 1. Table 1 - LBT M2 unit preliminary mass budget.

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+I to

d =zl

#I 94.34 @914

Figure 3 - Detail of the cold plate and back plate with electromagnetic actuators. The flexure that connects the reference plate and the aluminum one represented in a false orientation to show its components.

3. ADAPTIVE OPTICS UNIT DESIGN The major issues faced designing the adaptive secondary for the LBT are hereafter addressedin this paragraph. The actuators pattern is established with particular attention to provide sufficient actuator density at the mirror outer edge. An isostatic support system is designed to interface the back plate and the cold plate and then it is optimized to minimize the back plate reference surface RMS deformation. Finally, the entire adaptive secondary mechanical design is verified by static and dynamic analysis and the cooling system for both the actuators and the electronics is sized. 3,l Actuators layout The 918 actuators are distributed on the mirror surface according to a hexagonal pattern. The angular spacing between the actuator rows is 0.7388 deg, measured from the mirror axis. The envelope of each actuator is given by a 13 mm diameter cylinder, designed to work with a 11 mm diameter magnet glued on the mirror back surface. The radial separation between two adjacent actuators is 25.5 mm and it is also the minimum actuators separation. The distance between the outer actuators row axis and the external edge of the mirror is 12 mm, while the minimum gap between the edge and their holes is 5.5 mm. The distance between the first actuators row and the internal mirror edge is 10.2 mm while the minimum gap between the mirror edge and the actuators holes is 3.1 mm.

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Row

Number of

Angle from optical axis

Case A B C D \E

Thickness 50 mm 50mm 50 mm 50 mm 60 mm

I Boundary Conditions 3 supports @ 375 mm + 3 levers @ 375 mm + 3 levers @ 225 mm 3 supports - ---- @ 375 mm + 3 levers @ 225 mm 3 supports @ 375 mm + 3 levers @ 200 mm 3 supports @?325 mm + 3 levers @ 200 mm 3 supports @ 375 mm + 3 levers @ 225 mm

Table 3 - Reference plate configurations studied to optimize its RMS figure.

Elev, @et9 90 60 30 0

A (w-0

I3 (pm)

c (pm)

D (pm)

E (pm)

-0.28 -0.24 -0.14 -0.99 (*)

-0.62 -0.64 -0.55 -0.30

-0.80 -0.87 -0.72 -0.37

-0.79 -0.88 -0.74 -0.39

-0.44 -0.52 -0.45 -0.26

Table 4 - Reference plate maximum axial displacements for the five parametric models listed in Table 3. (*) m-7 lmm-s fnrw

in Z dire.ctinn.

Table 2 - Actuators layout.

3.2 Reference plate optimization The most stringent functional requirement for the reference plate is to minimize the reference surface figure RMS deformation at the different telescope pointing angles. This would permit to use the adaptive secondary in passive mode as well, that is correcting the telescope induced errors by keeping a stable shape for long periods. A preliminary analysis is run by modeling the reference plate as a continuous structure, i.e. the holes for the actuators are not described. To account for their effect on the plate stiffness the Young modulus is reduced by 30% with respect to its proper value. The scaling factor is derived from a study performed on the MMT adaptive secondary. In fact, the MMT has 336 15 mm diameter holes on a 420 mm diameter disk, while the LBT has 918 13 mm diameter holes on a 9 11 mm disk. The ratio between the disk area and the holes one is 5.42 for the MMT and 5.34 for the LBT. The material adopted for this analysis is Zerodur, to be consistent with the MMT study. The Young modulus adopted is E = 9060 x 0.7 = 6342~10~Pa. The density is scaled to account for the holes as well: 2050 Kg/m3. Given the reference plate external diameter, a parametric analysis is run to optimize both the thickness and the boundary conditions (fixed point and astatic levers). The merit ratio is the minimization of the reference surface max axial displacement. The “Case A” (see tables 3 and 4) is selected as reference plate baseline layout. A detailed FEM. of the reference plate is then produced to optimize its support system.

The material adopted for this final analysis is the actual reference plate one, namely ULE: E = 6600~10~ Pa ; p = 2200 Kg/m3 ; 2) = 0.17 ; a = o.12xIo-6 l/C . The radius of the three external astatic supports is

0.367 m and the internal supports one is 0.186 m.

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The deformations of the reference surface (reference plate concave face) are computed as function of the telescope elevation The reference surface RMS deformation at zenith pointing is equal to 244 nm. The reference surface max displacements for the selected case are resumed in the table 5. For the selected configuration the reaction forces D E F B Elev. Force A C on the six levers are computed (see table 6). (N) (N) (N) . (de& 09 W) (N) N _ c .m 90 Fx The gravity vector acts in the X2 plane. Fz 58.2 58.2 58.2 66.4 66.4 66.4 60 Fx -19.6 -18.9 -18.9 -29.1 -29.1 -21.3 Elev. (de@ 90 60 30 0 Fz 56.2 47.4 47.4 55.4 55.4 59.3 25(Pm) -0.32 (+) -0.34 -0.27 -0.64 (*I 30 Fx -32.3 -33.6 -33.6 -48.1 -48.1 -41.4 Table 5 - Reference surface maximum deformations. 1 Fz 39.3 24.1 24.1 30.4 30.4 37.3 (*I no levers force in Z direction; 0 FX -37.1 -41.5 -41.5 -50.5 -50.5 -50.4 (+Ino levers force in X direction. Fz I Table 6 - Reference plate reaction forces.

2.5207e-14 -&629e-08 -9.258e-08 -MS%-07 -lAmZe-07 -2.315~~07

3*;‘41”0”77 1

Figure 5 - Reference plate Z deformations (the concave reference surface is represented).

3.3 Adaptive secondary unit FEA The adaptive mirror is modeled together with the hexapod mechanism. The reference plate is mounted under the aluminum plate by means of a three flexures support. Each flexure is a 88mm x 1lmm INVAR plate 0.3mm thick. Such flexure allows decoupling the thermal differential deformations of the two plates. A thermal analysis is performed to evaluate the effectiveness of the described support. The resulting radial contraction of the reference plate is 4.4 pm, almost equal to the Aluminum plate one as it would be perfectly decoupled from the rest of the structure. The static analysis computes the max displacements of the reference plate as function of the telescope pointing. The results are reported in table 7. A modal analysis is run to study the dynamics of the adaptive secondary structure coupled with the hexapod one. Three lumped masses (15 Kg x 3) are added to the model to account for the three electronics crates. The results are reported in table 8.

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Elev. (deg) 90 60 30 0

Max X (pm) 200 173 100 0.3

Max Y (pm) 0.5 0.3 0.4 0.3

Max 2 (pm) 12.1 27.7 36.0 35.6

Table 7 - AdaDtive secondarv unit max displacements. Table 8 - Adaptive secondary natural frequencies.

FE3

Displacement 2.004Se-04 1.718e-04 1.4316e-04 l.l453e-04 8.5899e-05 5.7266e-05 ;*86SSe-05

Z:~~~~ji~~~~,~U~~~~~~~~~~~~~.~~~~jiii,D8:l;:1::~~:~~~~~~~::~~~i’i:~~.i:‘:0;:i~~~~::~::~~.:~~~:~~~~ ..:./ ..,:. :.,. ..: .,+.:,.A.(.. ..,...,:.,:: .... .:0.: :,, .,.,,,: ,,., :,.... .:A,/ ,/ ....:..,A;..:::,.. .,...:...

Figure 6 - Adaptive secondary unit static displacements with telescope pointing at horizon.

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Figure 7 - Adaptive secondary unit first bending mode (33.4 Hz).

3.4 Thermal issues The adaptive secondary thermal behavior is studied for the 0.5” seeing case. In such case the actuator RMS force is 0.3 N plus 0.05 N of gravity load (including mirror and magnets own weight). The actuator efficiency is set equal to 0.55 NI fi , based on MMT adaptive secondary actuator measured performances. The total power for each actuator is 600 mW, including 190 mW dissipated by the capacitive sensor board. Each crate dissipates 800 W in the same good seeing conditions. The cooling system gets from the telescope plant the input refrigerant some degree C below ambient temperature. The main pipe passesthrough spider shadow and it ends at the adaptive secondary distribution stage, located on the hub internal face at the Hexapod level. From the distribution box twelve parallel circuits feed the cold plate cooling lines, each one cooling an average of 76 actuators. Then, after passing through the cold plate the refrigerant pipes enter the crates, two pipes cooling each side wall of the crates. At the end all the twelve pipes converge into a single outlet box to exit the M2 hub. The cold plate must be kept at a temperature such as the RMS coil power is removed. The thermal conductance of the actuator is 0.290 (Watt/C), by assuming k = 200 (W / m C) for the AL conductivity. With these values, the temperature gradient needed between the coil and the cold plate to remove 600 mW is: ATF = 0.600 IO.29 = 2 C . This result demands that the input temperature of the refrigerant must be 2 C below ambient temperature. The LBT will be cooled with a 50 / 50 ethylene glycol and water solution, which thermal properties are: Cp=3609(J/KgC)andk=0.49-(W/mC). The fluid temperature increase along the cold plate channels is computed by considering the average of 76 actuators cooled by each one of the twelve lines. The channels section is 18 mm x 6 mm. The fluid velocity into the cold plate channels is chosen as design variable: vc = 1 m/s. The temperature increase along each channel results: ATp = q I ( AP x hp ) = (76 x 0.600) / (48.~10-~x 2698) = 0.35 C The total flow rate results: Q= 12x(vPxSP)= 12 x 1 x (0.018x0.006) = 77 (lit/min)

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Then, after removing the 0.600 x 918 = 550 Watt RMS actuator power from the cold plate, the refrigerant warms up from -2 to -1.7 C with respect to ambient temperature. Each crate contains 20 PCBs, each one controlling 16 actuators. Each coil cools half of a crate side wall, that is it removes one quarter of the crate power. Actually, all the pipes that cool the PCBs run in parallel inside each coil, thus reducing the pressure impedance and the temperature raise. Pipe internal diameter is 8 mm and the length of the contact with the PCB side is 15 mm. The fluid speed into the crate’s pipe is 2.1 m/set. The temperature increase across the crate is then: AT = (800/20/2) I ( 6419 x 3.8~10-~) = 0.8 C Thus, the refrigerant leaves the crates still 0.9 C below the ambient temperature. Further effort will be devoted to augment the actuators thermal conductivity to move the coolant temperature range toward the ambient one. Fianlly, given the following refrigerant properties: p = 1045 kg/m3 and v= 1.84x10m3(Pa s) the pressure drop into the overall adaptive secondary cooling circuit is Ap = 0.63 bar at ambient temperature.

4. CONCLUSIONS We reported on the preliminary design the LBT adaptive secondary mirror. The most relevant issues of the reference plate structural behavior have been successfully addressed. The overall thermal budget of the adaptive secondary has been studied and a suitable cooling system has been consequently designed. The concept of the adaptive secondary controlled by electromagnetic motors originally conceived for the MMT application seemsthen valid for the LBT case as well.

REFERENCES 1. 2. 3. 4. 5.

J. M. Hill, The University of Arizona and Piero Salinari, Osservatorio Astrofisico di Arcetri, “The Large Binocular Telescope Project”, paper No. 4004-07 in this conference; P. Salinari, C. Del Vecchio, V. Biliotti, “A study of an adaptive secondary mirror” in Active and Adaptive Optics, F. Merkle, Vol. 48, pp.247-253 of ES0 Conference Proceedings Series (ESO, Garching, Germany, 1993); A. Riccardi et al, “Adaptive secondary mirror for the 6.5 conversion of the multiple mirror telescope: delivery test results”, paper No. 4007-01 in this conference; C. Del Vecchio, D. Gallieni, “Numerical simulation of the LBT adaptive secondary mirror”, paper No. 4007-09 in this conference; G. Brusa and C. Del Vecchio, “Design of an adaptive secondary mirror: a global approach”, Applied Optics, Vol. 37, No. 21, pages 4656-4662.

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