OPTICAL CALIBRATION AND TEST OF THE VLTDEFORMABLE SECONDARY MIRRORRuna Briguglio1a, Marco Xompero1b, Armando Riccardi1c, Mario Andrighettoni2d, DietrichPescoller2e, Roberto Biasi2f, Daniele Gallieni3g, Elise Vernet4h, Johann Kolb4i, RobinArsenault4j, and Pierre-Yves Madec4k

1 INAF, Osservatorio Astrofisico di Arcetri, p.E. Fermi 5 50125 Firenze, Italy2 Microgate srl, Via Stradivari 4, 39100 Bolzano, Italy3 A.D.S International, via Roma 87, 23868 Valmadrera (Lc), Italy4 ESO, Karl-Schwarzschild-Str. 2, 85748 Garching bei Munchen, Germany

Abstract. modules of the new Adaptive Optics Facility (AOF) of ESO. The Deformable SecondaryMirror (DSM) for the VLT (ESO) represents the state-of-art of the large-format deformable mirror tech-nology. The paper reports the results of the optical characterization of the mirror unit with the ASSISTfacility located at ESO-Garching and executed in a collaborative effort by ESO, INAF-Osservatorio As-trofisico di Arcetri and the DSM manufacturing companies (Microgate s.r.l. and A.D.S. Internationals.r.l.).

1 Introduction

1.1 AOF and DSM

The Adaptive Optics Facility project [1] consists in transforming the fourth unit telescope ofthe VLT into an adaptive telescope. To this purpose an adaptive secondary mirror, the DSM, isimplemented replacing the M2-Dornier field stabilization mirror. Four 20 W sodium laser guidestars will be launched from the telescope centerpiece to provide the guide sources for the adap-tive optics modules GRAAL (feeding the large IR field of view imager Hawk-I) and GALACSI(feeding the integral field spectrograph MUSE). Using the DSM, the two AO modules providea Ground Layer Adaptive Optics correction while GALACSI also provides MUSE with a LaserTomography mode delivering a 5 to 10% strehl ratio in the visible. Details on the current statusof the AOF may be found in Arsenault & al., these proceedings [2].The DSM is equipped with a 1.2m diameter, 2 mm thickness glass shell and 1170 voice coil,contactless actuators [3], working in an internal closed loop with the feedback of co-located

a runa@arcetri.astro.itb marco@arcetri.astro.itc riccardi@arcetri.astro.itd mandri@microgate.ite dpescoller@microgate.itf rbiasi@microgate.itg gallieni@ads-int.comh evernet@eso.orgi jkolb@eso.orgj rarsenau@eso.orgk pmadec@eso.org

Third AO4ELT Conference - Adaptive Optics for Extremely Large TelescopesFlorence, Italy. May 2013ISBN: 978-88-908876-0-4DOI: 10.12839/AO4ELT3.13507

position capacitive sensors (capsens). The actuators stroke is as large as 100 µm to providechopping and field stabilization capabilities. For further details on the DSM mechanics andelectronics, we refer to Gallieni & Biasi, these proceedings [4].Within this paper we will report the preliminary results of the optical calibration and character-ization of the DSM installed on the ASSIST testbench at ESO.

1.2 ASSIST

ASSIST [5] is the test tower for the optical calibration of the DSM and the AOF. It is composedby two aspheric mirrors (a concave M1 and a convex M2) and a folding M3, that can be orientedto feed different focal stations. During the optical calibration of the DSM, M3 is reflectingthe collimated beam of a Twyman-Green, 4D-Technology dynamic interferometer. Because ofbudget constraints, the quality of the ASSIST optics is known to have a figuring error largerthan the specification on the DSM optical quality (15 nm RMS WF). The M1 figuring is 136nm RMS WFE on ASSIST, then it is required to filter out the M1 contribution from the DSMmeasurements; however, the very high orders from polishing have a spatial scale that is closeto the phasemap resolution and it was not possible to fully compensate them numerically in theverification of the DSM flattening.The DSM is kept in optical alignment with the interferometer by mean of an hexapod.

1.3 Calibration goal and test plan

The optical calibration procedure has been extensively tested and refined during the LBT andMagellan secondary mirrors commissioning [6]. The conceptual steps of the procedure are thecollection of the mirror influence functions (IF) and the computation of the flattening command:these steps provide the system with a local calibration for AO and seeing limited operations. Inorder to perform the large stroke field stabilization and chopping commands, as large as 60 µm,a full range absolute optical calibration of the capsens is needed. This procedure can be startedonly when a good flat is provided, then the full process turns to be iterative. We identifiedan optical test plan for the DSM based on the following steps: initial manual flattening; IFcollection and flattening refinement; actuator mapping in the images; capacitive sensor opticalcalibration and system reconfiguration; IF collection and final flattening; field stabilization test;long term stability test.In the following sections we will go through the steps of the procedures and the results obtained.

2 Initial characterization

2.1 Initial flattening

The first interferometric image of the DSM is shown in the left panel of Fig.1: such mirrorshape was obtained relaxing the actuator forces when the shell was kept floating by the internalcontrol loop. In order to have the full pupil visible, a set of gaussian commands centered on themost deformated spots was applied; then, the first low order stiffness modes were sampled andcorrected obtaining the mirror shape in the right panel of Fig.1. As the fringes density within theimage was as that stage low enough, the standard flattening procedure was started: the full set ofstiffness modes (1170), was sequentially sampled and corrected; the result of such preliminaryflattening is ∼ 100 nm WFE RMS.

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Fig. 1. Left panel: first interferometric image of the DSM, obtained by keeping the thin shell floating and relaxingthe actuator forces. Right panel: DSM shape after the preliminary flattening (22 modes).

2.2 Spider arms effects

The thick spider arms holding the ASSIST M2 mirror projects a 15 pixel wide obscuration onthe image. The immediate consequence is that 1 or 2 actuators per ring fall behind the spiders,for a total of roughly 100 actuators fully or partially masked. As a second effect, the phase re-construction algorithm recognizes separated islands in the image and is not able to join themcorrectly as a single surface, producing a differential piston error. This issue was addressed intwo different ways: for the correction of absolute images, the differential piston was evaluatedextrapolating the inter-segment gaps from circular profiles drawn across the image; for differ-ential images (which are captured when two opposite mirror commands are sampled), the apriori expected shape was subtracted to the frames and then the piston errors were computedand corrected.

2.3 Convection and vibration

ASSIST was characterized in terms of vibration and convection noise. Two measurement sce-narios were considered: the sampling of a differential frame and of an absolute frame. In thefirst case, 1000 frames were collected and the differential residual was computed after averag-ing together n differences. The results, separately for vibration and convection, is shown in Fig.2, showing that the WFE RMS due to convection is as large as 10 nm when averaging threedifferential frames (the standard sampling for the IF). With the same dataset, we evaluated thetypical coherence time of convection noise (10 s) by computing its structure function.The case of absolute images is more complicated because it is not possible to separate signaland error. The strategy is to collect frames over a long time span to average noise out (theacquisition of each individual frame must be separated by at least the coherence time): wedemonstrated however that the convection pattern changes over a time scale of tens of min-utes (non-stationarity) so that a very long averaging is not effective. We tested it by comparingtwo images, each of whom obtained averaging 600 frames over 4 hours and with the two setstaken at 4 hours time gap. The WFE of the difference is ∼40 nm RMS and is shown in the rightpanel of Fig. 2 where the convection residual is clearly visible; similarly, the differential WFEmeasured on a time scale of 30 minutes (60 frames averaged together) is of the same order ofmagnitude.

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Fig. 2. Left panel: residual tilt (black) and astigmatism (red) versus the number of differential frames averagedtogether. Middle panel: residual WFE (nm RMS) versus the number of differential frames averaged together.Black line: piston, tip, tilt and focus removed. Red line: astigmatism and trefoil removed. Right panel: differentialconvection pattern.

3 Capacitive sensor calibration

3.1 Concept

The calibration of the capacitive sensors consists in evaluating the parameters of the relation-ship between the capacitive sensor readings and the corresponding mirror positions, as mea-sured with an interferometer. A detailed description can be found in [7]; briefly, the calibrationconcept is based on the following points (Fig.3): the mirror is moved with trefoil-shaped com-mands to span the actuators working range; each command is applied and then sampled by theinterferometer with a differential procedure, to reduce convection noise; at each step, three actu-ators are kept at a fixed position and act therefore as fiducial points in the images; the resultingframes are combined together, using the information of the fiducial points, to obtain the currentabsolute mirror positions in the space.The procedure is based on the keypoint that the displacement of an uncalibrated actuator when azero command is given is actually zero within measurement noise of the sensor (< 5 nm RMS);also, the use of a trefoil shape and of three reference points provides the correction of the vibra-tion tip-tilt. The effect of the initial lack of calibration is to introduce high order deformationsin the mirror; the procedure must be therefore iterated with increased movement range as longa new set of calibration parameters is obtained.

3.2 Data collection

The fiducial actuators have been chosen close to the peak/valley of the trefoil shape to maximizethe command stroke; as they provide six constraints to the shape, the trefoil has been computedas a combination of six low order mirror modes: this ensures also that the requested actuatorforces are low. The fiducial actuators have been picked up on the third outermost ring to avoidborder effects.A total of three datasets were acquired, starting from an initial span of ±15 µm to a final totalspan of -30 µm +50 µm. The bottom limit position is defined by the saturation value of thecapacitive sensors ADC; the upper limit by the mirror stroke requested for field stabilization.For each trefoil command, 15 differential frames were collected; from Fig.2 convection noiseresiduals are estimated to be as low as 2 nm RMS surface. Vibration noise is corrected whilere-aligning the images on the fiducial points.

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Fig. 3. Left panel: the calibration concept, showing the sequence of the command shapes and the fiducial actuators.Right panel: final result of the calibration, showing the actuator position read by the interferometer vs that read bythe capacitive sensor.

Fig. 4. Optical position as measured by the interferometer vs electrical measurement by the capacitive sensor. Leftpanel: first iteration of the procedure; the departure between the two lines is the effect of the lack of calibration.Right panel: last iteration of the process, showing a good match between the two readings.

3.3 Results and discussion

The convergence of the calibration process is demonstrated in Fig.4: the discrepancy betweencapsens and interferometer position values is eventually corrected in the last measurement (rightpanel in the figure). The data fitting (capsens ADC versus optical positions) is shown in Fig.5together with the fitting error for act n.1169. The response has been modelled with a 3rd or-der polynomial function of 1

x , which gave the best compromise in terms of fitting error andimplementability in the DSP capsens firmware. The maximum fitting error is (typically) lowerthan 50 nm for all the actuators fully visible within the optical pupil. Those masked by the spi-der arms or by the central obscuration due to M2 have been calibrated with a lower accuracy,interpolating the interferometer signal with the surrounding pixels.

4 Preliminary test results

4.1 Mirror modal basis

Adopting the same approach used for the LBT secondaries, the DSM flattening calibration wasperformed with a basis of stiffness modes, rather than a zonal basis (made up of single actuators

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Fig. 5. Fitting result for actuator 1169. Upper panel: fitting of the optical position with the capacitive sensor ADC,based on the 3rd order 1

x polynomial. Lower panel: fitting residuals vs ADC value.

IF). The modal shapes have been measured with the push-pull technique at the highest (25Hz) interferometer frame rate, in order to enhance the noise rejection; 5 images have beencollected for each mode. The modal command amplitude has been maximized according toactuator force threshold and fringes density in the phasemap. For the very high order modes thetypical amplitude was ≈ 5nm WF RMS. In the left panel of Fig. 6 a sample of the mirror modeimages is shown: each mode has been corrected by compensating for the vibration tip/tilt.

4.2 Flattening results

The mirror has been flattened using the modal basis defined above. The reference shape forflattening was the average of 90 frames, collected every 10 s for a total sampling time of 15minutes: such parameters were adopted taking into account non-stationarity and coherence timeof convection as discussed in 2.3; the flattened mirror shape was sampled accordingly. In theright panel of Fig.6 the flattening result is shown; alignment aberration and low order mechani-cal modes (due to thermal drifts within the process) have been removed; M1 polishing residualshave been also compensated up to the spatial scale of a few pixels. The WFE is 29 nm RMSand is due to polishing features of the thin shell, to uncompensated residuals of M1 and to thedifferential convection pattern throughout the process.

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Fig. 6. Left panel: a sample of phasemaps showing the mirror modes. Right panel: phasemap of the DSM afterthe flattening process. Alignment and mechanical aberrations have been subtracted: the WFE is 29 nm RMS.

4.3 Field stabilization test

The accuracy of the tilt command required for the field stabilization has been tested at a smallstroke (2”, corresponding to a PtV of 10.5 µm) and at a large one (12”, 63 µm PtV; commandamplitude is expressed as surface =1

2 WF). The first test was performed by chopping the mirrorby 2” from the reference position at 10 Hz. The images have been analyzed computing the dif-ferential shapes: this provided an effective rejection of both air convection and vibrations. Theresulting high order deformation is 81 nm WFE RMS, and the tilt command accuracy is ∼ 1%.

The large stroke test was performed by moving the mirror to intermediate positions (3”,6”, 9”, 12”) and re-aligning it with the interferometer to compensate for the large tilt applied(that is out of the interferometer capturing range); the test was then repeated with a negative tiltcommand. We measured the mirror shape at the following sequence of position: 0 (referenceR1), 12” (T12′′), 0 (R2), -12” (T−12′′), 0 (R3); each image is the average of 30 frames captured in 5minutes integration time. The test result is given in Fig.7, showing (from the left)

(T1 −

(R1+R2)2

),(

T−1 −(R2+R3)

2

)and their sum. The WFE is respectively 133 and 124 nm RMS (after removing

alignment tip/tilt, focus and the 29 VLT active optics modes); for a comparison, the WFE of(R1+R2−R3−R4)

2 is 14 nm RMS because of air convection. The residual deformations are highlysimilar in the two images (the relative difference is shown in the right panel of the picture andis mostly air convection), this suggesting the possibility of compensating the deformation withan offset command.

4.4 Stability test

The DSM was tested for stability during a large number of overnight, unattended measure-ments, simulating a seeing limited observation. The system conditions (e.g. temperatures, ac-tuator forces) and shape were collected twice per minute. No hardware failures were detectedand no progressive degradation of the WFE was observed, with the exclusion of the focus andtrefoil coming from thermo-mechanical effects.

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Fig. 7. Left and central panel: DSM shape at ±12′′ tilt (respectively) after subtracting the shape at the referenceposition (i.e.the flat); right panel: difference between the two tilted shapes.

5 Conclusion

The DSM was installed on the ASSIST test bench at ESO to be optically tested. After calibrat-ing the capacitive sensors in a position span of 75 µm, the flattening command was computed,resulting in a WFE of 29 nm RMS, including also the residuals of air convection and M1 pol-ishing. The large stroke tilt requested for field stabilization was tested up to 12” correspondingto a PtV command of 63 µm: the residual WFE at the tilted position is 134 nm RMS. The longterm stability was demonstrated with a number of successfully completed overnight tests, withthe DSM being monitored by the interferometer.The refinement of the optical test is scheduled for the end of 2013.

References

1. Arsenault, R.; Madec, PY.; Paufique, J.; La Penna, P.,&al. Proc of the SPIE, Vol 8447,(2012)

2. Arsenault, R., Madec, P.Y., Paufique, J. &al., The ESO Adaptive Optics Facility under Test,AO4ELT3 Conference Proceedings (these proceedings).

3. Biasi, R., Gallieni, D., Salinari, P., Riccardi, A., Mantegazza, P., Proc. of the SPIE, Vol7736, (2010)

4. Gallieni, D., Biasi, R.: The new VLT-DSM M2 unit: construction and electromechanicaltesting. AO4ELT3 Conference Proceedings (these proceedings).

5. Stuik, R.; La Penna, P.; Dupuy, C.; de Haan, M.; Arsenault, R.;&al. Proc of the SPIE, Vol8447, (2012)

6. Riccardi, A., Xompero, M., Briguglio, R., &al, Proc. of the SPIE, Vol 7736, (2010)7. Briguglio, R.; Xompero, M.; Riccardi, A.; Biasi, R.; Andrighettoni, M., Proc. of the SPIE,

Vol 8447, (2012)

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