IMECE SINGLE CRYSTAL PIEZOELECTRIC ACTUATORS FOR ADVANCED DEFORMABLE MIRRORS

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1 Proceedings of IMECE ASME International Mechanical Engineering Congress and Exposition November 13-20, 2004, Anaheim, California USA IMECE SINGLE CRYSTAL PIEZOELECTRIC ACTUATORS FOR ADVANCED DEFORMABLE MIRRORS X.N. Jiang 1, P.W. Rehrig 1, W.S. Hackenberger 1, J. Moore 2, S. Chodimella 2, B. Patrick 2 1 TRS Technologies, Inc., 2820 East College Avenue, State College, PA SRS Technologies, 500 Discovery Drive, Huntsville, AL Keywords: Deformable mirror, single crystal piezoelectrics, piezoelectric actuator, adaptive optics ABSTRACT In this paper, single crystal piezoelectric actuators are developed and demonstrated as a means of increasing actuator authority while maintaining strain precision for adaptive optics used large throw deformable mirror applications. Single crystal (PMN-PT crystal) stack actuators with foot print size of 5 mm x 5 mm and height varied from 16 mm to 21 mm have been designed, fabricated and tested. The actuation stroke larger than 50 µm is obtained under driving electric field of 15 KV/cm for single crystal stack actuators. In-plane actuation stroke is about 25 µm under 8KV/cm for single crystal plate actuators. The characterization results show that the single crystal piezoelectric actuators hold enhanced stroke and coupling coefficient (>0.83) under lower driving field comparing with PZT counterpart, while keep the nature of piezoelectric actuations with high precision, high resolution, fast response under high preload stress. The potential benefits of incorporating these actuators in a deformable mirror (DM) design were demonstrated by system modeling using the Integrated Optical Design Analysis Software (IODA) developed by SRS. The modeling shows that low order aberrations with peak to valley errors as large as 40 microns could be corrected to diffraction limited performance with a reasonable number of actuators and acceptable actuator forces and face sheet stresses. In the case of DM correction with 20 microns of 1 st - Astigmatism-X error (Peak to valley: µm, RMS error: 8.13 µm), the corrected wavefront error was reduced to PV of 0.26 µm and RMS error of µm, which suggest promise for large throw DM applications. INTRODUCTION Various deformable mirrors (DM) have been used for wavefront control in systems such as space telescopes, airborne lasers, etc [1-3]. Actuators available for existing DMs (from Xinetics, Bifano, OKO, etc.) include piezoelectric/electrostrictive actuators and electrostatic actuators, and the stroke of these actuators are all less than 10 µm [1]. The future space missions [2] and focus-offload DM (FODM) for airborne wavefront control system [3] require actuator stroke around 20~50 µm, while still keep resolution less than 3nm, which is beyond the actuator performances for currently available DMs. As it is known that stroke of electrostatic actuators is limited by the compromising between the gap and driving voltage, some efforts have been put to increase the stroke of piezoelectric actuators by developing cofired multiplayer stacks so that larger stroke could be expected by the increased driving field, however, the stroke of piezoelectric and electrostrictive actuators are still small because of that fact that the piezoelectric coefficient of PZT and PMN ceramics are low in nature [4]. Single crystal piezoelectrics with 3~5 times higher piezoelectric coefficient than piezo ceramics are proposed for low profile, large stroke actuation for DMs [4-6]. Furthermore, the excellent low temperature properties of single crystal piezoelectrics are very attractive to cryogenic DM applications. In this paper, single crystal piezoelectric actuators with large stroke and high resolution are designed, fabricated, and tested. The large stroke and high precision stack actuators in 33 mode and in-plane actuators in 31 mode are desired for various DM mechanisms such as piston type DM and edge controlled DM, etc (Fig. 1). The potential benefits of incorporating these actuators in a deformable mirror (DM) design were demonstrated by system modeling. The Integrated Optical Design Analysis Software (IODA), developed by SRS, was used to evaluate the potential performance of a DM design that utilized the advanced single crystal actuators. 1 Copyright 2004 by ASME

2 The characterization results show that the single crystal piezoelectric actuators hold enhanced stroke and coupling coefficient (>0.83) under lower driving field comparing with PZT counterpart, while keep the nature of piezoelectric actuations with high precision, high resolution, fast response under high preload stress. E n d c a p B e C u S h i m T a b f o r S o l d e r i n g Face sheet Actuators Electroded Single Crystal Plate Membrane mirror E p o x y In-plane Actuators Figure 1. Schematic of DM. DM with stack actuators. DM with in-plane actuators. (c) EXPRIMENTAL PROCEDURES Single crystal piezoelectric actuators fabrication Both stack actuators and in-plane actuators were designed and fabricated. For stack actuators, PMN-PT crystal plates with dimension of 5 mm x 5 mm x 0.5 mm were diced from the PMN-PT crystal boule, and followed by 500 Å Cr/2000 Å Au sputtering on both sides of crystal plates to form electrodes (Fig. 2). The electroded plates were then poled at 10KV/cm, and the properties such as dielectric constant, dielectric loss and d 33 were then recorded. Thin copper shims with a thickness of 25 µm were designed and fabricated for electrode connection, the complete stack was composed of crystal plates, cu shim, endcaps and epoxy bonding layers, which were assembled as schematically shown in Fig. 2(c). For in-plane actuators, special cut PMN-PT crystal plates with dimension of 15 mm x 6 mm x 0.5 mm were prepared with Cr/Au electrodes (Fig. 2). Figure 2. Single crystal piezoactuators. PMN-PT plates for stack actuators; schematic view of a stack actuator; (c) <110> PMN-PT plate for in-plane actuators. Actuators characterization All single crystal plates were characterized for dielectric and ferroelectric properties. In detail, the capacitance and the loss tangent of the samples were measured using a Hewlett Packard 4274A multifrequency LCR meter. All the crystal samples were poled in fluorinert at room temperature under 10KV/cm unipolar electric field. The d 33 of crystal plates was LVDT Lock-in Amplifier High V Supplier Computer Actuator <110> <110> Figure 3. LVDT setup for actuator strain-electric field test. recorded using a d 33 meter. The strain-electric field performance of the stack actuators and in-plane actuators were investigated at 10KV/cm ~ 15KV/cm using an LVDT 2 Copyright 2004 by ASME

3 displacement measurement system (Fig. 3). The hysteresis and creep performance of actuators were also investigated using this LVDT system without pre-stress load. Resonance measurement was carried out to obtain dynamic response information, electromechanical coupling and mechanical compliance of stack and in-plane actuators. In the test, resonant frequency (f r ), anti-resonant frequency (f a ), capacitance, etc. were measured using an impedance analyzer and then the related performances were calculated. Preliminary DM Modeling The preliminary modeling was performed to help establish guidelines for evaluating the potential of these large throw single crystal actuators in an actual deformable mirror application. As schematically shown in Fig. 1, a DM with a conventional thin meniscus glass face sheet and stack actuators, in order to improve mirror shaping precision, actuator densities must be increased while at the same time the stress generated inside the face sheet must still be lower than the broken value by limiting relative stroke between adjacent actuators using a control algorithm. The objective of the study is to evaluate the magnitude of typical aberrations that can be corrected by taking advantage of the large dynamic range of the single crystal actuators. SRS IODA (Integrated Optical Design Analysis) program was used for this study. The IODA software interfaces with finite element models to define optical aberrations in terms of mirror surface deflections and integrates the aberrations into a format in which optical analysis can be performed. IODA uses the finite element model to generate actuator influence functions and can solve for the actuator positions that result in the minimum global surface figure error. IODA was initially developed for applications involving small perturbations that can be modeled using linear analysis tools. However, SRS has modified the software to allow the code to be used to evaluate nonlinear DM problems as well. The surface displacements generated in the finite element model can be translated into IODA, which then can display the optical path difference (OPD) plot. IODA can also convert this data into Zernike terms to isolate the problem aberrations that are producing the error [7]. Full aperture modeling for 127 mm (or 5 ) mirror with 25 actuators, 289 actuators and 541 actuators were investigated. Figure 4 shows the actuator layout for the 25 actuators case. The surface aberrations to be compensated in the modeling include focus error, 1 st -order Coma-X error and 1 st -order Astigmatism-X error, etc. Initially the error cases were specified in terms of number of waves error in the low order Zernike aberrations. Higher order errors will be evaluated using a Monte Carlo simulation approach. RESULTS AND DISCUSSIONS Single crystal actuators PMN-PT stacks with 20-layer, 30-layer, 36-layer and 40- layer 5mmx5mmx0.5mm plates were fabricated and tested. Figure 5 shows displacement vs. electric voltage for the 40- layer stack (~ 21mm long), good linearity between displacement and driving voltage is observed. Over 50 µm stroke is obtained with at driving voltage of 700 V, or the field of 14 KV/cm. The creep test is conducted by monitoring the Figure 4. Schematic view of DM. with actuators layout. displacement variation along with time under the same driving field. Figure 5 shows the creep performance of the stack for more than 20 minutes suggesting almost no displacement change. The hysteresis of stack actuator studied by measuring starin vs. field performance of stack actuator using LVDT system with the voltage increasing from 0 to peak and then decrease to 0 within 5 seconds. The strain performance and the hystereisis loop are shown in Fig. 5. The relative displacement hysteresis is defined here as L/L, where L is the displacement difference at the same diving voltage, and L is the dispalcement at the rising field. For the stack actuator, relative hysteresis is around The hysteresis of the single crystal piezoelectric actuators are comparable or smaller comparing with PZT actuators. The creep and hysteresis performanc ecould be impreoved by applying compressive preload during applications. Figure 5 shows the impedance and phase vs. frequency of a 30-layer stack actuator. The similar measurements were conducted with 20-layer, 30-layer and 36- layer stacks, but the 40-layer stack was broken before this measurement was done. So there is not resonant,easurement data for 40-layer stack. Clean modes are shown, and the elastic properties (compliance) calculated based on the measurement, as shown in Table 1, are close to the reported crystal properties, menaing the actuator assembly process is reliable. The compliance variation may be caused by the non-uniformity of crystal materials or the bonding thickness variation. The results from resonant measurement suggests the fast response and high efficient actuation of single crystal actuators. Displacement (µm) Driving Voltage (V) L L 127 mm mirror 3 Copyright 2004 by ASME

4 Displacement ( µm ) Displacement ( µm ) Time (Second) Driving Voltage (V) Impedance (Log) (Ohm) 4 9.0E E E E E E E E E E E+05 Frequency (Hz) Figure 5. Stack actuator characterization. strain vs. voltage of a 40-layer stack; creep test at 10 KV/cm; (c) impedance and phase vs. frequency of a 30-layer stack. Table 1. Resonance measurement for stack actuators. F r (KHz) f a (KHz) Coupling coefficient Elastic property (or compliance) 20- layer 30- layer 36- layer (c) (10-11 m 2 /N) The in-plane actuators (or plate actuators) were characterized using LVDT system for strain test and resonant method as well for impedance and phase test. The displacement vs. driving voltage of a plate actuator is shown in Fig. 6. Low hysteresis is found for single crystal plate actuators, e.g. the hysteresis of plate actuator at 400V is about A typical resonance mode of a plate actuator is shown in Fig. 6, and the average results are shown in Table 2, indicating efficient actuation by using special cut 31 mode of PMN-PT crystals. Phase (Degree) Impedance (Log) (Ohm) E E E E E E E+05 Frequency (Hz) 9.0E E E E E E+01 Figure 6. Plate actuator characterization. Displacement vs. voltage of a <110> PMN-PT plate actuator (15mmx6mmx0.5mm ); Impedance and phases vs. frequency of the plate actuator. Table 2. Resonance measurement for plate actuators. E S 11 Loss d 31 (pc/n) K 31 (10-11 m 2 /N) DM Modeling Full aperture modeling for 127 mm (5 inch) mirror with 25 actuators, 289 actuators and 541 actuators were investigated. As an example to see how the actuator density affects the figure correction, Figure 7 shows mirror surface before and after correction for a DM with 289 actuators in the case of 20 µm focus error. The input surface is with a 20 µm focus error with a PV of µm, and RMS error of µm. After correction, the PV is 0.52 µm, and RMS error is 0.07 µm, which is very promising due to the fact that no DM has been found for such a large focus error correction (>30 λ for nm wave). The required stroke is from µm to µm, and the force is from 1.16 N to 3.49 N, both stroke and force are within the actuator s capability. Table 3 presents the comparison of the correction precision in the case of different errors and different actuator densities. Phase (Degree) 4 Copyright 2004 by ASME

5 Number of Actuators 25 Table 3. Summary on modeling results. Case Summary Uncorrected figure (microns) PV RMS error Corrected figure (microns) PV RMS error 20µ focus µ focus Astigmatis m-x Coma-X µ focus Astigmatis m-x Coma-X CONCLUSIONS Figure 7. A 20 µm Focus error correction case for 127 mm (5 inch) mirror with 289 actuators. uncorrected surface; corrected surface. It is observed that increased actuator density leads to the improved precision of the corrected figure, however, it is also noticed that there seems to be an optimum actuator density for certain DM, for example, the corrected figure precision of the 5 DM with 289 actuators is very close to that of the case with 541 actuators. Larger than 50 microns of displacement could be achieved with a 20 mm long single crystal stack actuators with low dielectric loss (<0.1%) and low hysteresis under the driving field of 14 KV/cm. In-plane stroke of 24 microns has been achieved with 15 mm x 6 mm x 0.5 mm single crystal plates at driving field of 8 KV/cm. The potential benefits of incorporating these actuators in a deformable mirror (DM) design are demonstrated by using SRS Integrated Optical Design Analysis Software (IODA). The modeling shows that low-order aberrations with peak to valley errors as large as 40 microns could be corrected to diffraction limited performance with a reasonable number of actuators and acceptable actuator forces and face sheet stresses. In the case of DM correction with 20 microns of 1 st -order astigmatism, the input wavefront had a 20 micron 1 st - Astigmatism-X error (Peak to valley: µm, RMS error: 8.13 µm) the wavefront error was reduced to a PV of 0.26 µm and RMS error of µm. These results predict the single crystal piezoelectric DMs are promise for large throw DM applications. ACKNOWLEDGMENTS This work is sponsored by MDA/NAVY under contract No. N C The authors would thank Dr. Joseph Teter from Navy for his technical monitoring on this project. We also thank Hua Lei from TRS for her actuator assembly assistance. REFERENCES [1] Mansell, J.D., Sinha, S., and Byer, R.L., 2001, Silicon Deformable Mirrors for Laser Systems, SPIE Proceedings Vol Copyright 2004 by ASME

6 [2] NASA JWST Cryogenic Actuator Activities, Http//ngst.gsfc.nasa.gov/hardware/text/actuatoractivities.html. [3] Schall, H., Myers, A., Weight, D., Billman, K., and Cusumano, S., 2000, In-flight Calibration of an Airborne Wavefront Control Subsystem, SPIE Proceedings Vol [4] Mulvihill, M.L., Shawgo, R.J., Bagwell, R.B., and Ealey, M.A., 2002, Cryogenic Cofired Multilayer Actuator Development for a Deformable Mirror in the Next Generation Space Telescope, Journal of Electroceramics, 8, pp [5] Jiang, X.N., Rehrig, P.W., Hackenberger, W., and Shrout, T., 2003, Large Stroke and Low Profile Single Crystal Piezoelectric Actuators, SPIE Proceeding Vol.5053, pp [6] TRS Final Report for NASA Contract No. NAS [7] Moore, J.D., and Stallcup, M.A., 2001, Software for Integrated Optical Design Analysis, SPIE Proceeding Vol Copyright 2004 by ASME