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Membrane Mirrors with Boundary Located Electrostatic

Actuators for excitation of Multiple Modes

Lisa Robinson*, Miles Wickersham†, Umesh A. Korde‡

South Dakota School of Mines and Technology, Rapid City, SD, 57701

This paper investigates electrostatic boundary actuation of a circular deformable mirror

for use in beam shaping and adaptive optics. The circumferential electrostatic actuator electrode pattern used here is designed to produce multiple-mode mirror deformations. The design, analysis, and fabrication processes are described herein. Closed loop control to be applied is illustrated by means of an example involving a similar mirror with different actuation placement. A summarized discussion of previous closed loop results is also presented. It is shown that open loop control of this electrostatic actuation application is not feasible, and that closed loop actuation is necessary to meet design deflection requirements. This design enables several more aberration correction modes than any of our existing mirror designs, while making it possible to apply our current closed loop control approach with appropriate extensions.

I. Introduction Increasing demands on the performance of adaptive optic systems have led to many new actuation techniques as

well as different mirror designs. Some of the recent research on electrostatically actuated membrane optics may be found in references 1-7. The purpose of this research is to design, manufacture, and test a boundary actuated deformable mirror similar in principle to that of Moore et al1. The unique feature of this design is that the electrostatic actuation plates will be placed circumferentially around the outside edge of the deformable mirror as well inside the pivot ring area (see section II). This will create an edge-applied moment about the membrane, causing it to deform. This design is created to have several more aberration correction modes than our other designs. Current designs only allow for correction in one or two modes, and existing designs used in the field are restricted to smaller displacements due to the lack of stability and control. This design enables several more aberration correction modes while making it possible to apply our current closed loop control approach with appropriate extensions. One advantage of closed loop control is that it allows us substantially to extend the stable deflection range to utilize almost the entire available gap width.

II. Design The design for this deformable mirror uses electrostatic boundary actuation, in which twelve 19 x 19 mm

variable-area copper actuators are placed circumferentially around the outside rim of the mirror. There are also another twelve plates located on the inside of the pivot ring as seen in Figures I through III. These actuators, along with the eight traces leading from each actuator were milled out of copper coated printed circuit board. The advantage of this actuation configuration is that it allows the mirror to deform in both a convexed as well as a concaved manner. __________________ * Email: Lisa.Robinson@mines.sdsmt.edu † Email: Miles.Wickersham@mines.sdsmt.edu ‡ Email: Umesh.Korde@sdsmt.edu; Phone: 1-(605)355-3731

50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference <br>17th4 - 7 May 2009, Palm Springs, California

AIAA 2009-2114

Copyright © 2009 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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Figure I. Left: Actuator plates on top of board; Right: Actuator traces on back of board

The small circular area between the two rings of actuators features a small non-conductive pivot ring. This ring

is attached to the deformable mirror and serves as the pivot location for the deformable membrane. The goal is to achieve actuation stability as well as a deformation of the full gap size using closed loop control. Figures II & III (below) show the side view design schematic of the mirror assembly and the 3-dimensional mirror base assembly, respectively.

Figure II. Side view of circular deformable mirror design

Figure III. Circular mirror base configuration with circumferential actuators and pivot ring

A. Material Selection Initially, the mirror material was chosen to be 0.004” gage 6061 Aluminum foil. Aluminum foil was the ideal

material selected to give the mirror surface more flexural rigidity, keeping the foil from sagging on the edges and causing premature snap-down. Previous work with similar mirror designs called for Aluminum coated Kapton film. This material would require a conductive reinforcement ring to be placed on the underside of the mirror and on top

.1 mm

80 mm

22 mm

160 mm

Actuation Pads

Pivot Ring

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of the pivot ring to maintain the mirrors shape. The design changed, however, in consideration of numerous layers of glue and reinforcement rings that would reduce our initial 100 micrometer gap.

After several polishing techniques were attempted to create a mirrored surface while retaining surface integrity

and flatness, a thicker aluminum was chosen. Anolux Miro Silver was machined to the corresponding size and used in several preliminary tests. Anolux Miro-Silver is a new optical grade of machined aluminum that has a 98% reflectivity, 97% image clarity, and less than 6% diffuse deflection. Physical properties of this aluminum include a tensile strength of 29.0 ksi, yield strength of 26.1 ksi, and was made with an H-19 temper.

The pivot ring is made out of a non-conductive substrate, so as not to interfere with the electrostatic actuation. Several materials were assessed for their manufacturability, cost, conductivity, and thickness. Based on Grosso and Yellin, we learn that the key considerations for material selection include: i) ductility and tensile strength, ii) desired frequency response, which is related to high-yield strength and low density, iii) ability to be manufactured optically flat, and iv) ability to be coated with highly reflective coatings.1 The following table was created to aid in the consideration of material data.

Table I. Material Selection Chart

Pivot Ring Material

Thickness (µm) Conductive Manufacturability

Graphite Foil 127 - 1500 µm Not through

thickness No PVC Tape 150 - 190 µm No Yes

Polycarbonate Film 100 µm No Yes

Polyethylene Fishing Line 225 µm No Yes

Mirror

Material Thickness

(µm) Conductive Manufacturability Kapton (AL

Coated) 25, 76, 127

µm Only on AL side Yes Aluminum sheet 5 - 150 µm Yes Yes

Carbon Steel (1010) 50 - 500 µm Yes Yes

Nickel (201) 15 - 630 µm Yes Yes

Miro-Silver 304.8- 635 µm Yes Yes The pivot ring design required a material with insulative properties, high strength, precision thickness, and

manufacturability. Fabricating the ring and mirror base out of a solid block would be difficult to achieve a uniform thickness. So, the ring was outsourced to a local company called Precision Technologies, where several different materials were used. Graphite foil, borosilicate glass, PVC electrical tape, and composite plastics were all considered. The material selected for this pivot ring element was the polycarbonate film. This film was machined with adhesive on both sides, so uniform thickness was achieved.

Once the thicker Miro-Silver aluminum was chosen for the mirror surface; a different pivot ring was required to

keep a more precise gap between the mirror and substrate. In addition to the fact that the initial gap was altered, a single point of contact was needed to assume no interference in the deflection of mirror along the boundary. The next generation of the pivot ring was created with a circular cross section to ensure that only one point of contact exists on the mirror. Polyethylene fishing line was used to make a circular pivot ring, only increasing the initial gap by approximately 100 µm.

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Using the information from Table I, the Anolux Miro-Silver was selected as the material for the mirror surface. Metal foils are not typically selected for deformable mirror surface, but in review of Grosso and Yellin2 shows that titanium, titanium alloys, nickel, beryllium and molybdenum have all been used in deformable mirror applications. The mirror membranes used by Grosso and Yellin were formed from evaporating titanium material onto a substrate in a vacuum chamber, which was then tensioned onto a ring and epoxied in place.

B. Deformations Boundary actuation around the pivot ring will cause a local rotation of the membrane about the edge. Analyzing

the geometry of the mirror at maximum displacement gives an idea of the deformations that will need to occur along the outside edge of the mirror. We make the assumption that the mirror surface produces a linear deformation, allowing us to find the boundary displacement. This displacement is used to find the attractive force from the electrostatic actuation, as well as allowing us to find what area each actuator need to achieve this attractive force. Figure IV shows the geometry of mirror deformations.

Figure IV. Deformation geometry of deformed mirror (side view)

Where in Figure IV:

A = 0.205 m D0= 100 x 10-9 m B = 0.59 m D1 = 66 x 10-9 m C = 0.8 m Y = Boundary deformation

Analyzing this geometry we find:

A .205m:= B .59m:= C .8m:=

D0 100 109−

× m:= D1 66 109−m⋅:=

Solving for "X", the inner bent length of the deformable mirror:

X B2

D1( )2+:=

X 0.59m=

Solving for "Z", the outer bent length of the deformable mirror:

Z C X−:=

Z 0.21m=

Using a ratio of the triangles created by the deformed mirror:

X .625m:= D1 66 109−

× m:=

YZ D1⋅

X:=

Y 2.218 108−

× m=

C

A B

D0

Y

X D1

Z

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From this we can tell that the deformation at the boundary of the mirror, when maximum deflection in the center of the mirror occurs, is approximately 22 micrometers. This deflection allows us to find several important design parameters concerning the actuation pads. More on these equations are discussed our recent work.3

C. Actuation Electrostatic actuation has several advantages, including high actuation authority. Here we use variable-area as

opposed to variable-voltage actuation; given its potential advantages in applications where quick switching control is eases demands on the hardware. The main drawback of electrostatic actuation is the existence of the “snap-down" instability across the gap between the electroded substrate and the metallized membrane. When the electrostatic attractive force overpowers the system restoring forces, snap-down occurs, causing the membrane surface to collapse on to the substrate. Stable operation without closed-loop control is only possible as long as the electrostatic force remains smaller than the restoring force, which is generally possible when the membrane defection is less than 1/3(the full gap size).3

D. Simulation A test mirror as shown in Figure V & VI is made of 24 micrometer thick metallized Kapton film, with a 30

millimeter radius, and is constructed to provide an undetected gap size of 40 micrometers. The performance goals for the mirror are as follows:

• Detection range at mirror center approaching the full gap size G0 (G0 = 40 micrometers in these simulations)

• Tip/tilt detection approaching the maximum allowed by the full gap size • Response bandwidth of 500 Hz

Figure V. Electrode configuration used in this work for focus/defocus and tip/tilt defections. Cluster (i) causes

focus/defocus, and clusters (ii) and (iii) cause tip/tilt defections.

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Figure VI. Sectional schematic view through a 45 degree diagonal

The reference trajectory for the symmetric mode in the time domain is plotted below. Since the full available gap size is G0 = 40 micrometers, a peak velocity approaching 0.1 m/s is to be reached within about 0.25 ms, which corresponds to an average acceleration of 400 m/s2. The force variation causing this acceleration is directly proportional to the area variation for variable-area actuation. It is easily seen that a significant amount of area needs to be activated in the initial few instants to meet the acceleration requirement.

It was confirmed through the simulations that open-loop operation for the design requirements would be impractical because of snap-down instability. However, with closed-loop control, it is possible to satisfy the design conditions for continuous area variation. Thus, Figure VII plots the closed-loop response and compares it with the open-loop response, which shows snap-down at t ≈ 0.35 s without control. 3

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Figure VII. (a-d) The reference trajectory for the symmetric mode in the time domain. Also shown are the trajectory in phase space and the corresponding reference area variation.

The velocity response is shown below in Figure VIII, which also matches the reference velocity with closed-loop

control. The open loop velocity increases quickly until snap-down, after which it essentially remains locked at zero.

Figure VIII. (a-b) The actual displacement and velocity for the symmetric mode in the time domain. The figure compares the open loop and closed loop results.

Figure IX compares the closed-loop response with the open-loop behavior and the reference trajectory, and it is

seen again that almost the entire range of angular deflection can be exploited with the loop closed.

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Figure IX. The actual displacement and velocity for the antisymmetric mode in the time domain. The figure

compares the open loop and closed loop results.

Figure X. The actual displacement and velocity for the antisymmetric mode in the time domain. The figure

compares the open loop and closed loop results.

Since the results above are obtained for the simplest case of zero model error and continuous area variation, they confirm that, for stable operation closed-loop control is necessary over the deflection range of interest.

E. Testing First, the surface quality of the two different mirror samples were tested, comparing the hand-made reflective

mirror to the Anolux Miro-Silver8. The surface undulations of the Anolux aluminum mirror are measured at a maximum of 45.1 microns, and with the total desired deflection being approximately 200 microns we can safely say that these undulations are much less than the deflection and will not interfere with the actuation system.

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Figure XI. Surface Undulation of Anolux Miro-Silver and Hand Polished Prototype Mirrors The previously tested hand polished mirror showed surface undulations of a much greater magnitude, proving

that it does not have the tolerances to best meet our testing requirements. The first actuation configuration to be excited was done by applying the voltage to the outside ring of pads. In

this test, the hand-made mirror was used as part of the setup. Measurements were taken along several places from the outside edge of the mirror to the center to obtain a partial view of the actuated mirror profile. Next the inside rings were excited and also measured. Results can be found in Figure XII below.

Figure XII. Excitation of Inside and Outside Actuation Rings of Hand Polished Mirror It can be determined from these results that excitation of each respective ring produces the desired reaction.

Results from several different test trials produce similar results. An issue that arose using the hand polished mirrors is due to the fact that these mirrors are so thin, after one snap down the material has deformed plastically rendering it useless. So, each test must be conducted with a new, unbent mirror. This problem led to more testing using the Anolux Miro-Silver mirror that is much thicker with a higher modulus of elasticity.

The new Anolux Miro-Silver mirror was then used in similar testing, as we can better predict and control its

actuation movement. Initial inside actuator ring testing of this mirror showed a consistent snap down at an average of 250 Volts, with a deformation of 75 microns at the center at a stable 220 Volts.

The outside ring of actuation pads were excited to cause a snap down at an average of 320 Volts. Deformation at

the very outside edge of the mirror cannot be measured exceptionally accurately due to electrostatic pin connections

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that are in the way of measuring laser displacements. A next generation mirror is currently being produced to allow the measurement to be taken.

To better obtain a visual representation of the mirror and Zernike modes, a Shack-Hartmann wave front sensor

will later be employed. As this particular boundary actuated mirror system was created to correct higher modes, the Shack-Hartmann system will be ideal to observe these movements.

III. Conclusion This design enables several more aberration correction modes than our existing mirror designs, while also making

it possible to apply our current closed loop control approach with appropriate extensions. In the simulation results, the mirrors were driven by electrostatic actuators where the actuator area rather than voltage varied to control the generated force. This control method is particularly useful in applications where switching control of constant voltage signals to multiple lines is more convenient. The major design challenge outlined here was to maintain electrostatic actuation stability, avoiding the “snap down” effect. To achieve the design requirements and stability, it was proven necessary to use closed loop control. Experimental verification of the effectiveness of this boundary actuated mirror configuration lead us to continue with testing of different actuation configurations. As we see a constant snap down voltage through each actuation configuration, it can be said that the system is consistent enough to apply a sophisticated control system. Currently, this new control system is being designed to control each electrostatic actuation pad individually. Using this closed loop system, the boundary actuated deformable mirror design described above will be tested for control stability similar to the similar mirror prototype whose control system is in the final stages.

Acknowledgments This work is supported by the Air Force Research Laboratory, Space Vehicles Directorate (AFRL/RV). Particular thanks are due to Dr. Jeffry Welsh and Mr. Jeremy Banik of AFRL/RV for his insight and continued support. Much gratitude goes to Andrew Downs, Brian Fehrman and other co-workers at the School of Mines.

References 1 Moore, J., Patrick, S., Chodimella, D., Marker, B., deBlonk, B., “Meter-class actively controlled membrane mirror”, 5th Mirror Tech Days in Govt. Conference, Huntsville, AL, 2005 2 Grosso, Ronald P.; Yellin, Martin. “The membrane mirror as an adaptive optical element.” The Perkin-Elmer Corporation, Norwalk, Connecticult. 1977.

3 Korde, Umesh. A. “Large-Displacement Control of Variable Area Electrostatic Actuation for Membrane Reflectors.” J. Intelligent Material Systems and Structures, accepted. June 2008. 43Wang, P.K.C; Gutierrez, T.C.; Bartman, R.K. “A method for designing electrostatic-actuator electrode pattern in micromachined deformable mirrors.” Sensors and Actuators. 1996. 5Seeger, Joseph I.; Boser, Bernhard E. “Charge Control of Parallel-Plate, Electrostatic Actuators and the Tip-In Instability.” IEEE Journal of Microelectromechanical Systems, Vol. 12, No. 5, OCTOBER 2003. 6Zhu, Guchuan, Lévine, Jean; Praly, Laurent; Yves-Alain, Peter. ”Flatness-Based Control of Electrostatically Actuated MEMS With Application to Adaptive Optics: A Simulation Study.” IEEE Journal of Microelectromechanical Systems. Vol. 15, No. 5. October 2006. 7Mastrangelo, C. H. “Recent Advances in Electrostatic Microactuators for Mirror Steering.” Sullivan Park Scientific Research Laboratory. Corning Incorporated, Corning NY 14831. Proc. of SPIE Vol. 5719. 8 Alanod GmbH & Co. 18 Regan Road, Unit 25, Brampton, Ontario L7A 1C2 < http://www.anomet.com/reflective_products.html>