I. Introduction. II. Problem

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1 Wiring Deformable Mirrors for Curvature Adaptive Optics Systems Joshua Shiode Boston University, IfA REU 2005 Sarah Cook University of Hawaii, IfA REU 2005 Mentor: Christ Ftaclas Institute for Astronomy, University of Hawaii I. Introduction In order to get nearer to diffraction limited imaging, many ground-based telescopes today employ sophisticated adaptive optics systems. When starlight passes through the Earth s turbulent atmosphere, aberrations are introduced where the refractive index of the medium is different from its neighbors. What was once a planar wavefront becomes an aberrated mess. These aberrations have two basic properties that can be observed locally along the wavefront slope and curvature slope being the gradient of the phase function that describes the wave front, and curvature being the Laplacian of the same phase function. Adaptive optics (AO) systems use motions of a deformable mirror (DM) to correct these aberrations before the light is collected by science instruments. The systems image the telescope s pupil onto a DM, and in a closed-loop AO system, the light enters the wavefront sensor after reflecting off the DM. The wavefront sensor determines how the previous deformations of the DM have changed the wavefront and apply iterative corrections to the shape of the mirror to produce a wavefront as close to planar as possible. Curvature adaptive optics systems sense and correct for curvature aberrations of the wave front rather than tip-tilt (slope) aberrations, which most currently employed AO systems sense and correct. Most current curvature systems employ unimorph DMs made of two, millimeter thick wafers of piezoelectric ceramic material (PZT) laminated with electrodes on the back side and a reflective surface on the front. Each electrode on the DM s back controls the curvature of the mirror over a small, equally sized area of the full DM surface. In tip-tilt based AO systems, the wavefront reconstruction is done by the wavefront sensor by integrating the gradients it measures. Curvature AO systems, however, take measured curvature and scale it to applied voltages such that the DM physically reconstructs the wavefront without any complex calculations. Time is not wasted calculating the shape of the wavefront, and the bulk of the time in each cycle is available for applying and utilizing the effects of the corrections. II. Problem The Hokupa'a curvature AO system on the Gemini South telescope, with its 85-electrode DM (see figure 1), is the most advanced of its kind. The goal of AO is to advance imaging to near diffraction limits. Ultimately, electrodes would need to correspond to the size of coherent turbulence cells in the atmosphere over which the index of refraction is roughly constant which is about 10 cm in the near infrared. It is desirable to keep the DM about the same size as current curvature DMs to preserve its some of its known mechanical properties; however, for larger and larger telescopes, this will correspond to hundreds to thousands of electrodes with miniscule area. Another goal of AO in general is to produce systems that are effective for shorter wavelengths, but this again will correspond to much higher electrode densities. With these increased electrode densities, connecting the electrodes by conventional and manual methods

2 becomes more and more cumbersome and impractical. There is also an inverse correlation between the area of the electrode and the minimum radius of curvature it can apply, such that smaller electrodes can apply much less curvature to the DM. To combat this problem, one can use a true bimorph DM. Currently the DMs are bimorphs with one passive wafer and one active wafer, since voltage can only currently be applied to an exposed surface. A true bimorph has two PZT wafers with their polarization axes antiparallel. Driving voltages are applied to electrodes laminated onto the inner surface of each wafer, leaving the exposed surface of each wafer to be grounded. In a true bimorph, the wafers react oppositely, allowing for a much shorter radius of curvature. However, a true bimorph cannot be wired using current methods. Figure 1: This shows the back of the Hokupa a DM, with 61 gold coated electrodes within the inner 50 mm diameter circle corresponding to the dynamic optical surface on the front of the DM. The 24 outer electrodes, edge benders, control boundary curvature. The current wiring scheme leaves large uneven deposits of epoxy and solder on each of the DM s electrodes, which apply irregular and undesirable stresses on the DM. The new technique should draw the contact points for the electrodes away from the dynamic optical surface house in the inner 50mm of the 100mm diameter DM to combat this problem. It should also be easily expandable to systems with larger numbers of electrodes and provide the possibility of extension to bimorph configurations. We present a technique akin to replicating a flex circuit board onto the electrode containing surface of the DM in order to electrically connect the DM electrodes to their high voltage controllers as a solution that meets each of these goals. III. Methods 1. On-Site Technique The Hokupa a DM presents an interesting technical challenge, with many of its properties setting limits on any wiring process. Due to this and financial concerns, we found it desirable to design a wiring technique that could be completed entirely at our own facilities. For any wiring technique we might devise, the following conditions must be met: 1. DM temperature must not exceed 70 C, the glass temperature of the epoxy used to bond

3 the two PZT wafers that make up the DM. 2. No excessive stress can be placed on the DM which would cause its overall shape to deform, the gold electrodes debond, or result in inhibition of DM deformation. The first technique devised involved using a liquid dielectric that could be spun-on over the DM electrodes in a planar layer and subsequently etched using either photographic exposure or chemical etchant. We would spin-on this dielectric layer and cure it to its solid dielectric form; etch a pattern of vias (holes) into it, which bore through the layer to each of the DM electrodes; fill these vias with a conducting epoxy or gold. Upon this layer, we propose to apply a pattern of traces (canals) that bring the outermost electrodes out to a more convenient contact point away from the dynamic optical surface. A second dielectric layer on top of this, built up in the same way, would provide contact vias and traces for the remaining electrodes. We would cover the whole system with an encapsulating dielectric outfitted with vias at the new contact points (see figures 2 & 3). Figures 2 & 3: The left image depicts a cross-section of the flex circuit built directly on the back of the DM. The right image shows a view of the same flex circuit from the top if the dielectric layers were entirely transparent. It shows vias, traces and contact points for all 85 electrodes. As for the so-called convenient contact point, we worked out our design based on the assumption that we could fabricate a custom collar-like connector which would make contact with the traces at equal spacing along a circle 85% of the DM s radius. The idea was that the connector would contain spring loaded contact pins equally spaced around a 47mm radius circle, such that the pins would be slightly compressed when at rest and thus track the motion of the DM as it deforms. Unfortunately, there are no usable spin-on, curable dielectrics with a high enough dielectric strength to withstand the considerable electric fields that would be established between traces and electrodes as the voltage is run to a maximum +/- 400 V at 2 khz. Each either has a curing temperature greater than 80 C or would apply too much stress to the DM as it cured. We briefly investigated solid dielectric adhesive tapes, but found application to be nearly as cumbersome as the current wiring method. As a result, we were forced to abandon this design and the idea of onsite fabrication all-together. 2. Off-Site Technique

4 Having abandoned the idea of an on-site fabricated wiring scheme, we investigated partially and fully off-site wiring techniques. However, we stayed with the notion of using a flex circuit to wire the DM. In our investigation of materials for the above technique, we found that the established industry standards for flex-circuit fabrication broke all the limits set by the DM s materials, and knew we were unlikely to find a technique that could be fully completed off-site. We found the most desirable method is to fabricate the flex circuit separately off-site and off the DM. An engineer at the company MicroConnex suggested that it would then be possible to bond this flex circuit to the DM on-site and get good electrical contact between the circuit and DM (see figures 4 & 5). Figures 4 & 5: The left image depicts a cross-section of the separately fabricated flex circuit after bonding to the DM. The right image shows a preliminary design for the flex circuit, which contains 85 vias, traces and contact points in a nearly symmetrical arrangement. Note contact points are configured for conventional flex circuit connectors, and the whole circuit has a radius less than the DM. The flex circuit would have a set of vias and traces very similar to that previous design. The major difference being that the connection of the flex circuit to the DM would involve conventional flex circuit connectors rather than a custom design connector. Additionally, the flex circuit would be outfitted with three 10 micron tall gold pads corresponding to electrode. We could bond the circuit to the DM by applying an approximately 10 micron thick layer of adhesive and exerting uniform pressure over the whole circuit and DM. This would push enough adhesive out from beneath the gold pads to make electrical contact between pads on the circuit and DM electrodes with or without physical contact. However, we have only just recently begun to investigate this technique and have not had time to order circuits and test the feasibility of this bonding method. Despite a lack of experience with the flex circuits, we can speculate about what problems may arise when bonding the circuit to the DM. In designing our circuit we strived for flexibility and desired something whose thickness was miniscule compared to that of the DM. We also aimed for a symmetrical design for the trace and via pattern in order to promote isotropic mechanical properties in the flex circuit itself. This should minimize any mechanical effects that might result from bonding a circuit onto the DM. However, without testing we cannot say how the flex circuit will flex and deform once attached to the DM. Furthermore, it is possible that the DM could experience the same sort of deformation, or print-through, as it has previously with the current wiring system (i.e. we could see the stress from the circuit on the back of the mirror manifested

5 on the front optical surface). These would all be detrimental to the performance of the DM and must be investigated. IV. Conclusions It is clear from the enormous amount of time spent on materials research that it is not possible to build a wiring medium directly on the DM if we are to attack the problem using thin, flexible dielectric layers. However, pending further testing, it may be possible to attack this problem from this same angle if the flex circuit is fabricated separately and bonded later. This solution provides a much faster process for DM wiring and seems to solve the problem of uneven stresses on the dynamic optical surface of the DM, albeit so far only in theory. Our flex circuit by no means pushes the limits of the flex circuit fabrication industry s capabilities. The traces and vias are over designed and could easily be made thinner and be more tightly packed or even dispersed across more layers if necessary. This will allow easy adaptation of this technique to higher electrode DM s and more optimal curvature AO systems. And, more interestingly, this technique may be applicable in fabricating true bimorph mirrors. One could fabricate a flex-circuit, just like the one proposed, but which is equipped with contact pads on both sides. The circuit could then be bonded in between two electrode bearing wafers using the same technique described above, and the cables containing contact points for connectors can be left extending out the sides of the DM. The same problems in circuit design encountered for the unimorph DM will reappear in this application. Namely, mechanical effects and mirror stresses will need to be investigated and their severity assessed. Introducing a flex circuit between the two PZT wafers may also present a technical challenge for the subsequent steps of DM fabrication, but the technique still opens the door to renewed investigation of true bimorph DM development.

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