Demonstration of a Robust Curved Carbon Fiber Reinforced Polymer Deformable Mirror with Low Surface Error

Demonstration of a Robust Curved Carbon Fiber Reinforced Polymer Deformable Mirror with Low Surface Error Blake Coughenour a, S. Mark Ammons c, Michael Hart c, Robert Romeo d, Robert Martin d, Matt Rademacher c, Hop Bailey c a College of Optical Sciences, The University of Arizona, 1630 East University Blvd., Tucson, AZ, USA 85721-0094; c Steward Observatory, The University of Arizona, 933 North Cherry Avenue, Tucson, AZ, USA 85721-0065; d Composite Mirror Applications, 1638 S. Research Loop, Tucson, AZ, USA 85710; ABSTRACT Carbon fiber reinforced polymer (CFRP) composites provide several advantages as a substrate for thin-shell adaptive secondary mirrors, including high stiffness-to-weight ratio and low coefficient of thermal expansion (CTE). We have addressed some of these concerns using a prototype CFRP mirror under actuation. Using 4D and Newton interferometry, we present measurements of surface quality at a range of temperatures. Under actuator relaxation at room temperature, its surface error is low (92 nm RMS) and dominated by edge curvature. This error is reduced further under best actuator correction to 43 nm RMS, placing it into consideration for use in near-ir astronomy. The low surface error internal to the outer ring of actuators - 17 nm RMS at 60 F and 33 nm RMS at 20 F - suggests that larger mirrors will have a similar figure quality under actuator correction on ground-based AO systems. Furthermore, the actuator forces required to correct the figure are small compared to the dynamic range of voice coil actuators (~0.1 N). In addition, surface roughness is characterized to address the effects of high spatial frequency errors. Keywords: adaptive optics, carbon fiber, reinforced polymer, substrate, thin-shell, deformable, secondary mirrors 1.1 Deformable Secondary Mirrors for Astronomy 1. INTRODUCTION In the coming decades, ground-based Extremely Large Telescopes (ELTs) will deliver the best available spatial resolution in the mid-infrared (IR). The James Webb Space Telescope (JWST) will be quite sensitive to faint objects at mid-ir wavelengths, but its spatial resolution is limited by primary mirror size (6.5m) and will be 4-6 worse than that of ground based ELTs. Reaching the diffraction limit at mid-ir wavelengths will require advanced Adaptive Optics (AO) systems for ELTs. Ground-based Adaptive Optics instruments on large telescopes are currently providing spatial resolution at near-infrared wavelengths that matches or exceeds that available from space at visible wavelengths. AO systems equipped with deformable secondary mirrors have particular advantages; compared to systems with internal deformable mirrors, they have fewer warm optics, greater total throughput, and thus the higher sensitivities in the mid-ir 1. The Giant Magellan Telescope (GMT) is envisioned at the union of seven 8.4-m circular primary mirrors, which will combine to give the spatial resolution of a 24.5-meter telescope when phased. Studied AO modes for the GMT include Ground Layer AO (GLAO), Multi-Conjugate AO (MCAO), Laser Tomographic AO (LTAO), and Extreme AO for direct detection of extrasolar planets. These AO instruments will rely on a deformable secondary with seven segments matched to the seven 8.4-meter primaries. These secondaries must possess excellent wavefront quality while being robust to transportation, installation, and operation over the long-term. The need for such a reliable substrate can be met with advancements in new fabrication techniques of carbon fiber reinforced polymer mirrors. Adaptive Optics Systems II, edited by Brent L. Ellerbroek, Michael Hart, Norbert Hubin, Peter L. Wizinowich, Proc. of SPIE Vol. 7736, 77363I 2010 SPIE CCC code: 0277-786X/10/$18 doi: 10.1117/12.856326 Proc. of SPIE Vol. 7736 77363I-1

1.2 Properties of Carbon Fiber Composites Carbon fiber reinforced polymer (CFRP) is an attractive material for fabrication of optical systems. CFRP has a number of material properties that make it advantageous for structures, including: The stiffness-to-weight ratio of CFRP is about 5 times greater than steel. The Young s modulus is on the order of steel s while the density of CFRP is much lower. Thus, CFRP is an excellent material for fabricating stiff, lightweight structures. The coefficient of thermal expansion (CTE) for CFRP is very low at 1-2 ppm/ C, roughly 20 times lower than that of aluminum. Structures fabricated with CFRP are dimensionally stable with respect to thermal changes. By customizing the layup of the unidirectional pre-impregnated composite fiber ( prepreg ), the CTE can be made to be near zero for key components. Athermal structural designs are possible with CFRP. The thermal conductivity of CFRP is similar to steel. This property, coupled with the lower mass of a CFRP structure, results in rapid thermalization and a minimum of thermal gradients in the piece. CFRP structural elements are fabricated as a lay-up of unidirectional prepreg fiber. The structural elements can be optimized to take advantage of the CFRP non-isotropic properties or can be tailored to yield quasi-isotropic behavior. 1.3 Advancements in CFRP Mirror Fabrication Figure 1. Block diagram of CFRP mirror lay-up and fabrication process. Composite Mirror Applications (CMA) of Tucson, AZ has invested considerable effort in the development of lightweight, CFRP optics. The fabrication process involves the creation of a precision optical surface through replication of a mandrel with the inverse shape (Figure 1). Layers of unidirectional, CFRP prepreg are layered over a mandrel that has the complementary shape of the desired mirror. After curing of the lay-up structure and removal from the mandrel, the mirror surface is aluminized in the same manner as conventional glass mirrors. The mandrel can be reused to generate multiple copies of the same mirror shape. The quality of the optical surface now produced with this technique is limited only by the quality of the mandrel 2. The CFRP optics produced at CMA for telescope systems are an order of magnitude lighter than similar mirrors made with traditional glass. The reasons for this recent success include: Commercially available CFRP prepregs have improved rapidly over the past decade. The layup schedules for the unidirectional prepreg optimize the performance for mirror substrates. The resulting coefficient of thermal expansion (CTE) can be near zero in-plane, close to zerodur, resulting in a mirror with outstanding thermal stability properties. Release of the CFRP replica from the mandrel is an important step in fabrication that can easily change the mirror surface; CMA has made proprietary developments in this process that preserve the replica figure. The designs of the mirror faceplates and core structure have been important developments. The result is a replicated mirror which is free of fiber and core print through issues that have plagued earlier development efforts by other institutions. CMA has developed the techniques for coating the CFRP polymer surface. The adhesion and durability of these coatings surpasses similar coatings on a glass surface in most cases. These coatings have been applied on the CFRP composite mirrors for various applications over the wavelength range from UV (200nm) to microwaves (1cm). Proc. of SPIE Vol. 7736 77363I-2

1.4 Advantages of CFRP as a Deformable Secondary Substrate CFRP holds great promise as a mirror substrate for astronomical applications due to its high strength, stiffness, and thermal conductivity, low coefficient of thermal expansion (CTE), and robustness. Our work seeks to combine a key benefit of deformable secondary technology removal of low spatial frequency errors with the resistance to breakage inherent to CFRP. There are multiple advantages to the use of CFRP as a substrate for deformable secondaries in near-ir astronomical adaptive optics: Inherent toughness with zero CTE. At substrate thicknesses of 1-3mm, a CFRP thin shell is less likely to break under shock than a comparable Zerodur shell. Fabrication, transportation, installation, and servicing are considerably less risky with a CFRP substrate. CFRP requires similar actuator force to Zerodur. Although CFRP is a robust material, little extra actuator force is required to deform it a given amount compared to Zerodur. The introduced curvature of a thin circular plate under a point force load F is C F Et 3 (1) where E is the Young s modulus of the material and t is the material thickness. The Young s modulus of a CFRP thin-shell is 150 GPa perpendicular to the carbon ply, while it is ~90 GPa for Zerodur. From equation (1), a CFRP thin-shell will require the same forces to achieve a given deformation as Zerodur if the thickness is reduced by 19%. Replicability. Following the polishing of the mandrel optic, fabrication of new CFRP replicas is limited only by the cost of new materials. The mandrel, pressing tools, and other fixtures only need to be constructed and tested once. This is useful for applications that require multiple copies of the same piece, e.g., the GMT secondary segments. For deformable mirror applications, CMA uses high modulus carbon fibers held together with a cyanate ester thermosetting resin as the matrix. The design of thin-shelled mirrors requires a specific ply-orientation to be used in order to maintain quasi-isotropy in-plane. This will ensure that mechanical and thermal properties are relatively consistent radially. This is important for predicting the behavior of the mirror under high stresses. 1.5 Questions to be Addressed Thin-shell CFRP mirrors have already been proven at mid-infrared and sub-millimeter wavelengths, where the optical quality requirements are less stringent than in the near-ir 1. Operation at near-infrared wavelengths will require good optical quality (< 100 nm RMS) without sacrificing actuator dynamic range (~1-2 N). We verify a new fabrication technique that enables near-infrared wavelengths to be examined using deformable secondaries by answering several questions: Is the natural, un-mounted figure quality of a CFRP thin-shell suitable for near-ir astronomy? What fraction of the figure error can be removed with mounted actuators? What actuator forces are needed to remove low spatial frequency errors caused by environmental fluctuation? How would the optical figure of a CFRP thin shell change as a function of temperature and humidity? 2.1 Manufacture 2. METHODOLOGY In collaboration with CMA, we have manufactured a thin-shell CFRP mirror using the technique detailed in Section 1.3. The mandrel is an 8 cm spherical plano-convex lens of BK7 glass, with figure specification of 130 nm P-V surface error. From this, we have constructed an 8 cm diameter concave, spherical thin-shell CFRP mirror with 1.6 mm substrate thickness (Figure 2). Proc. of SPIE Vol. 7736 77363I-3

2.2 Actuation To permit figure testing, position actuators must be attached to the back surface of the mirror. Seven neodymium magnets are bonded to the rear surface in a hexapolar pattern, with 2.8 cm separations. Low-friction sapphire windows are bonded to the magnets to create a smooth surface for actuator contact. Six New Focus picomotors are used as position actuators, i.e., individual constraints on z-position. The sapphire windows permit some movement along the plane of the window, so that 3 of 6 position and rotation coordinates are left free. However, the coefficient of static friction between the window and the actuator point is not exactly zero ("stiction" keeps the mirror fixed) so that the full 6-degree position and rotation can be constrained quasi-staticly. This mounting strategy allows us to use the actuators to change the surface figure without over-constraining the piece, which would induce intolerable stresses. A nonautomated, threaded spindle is used for the central actuator. The actuators are mounted with an aluminum back plate. Figure 2 shows the 8 cm mirror mounted to the actuator control apparatus for figure testing. Figure 2. 8 cm thin-shell CFRP mirror (left). Mounting apparatus (center). Mirror under actuation control (right). 2.3 Relaxed Figure Characterization We characterize the magnitude of high-frequency errors (on 1-100 microns scales), or surface roughness, using a Veeco vertical scanning white-light interferometer focused on the mirror surface. At the Vecco spatial resolution of ~1 micron, imperfections from the carbon fiber strands on the substrate can be directly seen. Full-aperture optical figure quality is characterized using a Twyman-Green simultaneous phase-measurement interferometer. Three control actuators are removed from contact with the magnets on the rear surface, leaving three supporting actuators in contact. This mounting procedure fully constrains the mirror position and rotation without applying localized forces, allowing us to characterize the "relaxed" figure. Tip and tilt aberrations are removed in software; absolute curvature error at room temperature is negligible, based on contact fringe measurements. Figure 3. 8 cm thin-shell CFRP mirror in optical alignment with interferometer in environmental chamber. 2.4 Corrected Figure and Environmental Testing Using the simultaneous phase-measurement interferometer, the surface figure can be adjusted using more actuators. Careful manual application of all 6 outside actuators permits aberrations of astigmatism and coma to be reduced. In testing, the central non-automated actuator is not in contact with the mirror and so our actuation is not optimized for curvature removal. Curvature for the corrected figure is removed in software. A surface analysis mask is used to mask the errors that are caused by actuator print-through and edge curvature. Proc. of SPIE Vol. 7736 77363I-4

Temperature and humidity are regulated using an environmental chamber that surrounds the actuator control apparatus (Figure 3). As temperature is decreased, humidity is regulated using a fan that cycles the air through a dried desiccant. A window covered with a microscope slide provides the beam path from the interferometer into the chamber. Temperatures ranging from 60 F down to 20 F are examined. The chamber humidity was constrained to be less than 40% at all temperatures, preventing condensation onto the CFRP mirror and window. 3. RESULTS 3.1 Surface Roughness Surface figure measured with vertical-scanning white light interferometry is shown in Figure 4. The absolute curvature of the mirror is responsible for the low spatial frequency trend across the surface map. A cross-section of the surface profile near the center is shown in Fig 4c to indicate the spatial scale and magnitude of error induced by the individual carbon fiber strands. At room temperature, the P-V surface error of the carbon fiber strands appears to be approximately 3 nm at maximum. Figure 4. Surface roughness of 8 cm thin-shell CFRP mirror. 3D plot of 155x116μm surface patch (a), 2D surface patch (b), and selected cross-section of 2D plot showing peak-valley error of multiple fiber strands (c). 3.2 Full Surface Figure Figure 5a displays the wavefront error of the 8 cm piece when supported by 3 actuators indicating its natural, relaxed state. Overall curvature cannot be measured in this test, although Newton Interferometric tests that compare the piece's figure to that of the original optical mandrel indicate that the absolute, uncontrolled curvature error at room temperature Proc. of SPIE Vol. 7736 77363I-5

is less than 80 nm RMS surface. Print-through errors are visible, which are due to glue stresses from magnet bonding. The print-through errors are ~75 nm P-V on the surface. Measurements of the relaxed figure yield 91.58 ± 0.76 nm RMS surface error. Figure 5b displays the wavefront error of the 8 cm piece corrected by the six picomotor actuators. Figure 5c displays interference fringes of the 8 cm piece under the best qualitative actuator correction. Measurements of the corrected full figure yield 42.99 ± 0.43 nm RMS surface error (curvature removed). Most of the error appears to be edge curvature, beyond the correctable radius of the actuators. This suggests that the majority of the error does not scale strongly with mirror size. The forces required to correct the natural, relaxed shape of the 8 cm CFRP piece are estimated to be ~0.1 N for each actuator. These values are well within the dynamic range of voice coils (1-2 N), which are commonly used as deformable secondary actuators. a. b. Figure 5. Wavefront error of 8 cm thin-shell CFRP mirror with tip and tilt removed. Relaxed figure wavefront error (a), wavefront error under actuator correction with curvature removed (b), and interference fringes (c). 3.3 Intra-Actuator Surface Figure Figure 6 displays an analysis mask applied to the interior surface shown at different temperatures. By masking out edge curvature beyond the correctable radius of the actuators and the locations of the seven actuator mount points, non-linear errors resulting from edge curvature and actuator print-through are ignored. The full aperture error of a larger CFRP mirror (d >.5 m) with actuator densities comparable to this piece would be dominated by the intra-actuator error for two reasons: (1) low-frequency errors can be corrected by actuators and (2) the area beyond the last ring of actuators, dominated by edge curvature, represents a small fraction of the area of a large mirror. Analysis of our 8 cm piece with this mask allows us to understand how errors will scale with mirror diameter. Figure 6. Interior analysis mask with actuator print through removed shown at different temperatures Proc. of SPIE Vol. 7736 77363I-6

The surface error is reduced by manual actuator correction at 60 F. Without actuator adjustment, an error drift is measured as the temperature is slowly reduced to 20 F. By maintaining temperature quasi-equilibrium at set locations, the surface error is further reduced by actuator correction in 10 F steps. RMS surface error as a function of temperature during drift and after actuator correction is shown in Figure 7. Normalized surface figures showing the error over a range of temperatures during drift from 60 F are also shown at the bottom of the figure. RMS surface error after actuator correction is measured at quasi-equilibrium during multiple measurements (Table 1). The average error reduction due to actuator correction is also shown, computed in quadrature. Figure 7. Masked wavefront error of 8 cm thin-shell CFRP mirror with tilt and power removed. RMS surface error as a function of temperature (Top). Normalized wavefront figures at quasi-equilibrium locations (Bottom). Table 1. RMS surface error after actuator correction at temperature quasi-equilibrium states. Temp RMS Surface Error Average Error Reduction 60 F 17.39 ± 1.69 nm 0 50 F 18.54 ± 2.62 nm 12.45 nm 40 F 22.02 ± 3.01 nm 17.30 nm 30 F 28.00 ± 3.54 nm 17.46 nm 20 F 33.17 ± 3.88 nm 22.54 nm Proc. of SPIE Vol. 7736 77363I-7

4.1 Astronomy Considerations 4. CONCLUSIONS These experiments show the following, that a natural, relaxed CFRP optical figure can be manufactured close (~90 nm RMS surface) to the prescribed mandrel figure. When the mirror figure is compared to that of its optical mandrel with Newton Interferometry, providing a more sensitive measure of the mirror's absolute full-aperture curvature error, the RMS errors are similar. This suggests that the natural curvature error is tolerable and correctable by actuators. High frequency surface deformations (~3 nm P-V surface) are well within the tolerable range for near-ir use. Relaxation of CFRP's internal stresses produces tolerable deformations. These low-amplitude deformations are dominated by curvature that can be dramatically reduced by actuator correction. The optical figure under the best qualitative actuator correction (~40 nm RMS full surface) places it into consideration for use in near-ir astronomy. The contribution of this error term alone only reduces K-band Strehl to 94%. The actuator forces required to correct the figure (~0.1 N) are small compared to the dynamic range of voice coil actuators. Therefore, we conclude that the natural, un-mounted figure quality of a CFRP thin-shell is suitable for near-ir astronomy. While the interior surface error increases linearly at lower temperatures, we have shown that actuator adjustment can only reduce the surface error down to a fraction of that near room temperature. Actuator print-through is small at room temperature (~75 nm P-V surface), but increases due to glue stresses as temperature decreases. This error may be the cause for the nearly linear increase in surface error at low temperature, and may be removed in the future by using different actuator mounting techniques. Most importantly, the intra-actuator error at mid- to high- spatial frequencies remains tolerable (< 25 nm RMS surface) at temperatures ranging down to 20 F. This suggests that the error of larger mirrors, up to several meters in diameter, would be tolerable under sufficient actuator correction. The high actuator densities (10 cm 2 per actuator) already required for near-ir adaptive optics with adaptive secondaries is sufficient to correct the low-frequency errors in CFRP. 4.2 Continued Testing of CFRP Mirrors However, there are still outstanding questions that need to be addressed. It remains to be seen that a large, thin-shell CFRP deformable secondary mirror for astronomical use, i.e., a convex and hyperbolic surface, will retain good surface quality in a mountaintop environment over many years of operation. Environmental cycling of the optical figure needs to be performed under a broader range of humidity and temperature conditions. It is also important to show that the natural, relaxed figure error of thin-shell CFRP pieces does not scale sharply with mirror diameter (> d 2 ), as this may saturate the dynamic range of voice coil actuators. CFRP has great potential for secondaries and active primaries in astronomy, both for ground-based and space-based telescopes. In space, lightweight, stiff primary mirrors are of utmost importance. Future large telescopes in space (> 8 m) will use active segmented primaries similar to that of the JWST. These segments are chiefly off-axis aspheres whose manufacture benefits immensely from replication. For a JWST-style mirror with 18 segments, there are four types of figure prescriptions. Once mandrels are polished, they can be used for multiple CFRP fabrications. The same potential holds for ground-based segmented telescopes. The GMT will have a segmented secondary composed of seven 1.1 meter adaptive thin shells. Six of these segments have the same optical figure and can be replicated from the same mandrel optic. Continued environmental and lifecycle testing will be critical to realizing CFRP's potential as a deformable secondary substrate for ELTs on the ground and in space. Proc. of SPIE Vol. 7736 77363I-8

ACKNOWLEDGEMENTS The authors wish to thank Buddy Martin, Mike Tuell, and Jeff Kingsley for the use of a Twyman-Green 4D Interferometer over the duration of the experiment. We also thank Peter Strittmatter for financial support. SMA acknowledges financial support from the Space Telescope Science Institute through the Hubble Postdoctoral Fellowship. REFERENCES [1] Lloyd-Hart, M., Thermal Performance Enhancement of Adaptive Optics by Use of a Deformable Secondary Mirror, PASP 112, 264 (2000). [2] Romeo, R. and Martin, R., Progress in 1m-class lightweight CFRP composite mirrors for the ULTRA telescope, Proc. SPIE 6273, 62730S (2006). Proc. of SPIE Vol. 7736 77363I-9