Wavefront Correction

Transcription

1 Wavefront Correction 2009 CfAO Short Course Santa Cruz, CA Joel Kubby

2 Wavefront Correction Claire Max, Astronomy 289C -- Adaptive Optics

3 Outline 1) Overview of deformable mirrors and wavefront correction Coherence length/degrees of freedom Fitting error Requirements 2) Types of deformable mirrors Conventional Emerging 3) Conclusions

4 Coherence length r 0 sets the number of degrees of freedom of an AO system Divide primary mirror into subapertures of diameter r 0 Number of subapertures ~ (D / r 0 ) 2 where r 0 is evaluated at the desired observing wavelength Claire Max, Astro 289C, UCSC

5 Overview of wavefront correction Divide pupil into regions of ~size r 0, best fit to wavefront. Diameter of subaperture = d s Several types of deformable mirror (DM), each has its own characteristic fitting error σ fitting 2 = a F (d s / r 0 ) 5/3 rad 2 Claire Max, Astro 289C, UCSC

6 Fitting error σ fitting 2 = a F (d s / r 0 ) 5/3 rad 2 Physical interpretation: If we assume continuous face-sheet DM does a perfect correction of all modes with spatial frequencies < 1 / r 0 and does NO correction of any other modes, then a F = 0.26 Equivalent to assuming that a DM is a high-pass filter : Removes all disturbances with low spatial frequencies, does nothing to correct modes with spatial frequencies higher than 1/r 0 Claire Max, Astro 289C, UCSC

7 Fitting errors for various DM designs σ fitting 2 = a F (d s /r 0 ) 5/3 rad 2 DM Design a F Actuators /Seg Piston only, square segments Piston+tilt, Square segments Continuous DM Claire Max, Astro 289C, UCSC

8 Consequences: different types of DMs need different actuator counts, for same conditions To equalize fitting error for different types of DM, number of actuators must be in ratio N 1 N 2 = d 2 d 1 So a piston-only segmented DM needs ( 1.26 / 0.28 ) 6/5 = 6.2 times more actuators than a continuous face-sheet DM Segmented mirror with piston and tilt requires 1.8 times more actuators than continuous face-sheet mirror to achieve same fitting error: 2 = a F 1 a F2 6/5 N 1 = 3N 2 ( 0.18 / 0.28 ) 6/5 = 1.8 N 2 Claire Max, Astro 289C, UCSC

9 DM Requirements Dynamic range: Stroke (total up and down range) Typical stroke for astronomy depends on telescope diameter: ± several microns for 10 m telescope ± microns for 30 m telescope For vision science microns Temporal frequency response: DM must respond faster than a fraction of the coherence time τ 0 Influence function of actuators: Shape of mirror surface when you push just one actuator Claire Max, Astro 289C, UCSC

10 DM Requirements Surface quality: Small-scale bumps can t be corrected by AO Hysteresis of actuators: Repeatability Want actuators to go back to same position when you apply the same voltage Power dissipation: Don t want too much resistive loss in actuators, because heat is bad ( seeing, distorts mirror) Lower voltage is better (easier to use, less power dissipation) DM size: Not so critical for current telescope diameters For 30-m telescope need big DMs: at least 30 cm across Consequence of the Lagrange invariant y 1 ϑ 1 = y 2 ϑ 2 Claire Max, Astro 289C, UCSC

11 Segmented Made of separate segments with small gaps Each segment has 1-3 actuators and can correct: Piston only (in and out), or Piston plus tip-tilt (three degrees of freedom) Continuous face-sheet Thin glass sheet with actuators glued to the back Bimorph Types of deformable mirrors: Conventional 2 piezoelectric wafers bonded together with array of electrodes between them. Front surface acts as mirror. Claire Max, Astro 289C, UCSC

12 Types of deformable mirrors: Small and/or unconventional Liquid crystal spatial light modulators Technology similar to LCDs for computer screens Applied voltage orients long thin molecules, changes index of refraction Good for lab experiments; not yet ready for astronomy (too slow, polarization dependent) MEMS (Micro-Electro-Mechanical Systems) Fabricated using microfabrication methods of the integrated circuit industry Many mirror configurations possible Potential to be very inexpensive Claire Max, Astro 289C, UCSC

13 Current AO Technology Piezoelectric Actuators

14 Typical role of actuators in a conventional continuous face-sheet DM Actuators are glued to back of thin glass mirror When you apply a voltage to the actuator (PZT, PMN), it expands or contracts in length, thereby pushing or pulling on the mirror V Claire Max, Astro 289C, UCSC

15 Types of actuator: Piezoelectric Pies' from Greek for Pressure PZT (lead zirconate titanate) gets longer or shorter when you apply V Stack of PZT ceramic disks with integral electrodes Displacement linear in voltage Typically 150 Volts Δx ~ 10 microns 10-20% hysteresis

16 In general, hysteresis is bad for AO Want response to voltage to be linear and one-to-one With hysteresis, response is nonlinear and non-unique Can compensate to some extent in a closed-loop system, because you are always sensing and correcting Claire Max, Astro 289C, UCSC

17 Piezo DM Challenges They are hand assembled, leading to high cost per channel ($500-$1,000/channel), limiting the number of channels that are available The actuators are large, limiting the interactuator spacing to 5-7 mm The resulting array is large, increasing the size of the optical system Piezo electric materials have hysteresis so the displacement is dependent on their past history

18 Types of actuator: PMN Lead magnesium niobate (PMN) Electrostrictive: Material gets longer in response to an applied electric field Quadratic response (non-linear) Can push and pull if a bias is applied Hysteresis can be lower than PZT in some temperature ranges Both displacement and hysteresis depend on temperature (PMN is more temperature sensitive than PZT) Claire Max, Astro 289C, UCSC

19 Segmented deformable mirrors Each actuator can move just in piston (in and out), or in piston plus tip-tilt (3 degrees of freedom) Fitting error: σ 2 fitting = a F (d s /r 0 ) 5/3 Piston only: a F = degrees of freedom: a F = 0.18 actuators Light Claire Max, Astro 289C, UCSC

20 Segmented deformable mirrors NAOMI (William Herschel Telescope, UK): 76 element segmented mirror Each square mirror is mounted on 3 piezos, each of which has a strain gauge Strain gauges provide independent measure of movement, are used to reduce hysteresis to below 1% (piezo actuators have ~10% hysteresis). Claire Max, Astro 289C, UCSC

21 Largest segmented DM: Thermotrex 512 segments Each with 3 DOF Overall diam. 22 cm Built in early 1990 s for military Credit: Michael Lloyd-Hart lectures Claire Max, Astro 289C, UCSC

22 Continuous face-sheet DM s Facesheet thickness must be large enough to maintain flatness during polishing, but thin enough to deflect when pushed or pulled by actuators Thickness also determines influence function Response of mirror shape to push by 1 actuator Thick face sheets broad influence function Thin face sheets more peaked influence function Actuators have to be stiff, so they won t bend sideways as the mirror deflects Claire Max, Astro 289C, UCSC

23 Continuous face-sheet DM s: Fitting error σ fitting 2 = a F (d s / r 0 ) 5/3 rad 2 where a F = 0.28 Claire Max, Astro 289C, UCSC

24 Continuous face-sheet DM s: Xinetics product line Claire Max, Astro 289C, UCSC

25 Xinetics/Keck 146mm clear aperture 349 actuators on 7 mm spacing

26 Influence functions for Xinetics DM Push on four actuators, measure deflection with an optical interferometer Vertical scale exaggerated! Claire Max, Astro 289C, UCSC

27 Compagnie Industrielle des Lasers (CILAS) SAM 416 9x9 subscale prototype DM stroke of 11 μm, surface flatness of 13 nm RMS, and hysteresis of 5-6% A deformable mirror with 1,377 piezoelectric actuators has been developed for the European Southern Observatory (ESO). 2.5 m, 5,000-10,000 actuator mirror planned for E-ELT

28 CILAS continuous face sheet DM Credit: Michael Lloyd-Hart Lectures Claire Max, Astro 289C, UCSC

29 Bimorph mirrors Bimorph mirror made from 2 piezoelectric wafers with an electrode pattern between the two wafers to control deformation Front and back surfaces are electrically grounded. When V is applied, one wafer contracts as the other expands, inducing curvature Claire Max, Astro 289C, UCSC

30 Bimorph mirror construction Credit: Michael Lloyd-Hart Claire Max, Astro 289C, UCSC

31 Bimorph mirrors well matched to curvature sensing AO systems Electrode pattern can be shaped to match sub-apertures in curvature sensor Mirror shape W(x,y) obeys Poisson Equation wh2 ( ) 2 W + AV = 0 re,isthevoltagedistributoev i(x y )nclaire Max, Astro 289C, UCSC

32 Liquid crystal devices (LCD s = spatial light modulators) Pattern of phase delay is written onto back of LCD with light. Changes voltage at each pixel, which changes index of refraction in liquid crystal. Incident light shines onto front of LCD. It reflects from the dielectric mirror, and doublepasses through the liquid crystal. Spatial resolution is very high (480x480 pixels). Can correct large number of spatial modes. But: Corrects only piston, needs polarized light, limited dynamic range, odd behavior at edges of pixels Problem: slow response time Claire Max, Astro 289C, UCSC

33 Hamamatsu Liquid Crystal SLM at UCSC s Lab for AO Claire Max, Astro 289C, UCSC

34 Deformable Secondary Mirrors Pioneered by U. Arizona and Arcetri Observatory in Italy Newest entry in field: Microgate (Italy) Recently installed on U. Arizona s MMT Upgrade telescope (6.5 m primary), where it is working very well Next steps: Large binocular telescope (Mt. Graham, AZ), VLT laser facility (Chile) Claire Max, Astro 289C, UCSC

35 Cassegrain telescope concept Claire Max, Astro 289C, UCSC

36 Adaptive secondary mirrors Make the secondary mirror into the deformable mirror Curved surface ( ~ hyperboloid) tricky Advantages: No additional mirror surfaces Lower emissivity. Ideal for thermal infrared. Higher reflectivity. More photons hit science camera. Common to all imaging paths except prime focus High stroke Disadvantages: Harder to build: heavier, larger actuators, convex. Harder to handle (break more easily) Difficult to control mirror s edges (no outer ring of actuators outside the pupil) Claire Max, Astro 289C, UCSC

37 MMT-Upgrade: adaptive secondary Magnets glued to back of thin mirror, under each actuator. On end of each actuator is coil through which current is driven to provide bending force. Within each copper finger is small bias magnet, which couples to the corresponding magnet on the mirror. Claire Max, Astro 289C, UCSC

38 Deformable secondaries: Magnets and actuators Prototype for LBT Upgrade DM for MMT Claire Max, Astro 289C, UCSC

39 Adaptive secondary for MMT Upgrade telescope U. Arizona + Arcetri Observatory (Italy) > 300 actuators Laird Close and Francois Wildi Claire Max, Astro 289C, UCSC

40 It Works! Claire Max, Astro 289C, UCSC

41 Cost scaling will be important for future giant telescopes Conventional DMs About $1000 per degree of freedom So $1M for 1000 actuators Adaptive secondaries cost even more. Replace existing secondary mirrors VLT adaptive secondaries in range $12-14M each MEMS (infrastructure of integrated circuit world) Less costly, especially in quantity Currently ~ $100 per degree of freedom So $100,000 for 1000 actuators Potential to cost 10 s of $ per degree of freedom Claire Max, Astro 289C, UCSC

42 Cost-Performance

43 MEMS Fabrication Processes

44 MEMS Fabrication Flow

45 MEMS Fabrication Processes Tronics NMRC Bishnu Gogci, Sensors Product Division, Motorola

46 Bulk Micromachining

47 Benefits of Bulk Micromachining Metallized single crystal silicon makes excellent mirror surfaces (flat, thick) Single crystal silicon has excellent and reproducible electrical and mechanical properties Wafer bonding can be used to make large actuator gap to enable large stroke

48 Limitations of Bulk Micromachining Sloped sidewalls minimize actuator packing density Has only been used in AO for membrane mirrors with low spatial frequency that do not require high packing density

49 Surface Micromachining

50 Benefits of Surface Micromachining Stacked layers enables broad functionality Polysilicon (structural, conductors) Nitride (insulator, dielectric) Oxide (sacrificial, dielectric) Metal (conductors, optical coatings) Dry etching enables design freedom Non-crystallographic Anisotropic

51 Limitations of Surface Micromachining The layer thicknesses have been limited to a few microns, limiting the mirror thickness and the actuator stroke If the layers are made thicker, processing becomes more challenging Print-through from conformal coating creates surface topography on the mirror Residual stress and stress gradients can lead to mirror curvature

52 Thin Layers Deposited thin film sacrificial layers (oxide) define the actuaor gap and limits the available stroke.

53 Residual Stress and Stress Gradients Stress Gradients Metallization of thin films

54 Topography from Conformal Coating

55 MEMS Actuation Mechanisms

56 MEMS Actuation Mechanisms

57 Electrostatic Actuation +V F m Moveable plate -V F e z g Lower plate is fixed, upper plate can move Fixed plate Attractive force between the plates is balanced by restoring force of the spring

58 Electrostatic Force z C V F C V z F C V z F C V Δ Δ = Δ = Δ Δ + Δ = Δ Mechanical Work Electrical Work (Battery) Change in the Total Energy Stored in Capacitor

59 Electrostatic Force ( ) ( ) ) ( 2 z g AV F z g A dz dc z g A C e = = = ε ε ε g +Q -Q g +Q -Q A g z z g +Q -Q g +Q -Q A g z z

60 Force Balance F m = F e 2 ε 0 AV m = kz = F 2 e F = 2( g z) Solve for V as a function of z; V = 2kz( g ε 0 A z) 2 1/ 2

61 Force Balance F m = F e kz 2 0 AV = ε 2( g z) 2 z

62 Force Imbalance No equilibrium above critical voltage, electrostatic force is always larger kz 2 0 AV < ε 2( g z) 2 z

63 Pull-In z/g z V pull in = g 3 = 2kz( g ε 0 A z 2 ) 1/ 2 = 8 kg V pi ε A Stable region V g A ε 0 2gk

64 Leveraged Bending Cantilever Beam (CB) Fixed-Fixed Beam (FB) Non-linear effects Increases the useable gap but drives up the required voltage Elmer S. Hung and Stephen D. Senturia, JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 8, NO. 4, P. 497 (1999).

65 DM Requirements

66 Thirty Meter Telescope Jerry Nelson, Don Gavel 2004 August 19 MEMS workshop UCSC

67 Terminology Stroke The DM must match the wavefront error +V F m z/g z V pull in = g 3 = 2 kz ( g z ) ε 0 A 2 1/ 2 8 kg 3 V pi = 0 27 ε A -V F e z g Stable region V g A ε 0 2 gk Would like stroke 10 μm

68 Terminology Actuator spacing Sets the highest spatial frequency controlled d d

69 Terminology Continuous face-plate Segmented mirrors Electrostatically actuated diaphragm Attachment post Continuous mirror Segmented mirrors (piston) Membrane mirror

70 Terminology Nanolaminate face sheet Nanolaminate materials are engineered at the atomic level to provide optimal strength, stiffness, and surface properties for lightweight optics Lawrence Livermore National Laboratory (LLNL)

71 MEMS Deformable Mirrors Electrostatic and Magnetic Actuation

72 Boston Micromachines/Boston University

73 Boston Micromachines Electrostatically actuated diaphragm Attachment post Membrane mirror Continuous mirror

74 Boston Micromachines: 1000 actuator MEMS DM Currently under testing in Lab for AO, UCSC About 2 microns of stroke Next steps: 4000 actuators; 4 microns of stroke Claire Max, Astro 289C, UCSC

75 Boston Micromachines

76 Boston Micromachines

77 6um of stroke achieved Displacement, nm Displacement (nm) Voltage, V Voltage (V)

78 Long Stroke MEMS Mirrors for Biological Imaging Goal: To produce a MEMS deformable mirror with 6μm of physical stroke (12 μm phase) for highresolution, high-contrast retinal imaging systems. This work was partially funded by The Center for Adaptive Optics and NSF Science and Technology Center and a National Eye Institute Grant Number: 1 R43 EY Mirror Array Characteristics Number of actuators/array Actuator pitch Actuator stroke Maximum actuation voltage Aperture (140 element array) µm 6µm 250V 5.5mm

79 Boston Micromachines

80 Boston Micromachines

81 First 18 Zernike modes produced by Boston Micromachines MEMS DM Claire Max, Astro 289C, UCSC

82 MEMS testing at LAO: looks very promising Credit: Morzinski, Severson, Gavel, Macintosh, Dillon (UCSC) Claire Max, Astro 289C, UCSC

83 Boston Micromachines Large stroke obtained by using thicker sacrificial layers and leveraged bending Scaling up from proven designs at lower stroke Challenging process development for surface micromachining of thick films Operating voltage is high (>250V) High voltage can drive electrochemical corrosion in humid environment

84 Iris AO

85 Iris AO MEMS Segmented DM

86 Iris AO MEMS Segmented DM

87 Iris AO MEMS Segmented DM

88 Iris AO MEMS Segmented DM 2 nd Generation assembled mirrors

89 Iris AO MEMS Segmented DM 2 nd Generation assembled mirrors

90 Iris AO MEMS Segmented DM Scalable Assembly: 367 Segment Demo

91 Iris AO MEMS Segmented DM Large stroke obtained by elevating mirror Good match to large stroke requirements for vision science Segmented mirror does not meet TMT requirement for continuous face sheet

92 Membrane Mirrors

93 AgilOptics

94 AgilOptics

95 AgilOptics

96 AgilOptics

97 AgilOptics

98 OKO Technologies/Delft

99 OKO Technologies/Delft

100 Imagine Optic

101 Imagine Optic

102 Imagine Optic

103 Imagine Optic

104 Membrane Mirrors Large stroke and continuous face sheet meets the requirements for TMT Low spatial frequency and channel count do not meet the requirements for TMT, but could be used as a woofer in a woofertweeter combination Tweeter gives high spatial frequency with low stroke Surface micromachined MEMS Woofer gives large stroke at low spatial frequency Bulk membrane MEMS

105 Challenges Surface Micromachined MEMS (BMM) Stroke limited by sacrificial layer thickness Conformal coatings lead to print-through Limited to semiconductor materials, processing and substrates Bulk Micromachined MEMS (OKO, Imagine Optics) Membrane mirrors with limited spatial frequency Currently used as large stroke woofers with limited stroke surface micromachined tweeters

106 Issues for MEMS DM devices Need more stroke (aiming at 10 microns) Snap-down If displacement is too large, top sticks to bottom and mirror is broken ( stiction ) Robustness not well tested on telescopes yet Sensitive to humidity (seal using windows) Internal failure modes? Defect-free fabrication Current 1024 devices have 0 to a few bad actuators Claire Max, Astro 289C, UCSC

107 UCSC

108 UCSC Research Goals Increase the stroke of Micro-Electro-Mechanical Systems (MEMS) continuous face sheet Deformable Mirrors (DM) to meet the needs of future extremely large telescopes (30 m): Required stroke 10 μm Use high aspect ratio micromachining process (LIGA) Increase the order of MEMS deformable mirrors to 10,000 actuators Through wafer interconnects Scalable glass-ceramic substrate Increase the robustness of the DM to survive the telescope environment Inert gold face plate and actuators Inert glass-ceramic substrate

109 LIGA High Aspect Ratio Process Synchrotron Radiation X-ray Mask PMMA 1)Expose Plating Base Substrate 2)Develop 3)Electroform 4)Planarize 5)Remove PMMA 6)Release

110 High Aspect Ratio MEMS Processing Multilayer DXRL Processing Christenson, T.R., and Schmale, D.T. (1999) A Batch Wafer Scale LIGA Assembly and Packaging Technique via Diffusion Bonding, Proc. IEEE MEMS Workshop, pp

111 Design μm Gap 5-8 μm Spring Layer 30 μm Gap 4 μm Mirror Layer Al 2 O 3 Substrate 32x32 BGA 1.0 mm pitch Counter Electrode

112 Actuator Modeling 4 Spring Actuator 8 Spring Actuator Circle Actuator 6 152V = 9.81μm 156V = 9.76μm 167V = 9.871μm

113 Face Plate Modeling 8 Spring Circle 7 190V = 9.91μm 206V = 9.76μm

114 Face Plate Modeling

115 Actuator Fabrication 30 μm gap

116 Actuator Testing 4 Spring 133V = 8.19μm

117 Face Plate Characterization

118 Current status We have been able to fabricate large stoke actuators using high-aspect ratio LIGA processing Their performance is in good agreement with modeling results We have been able to fabricate face plates in the same LIGA process with nm RMS roughness We are now working on bonding the face plate to the actuators

119 Conclusions Deformable mirror acts as a high-pass filter Can t correct shortest-wavelength perturbations Different types of mirror do better/worse jobs Segmented DMs need more actuators than continuous face-sheet DMs Design of DMs balances stiffness and thickness of face sheet, stroke and strength of actuators, hysteresis, ability to polish mirror with high precision Large DMs are now proven (continuous face sheet, bimorph, adaptive secondary) MEMs DMs hold promise of lower cost, more actuators Claire Max, Astro 289C, UCSC

120 Acknowledgements Center for Adaptive Optics UCSC s MEMS DM Research Group: Bautista Fernandez (analysis, modeling, design, layout, testing) Oscar Azucena (modeling using energy methods) Darwin Fernandez, Janelle Young (undergraduate interns) This work has been supported in part by the National Science Foundation Science and Technology Center for Adaptive Optics, managed by the University of California at Santa Cruz under cooperative agreement No. AST This research was also supported in part by a Special Research Grant from the University of California, Santa Cruz.

121 That s All Folks!