Shaping Thin Glass Mirrors using Air Bearings Mark L. Schattenburg, Mireille K. Akilian and Ralf K. Heilmann Space Nanotechnology Laboratory Kavli Institute for Astrophysics and Space Research Massachusetts Institute of Technology, Cambridge, MA International Workshop on Astronomical X-Ray Optics Prague, Czech Republic Dec. 9, 2009

Thin Sheet Glass is Produced in High Volume with High Quality Hard Disk DrivesLiquid Crystal Displays

Sheet Glass Manufacturing Processes Corning’s Fusion Process Slot Draw Process

Traditional Slumping Technology Large thermal asymmetry: Very long slumping cycles Edge curl up CTE mismatch ripples

Problems with Conventional Slumping Technology Glass sheet slumped on dusty mandrel The traditional approach is not working … We need a new idea! Sticking Dust particles, ripples … Large thermal asymmetry Long thermal cycles (days)

Problem: How to faithfully replicate mandrel surface. Solution: Porous air bearing prevents glass from touching mandrel. Glass surface from manufacturer Glass surface after slumping Flatness ~400 μ m P-V (Peak-to-Valley)Flatness <0.4 μ m RMS

Air Bearing Slumping Concept Glass centerline is forced to bearing mid-point Glass sheet is mechanically supported by tungsten wires 100 mm

Fluid Dynamics Governing Equations Flow inside porous mandrel Flow in gap Where k : permeability p’ : pressure in porous mandrel p : pressure in gap h : air gap height H : porous mandrel thickness h = 5 μm h = 10 μm h = 15 μm

Glass is Pushed to Centerline with 1/h 3 Restoring Force Assume: h is constant k x =k y =k z =k Fact: permeability k << h 2 h 1 > h 2 p 1 < p 2

Slumping onto Flat Surfaces Easiest Plan to Start OUR THREE-PART PLAN Crawl:Slump onto flat mandrels: Low cost mandrels Simplified metrology Develop understanding of fluid dymamics Walk:Slump onto Wolter mandrels (new effort) Run:Continuous slumping process

Prototype Mandrel Assembly Concept MIT-Kavli Institute Tantalum spacers maintain 50  m glass-mandrel gaps (temporary solution). Spacers eliminated in future design.

Assembly Steps

Assembly Steps (Continued)

Mandrel Plumbing Layout All experiments to date performed with open-loop pressure control. Closed-loop control has been implemented and is under test.

Slumping Results: Glass Sheet Surface Metrology Frequency P-V 2.26 μm; RMS 0.39 μm Frequency RMS 7.53 arcsec Frequency RMS arcsec

Slumping Repeatability: Sheet-to-Sheet Frequency RMS 0.35 μm Frequency RMS 3.30 arcsec RMS 8.13 arcsec Frequency

Deep-UV ( =250 nm) Shack-Hartmann Metrology Tool Repeatability ~ 40 nm P-V

Thin Optic Constraint Double-sided flexures (3) Vertical tilt stage Reference block Antenna flexures (4) Horizontal tilt stage Silicon wafer Repeatability 55 nm

The Next Steps for Air Bearing Slumping … (2) Eliminate spacers (3) Develop continuous processing of Wolter Optics (1)Implement closed-loop pressure control. (Completed and under test.)

Summary Demonstrated a new method for slumping glass using porous air bearings. Eliminates high-frequency errors due to dust particles 1/h 3 restoring force. Demonstrated sheet-to-sheet repeatability of 3.3 arc sec. New funding source obtained ( ) Two new Mech. E. Ph.D. students hired Larger slumping facility under development We are grateful to the NASA ROSES program for financial support.