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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 02139

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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 02139

International Workshop on Astronomical X-Ray Optics

Prague, Czech Republic

Dec. 9, 2009

thin sheet glass is produced in high volume with high quality
Thin Sheet Glass is Produced in High Volume with High Quality

Hard Disk Drives

Liquid Crystal Displays

sheet glass manufacturing processes
Sheet Glass Manufacturing Processes

Slot Draw Process

Corning’s Fusion Process

traditional slumping technology
Traditional Slumping Technology
  • Large thermal asymmetry:
  • Very long slumping cycles
  • Edge curl up
  • CTE mismatch ripples
problems with conventional slumping technology
Problems with Conventional Slumping Technology
  • Sticking
  • Dust particles, ripples …
  • Large thermal asymmetry
  • Long thermal cycles (days)

The traditional approach is not working …

We need a new idea!

Glass sheet slumped on dusty mandrel

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 μm P-V (Peak-to-Valley)

Flatness <0.4 μm RMS

air bearing slumping concept
Air Bearing Slumping Concept

Glass sheet is mechanically supported by tungsten wires

100 mm

Glass centerline is forced to bearing mid-point

fluid dynamics governing equations
Fluid Dynamics Governing Equations

Flow inside porous mandrel

Where k: permeability

p’: pressure in porous mandrel

p: pressure in gap

h: air gap height

H: porous mandrel thickness

Flow in gap

h = 15 μm

h = 5 μm

h = 10 μm

glass is pushed to centerline with 1 h 3 restoring force
Glass is Pushed to Centerline with 1/h3 Restoring Force

Assume: h is constant


Fact:permeability k << h2

h1 > h2 p1 < p2

slumping onto flat surfaces easiest plan to start
Slumping onto Flat Surfaces Easiest Plan to Start
  • Crawl: Slump onto flat mandrels:
      • Low cost mandrels
      • Simplified metrology
      • Develop understanding of fluid dymamics
  • Walk: Slump onto Wolter mandrels (new effort)
  • Run: Continuous slumpingprocess
prototype mandrel assembly concept
Prototype Mandrel Assembly Concept
  • Tantalum spacers maintain 50 mm glass-mandrel gaps
  • (temporary solution).
  • Spacers eliminated in future design.

MIT-Kavli Institute

mandrel plumbing layout
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
Slumping Results: Glass Sheet Surface Metrology

P-V 2.26 μm; RMS 0.39 μm


RMS 12.22 arcsec

RMS 7.53 arcsec



slumping repeatability sheet to sheet
Slumping Repeatability: Sheet-to-Sheet

RMS 0.35 μm


RMS 8.13 arcsec

RMS 3.30 arcsec



Thin Optic Constraint


flexures (3)

Silicon wafer

Reference block


55 nm

Vertical tilt stage

Antenna flexures (4)

Horizontal tilt stage

the next steps for air bearing slumping
The Next Steps for Air Bearing Slumping …
  • Implement closed-loop pressure control.
  • (Completed and under test.)

(3) Develop continuous processing

of Wolter Optics

(2) Eliminate spacers

  • Demonstrated a new method for slumping glass using porous air bearings.
  • Eliminates high-frequency errors due to dust particles

1/h3 restoring force.

  • Demonstrated sheet-to-sheet repeatability of 3.3 arc sec.
  • New funding source obtained (2010-2014)

Two new Mech. E. Ph.D. students hired

Larger slumping facility under development

We are grateful to the NASA ROSES program

for financial support.