Shaping Thin Glass Mirrors using Air Bearings

Mark L. Schattenburg, Mireille K. Akilian and Ralf K. Heilmann

Space Nanotechnology LaboratoryKavli Institute for Astrophysics and Space Research

Massachusetts Institute of Technology, Cambridge, MA 02139

International Workshop on Astronomical X-Ray OpticsPrague, Czech Republic

Dec. 9, 2009

Thin Sheet Glass is Produced in High Volume with High Quality

Hard Disk Drives Liquid 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 manufacturerGlass surface after slumping

Flatness ~400 μm P-V (Peak-to-Valley) Flatness <0.4 μm 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

0'''

2

2

2

2

2

2

z

pk

y

pk

x

pk zyx

Flow inside porous mandrel

Flow in gap

Hz

zyx z

pk

y

pkhh

yx

pkhh

x

'

1266 22

Where k: permeabilityp’: pressure in porous mandrelp: pressure in gaph: air gap heightH: porous mandrel thickness

h = 5 μm h = 10 μm h = 15 μm

Glass is Pushed to Centerline with 1/h3 Restoring Force

Hz

zyx z

pk

y

pkhh

yx

pkhh

x

'

1266 22

Assume: h is constant kx=ky=kz=k

Fact: permeability k << h2

Hzz

p

h

k

y

p

x

p

'12

32

2

2

2

h1 > h2 p1 < p2

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

Fre

quen

cy P-V 2.26 μm; RMS 0.39 μm

Fre

quen

cy RMS 7.53 arcsecF

requ

ency RMS 12.22 arcsec

Slumping Repeatability: Sheet-to-Sheet

Fre

quen

cy RMS 0.35 μm

Fre

quen

cy RMS 3.30 arcsec RMS 8.13 arcsecF

requ

ency

Deep-UV (=250 nm) Shack-Hartmann Metrology ToolRepeatability ~ 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/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.