Development of optimal grinding and polishing tools for aspheric surfaces

Marty Valente

Jim Burge, Bill Anderson, Scott Benjamin,

Myung Cho, Koby SmithOptical Sciences Center

University of Arizona

Fabrication of spherical surfaces

• Spheres are natural and easy, as long as you use– large stiff tools– good supports– smart polishing strokes,

• The tool and the part tend to wear to form mating spheres– The tool always fits the surface, giving rapid convergence,

excellent surface

• Measurement is easy - interferometer, spherometer

The process itself results in a spherical surface

The largest lens (in the world?)

• 1.8-m diameter test plate for measuring the MMT wide field secondary mirror

• Both sides spherical, concave side requires high accuracy• Polished at OSC to achieve slope spec of 0.01 waves/cm • Now has computer generated hologram on concave surface

polishing handling Final figure

Grinding and polishing aspheric surfaces

• The process by itself does not converge to make the correct shape

• It is necessary to set up an accurate test, and work the surface based on the measurement

• The laps generally do not fit the aspheric surface so– there is no tendency towards the correct shape– special attention must be paid to the surface finish

General lap misfit for aspheres

•Circular lap radius a•off center by bAspheric departure is

dominated by lowest modes, with P-V deviation from vertex fit of

The grinding and polishing tool must always accommodate the misfit, as the tool is rotated and stroked over the part

Mechanisms for working aspheric surfaces

• Lapping relies on two mechanisms for correcting shape errors:– Directed figuring : rubbing more, or pressing harder on the

high spots– Natural smoothing : Using a stiff lap, small scales bumps

are naturally worn down

• Optimal tooling will take natural smoothing as far as possible to maximize efficiency

Control of small scales by smoothing

Stiffness of lap

Grinding and polishing of aspheres, always fighting between two issues:

#1) Desire to use large, rigid laps for passive smoothing#2) Requirement that the lap conform to the asphere

– usually leads to small tools or flexible tools at the expense of #1– for small parts, it can be economic to use small tools under computer

control

Optimal lap, controlled to fit the asphere, and very stiff to figure errors

Next best thing, lap is compliant in modes necessary to fit the asphere, yet remains stiff to figure errors

Large tool for aspheres - stressed lap

• Used at Steward Observatory Mirror Lab for f/1 mirrors• 1.2-m, 60 cm, and 30 cm stressed laps are in operation• bent by actuators as the lap is moved, • NC shape changes every msec so it always fits desired asphere • bends up to 1 mm 6.5-m f/1.25 14 nm rms

Active vs. passive laps

• The actively controlled stressed lap works extremely well, yet requires significant initial investment and maintenance.

• Is it possible to design a lap that is naturally compliant to the modes required to fit the asphere, yet remains stiff enough for natural smoothing?

The magic of rings

Power Coma

Function a2r2 a31r

3cos = a31r

2x

for rings ofconstant r

ring shifts withr2 dependence

ring tilts withr2 dependence

Shape

Cross section

If the lap is shaped like a ring, power and coma terms go away

Bending required for ring tool - Astigmatism

Astigmatic bending

• Rings bend easily in astigmatism if the cross section is compliant in torsion

• Use geometry to make rings stiff locally in one direction

• Analogy, bandsaw blade. – Totally compliant for astigmatism– Very rigid over scales of few inches

• So a lap made from thin rings will fit the asphere!Power and coma are taken up by rigid body motion and astigmatism is easily bent in

An important detail for the rings - coning

Cylindrical rings, pressure aligned for maximum stiffnessfor near-flat surfaces only

For curved surfaces, tilted interface causes torsion, too compliant!

Solution:Tilt the beam, rings then become sections of a cone, rather than a cylinder

Cross-section of ring

Polishing pressure

Grinding or polishing pad

Flexible, incompressible joint

Ring tool design

We need to use nested rings to get sufficient polishing area

The rings can be faced with either grinding or polishing pads

The cross sectional height and width of the rings are chosen using finite element modeling to determine the stiffness.

4.0 m

0.6 m

1.5 m

0.9 m

Calculation of ring geometry

Using finite element modeling, we created an empirical model of ring stiffness as function of cross section geometry

Then, for each ring in the nested set:

The aspheric departure is calculated to determine the amount of astigmatic bending required for each ring, at the end of its stroke.

Choose ring cross section to allow the ring to bend by the required amount, forced by pressure variations small compared to the nominal polishing pressure.

Software for designing ring tools

User enters parameters for asphere and desired tool size and stroke

Software calculates the corresponding ring geometry

Attachments of rings

• Allow vertical motion using guide rods in linear bearings

• Allow rotation using spherical joint• Constrain lateral motion• Lateral force near polishing surface

to minimize moments• Supply drive force in circumferential

direction• Apply force using weights• Designed for fabrication ease

ring

Support frame

weight

Teflon bearing

spring

guide rod

ball joint

Teflon bearing

Grinding interface• Use pads, small enough to always fit

asphere • Stiff attachment to ring• Pivot on ball bearing• Held on by silicone• Grinding surface - metal • Polishing surface - urethane • Design for fabrication ease• Maintenance is important

ring

ball joint

guide rod

Aluminum pad with seat for bearing

RTV

grinding/polishing surface

ball bearing

Prototype ring tool

Working 40 cm f/0.5 asphere

Preliminary results from ring tool

• The tool is basically well-behaved– not problems at edge– no problems with chatter

• Fits the aspheric surface• Good smoothing achieved

Initial Ronchigram, after aspherizing with full size compliant tool

Ronchigram, after 4 hr run with the prototype ring tool

Ring tool frame

• Connects drive pin to rings• Has bearings for guide rods• Frame “floats” on rings using soft

springs• Drive torque and lateral forces

taken at hub• Lifting eyes are used to hoist frame

3-m tool for 4-m f/0.5 paraboloid

Membrane laps

• Smaller laps can achieve a good compromise between desired stiffness for smoothing and compliance to fit the asphere using laps faced with membranes

Pin, connecting to polishing machine

Compliant interface (CC neoprene foam)

Membrane

Grinding or polishing pads

Rigid tool

Membrane stiffness

• Finite element used to establish modal stiffness of membrane• Solve for membrane thickness for a given tool, stroke, and membrane

material• Membrane stiffness goes as t3

• Stiffness to ripples on the surface goes as L-4

– L is the period of the ripple

• Membranes with the correct curves can be made by – direct machining– hot-forming plastic sheets onto surface– casting, layup on surface

Membrane Tool’sAspheric Misfit

Analysis using modal decomposition

Displacement

Displacement

Displacement

Displacement

Pressure Distribution

Pressure Distribution

Pressure Distribution

Pressure Distribution

Required Pressure Distribution

Displacement Pressure

The modal stiffness was calculated using a finite element model

Note that the dominant pressure variations are at the edge of the tool

Software for designing membrane tools

User enters parameters for asphere, desired tool size and stroke

Given membrane, software calculates pressure distribution under lap

or given allowable pressure distribution, software calculates membrane thickness

Experience with membranes

Initial Ronchigram

After 5 hours directed figuring with membrane toolFor f/0.5 convex

asphere

(tested in transmission)

Tool made by hot forming plastic sheet, faced with grinding pads

Conclusion

• There is much activity and interest at the University of Arizona in the area of fabrication of aspheric surfaces.

• Stay tuned! Things develop very quickly