Transcript Grinding and polishing aspheric surfaces

Development of optimal grinding and
polishing tools for aspheric surfaces
Marty Valente
Jim Burge, Bill Anderson, Scott Benjamin,
Myung Cho, Koby Smith
Optical 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 b
Aspheric departure is
dominated by lowest modes, with P-V
deviation from vertex fit of
Power
Astig
Coma
Ka 2 b 2
2R 3
Ka 2 b 2
2R 3
Ka 3b
3R 3
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
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• 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
If the lap is shaped like a ring, power and coma
terms go away
Power
Coma
Function
a2r2
a31r3cos
= a31r2x
for rings of
constant r
ring shifts with
r2 dependence
ring tilts with
r2 dependence
Shape
Cross section
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
stiffness
for near-flat surfaces only
For curved surfaces, tilted
interface causes torsion,
too compliant!
Cross-section
of ring
Flexible,
incompressible
joint
Grinding or
polishing pad
Polishing
pressure
Solution:
Tilt the beam, rings then
become sections of a cone,
rather than a cylinder
Ring tool design
We need to use nested rings to get
sufficient polishing area
1.5 m
The rings can be faced with either grinding
or polishing pads
4.0 m
The cross sectional height and width of the
rings are chosen using finite element
modeling to determine the stiffness.
0.9 m
0.6 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
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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
weight
Teflon bearing
Support frame
Teflon bearing
spring
ring
guide rod
ball joint
Grinding interface
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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
guide rod
ring
ball joint
ball bearing
RTV
Aluminum pad with seat for bearing
grinding/polishing
surface
Prototype ring tool
Working 40 cm f/0.5 asphere
Preliminary results from ring tool
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The tool is basically well-behaved
– not problems at edge
– no problems with chatter
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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
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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
Rigid tool
Compliant interface (CC neoprene foam)
Membrane
Grinding or polishing pads
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
Analysis using modal decomposition
Displacement
Di spl acement
Di spl acement
P r essur e Di str i buti on
Pressure
P r essur e Di str i buti on
Required Pressure
Distribution
Membrane Tool’s
Aspheric Misfit
P r essur e Di str i buti on
Di spl acement
Di spl acement
Di spl acement
The modal stiffness
was calculated using a
finite element model
P r essur e Di str i buti on
P r essur e Di str i buti on
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
Tool made by hot forming
plastic sheet, faced with
grinding pads
For f/0.5 convex
asphere
(tested in
transmission)
After 5 hours directed
figuring with membrane
tool
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