Jim Burge, Bill Anderson, Scott Benjamin, 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 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 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 stiffness for 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 Flexible, incompressible joint Grinding or polishing pad Polishing pressure

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.

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 weight Teflon bearing Support frame Teflon bearing spring ring guide rod ball joint

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 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 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 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 Pressure Required Pressure Distribution Membrane Tool’s Aspheric Misfit 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 Tool made by hot forming plastic sheet, faced with grinding pads After 5 hours directed figuring with membrane tool For f/0.5 convex asphere (tested in transmission)

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