A 2024 demonstration at the Changchun Institute of Optics, Fine Mechanics and Physics (CIOMP) polished a ⌀4 m silicon carbide (SiC) aspheric mirror to better than 0.024λ RMS using an error-map-dividing strategy that assigns low-order errors to a ⌀400 mm tool and high-order errors to a ⌀100 mm tool in computer-controlled optical surfacing (CCOS). The authors acknowledge that the strategy rests on simulation: the relationship between grinding-head size and the controllable spatial-frequency band has not been measured, actual outcomes deviate from predictions (simulation forecast ~120 days of pure machining where ~180 were needed, attributed to tool wear, SiC-specific removal behavior, edge-effect control, and process instability), and metrology consumed over half of the 377 processing-and-measurement days. The open problem is to make multi-tool CCOS of multi-meter SiC aspheres deterministic: empirically establish the tool influence functions and their stability for the tool set used, replace the simulation-only tool-size/frequency-control curves with measured ones, and refine the process models so that predicted and achieved convergence agree on real fabrication runs.

Background

Silicon carbide (SiC) has become the material of choice for lightweight mirrors in space telescopes and large ground-based instruments because of its high specific stiffness (stiffness-to-mass ratio) and dimensional stability; figuring monolithic SiC aspheres with apertures of several meters is a manufacturing frontier. The surface is shaped by computer-controlled optical surfacing (CCOS): a planar-rotary tool — a sub-aperture polishing head (a tool much smaller than the mirror aperture) that spins about its own axis while that axis is swept across the surface — dwells at each location for a time computed from a removal model, classically Preston's equation, under which the removed depth dz/dtdz/dt is proportional to the local polishing pressure PP and the relative tool–surface velocity vv (dz/dt=kPvdz/dt = kPv). The spatial footprint of the tool's removal rate is the tool influence function (TIF); figure correction amounts to convolving the TIF with a computed dwell-time map. Two tool-related facts dominate practice: the material removal rate grows with tool size, while the ability to correct fine detail falls. Small tools can correct mid-to-high spatial frequencies — the mid-spatial-frequency (MSF) regime, with periods from millimeters to tens of centimeters, that scatters light and degrades image quality — but need impractically long dwell times to remove large error volumes, while large tools are fast but cannot follow short-period errors and misfit aspheric curvature.

Liu et al. (2024), from the CIOMP group that produced the world's largest SiC aspheric mirror (⌀4.03 m; Zhang et al. 2022), demonstrated a strategy for this trade-off on a 4 m SiC parabolic mirror polished on a 4.5 m-capacity CCOS machine. The residual error map is split by a 36-term Zernike polynomial fit (Zernike polynomials being the standard orthogonal basis on the unit disk for describing optical surface errors) into a low-order map removed by a ⌀400 mm tool and a high-order map removed by a ⌀100 mm tool, with magnetorheological finishing (MRF — polishing with a magnetically stiffened fluid spot) used in later stages; the group's tool set also included a ⌀600 mm head. Simulation predicted one-iteration convergence from 0.2λ0.2\lambda to 0.071λ0.071\lambda RMS and a combined convergence-efficiency metric of 1.84 (versus 0.72 and 0.51 for the single small and large tools); in the actual run the error converged from 0.207λ0.207\lambda to 0.109λ0.109\lambda RMS (47%) in one iteration, and the final figure was better than 0.024λ0.024\lambda RMS; the same simulation estimated roughly 300 days of pure machining had the ⌀100 mm tool been used alone. (The program's earlier comprehensive account of the ⌀4.03 m mirror, Zhang et al. 2022, already reported a 15.2 nm RMS final figure, so the final accuracy itself was not a first; the novel element was the error-dividing multi-tool strategy and its measured efficiency.)

The authors are explicit about what the demonstration did not establish. First, the relationship between grinding-head size and the controllable spatial-frequency band was established entirely by simulation — synthetic sinusoidal error maps with periods from 50 to 1000 mm figured by modeled TIFs of different tool diameters — and not by systematic measurement. Second, actual outcomes deviated from the model: simulation predicted about 120 days of pure machining where about 180 days were needed, a gap the authors attribute to process instability — tool behavior variability, tool wear, unforeseen SiC removal behavior, and edge-effect control (the disturbance of the TIF where the tool overhangs the aperture boundary). Third, the schedule was dominated not by polishing but by measurement: of 377 days of processing-plus-measurement activity, metrology consumed over half, because obtaining stable, trustworthy full-aperture data on a 4 m-class asphere is itself difficult. The open problem is therefore the process-certainty gap of multi-tool CCOS of large SiC aspheres: replacing simulation-only relationships with empirically validated ones so that the strategy becomes predictively accurate.

Problem Statement

For multi-tool, error-map-dividing computer-controlled optical surfacing (CCOS) of multi-meter silicon carbide (SiC) aspheric mirrors, make the process deterministic — close the gap between simulated and actual processing outcomes — by: (1) empirical establishment on SiC of the tool influence functions (TIFs) of the planar-rotary tools used in multi-meter SiC aspheric CCOS (diameters on the order of 100–600 mm, at the strokes and kinematic modes employed), including their stability over tool life (wear), their material-specific removal behavior, and their modification near the aperture edge, and from these measurements the experimentally determined relationship between different tool sizes and the controllable spatial-frequency band (the convergence rate as a function of error period and tool size) that presently exists only in simulation; and (2) refinement of the removal/process models to incorporate the measured TIFs, tool wear, and edge effects, such that predicted dwell times, convergence rates, and residual errors agree with actual processing outcomes on real large-SiC-aspheric fabrication runs. Both serve one overarching objective, predictive fabrication of large SiC aspheres.

References

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