Aspherical surface polishing with a ring polisher

Gih-Horng Chen; Duncan T. Moore

doi:10.1364/AO.18.000559

Applied Optics
Vol. 18,
Issue 4,
pp. 559-562
(1979)
•https://doi.org/10.1364/AO.18.000559

Aspherical surface polishing with a ring polisher

Gih-Horng Chen and Duncan T. Moore

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Gih-Horng Chen and Duncan T. Moore, "Aspherical surface polishing with a ring polisher," Appl. Opt. 18, 559-562 (1979)

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Abstract

The ring-shaped polisher analyzed by Vinokur is modified to be a high-speed polisher for aspherical surfaces. The mathematical modeling of the ring polisher has been reformulated to examine the uniformity of surface polishing over the workpiece. The fabrication of a ring polisher is described, and experimental results of direct polishing of ground aspherical surfaces are discussed.

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(A) If R ≥ e ≥ R₁, i.e., the workpiece center is closer to the polisher’s inner rim.
	$0 \leq ξ \leq ɛ - \frac{R_{1}}{ρ_{m}}$	$ɛ - \frac{R_{1}}{ρ_{m}} \leq ξ \leq \frac{R_{2}}{ρ_{m}} - ɛ$	$\frac{R_{2}}{ρ_{m}} - ɛ \leq ξ \leq 1$
ω ≥ Ω	$γ = Ω e (1 + λ ξ) E (\frac{π}{2}, K)$	$γ = Ω e (1 + λ ξ) [E (\frac{π}{2}, K) - E (ϕ_{1}, K)]$	γ = Ωe(1 + λξ)[E(ϕ₂,K) − E(ϕ₁,K)]
Ω ≥ ω	$γ = Ω e (1 + λ ξ) E (\frac{π}{2}, K)$	γ = Ωe(1 + λξ)E(ψ₁, K)	γ = Ωe(1 + λξ)[E(ψ₁,K) − E(ψ₂,K)]

(B) If R₂ ≥ e ≥ R, i.e., the workpiece center is closer to the polisher’s outer rim.
	$0 \leq ξ \leq \frac{R_{2}}{ρ_{m}} - ɛ$	$\frac{R_{2}}{ρ_{m}} - ɛ \leq ξ \leq ɛ - \frac{R_{1}}{ρ_{m}}$	$ɛ - \frac{R_{1}}{ρ_{m}} \leq ξ \leq 1$
ω ≥ Ω	$γ = Ω e (1 + λ ξ) E (\frac{π}{2}, K)$	γ = Ωe(1 + λξ)E(ϕ₂,K)	γ = Ωe(1 + λξ)[E(ϕ₂,K) − E(ϕ₁,K)]
Ω ≥ ω	$γ = Ω e (1 + λ ξ) E (\frac{π}{2}, K)$	$γ = Ω e (1 + λ ξ) [E (\frac{π}{2}, K) - E (ψ_{1}, K)]$	γ = Ωe(1 + λξ)[E(ψ₁,K) − E(ψ₂,K)]

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Applied Optics