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References

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  1. G.-H. Chen, D. T. Moore, Appl. Opt. 18559 (1979).
    [CrossRef] [PubMed]
  2. S. I. Vinokur, in Generation of Optical SurfacesK. G. Kumanin, Ed. (Focal Press, London, 1962), pp. 371, 378.
  3. F. Cooke, N. Brown, E. Prochnow, Opt. Eng. 15, 407 (1976).
    [CrossRef]

1979 (1)

1976 (1)

F. Cooke, N. Brown, E. Prochnow, Opt. Eng. 15, 407 (1976).
[CrossRef]

Brown, N.

F. Cooke, N. Brown, E. Prochnow, Opt. Eng. 15, 407 (1976).
[CrossRef]

Chen, G.-H.

Cooke, F.

F. Cooke, N. Brown, E. Prochnow, Opt. Eng. 15, 407 (1976).
[CrossRef]

Moore, D. T.

Prochnow, E.

F. Cooke, N. Brown, E. Prochnow, Opt. Eng. 15, 407 (1976).
[CrossRef]

Vinokur, S. I.

S. I. Vinokur, in Generation of Optical SurfacesK. G. Kumanin, Ed. (Focal Press, London, 1962), pp. 371, 378.

Appl. Opt. (1)

Opt. Eng. (1)

F. Cooke, N. Brown, E. Prochnow, Opt. Eng. 15, 407 (1976).
[CrossRef]

Other (1)

S. I. Vinokur, in Generation of Optical SurfacesK. G. Kumanin, Ed. (Focal Press, London, 1962), pp. 371, 378.

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Figures (2)

Fig. 1
Fig. 1

Geometry of an aspheric polishing technique for producing equal relative velocity at all points between lens surface and polisher. L, axis of rotation of lens; T, axis of rotation of tool; P, arbitrary point on lens–polisher interface. The parallelogram represents the relative velocity vectors at point P.

Fig. 2
Fig. 2

Comparison of aspheric surface shapes.

Equations (8)

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V 2 + v l 2 + v t 2 + 2 v l v t cos ( γ ) .
γ = π / 2 - ψ cos ( π / 2 - ψ ) = sin ψ v 1 = r ω l v t = a ω t ω l = angular lens velosity ω t = angular polisher velocity V 2 = r 2 ω l 2 + a 2 ω t 2 + 2 a r ω l ω t sin ψ }
tan ψ = r / ( d r / d θ ) .
( r cos θ - d ) 2 + r 2 sin 2 θ = a 2 .
d r / d θ = r d sin θ / ( d cos θ - r ) .
sin ψ = [ ( d cos θ - r ) / d sin θ ] [ 1 + ( d cos θ - r ) 2 / ( d sin θ ) 2 ] 1 / 2 .
a 2 = d 2 + r 2 - 2 r d cos θ .
V 2 = d 2 ω t 2 + ( ω l - ω t ) 2 r 2 + 2 r d ( cos θ ) ω t ( ω l - ω t ) .

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