Abstract

We present a method to obtain the optimum surface shape for use as a starting point for the machining of aspherical surfaces of revolution. Applying this method, the volume that remains to be machined away can be set below an acceptable value. Subsequently, it is shown how this method can be applied for conic surfaces.

© 1997 Optical Society of America

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References

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  1. T. Nakasuji et al., “Diamond turning of brittle materials for optical components,” Annals of the CIRP 39, 89–92 (1990).
    [CrossRef]
  2. R.A. Jones, “Computer simulation of smoothing during computer-controlled optical polishing,” Appl. Opt. 34, 1162–1169 (1995).
    [CrossRef] [PubMed]
  3. T.W. Drueding et al., “Ion beam figuring of small optical components,” Opt. Eng. 34, 3565–3571 (1995).
    [CrossRef]
  4. O.W. Fähnle et al., “Loose abrasive line-contact machining of aspherical optical surfaces of revolution,” accepted for publication in Appl. Opt.

1995 (2)

T.W. Drueding et al., “Ion beam figuring of small optical components,” Opt. Eng. 34, 3565–3571 (1995).
[CrossRef]

R.A. Jones, “Computer simulation of smoothing during computer-controlled optical polishing,” Appl. Opt. 34, 1162–1169 (1995).
[CrossRef] [PubMed]

1990 (1)

T. Nakasuji et al., “Diamond turning of brittle materials for optical components,” Annals of the CIRP 39, 89–92 (1990).
[CrossRef]

Drueding, T.W.

T.W. Drueding et al., “Ion beam figuring of small optical components,” Opt. Eng. 34, 3565–3571 (1995).
[CrossRef]

Fähnle, O.W.

O.W. Fähnle et al., “Loose abrasive line-contact machining of aspherical optical surfaces of revolution,” accepted for publication in Appl. Opt.

Jones, R.A.

Nakasuji, T.

T. Nakasuji et al., “Diamond turning of brittle materials for optical components,” Annals of the CIRP 39, 89–92 (1990).
[CrossRef]

Annals of the CIRP (1)

T. Nakasuji et al., “Diamond turning of brittle materials for optical components,” Annals of the CIRP 39, 89–92 (1990).
[CrossRef]

Appl. Opt. (1)

Opt. Eng. (1)

T.W. Drueding et al., “Ion beam figuring of small optical components,” Opt. Eng. 34, 3565–3571 (1995).
[CrossRef]

Other (1)

O.W. Fähnle et al., “Loose abrasive line-contact machining of aspherical optical surfaces of revolution,” accepted for publication in Appl. Opt.

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Figures (2)

Figure 1
Figure 1

The touching sphere at point P of a concave aspherical surface of revolution, also indicating the speci al case only valid for paraboloidal surfaces where R equals the length of the hypothenuse of the right-angled triangle, the two other sides are given by p and ro.

Figure 2
Figure 2

Computer simulation of the determination of the starting surface fs(r) for the production process of a concave hyper boloidal surface of revolution, (a) and (b) the distance of fs(r) to fa(r) for the first ni rie iteration steps, which lead to t lie first five sequences of peaks ((a) showing the first four sequences and (b) the fifth sequence after which the process is stopped.), (c) the mass of material (BK7) that still has to be removed to reach fa(r) depending on the sequence, that is reached, (d) the maximal distance Δ of fs(r) to fa(r) for the first five sequences of peaks.

Equations (11)

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f t r = ± [ h - R 2 - r 2 1 / 2 ] ,
h = R 2 - r o 2 1 / 2 + | f a r o | ,
R = R r o = r o [ 1 + f a r o / r 2 ] 1 / 2 ,
A ) f t r f a r B ) f t r o = f a r o C ) if   f a r   concave:   ρ r o R r o   if   f a r   convex:   ρ r o R r o
D ) lim   R r o = ρ 0   r o 0
f s r Δ = [ f a r n / r ] 1 r Δ - r n + f a r n ,
d = [ r n - r Δ 2 + f s r Δ - f a r n 2 ] 1 / 2
V = r f s r - f a r d r d ϕ
f c r = ± r 2 / p + [ p 2 - r 2 k + 1 ] 1 / 2
f c r = f c r / r = ± r / [ p 2 - r 2 k + 1 ] 1 / 2
f c r = f c r / r = p 2 / [ p 2 - r 2 k + 1 ] 3 / 2

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