Abstract

A mathematical model has been developed that predicts the aspheric surface that a typical optical surfacing machine will produce. The model, which combines two basic assumptions concerning material wear with the kinematics of the machine, has been verified experimentally for the grinding process. In region of the surface where the tool extends beyond the edge of the workpiece, pressure becomes nonuniform, and the model must be altered. The established model has been used to synthesize those machine strokes required to produce a desired aspheric surface.

© 1974 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. J. Rupp, Feinwerktecknik 67, 295 (1963).
  2. W. J. Rupp, Appl. Opt. 4, 743 (1965).
    [CrossRef]
  3. W. Rupp, Optica Acta 18, 1 (1971).
    [CrossRef]
  4. W. Rupp, Appl. Opt. 11, 2797 (1972).
    [CrossRef] [PubMed]
  5. R. Aspden, R. McDonough, F. R. Nitchie, Appl. Opt. 11, 2739 (1972).
    [CrossRef] [PubMed]
  6. R. L. Luckett, Manufacturing Optics Intl. (Sept.1972), p. 613.
  7. F. W. Preston, J. Glass Tech. 11, 124 (1927).

1972 (2)

1971 (1)

W. Rupp, Optica Acta 18, 1 (1971).
[CrossRef]

1965 (1)

1963 (1)

W. J. Rupp, Feinwerktecknik 67, 295 (1963).

1927 (1)

F. W. Preston, J. Glass Tech. 11, 124 (1927).

Aspden, R.

Luckett, R. L.

R. L. Luckett, Manufacturing Optics Intl. (Sept.1972), p. 613.

McDonough, R.

Nitchie, F. R.

Preston, F. W.

F. W. Preston, J. Glass Tech. 11, 124 (1927).

Rupp, W.

Rupp, W. J.

W. J. Rupp, Appl. Opt. 4, 743 (1965).
[CrossRef]

W. J. Rupp, Feinwerktecknik 67, 295 (1963).

Appl. Opt. (3)

Feinwerktecknik (1)

W. J. Rupp, Feinwerktecknik 67, 295 (1963).

J. Glass Tech. (1)

F. W. Preston, J. Glass Tech. 11, 124 (1927).

Optica Acta (1)

W. Rupp, Optica Acta 18, 1 (1971).
[CrossRef]

Other (1)

R. L. Luckett, Manufacturing Optics Intl. (Sept.1972), p. 613.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Kinematics of a typical optical surfacing machine.

Fig. 2
Fig. 2

Geometry used to determine relative velocities.

Fig. 3
Fig. 3

Material removal when grinding a polished surface.

Fig. 4
Fig. 4

Material removal when grinding a surface with the central region originally polished and the outer region ground.

Fig. 5
Fig. 5

Material removal when grinding a surface with the outer region originally polished and the central region ground.

Fig. 6
Fig. 6

Material removal when grinding a ground surface.

Fig. 7
Fig. 7

Nonuniform pressure distribution when the tool extends beyond the edge of the workpiece.

Fig. 8
Fig. 8

Material removal predicted using a properly weighted linear combination of three individual removal curves.

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

W = K wear p f V p d t ,
W = p f K wear V p d t .
W ( r ) = 1 2 π 0 2 π W 1 ( r , θ ) d θ .
L ( t ) = L 0 ( t ) exp ( - i ω w t ) .
V t = d L / d t = [ d L 0 d t - i ω w L 0 ] exp ( i ω w t ) .
R = r e i θ - L 0 exp ( - i ω w t ) .
V t p = i R ω t
( V p / ω w B ) = [ η ( d L / d τ ) - iL ( 1 + ω ) ] exp ( - i τ / η ) + i ω k exp ( i θ ) ,
L = L 0 / B , τ = ω e t , τ ( 0 , 2 π ) , η = ω e / ω w , k = r / B , k ( 0 , 1 ) , Ω = ω t / ω w , θ = θ , θ ( 0 , 2 π ) .
W 1 ( k , θ ) = p f K wear ( B / η ) Q ( k , θ , τ ) d τ .
α 2 | R B | 2 = k 2 + L 2 - 2 k [ Re { L } cos ( τ / η + θ ) + Im { L } sin ( τ / η + θ ) ] .
w 1 ( k , θ ) = W 1 / T = p f K wear ω w B ( 1 2 π ) 0 2 π Q ( k , θ , τ ) d τ .
w ( k ) = K wear p f ω w B ( 1 2 π ) 2 0 2 π 0 2 π Q d τ d θ .
w ( k ) = K wear p f ω w B ( 1 2 π ) 2 0 2 π 0 2 π p ( x ) p f Q d τ d θ .
W ( k ) = a 1 w 1 ( k ) + a 2 w 2 ( k ) + + a i w i ( k ) .

Metrics