Abstract

The fabrication of a conic surface begins with the grinding of a best-fit sphere. The desired conic surface can then be obtained by further grinding with a subaperture tool. Finally, the surface is polished. Normally the best-fit sphere is chosen so as to minimize the second grinding step. However, this method tends to produce mid-spatial frequency errors near the edge of the surface and can cause errors in the paraxial radius of curvature. This paper presents an alternative method of calculating the initial sphere so as to avoid these errors. It requires more grinding time but far less time for polishing.

© 1999 Optical Society of America

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References

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  1. A.V. Kuznetsov, B. A. Chunin, “Methods of making aspherical surfaces,” Sov. J. Opt. Technol., 43, No. 5, 319–24, (1976).
  2. Gunter Schultz, “Spherical surfaces,” Progress in Optics, 25,349–415, (1988).
    [CrossRef]
  3. G.M. Sanger, “Perspective on precision machining, polishing, and optical requirements,” SPIE, 306,90–99, (1981).
    [CrossRef]
  4. Robert E. Parks, “Overview of optical manufacturing methods,” SPIE, 306,2–12, (1981).
    [CrossRef]
  5. Theodore W. J. Unti, “Best-Fit Sphere Approximation to a General Aspheric Surface,” Applied Optics, 5, No. 2, 319–21, (1966).
    [CrossRef] [PubMed]
  6. J.D. Briers, “Best-fit spheres and conics as an aid in the manufacture and testing of diamond-turned aspherics optics,” Optica Acta, 32, No. 2, 169–78, (1985).
    [CrossRef]
  7. D. Malacara, “An optical surface and its characteristics,” Appendix 1, Optical Shop Testing, D. Malacara, Ed., John Wiley & Sons, Inc., New York, 1992.

1988

Gunter Schultz, “Spherical surfaces,” Progress in Optics, 25,349–415, (1988).
[CrossRef]

1985

J.D. Briers, “Best-fit spheres and conics as an aid in the manufacture and testing of diamond-turned aspherics optics,” Optica Acta, 32, No. 2, 169–78, (1985).
[CrossRef]

1981

G.M. Sanger, “Perspective on precision machining, polishing, and optical requirements,” SPIE, 306,90–99, (1981).
[CrossRef]

Robert E. Parks, “Overview of optical manufacturing methods,” SPIE, 306,2–12, (1981).
[CrossRef]

1976

A.V. Kuznetsov, B. A. Chunin, “Methods of making aspherical surfaces,” Sov. J. Opt. Technol., 43, No. 5, 319–24, (1976).

1966

Theodore W. J. Unti, “Best-Fit Sphere Approximation to a General Aspheric Surface,” Applied Optics, 5, No. 2, 319–21, (1966).
[CrossRef] [PubMed]

Briers, J.D.

J.D. Briers, “Best-fit spheres and conics as an aid in the manufacture and testing of diamond-turned aspherics optics,” Optica Acta, 32, No. 2, 169–78, (1985).
[CrossRef]

Chunin, B. A.

A.V. Kuznetsov, B. A. Chunin, “Methods of making aspherical surfaces,” Sov. J. Opt. Technol., 43, No. 5, 319–24, (1976).

Kuznetsov, A.V.

A.V. Kuznetsov, B. A. Chunin, “Methods of making aspherical surfaces,” Sov. J. Opt. Technol., 43, No. 5, 319–24, (1976).

Malacara, D.

D. Malacara, “An optical surface and its characteristics,” Appendix 1, Optical Shop Testing, D. Malacara, Ed., John Wiley & Sons, Inc., New York, 1992.

Parks, Robert E.

Robert E. Parks, “Overview of optical manufacturing methods,” SPIE, 306,2–12, (1981).
[CrossRef]

Sanger, G.M.

G.M. Sanger, “Perspective on precision machining, polishing, and optical requirements,” SPIE, 306,90–99, (1981).
[CrossRef]

Schultz, Gunter

Gunter Schultz, “Spherical surfaces,” Progress in Optics, 25,349–415, (1988).
[CrossRef]

Unti, Theodore W. J.

Theodore W. J. Unti, “Best-Fit Sphere Approximation to a General Aspheric Surface,” Applied Optics, 5, No. 2, 319–21, (1966).
[CrossRef] [PubMed]

Applied Optics

Theodore W. J. Unti, “Best-Fit Sphere Approximation to a General Aspheric Surface,” Applied Optics, 5, No. 2, 319–21, (1966).
[CrossRef] [PubMed]

Optica Acta

J.D. Briers, “Best-fit spheres and conics as an aid in the manufacture and testing of diamond-turned aspherics optics,” Optica Acta, 32, No. 2, 169–78, (1985).
[CrossRef]

Progress in Optics

Gunter Schultz, “Spherical surfaces,” Progress in Optics, 25,349–415, (1988).
[CrossRef]

Sov. J. Opt. Technol.

A.V. Kuznetsov, B. A. Chunin, “Methods of making aspherical surfaces,” Sov. J. Opt. Technol., 43, No. 5, 319–24, (1976).

SPIE

G.M. Sanger, “Perspective on precision machining, polishing, and optical requirements,” SPIE, 306,90–99, (1981).
[CrossRef]

Robert E. Parks, “Overview of optical manufacturing methods,” SPIE, 306,2–12, (1981).
[CrossRef]

Other

D. Malacara, “An optical surface and its characteristics,” Appendix 1, Optical Shop Testing, D. Malacara, Ed., John Wiley & Sons, Inc., New York, 1992.

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Figures (3)

Figure 1
Figure 1

Conic surface (solid line), and initial sphere, (broken line) using the Unti equation.

Figure 2
Figure 2

Conic surface (solid line) and initial sphere, (broken line) using the equation (6).

Figure 3
Figure 3

r2 − r1, as function of the f#.

Tables (1)

Tables Icon

Table 1 Comparison between a calculation using the Unti equation and the equation proposed by the authors. The units are millimeters and for Yt the numbers are a percentage of the aperture of the surface.

Equations (12)

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z = C 1 S 2 1 + [ 1 - ( k + 1 ) C 1 S 2 ] 1 / 2 ,
d z d S = C 1 S [ 1 - ( k + 1 ) C 1 S 2 ] ,
d z d S = C 2 S [ 1 - C 2 S 2 ] 1 / 2 .
C 1 ( D 2 ) [ 1 - ( k + 1 ) C 1 2 ( D 2 ) 2 ] 1 / 2 = C 2 ( D 2 ) [ 1 - ( k + 1 ) C 2 2 ( D 2 ) 2 ] 1 / 2 ,
C 2 = 2 C 1 [ 4 - k D 2 C 1 2 ] 1 / 2 ;
r 2 = 1 2 [ 4r 1 2 - k D 2 ] 1 / 2 .
1 2 [ 4r 1 2 - k D 2 ] 1 / 2     r 1 ,
k     0.
r 2 = D 2   [ 16 ( f # ) 2 - k ] 1 / 2 ,
V   =   2 π 0 D / 2 ( Δ z ) y d y ,
V   =   2 π { r 1 3 3 ( k + 1 ) 2 - D 2 ( Q + 4 r 1 2 ) 16 ( k + 1 ) r 1 - Q 3 / 2 24 ( k + 1 ) 2 - ( Q + D 2 ) 24 + D 2 Q 1 / 2 16 + Q 3 / 2 24 } ,
V   =   2 π { D 4 128 r 1 + r 1 D 2 8 + r 1 3 3 - ( 4 r 1 2 + D 2 ) 24 } .

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