Abstract

Two separate geometric design procedures are presented for calculating aspheric surfaces. The first calculates individual reflecting surfaces for correcting the optical path length (OPL) of a system. The second jointly calculates pairs of surfaces for the simultaneous correction of OPL and offense against the sine condition (OCS). The procedures remain valid for extreme focal ratios. Applications of these procedures are made to the design of Arecibo-style (stationary spherical primary) telescopes, coma-correctors for such telescopes, three-mirror aplanats with deep spherical primaries, and two-mirror aplanats. Unusual new forms of aplanatic telescope and microscope objectives have emerged from these applications.

© 1979 Optical Society of America

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References

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  1. W. H. Southwell, Appl. Opt. 18, 1240 (1979).
    [Crossref] [PubMed]
  2. P. N. Robb, L. Mertz, Proc. Soc. Photo-Opt. Soc. Am. 172, 15 (1979).
  3. A. K. Head, Proc. Phys. Soc. London 70, 945 (1957); Proc. Phys. Soc. London 71, 546 (1958).
    [Crossref]
  4. L. Mertz, in Optical Instruments and Techniques, J. H. Dickson, Ed. (Oriel, Boston, 1969), p. 507.
  5. A. E. Conrady, Applied Optics and Optical Design, Part 2 (Dover, New York, 1960), p. 793.
  6. S. Rosin, Appl. Opt. 5, 675 (1966).
    [Crossref] [PubMed]

1979 (2)

W. H. Southwell, Appl. Opt. 18, 1240 (1979).
[Crossref] [PubMed]

P. N. Robb, L. Mertz, Proc. Soc. Photo-Opt. Soc. Am. 172, 15 (1979).

1966 (1)

1957 (1)

A. K. Head, Proc. Phys. Soc. London 70, 945 (1957); Proc. Phys. Soc. London 71, 546 (1958).
[Crossref]

Conrady, A. E.

A. E. Conrady, Applied Optics and Optical Design, Part 2 (Dover, New York, 1960), p. 793.

Head, A. K.

A. K. Head, Proc. Phys. Soc. London 70, 945 (1957); Proc. Phys. Soc. London 71, 546 (1958).
[Crossref]

Mertz, L.

P. N. Robb, L. Mertz, Proc. Soc. Photo-Opt. Soc. Am. 172, 15 (1979).

L. Mertz, in Optical Instruments and Techniques, J. H. Dickson, Ed. (Oriel, Boston, 1969), p. 507.

Robb, P. N.

P. N. Robb, L. Mertz, Proc. Soc. Photo-Opt. Soc. Am. 172, 15 (1979).

Rosin, S.

Southwell, W. H.

Appl. Opt. (2)

Proc. Phys. Soc. London (1)

A. K. Head, Proc. Phys. Soc. London 70, 945 (1957); Proc. Phys. Soc. London 71, 546 (1958).
[Crossref]

Proc. Soc. Photo-Opt. Soc. Am. (1)

P. N. Robb, L. Mertz, Proc. Soc. Photo-Opt. Soc. Am. 172, 15 (1979).

Other (2)

L. Mertz, in Optical Instruments and Techniques, J. H. Dickson, Ed. (Oriel, Boston, 1969), p. 507.

A. E. Conrady, Applied Optics and Optical Design, Part 2 (Dover, New York, 1960), p. 793.

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Figures (10)

Fig. 1
Fig. 1

Geometry for procedure I.

Fig. 2
Fig. 2

Alternate geometry for procedure I.

Fig. 3
Fig. 3

Arecibo-style telescope with secondary calculated by procedure I.

Fig. 4
Fig. 4

Variation of effective focal length with zone for Arecibo-style telescope.

Fig. 5
Fig. 5

Auxiliary coma-correcting system for Arecibo-style telescope; initial design.

Fig. 6
Fig. 6

Geometry leading to pivot point P for procedure II.

Fig. 7
Fig. 7

Geometry for prolonging reflecting surface from R1 to R2 in procedure II.

Fig. 8
Fig. 8

Geometry to apply procedure II directly after spherical primary.

Fig. 9
Fig. 9

Aplanatic telescopes with deep spherical primaries followed by two aspheric correcting mirrors as calculated by procedure II.

Fig. 10
Fig. 10

10× aplanatic microscope objective. Numerical aperture equals refractive index of operating medium.

Equations (2)

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r = a ( 1 - e 2 ) ( 1 + e cos ϕ ) ,
r = a / ( 1 + cos θ ) ,

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