Abstract

A doublet of choice glasses may be located in the converging focal cone of the infinity-focused parabola to yield an aplanatic telescope or camera. The resulting angular field is limited by high astigmatism but is significantly larger than that of the coma-limited parabola. The spherical and chromatic aberrations are so well corrected and the coma so well balanced that the doublet may be used unaltered with a parabola of arbitrary focal length and speed with excellent results for the unvignetted rays. A second doublet nearer to the focus and designed independently of the first corrects the system’s astigmatism while preserving its aplanaticism. It may also be designed for flattening the field. This arrangement may allow for greater flexibility in the placing of optical elements than does Wynne’s triplet for modest-aperture systems. Equations are presented for choosing candidate glasses for the first doublet from the very limited manifold of solving glasses.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. D. J. Schroeder, “Wynne Triplets,” in Astronomical Optics (Academic, San Diego, Calif., 1987), pp. 169–170.
  2. W. J. Smith, “Image formation: geometrical and physical optics,” in Handbook of Optics, W. G. Driscoll, W. Vaughan, eds. (McGraw-Hill, N.Y., 1978), p. 2–22.
  3. R. Kingslake, “A parabolic mirror,” in Lens Design Fundamentals (Academic, New York, 1978), p. 302.
  4. A. E. Gee, “The design of telescope objectives by the G-sum method,” in Amateur Telescope Making III, A. G. Ingalls, ed. (Scientific, Princeton, N.J., 1953), p. 208.
  5. In Ref. 3, “Primary spherical aberration of a thin lens,” pp. 116–117.
  6. M. Born, E. Wolf, in “The Herschel Condition,” Principles of Optics, 6th ed. (Pergamon, Elmsford, N.Y., 1980), p. 169.
  7. In Ref. 3, “The coma G-sum,” pp. 164–165.
  8. In Ref. 3, “Thin lens contributions,” p. 207.
  9. H. Rutten, M. van Venrooij, “Presentation of image aberrations with spot diagrams,” in Telescope Optics (Willmann-Bell, Richmond, Va., 1988), p. 36.

Born, M.

M. Born, E. Wolf, in “The Herschel Condition,” Principles of Optics, 6th ed. (Pergamon, Elmsford, N.Y., 1980), p. 169.

Gee, A. E.

A. E. Gee, “The design of telescope objectives by the G-sum method,” in Amateur Telescope Making III, A. G. Ingalls, ed. (Scientific, Princeton, N.J., 1953), p. 208.

Kingslake, R.

R. Kingslake, “A parabolic mirror,” in Lens Design Fundamentals (Academic, New York, 1978), p. 302.

Rutten, H.

H. Rutten, M. van Venrooij, “Presentation of image aberrations with spot diagrams,” in Telescope Optics (Willmann-Bell, Richmond, Va., 1988), p. 36.

Schroeder, D. J.

D. J. Schroeder, “Wynne Triplets,” in Astronomical Optics (Academic, San Diego, Calif., 1987), pp. 169–170.

Smith, W. J.

W. J. Smith, “Image formation: geometrical and physical optics,” in Handbook of Optics, W. G. Driscoll, W. Vaughan, eds. (McGraw-Hill, N.Y., 1978), p. 2–22.

van Venrooij, M.

H. Rutten, M. van Venrooij, “Presentation of image aberrations with spot diagrams,” in Telescope Optics (Willmann-Bell, Richmond, Va., 1988), p. 36.

Wolf, E.

M. Born, E. Wolf, in “The Herschel Condition,” Principles of Optics, 6th ed. (Pergamon, Elmsford, N.Y., 1980), p. 169.

Other (9)

D. J. Schroeder, “Wynne Triplets,” in Astronomical Optics (Academic, San Diego, Calif., 1987), pp. 169–170.

W. J. Smith, “Image formation: geometrical and physical optics,” in Handbook of Optics, W. G. Driscoll, W. Vaughan, eds. (McGraw-Hill, N.Y., 1978), p. 2–22.

R. Kingslake, “A parabolic mirror,” in Lens Design Fundamentals (Academic, New York, 1978), p. 302.

A. E. Gee, “The design of telescope objectives by the G-sum method,” in Amateur Telescope Making III, A. G. Ingalls, ed. (Scientific, Princeton, N.J., 1953), p. 208.

In Ref. 3, “Primary spherical aberration of a thin lens,” pp. 116–117.

M. Born, E. Wolf, in “The Herschel Condition,” Principles of Optics, 6th ed. (Pergamon, Elmsford, N.Y., 1980), p. 169.

In Ref. 3, “The coma G-sum,” pp. 164–165.

In Ref. 3, “Thin lens contributions,” p. 207.

H. Rutten, M. van Venrooij, “Presentation of image aberrations with spot diagrams,” in Telescope Optics (Willmann-Bell, Richmond, Va., 1988), p. 36.

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 (6)

Fig. 1
Fig. 1

System configured as Newtonian.

Fig. 2
Fig. 2

Longitudinal aberration.

Fig. 3
Fig. 3

Ray-fan plots.

Fig. 4
Fig. 4

Longitudinal aberration.

Fig. 5
Fig. 5

Ray-fan plots.

Fig. 6
Fig. 6

Longitudinal astigmatism and field curvature.

Tables (2)

Tables Icon

Table 1 Specifications: First Doublet

Tables Icon

Table 2 Specifications: Second Doublet

Equations (24)

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

OSCn=-1/4F/number2=-yn/2fn2,
G1=n2n-1/2, G2=2n+1n-1/2,G3=3n+1n-1/2, G4=n+2n-1/2n,G5=2n2-1/n, G6=3n+2n-1/2n,G7=G2/n, G8=G1/n.
SCd=0 =G1aca3+G1bcb3-ϕaG3aca2-G3bcb2+ϕa2G6aca+G6bcb+c2G2aca2-G2bcb2-ϕaG5aca+G5bcb+c22G4aca+G4bcb,
SCd=0 =G1aca3+G1bcb3-v2G3aca2-G3bcb2+v22G6aca+G6bcb+c2G2aca2-G2bcb2-v2G5aca+G5bcb+c22G4aca+G4bcb.
ϕa+v2=G3aca2-G3bcb2+G5acac2+G5bcbc2/G6aca+G6bcb.
OSCd=yn/2fn2 =yd2G5acac2/4-G7acav2+G8aca2+G5bcbc2/4-G7bcbv2-G8bcb2,
v2=-yn/2ydfn2+G8aca2-G8bcb2+G5aca+G5bcbc2/4/G7aca+G7bcb.
g1=G1a-G1bdb/da3, g2=G2a-G2bdb/da2,g3=G3a-G3bdb/da2, g4=G4a-G4bdb/da,g5=G5a-G5bdb/da, g6=G6a-G6bdb/da,g7=G7a-G7bdb/da, g8=G8a-G8bdb/da2.
SCd:ca2g1-na-1g3+na-12g6+c2cag2-na-1g5+c22g4=0,
OSC:yd2cag7v2-g8ca-g5c2/4-yn/2fn2=0,
OSC:yd2cag7v2-g8ca-g5c2/4-v2-ϕa2/4=0.
c2=g6v2+ϕa-cag3/g5.
K2-4g7-g6-2na-1K-D=0,
B-g2-na-1g5-2g4g3/g5A-g4A2=0,
K=g5/g6A-na-1.
v6=1/l5+ϕa,
SCd=0=g1ca2+g2ca-g3v6ca+g4-g5v6+g6v62,
OSCd=0=g5-4g7v6+4g8ca,
g2=G2ac2-G2bc3db/da2,g4=G4ac22-G4bc32db/da,g5=G5ac2-G5bc3db/da.
AC=0= 1/f,PC=0= 1/nf,
ϕa+ϕb2=-ϕa+ϕb1- ϕn,
ϕa/na+ϕb/nb2=-ϕa/na+ϕb/nb1- ϕn/nn,
ϕa2=-ϕa+ϕb1+ ϕn/1-J2,
ϕa2=-ϕa/na+ϕb/nb1+ ϕn/nn/1/na-J/nb2,

Metrics