Abstract

I show that it is possible to choose the eikonals for the lens groups of a zoom lens such that extended objects at infinity are imaged perfectly, without any aberrations, at all zoom settings.

© 2001 Optical Society of America

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References

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  1. A. Walther, “Zoom lenses and computer algebra,” J. Opt. Soc. Am. A 16, 198–204 (1999).
    [CrossRef]
  2. R. Kingslake, A History of the Photographic Lens (Academic, New York, 1989), p. 161.
  3. For a general introduction to eikonal functions see Refs. 4-7.
  4. M. Herzberger, Strahlenoptik (Springer, Berlin, 1931).
  5. R. Luneburg, Mathematical Theory of Optics (University of California Press, Los Angeles, Calif., 1964).
  6. H. A. Buchdahl, An Introduction to Hamiltonian Optics (Cambridge University Press, Cambridge, UK, 1970).
  7. A. Walther, The Ray and Wave Theory of Lenses (Cambridge University Press, Cambridge, UK, 1995).
  8. T. Smith, “The changes in aberrations when the object and stop are moved,” Trans. Opt. Soc. 23, 139–153 (1921/1922).
  9. These calculations were carried out with the Oslo Six lens design program. Oslo Six is a registered trade mark of Sinclair Optics Inc., Fairport, New York.
  10. See, e.g., Ref. 7, pp. 228–229.

1999

Buchdahl, H. A.

H. A. Buchdahl, An Introduction to Hamiltonian Optics (Cambridge University Press, Cambridge, UK, 1970).

Herzberger, M.

M. Herzberger, Strahlenoptik (Springer, Berlin, 1931).

Kingslake, R.

R. Kingslake, A History of the Photographic Lens (Academic, New York, 1989), p. 161.

Luneburg, R.

R. Luneburg, Mathematical Theory of Optics (University of California Press, Los Angeles, Calif., 1964).

Smith, T.

T. Smith, “The changes in aberrations when the object and stop are moved,” Trans. Opt. Soc. 23, 139–153 (1921/1922).

Walther, A.

A. Walther, “Zoom lenses and computer algebra,” J. Opt. Soc. Am. A 16, 198–204 (1999).
[CrossRef]

A. Walther, The Ray and Wave Theory of Lenses (Cambridge University Press, Cambridge, UK, 1995).

J. Opt. Soc. Am. A

Trans. Opt. Soc.

T. Smith, “The changes in aberrations when the object and stop are moved,” Trans. Opt. Soc. 23, 139–153 (1921/1922).

Other

These calculations were carried out with the Oslo Six lens design program. Oslo Six is a registered trade mark of Sinclair Optics Inc., Fairport, New York.

See, e.g., Ref. 7, pp. 228–229.

R. Kingslake, A History of the Photographic Lens (Academic, New York, 1989), p. 161.

For a general introduction to eikonal functions see Refs. 4-7.

M. Herzberger, Strahlenoptik (Springer, Berlin, 1931).

R. Luneburg, Mathematical Theory of Optics (University of California Press, Los Angeles, Calif., 1964).

H. A. Buchdahl, An Introduction to Hamiltonian Optics (Cambridge University Press, Cambridge, UK, 1970).

A. Walther, The Ray and Wave Theory of Lenses (Cambridge University Press, Cambridge, UK, 1995).

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Figures (1)

Fig. 1
Fig. 1

Schematic of a Donders system with a ray coming from the axial point at infinity.

Equations (40)

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sin(θ2/2)sin(θ3/2)=G,
Li=sin θi,ti=sin(θi/2),i=1  4.
Hi=Li+a3Li3+a5Li5+  
W1=n=0H1nFn(θ2).
x1=W1L1=n=1nH1n-1dH1dL1 Fn(θ2).
x1=-2f1t2=F1(θ2),
W1=-2f1H1t2+n=2H1nFn(t2).
W3=-2f1H4t3+n=2H4nFn(t3).
W2=-4f2sin(θ2/2)sin(θ3/2)=-4f2t2t3.
z=-f2/G,z=-Gf2,
E=W1+z cos θ2-z+W2+zcos θ3-z+W3.
z cos θ2-z=-z(1-cos θ2)=-2z sin2(θ2/2)=-2zt22.
E=-2f1H1t2+2H1nFn(t2)+2 f2G t22-4f2t2t3+ 2Gf2t32-2f1H4t3+2H4nFn(t3).
-2f1H1+2H1nFn(t2)t2+4f2G t2-4f2t3=0,
-2f1H4+2H4nFn(t3)t3+4Gf2t3-4f2t2=0.
-2f1(-GH1)-G2H1nFn(t2)t2+4Gf2t3-4f2t2=0.
W1=-2f1H1t2,W2=-4f2t2t3,
W3=-2f1H4t3,
E=2f2Gt2-Gt3-Gf1H12f22-Gf12H122f2.
t2-Gt3-Gf1H12f2=0,
a=(L22+M22)/2,b=L2L3+M2M3,
c=(L32+M32)/2.
L2=sin θ2cos ϕ2,M2=sin θ2sin ϕ2,
L3=sin θ3cos ϕ3,M3=sin θ3sin ϕ3.
a=(sin2 θ2)/2,b=sin θ2sin θ3cos(ϕ2-ϕ3),
c=(sin2 θ3)/2.
a=2 sin2(θ2/2)cos2(θ2/2)=2t22(1-t22),
b=4 sin(θ2/2)cos(θ2/2)sin(θ3/2)cos(θ3/2)×cos(ϕ2-ϕ3)=4t2t31-t221-t32cos(ϕ2-ϕ3),
c=2 sin2(θ3/2)cos2(θ3/2)=2t32(1-t32).
W1=-2f1H1t2cos(ϕ1-ϕ2),
W2=-4f2t2t3cos(ϕ2-ϕ3),
W3=-2f1H4t3cos(ϕ4-ϕ3),
E=-2f1H1t2cos ϕ2+2 f2G t22-4f2t2t3cos(ϕ2-ϕ3)+2Gf2t32-2f1(-GH1)t3cos ϕ3.
E=2 f2Gt2cos ϕ2-Gt3cos ϕ3-Gf12f2 H12+2 f2G (t2sin ϕ2-Gt3sin ϕ3)2-G f122f2 H12.
t2cos ϕ2-Gt3cos ϕ3-Gf12f2 H1=0,
t2sin ϕ2-Gt3sin ϕ3=0.
E=-G f122f2 H12,
W1=-2f1b1-2a2(1+1-2c),
W2=-2f2b1+1-2a1+1-2c,
W3=-2f1b1-2c2(1+1-2a).

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