Abstract

Third-order aberration contributions of aspheric surfaces are derived from the point of view of wave theory. The design of a double aspheric curved field anastigmat based on third-order theory is then presented and its performance compared to a similar (Petzval) system consisting solely of spherical surfaces. The control of higher order aberrations and the possibility of increasing the relative aperture of the system with the aid of aspherics are discussed.

© 1956 Optical Society of America

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References

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  1. L. C. Martin, Technical Optics (J. Pitman and Sons, Ltd, London, New York, 1948), Vol. II, Chapters II and VIII.
  2. C. R. Burch, Proc. Phys. Soc. (London) 55, 433 (1943).
    [CrossRef]
  3. H. H. Hopkins, Wave Theory of AberrationsOxford University Press, New York, 1950), p. 151.
  4. D. P. Feder, J. Opt. Soc. Am. 41, 630 (1951).
    [CrossRef]

1951 (1)

1943 (1)

C. R. Burch, Proc. Phys. Soc. (London) 55, 433 (1943).
[CrossRef]

Burch, C. R.

C. R. Burch, Proc. Phys. Soc. (London) 55, 433 (1943).
[CrossRef]

Feder, D. P.

Hopkins, H. H.

H. H. Hopkins, Wave Theory of AberrationsOxford University Press, New York, 1950), p. 151.

Martin, L. C.

L. C. Martin, Technical Optics (J. Pitman and Sons, Ltd, London, New York, 1948), Vol. II, Chapters II and VIII.

J. Opt. Soc. Am. (1)

Proc. Phys. Soc. (London) (1)

C. R. Burch, Proc. Phys. Soc. (London) 55, 433 (1943).
[CrossRef]

Other (2)

H. H. Hopkins, Wave Theory of AberrationsOxford University Press, New York, 1950), p. 151.

L. C. Martin, Technical Optics (J. Pitman and Sons, Ltd, London, New York, 1948), Vol. II, Chapters II and VIII.

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Figures (7)

Fig. 1
Fig. 1

Schematic representation of a fourth-order aspheric.

Fig. 2
Fig. 2

Double aspheric curved field anastigmat.

Fig. 3
Fig. 3

Rim ray curves of double aspheric on sagittal focus.

Fig. 4
Fig. 4

Field curves for double aspheric curved field anastigmat.

Fig. 5
Fig. 5

Meridional ray curves for Petzval lens.

Fig. 6
Fig. 6

Field curves for Petzval lens.

Fig. 7
Fig. 7

Effect of higher orders on rim ray curves.

Tables (2)

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Table I a Third-order aberrations.

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Table II a,b Third-order aberrations.

Equations (9)

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x = a s 2 + b s 4 + c s 6 + ,
x = s 2 2 r + s 4 8 r 3 + s 6 16 r 5 + .
S C = - 8 k 4 ( n - n ) y 4 2 n 0 u 0 2
T C = S C · u 0 = - 8 k 4 ( n - n ) y 4 2 n 0 u 0
C C = y p y · S C · u 0 = y p y · T C
A C = ( y p y ) 2 · S C = ( y p y ) 2 · T C u 0
D C = ( y p y ) 3 · S C · u 0 = ( y p y ) 3 · T C
B = - 8 ( n - n ) k 4 y 4 , F = ρ · B , C = ρ 2 · B , D = ρ 3 · B ,             where             ρ = y p / y .
( y p y ) 1 2 · B 1 + ( y p y ) 2 2 · B 2 = - C , ( y p y ) 1 3 · B 1 + ( y p y ) 2 3 B 2 = 0 ,