Abstract

Fermat’s principle dictates that aberrations are inevitable when a lens must be used to image more than one object plane. We present a numerical method to evaluate the effect of this basic limitation in cases of practical interest.

© 1970 Optical Society of America

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References

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  1. Of T. Smith’s many papers, we quote in particular Trans. Opt. Soc. (London) 23, 311 (1921, 22) and a paper in La Theorie des Images, edited by P. Fleury (Editions de la Revue d’Optique, Paris, 1949), p. 18.
    [Crossref]
  2. A. Walther, Am. J. Phys. 35, 808 (1967).
    [Crossref]
  3. A. Walther, J. Opt. Soc. Am. 59, 1325 (1969).
    [Crossref]
  4. C. Caratheodory, Geometrische Optik (Springer, Berlin, 1937), p. 36.

1969 (1)

1967 (1)

A. Walther, Am. J. Phys. 35, 808 (1967).
[Crossref]

Caratheodory, C.

C. Caratheodory, Geometrische Optik (Springer, Berlin, 1937), p. 36.

Smith, T.

Of T. Smith’s many papers, we quote in particular Trans. Opt. Soc. (London) 23, 311 (1921, 22) and a paper in La Theorie des Images, edited by P. Fleury (Editions de la Revue d’Optique, Paris, 1949), p. 18.
[Crossref]

Walther, A.

Am. J. Phys. (1)

A. Walther, Am. J. Phys. 35, 808 (1967).
[Crossref]

J. Opt. Soc. Am. (1)

Trans. Opt. Soc. (London) (1)

Of T. Smith’s many papers, we quote in particular Trans. Opt. Soc. (London) 23, 311 (1921, 22) and a paper in La Theorie des Images, edited by P. Fleury (Editions de la Revue d’Optique, Paris, 1949), p. 18.
[Crossref]

Other (1)

C. Caratheodory, Geometrische Optik (Springer, Berlin, 1937), p. 36.

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Figures (4)

Fig. 1
Fig. 1

Can Q be imaged perfectly?

Fig. 2
Fig. 2

Astigmatism and meridional asymmetry error corrected.

Fig. 3
Fig. 3

Astigmatism and meridional intercept of the sagittal trace corrected. The sagittal-ray intercepts for the sagittal trace are too small to be shown in the figure.

Fig. 4
Fig. 4

Point on axis corrected perfectly.

Equations (15)

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L = - V / x ,             M = - V / y ,
x = - V / L ,             y = - V / M ,
2 V x L Δ L + 2 V x M Δ M = - L - V , x ,
2 v y L Δ L + 2 V y M Δ M = - M - V y .
- V / L = x = - x , - V / M = y = - y ,
V = u 2 + f ( u 1 ) ,
u 1 = 1 2 ( x 2 + y 2 ) , u 2 = x L + y M .
V = u 2 + A u 1 + 1 2 B u 1 2 + 1 3 C u 1 3 + ,
V / x = - L = L + A x + x ( B u 1 + C u 1 2 + ) ,
L = - L - x - x ( B u 1 + C u 1 2 ) ,
M = - M - y - y ( B u 1 + C u 1 2 ) ,
x = - x ,
y = - y .
Δ = [ ( x Q - x ) 2 + ( y Q - y ) 2 + z Q 2 ] 1 2 + V ( x , y , L , M ) + L x Q + M y Q + N z Q ,
V = u 2 + ( 0.5625 + 2 u 1 ) 1 2 - ( 9 + 2 u 1 ) 1 2 .