Abstract

Calculations of the light flux distribution in the defocused star image suggest that λ/60 of sharply varying aberration and λ/20 of slowly varying aberration can be detected.

© 1960 Optical Society of America

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References

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  1. L. C. Martin, Technical Optics (London, 1950), Vol. II.
  2. E. H. Linfoot, Proc. Roy. Soc. (London) A186, 72 (1946).
  3. E. H. Linfoot, Proc. Phys. Soc. 58, 759 (1946).
    [Crossref]
  4. H. D. Taylor, The Adjustment and Testing of Telescope Objectives (Newcastle upon Tyne, 1947), fourth edition. This is a most detailed treatment of the method.
  5. K. Lommel, Abhandl. bayer. Akad. Wiss. Math.-Naturw. Kl. 15(1886).
  6. F. Zernike and B. R. A. Nijboer, contribution to “La théorie des Images Optiques” (Paris, 1949), p. 217.

1946 (2)

E. H. Linfoot, Proc. Roy. Soc. (London) A186, 72 (1946).

E. H. Linfoot, Proc. Phys. Soc. 58, 759 (1946).
[Crossref]

1886 (1)

K. Lommel, Abhandl. bayer. Akad. Wiss. Math.-Naturw. Kl. 15(1886).

Linfoot, E. H.

E. H. Linfoot, Proc. Roy. Soc. (London) A186, 72 (1946).

E. H. Linfoot, Proc. Phys. Soc. 58, 759 (1946).
[Crossref]

Lommel, K.

K. Lommel, Abhandl. bayer. Akad. Wiss. Math.-Naturw. Kl. 15(1886).

Martin, L. C.

L. C. Martin, Technical Optics (London, 1950), Vol. II.

Nijboer, B. R. A.

F. Zernike and B. R. A. Nijboer, contribution to “La théorie des Images Optiques” (Paris, 1949), p. 217.

Taylor, H. D.

H. D. Taylor, The Adjustment and Testing of Telescope Objectives (Newcastle upon Tyne, 1947), fourth edition. This is a most detailed treatment of the method.

Zernike, F.

F. Zernike and B. R. A. Nijboer, contribution to “La théorie des Images Optiques” (Paris, 1949), p. 217.

Abhandl. bayer. Akad. Wiss. Math.-Naturw. Kl. (1)

K. Lommel, Abhandl. bayer. Akad. Wiss. Math.-Naturw. Kl. 15(1886).

Proc. Phys. Soc. (1)

E. H. Linfoot, Proc. Phys. Soc. 58, 759 (1946).
[Crossref]

Proc. Roy. Soc. (London) (1)

E. H. Linfoot, Proc. Roy. Soc. (London) A186, 72 (1946).

Other (3)

L. C. Martin, Technical Optics (London, 1950), Vol. II.

H. D. Taylor, The Adjustment and Testing of Telescope Objectives (Newcastle upon Tyne, 1947), fourth edition. This is a most detailed treatment of the method.

F. Zernike and B. R. A. Nijboer, contribution to “La théorie des Images Optiques” (Paris, 1949), p. 217.

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Figures (2)

Fig. 1
Fig. 1

Flux in out-of-focus star image. Curve 1, no spherical aberration, p=±10; curve 2, under-corrected spherical aberration, γ=0.2, outside focus (p=+10); curve 3, under-corrected spherical aberration, γ=0.2, inside focus (p=−10).

Fig. 2
Fig. 2

Flux in out-of-focus star image. Curve 1, no spherical aberration, p=±18; curve 2, under-corrected spherical aberration, γ=0.2, outside focus (p=+18); curve 3, under-corrected spherical aberration, γ=0.2, inside focus (p=−18).

Equations (5)

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A 0 ( p , q ) + i B 0 ( p , q ) = a 2 π 0 2 π 0 1 exp i { p r 2 + q r cos θ } r d r d θ ,
p = π λ ( N A ) 2 · z ;             q = 2 π λ ( N A ) · R ,
A 0 ( p , q ) + i B 0 ( p , q ) + ρ 2 ( e i β - 1 ) × { A 0 ( ρ 2 p , ρ q ) + i B 0 ( ρ 2 p , ρ q ) } .
I ( p , q ) = A 0 2 ( p , q ) + B 0 2 ( p , q ) + 2 ρ 2 β { A 0 ( ρ 2 p , ρ q ) B 0 ( p , q ) - B 0 ( ρ 2 p , ρ q ) A 0 ( p , q ) } + O ( β 2 ) .
exp i { p r 2 + q r cos θ + γ R 4 0 ( r ) } ,