Abstract

In the paraxial form of the Debye integral for focusing, higher order defocus terms are ignored, which can result in errors in dealing with aberrations, even for low numerical aperture. These errors can be avoided by using a different integration variable. The aberrations of a glass slab, such as a coverslip, are expanded in terms of the new variable, and expressed in terms of Zernike polynomials to assist with aberration balancing. Tube length error is also discussed.

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References

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  1. M. Born and E. Wolf, Principles of Optics, 6th ed.(Pergamon, 1993).
  2. Y. Li and E. Wolf, J. Opt. Soc. Am. A 1, 801 (1984).
    [CrossRef]
  3. C. J. R. Sheppard and P. Török, J. Opt. Soc. Am. A 15, 3016 (1998).
    [CrossRef]
  4. C. J. R. Sheppard, Opt. Lett. 25, 1660 (2000).
    [CrossRef]
  5. H. H. Hopkins, Proc. Phys. Soc. London 55, 116 (1943).
    [CrossRef]
  6. B. Richards and E. Wolf, Proc. R. Soc. London A 253, 358 (1959).
    [CrossRef]
  7. R. Kant, J. Modern Opt. 40, 2293 (1993).
    [CrossRef]
  8. C. J. R. Sheppard, Optik 105, 29 (1997).
  9. C. J. R. Sheppard and M. Gu, J. Modern Opt. 40, 1631(1993).
    [CrossRef]
  10. C. J. R. Sheppard, Appl. Opt. 27, 4782 (1988).
    [CrossRef]
  11. C. J. R. Sheppard and H. J. Matthews, J. Opt. Soc. Am. A 4, 1354 (1987).
    [CrossRef]
  12. P. Török, P. Varga, Z. Laczik, and G. R. Booker, J. Opt. Soc. Am. A 12, 325 (1995).
    [CrossRef]
  13. P. Török, P. Varga, and G. Németh, J. Opt. Soc. Am. A 12, 2660 (1995).
    [CrossRef]

2000

1998

1997

C. J. R. Sheppard, Optik 105, 29 (1997).

1995

1993

R. Kant, J. Modern Opt. 40, 2293 (1993).
[CrossRef]

C. J. R. Sheppard and M. Gu, J. Modern Opt. 40, 1631(1993).
[CrossRef]

1988

1987

1984

1959

B. Richards and E. Wolf, Proc. R. Soc. London A 253, 358 (1959).
[CrossRef]

1943

H. H. Hopkins, Proc. Phys. Soc. London 55, 116 (1943).
[CrossRef]

Booker, G. R.

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed.(Pergamon, 1993).

Gu, M.

C. J. R. Sheppard and M. Gu, J. Modern Opt. 40, 1631(1993).
[CrossRef]

Hopkins, H. H.

H. H. Hopkins, Proc. Phys. Soc. London 55, 116 (1943).
[CrossRef]

Kant, R.

R. Kant, J. Modern Opt. 40, 2293 (1993).
[CrossRef]

Laczik, Z.

Li, Y.

Matthews, H. J.

Németh, G.

Richards, B.

B. Richards and E. Wolf, Proc. R. Soc. London A 253, 358 (1959).
[CrossRef]

Sheppard, C. J. R.

Török, P.

Varga, P.

Wolf, E.

Y. Li and E. Wolf, J. Opt. Soc. Am. A 1, 801 (1984).
[CrossRef]

B. Richards and E. Wolf, Proc. R. Soc. London A 253, 358 (1959).
[CrossRef]

M. Born and E. Wolf, Principles of Optics, 6th ed.(Pergamon, 1993).

Appl. Opt.

J. Modern Opt.

R. Kant, J. Modern Opt. 40, 2293 (1993).
[CrossRef]

C. J. R. Sheppard and M. Gu, J. Modern Opt. 40, 1631(1993).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Lett.

Optik

C. J. R. Sheppard, Optik 105, 29 (1997).

Proc. Phys. Soc. London

H. H. Hopkins, Proc. Phys. Soc. London 55, 116 (1943).
[CrossRef]

Proc. R. Soc. London A

B. Richards and E. Wolf, Proc. R. Soc. London A 253, 358 (1959).
[CrossRef]

Other

M. Born and E. Wolf, Principles of Optics, 6th ed.(Pergamon, 1993).

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Figures (1)

Fig. 1.
Fig. 1.

Axial intensity in the focus of a lens with PSA. (a) Paraxial result. (b) Scalar hNA theory. (c) As in (b) but without aplanatic weighting. (d) Scalar hNA theory for hNA PSA. (e) As in (d) but without aplanatic weighting.

Equations (15)

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U(r,z)=ikf0αeikΨJ0(krsinθ)exp(ikzcosθ)cos1/2θsinθdθ,
U(r,z)=ikfexp(ikz)0αeikΨJ0(krsinθ)×exp[2ikzsin2(θ/2)]cos1/2θsinθdθ.
U(r,z)=i2πNexp(ikz)×01eikΨJ0(vρ)exp(iuρ22)ρdρ,
Ψ=A40λsin4θsin4α,
kzcosθ2πA40ρ4=kzρ2kzsin2α2ρ4(kzsin4α+2πA40)8ρ6kzsin6α16+.
kΨ=p=0A2p,0ρ2p.
kΨ=p=0B2p,0σ2p,
U(0,z)=ikfexp(ikz)sec2α2×01eikΨexp(iuhσ22)(12σ2)1/2σdσ,
ρ2=σ2(1D2/4)(1D2σ24).
B20=1(1D2/4)A20,B40=1(1D2/4)2(A40(NA)2A204),B60=1(1D2/4)3(A60(NA)2A402),B80=1(1D2/4)4(A803(NA)2A604+(NA)2A404),.
Ψ=d[(n2sin2θ)1/2cosθ],
Ψ=d[(n1)+(n1)(NA)2ρ22n+(n31)(NA)4ρ48n3+(n51)(NA)6ρ616n5+].
Ψ=d(n1)[1+D2σ22n+(n+1)D4σ48n3+(n+1)D6σ616n5+],
ρnRnm(ρ)(n+m2)!(nm2)!n!,
Ψ=d(n1)[R00(σ)+D4nR20(σ)+(n+1)D248n3R40(σ)+(n+1)D3320n5R60(σ)+].

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