Abstract

The effect on confocal imaging of spherical aberration caused by a weak refractive-index mismatch is discussed. Aberration balancing that uses a change in the objective’s tube length is studied. It is found that the range of depths that can be imaged satisfactorily by a high-numerical-aperture objective with compensation is an order of magnitude greater than that without compensation. The aberration balancing tends to break down for extremely high numerical apertures.

© 2000 Optical Society of America

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References

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  1. C. J. R. Sheppard, C. J. Cogswell, “Three-dimensional image formation in confocal microscopy,” J. Microsc. 159, 179–194 (1990).
    [CrossRef]
  2. C. J. R. Sheppard, M. Gu, “Aberration compensation in confocal microscopy,” Appl. Opt. 30, 3563–3568 (1991).
    [CrossRef] [PubMed]
  3. C. J. R. Sheppard, M. Gu, K. Brain, H. Zhou, “Influence of spherical aberration on axial imaging of confocal microscopy,” Appl. Opt. 33, 616–624 (1994).
    [CrossRef] [PubMed]
  4. P. Török, S. J. Hewlett, P. Varga, “The role of specimen-induced spherical aberration in confocal microscopy,” J. Microsc. 188, 158–172 (1997).
    [CrossRef]
  5. C. J. R. Sheppard, T. Wilson, “Effects of high angles of convergence on V(z) in the scanning acoustic microscope,” Appl. Phys. Lett. 38, 858–859 (1981).
    [CrossRef]
  6. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1993).

1997 (1)

P. Török, S. J. Hewlett, P. Varga, “The role of specimen-induced spherical aberration in confocal microscopy,” J. Microsc. 188, 158–172 (1997).
[CrossRef]

1994 (1)

1991 (1)

1990 (1)

C. J. R. Sheppard, C. J. Cogswell, “Three-dimensional image formation in confocal microscopy,” J. Microsc. 159, 179–194 (1990).
[CrossRef]

1981 (1)

C. J. R. Sheppard, T. Wilson, “Effects of high angles of convergence on V(z) in the scanning acoustic microscope,” Appl. Phys. Lett. 38, 858–859 (1981).
[CrossRef]

Born, M.

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

Brain, K.

Cogswell, C. J.

C. J. R. Sheppard, C. J. Cogswell, “Three-dimensional image formation in confocal microscopy,” J. Microsc. 159, 179–194 (1990).
[CrossRef]

Gu, M.

Hewlett, S. J.

P. Török, S. J. Hewlett, P. Varga, “The role of specimen-induced spherical aberration in confocal microscopy,” J. Microsc. 188, 158–172 (1997).
[CrossRef]

Sheppard, C. J. R.

C. J. R. Sheppard, M. Gu, K. Brain, H. Zhou, “Influence of spherical aberration on axial imaging of confocal microscopy,” Appl. Opt. 33, 616–624 (1994).
[CrossRef] [PubMed]

C. J. R. Sheppard, M. Gu, “Aberration compensation in confocal microscopy,” Appl. Opt. 30, 3563–3568 (1991).
[CrossRef] [PubMed]

C. J. R. Sheppard, C. J. Cogswell, “Three-dimensional image formation in confocal microscopy,” J. Microsc. 159, 179–194 (1990).
[CrossRef]

C. J. R. Sheppard, T. Wilson, “Effects of high angles of convergence on V(z) in the scanning acoustic microscope,” Appl. Phys. Lett. 38, 858–859 (1981).
[CrossRef]

Török, P.

P. Török, S. J. Hewlett, P. Varga, “The role of specimen-induced spherical aberration in confocal microscopy,” J. Microsc. 188, 158–172 (1997).
[CrossRef]

Varga, P.

P. Török, S. J. Hewlett, P. Varga, “The role of specimen-induced spherical aberration in confocal microscopy,” J. Microsc. 188, 158–172 (1997).
[CrossRef]

Wilson, T.

C. J. R. Sheppard, T. Wilson, “Effects of high angles of convergence on V(z) in the scanning acoustic microscope,” Appl. Phys. Lett. 38, 858–859 (1981).
[CrossRef]

Wolf, E.

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

Zhou, H.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

C. J. R. Sheppard, T. Wilson, “Effects of high angles of convergence on V(z) in the scanning acoustic microscope,” Appl. Phys. Lett. 38, 858–859 (1981).
[CrossRef]

J. Microsc. (2)

P. Török, S. J. Hewlett, P. Varga, “The role of specimen-induced spherical aberration in confocal microscopy,” J. Microsc. 188, 158–172 (1997).
[CrossRef]

C. J. R. Sheppard, C. J. Cogswell, “Three-dimensional image formation in confocal microscopy,” J. Microsc. 159, 179–194 (1990).
[CrossRef]

Other (1)

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

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Figures (6)

Fig. 1
Fig. 1

Variance of the aberration from a slab of a weakly aberrating medium.

Fig. 2
Fig. 2

Optimum values of B/A and knz/A (which are dimensionless) for balancing of the spherical aberration of a weakly aberrating medium.

Fig. 3
Fig. 3

Residual aberration at the Zernike balance for A = 1 and α = 60°.

Fig. 4
Fig. 4

Variance of the residual aberration at the Zernike balance.

Fig. 5
Fig. 5

Variation in the peak intensity with parameter A for a value of α = 60° before and after Zernike balancing and optimum balancing.

Fig. 6
Fig. 6

Approximate value of B for optimum balancing as a function of the parameter A for a value of α = 60°C. The Zernike treatment predicts a linear relation, as shown by the dashed line.

Equations (13)

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ϕ=kt[(n+Δn)cos θ2-n cos θ],
n sin θ=(n+Δn)sin θ2,
cos θ2=cos θ(1+Δnn tan2 θ).
ϕ=A sec θ,
A=ktΔn.
Iz=0α exp2i(ϕ+knz cos θ)sin θ cos θ dθ,
c=cos θ,
Iz=cos α1 exp2iAc+knzccdc2.
ϕ=B sin2 θ=B1-c2,
B=-kf2Δ1/l2.
Iz=01 exp2iA1-ρ2 sin2 α1/2+Bρ2×sin2 α+kz1-ρ2 sin2 α1/2ρdρ,
ρ=sin θ/sin α
B=2.465A,  knx=5.6A.

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