Abstract

Confocal and multiphoton microscopes are particularly sensitive to specimen- or system-induced aberrations, which result in decreased resolution and signal-to-noise ratio. The inclusion of an adaptive optics correction system could help overcome this limitation and restore diffraction-limited performance, but such a system requires a suitable method of wave-front measurement. By extending the concept of a modal wave-front sensor previously described by Neil et al. [J. Opt. Soc. Am. A 17, 1098–1107 (2000)], we present a new sensor capable of measuring directly the Zernike aberration modes introduced by a specimen. This modal sensor is particularly suited to applications in three-dimensional microscopy because of its inherent axial selectivity; only those wave fronts originating in the focal region contribute to the measured signal. Four wave-front sensor configurations are presented and their input response is characterized. Sensitivity matrices and axial responses are presented.

© 2002 Optical Society of America

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References

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  1. T. Wilson, C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, London, 1984).
  2. T. Wilson, ed., Confocal Microscopy (Academic, London, 1990).
  3. W. Denk, J. H. Strickler, W. W. Webb, “Two-photon laser scanning confocal microscopy,” Science 248, 73–76 (1990).
    [CrossRef] [PubMed]
  4. M. J. Booth, M. A. A. Neil, T. Wilson, “Aberration correction for confocal imaging in refractive index mismatched media,” J. Microsc. 192, 90–98 (1998).
    [CrossRef]
  5. J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford U. Press, Oxford, UK, 1998).
  6. R. K. Tyson, Principles of Adaptive Optics (Academic, London, 1991).
  7. M. A. A. Neil, M. J. Booth, T. Wilson, “New modal wave-front sensor: a theoretical analysis,” J. Opt. Soc. Am. A 17, 1098–1107 (2000).
    [CrossRef]
  8. M. A. A. Neil, M. J. Booth, T. Wilson, “Closed-loop aberration correction using a modal Zernike wave-front sensor,” Opt. Lett. 25, 1083–1085 (2000).
    [CrossRef]
  9. M. A. A. Neil, R. Juskaitis, M. J. Booth, T. Wilson, T. Tanaka, S. Kawata, “Adaptive aberration correction in a two-photon microscope,” J. Microsc. 200, 105–108 (2000).
    [CrossRef] [PubMed]
  10. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, London, 1996).
  11. Min Gu, Principles of Three-Dimensional Imaging in Confocal Microscopes (World Scientific, Singapore, 1996).
  12. M. J. Booth, M. A. A. Neil, R. Juskaitis, T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. USA 99, 5788–5792 (2002).
    [CrossRef] [PubMed]

2002 (1)

M. J. Booth, M. A. A. Neil, R. Juskaitis, T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. USA 99, 5788–5792 (2002).
[CrossRef] [PubMed]

2000 (3)

1998 (1)

M. J. Booth, M. A. A. Neil, T. Wilson, “Aberration correction for confocal imaging in refractive index mismatched media,” J. Microsc. 192, 90–98 (1998).
[CrossRef]

1990 (1)

W. Denk, J. H. Strickler, W. W. Webb, “Two-photon laser scanning confocal microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

Booth, M. J.

M. J. Booth, M. A. A. Neil, R. Juskaitis, T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. USA 99, 5788–5792 (2002).
[CrossRef] [PubMed]

M. A. A. Neil, M. J. Booth, T. Wilson, “Closed-loop aberration correction using a modal Zernike wave-front sensor,” Opt. Lett. 25, 1083–1085 (2000).
[CrossRef]

M. A. A. Neil, M. J. Booth, T. Wilson, “New modal wave-front sensor: a theoretical analysis,” J. Opt. Soc. Am. A 17, 1098–1107 (2000).
[CrossRef]

M. A. A. Neil, R. Juskaitis, M. J. Booth, T. Wilson, T. Tanaka, S. Kawata, “Adaptive aberration correction in a two-photon microscope,” J. Microsc. 200, 105–108 (2000).
[CrossRef] [PubMed]

M. J. Booth, M. A. A. Neil, T. Wilson, “Aberration correction for confocal imaging in refractive index mismatched media,” J. Microsc. 192, 90–98 (1998).
[CrossRef]

Denk, W.

W. Denk, J. H. Strickler, W. W. Webb, “Two-photon laser scanning confocal microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, London, 1996).

Gu, Min

Min Gu, Principles of Three-Dimensional Imaging in Confocal Microscopes (World Scientific, Singapore, 1996).

Hardy, J. W.

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford U. Press, Oxford, UK, 1998).

Juskaitis, R.

M. J. Booth, M. A. A. Neil, R. Juskaitis, T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. USA 99, 5788–5792 (2002).
[CrossRef] [PubMed]

M. A. A. Neil, R. Juskaitis, M. J. Booth, T. Wilson, T. Tanaka, S. Kawata, “Adaptive aberration correction in a two-photon microscope,” J. Microsc. 200, 105–108 (2000).
[CrossRef] [PubMed]

Kawata, S.

M. A. A. Neil, R. Juskaitis, M. J. Booth, T. Wilson, T. Tanaka, S. Kawata, “Adaptive aberration correction in a two-photon microscope,” J. Microsc. 200, 105–108 (2000).
[CrossRef] [PubMed]

Neil, M. A. A.

M. J. Booth, M. A. A. Neil, R. Juskaitis, T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. USA 99, 5788–5792 (2002).
[CrossRef] [PubMed]

M. A. A. Neil, M. J. Booth, T. Wilson, “Closed-loop aberration correction using a modal Zernike wave-front sensor,” Opt. Lett. 25, 1083–1085 (2000).
[CrossRef]

M. A. A. Neil, M. J. Booth, T. Wilson, “New modal wave-front sensor: a theoretical analysis,” J. Opt. Soc. Am. A 17, 1098–1107 (2000).
[CrossRef]

M. A. A. Neil, R. Juskaitis, M. J. Booth, T. Wilson, T. Tanaka, S. Kawata, “Adaptive aberration correction in a two-photon microscope,” J. Microsc. 200, 105–108 (2000).
[CrossRef] [PubMed]

M. J. Booth, M. A. A. Neil, T. Wilson, “Aberration correction for confocal imaging in refractive index mismatched media,” J. Microsc. 192, 90–98 (1998).
[CrossRef]

Sheppard, C. J. R.

T. Wilson, C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, London, 1984).

Strickler, J. H.

W. Denk, J. H. Strickler, W. W. Webb, “Two-photon laser scanning confocal microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

Tanaka, T.

M. A. A. Neil, R. Juskaitis, M. J. Booth, T. Wilson, T. Tanaka, S. Kawata, “Adaptive aberration correction in a two-photon microscope,” J. Microsc. 200, 105–108 (2000).
[CrossRef] [PubMed]

Tyson, R. K.

R. K. Tyson, Principles of Adaptive Optics (Academic, London, 1991).

Webb, W. W.

W. Denk, J. H. Strickler, W. W. Webb, “Two-photon laser scanning confocal microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

Wilson, T.

M. J. Booth, M. A. A. Neil, R. Juskaitis, T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. USA 99, 5788–5792 (2002).
[CrossRef] [PubMed]

M. A. A. Neil, M. J. Booth, T. Wilson, “Closed-loop aberration correction using a modal Zernike wave-front sensor,” Opt. Lett. 25, 1083–1085 (2000).
[CrossRef]

M. A. A. Neil, M. J. Booth, T. Wilson, “New modal wave-front sensor: a theoretical analysis,” J. Opt. Soc. Am. A 17, 1098–1107 (2000).
[CrossRef]

M. A. A. Neil, R. Juskaitis, M. J. Booth, T. Wilson, T. Tanaka, S. Kawata, “Adaptive aberration correction in a two-photon microscope,” J. Microsc. 200, 105–108 (2000).
[CrossRef] [PubMed]

M. J. Booth, M. A. A. Neil, T. Wilson, “Aberration correction for confocal imaging in refractive index mismatched media,” J. Microsc. 192, 90–98 (1998).
[CrossRef]

T. Wilson, C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, London, 1984).

J. Microsc. (2)

M. J. Booth, M. A. A. Neil, T. Wilson, “Aberration correction for confocal imaging in refractive index mismatched media,” J. Microsc. 192, 90–98 (1998).
[CrossRef]

M. A. A. Neil, R. Juskaitis, M. J. Booth, T. Wilson, T. Tanaka, S. Kawata, “Adaptive aberration correction in a two-photon microscope,” J. Microsc. 200, 105–108 (2000).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (1)

Opt. Lett. (1)

Proc. Natl. Acad. Sci. USA (1)

M. J. Booth, M. A. A. Neil, R. Juskaitis, T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. USA 99, 5788–5792 (2002).
[CrossRef] [PubMed]

Science (1)

W. Denk, J. H. Strickler, W. W. Webb, “Two-photon laser scanning confocal microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

Other (6)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, London, 1996).

Min Gu, Principles of Three-Dimensional Imaging in Confocal Microscopes (World Scientific, Singapore, 1996).

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford U. Press, Oxford, UK, 1998).

R. K. Tyson, Principles of Adaptive Optics (Academic, London, 1991).

T. Wilson, C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, London, 1984).

T. Wilson, ed., Confocal Microscopy (Academic, London, 1990).

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of a confocal microscope with an aberrating specimen. Planes I, II and III are all conjugate to the pupil of the objective lens (the matching optics have been omitted for clarity) and represent possible locations of biasing and correction elements. The specimen-induced aberrations can be modeled by an equivalent phase plate situated in plane II.

Fig. 2
Fig. 2

Schematic descriptions of different confocal wave-front sensor biasing configurations where biasing occurs in A, illumination and emission path; B, illumination path only; C, emission path only. Configuration D, suitable for two-photon microscopy, uses illumination-path biasing and a large-area detector.

Fig. 3
Fig. 3

Output signals for a fluorescent plane object in each wave-front sensor configuration. For configuration A, νp=π and b=0.5. For configuration B/C, νp=π and b=0.5. For configuration D, b=0.55.

Fig. 4
Fig. 4

Graphical representation of the sensitivity matrices for each configuration when the object is a fluorescent volume.

Fig. 5
Fig. 5

Axial response to a defocused fluorescent plane for each wave-front sensor configuration. For configuration A, νp=π and b=0.5. For configuration B/C, νp=π and b=0.5. For configuration D, b=0.55.

Tables (1)

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Table 1 Zernike Circle Polynomials

Equations (34)

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g˜(r, θ)=g(r, θ+π).
f(ν, ξ)=|F[Pf(r, θ)]|2,
h(ν, ξ)=|F[Ph(r, θ)]|2.
W1,2=02π0νp(f1,2 * h1,2)νdνdξ,
ΔWik=W1-W2=02π0νp[(f1 * h1)-(f2 * h2)]νdνdξ.
Sik=-ΔWikaa=0=-02π0νpa[(f1 * h1)
-(f2 * h2)]a=0νdνdξ,
w=Sa,
W1,2=02π0νpF-1[F1,2H1,2]νdνdξ,
F1,2(r, θ)=P1,2f(r, θ)P1,2f(r, θ)*,
H1,2(r, θ)=P1,2h(r, θ)P1,2h(r, θ)*,
W1,2=νp2π302π02F1,2H1,2J1(rνp)drdθ,
F1,2(r, θ+π)=F1,2(r, θ)*,
W1,2=νpπ30π02 Re[F1,2H1,2]J1(rνp)drdθ.
ΔWik=νpπ30π02{Re[F1H1]-Re[F2H2]}J1(rνp)drdθ
Sik=-νpπ30π02a{Re[F1H1]-Re[F2H2]}a=0J1(rνp)drdθ.
u=πD2z2λL28πλz sin2α2,
P1,2f(r, θ)=expjaZ˜k±jbZ˜i+jur22,
P1,2h(r, θ)=expjaZk±jbZi+jur22.
F1,2(r, θ)=H˜1,2(r, θ)=H1,2(r, θ)*.
ΔWik=νpπ30π02[|H1|2-|H2|2]J1(rνp)drdθ.
P1,2f(r, θ)=expjaZ˜k+jur22,
P1,2h(r, θ)=expjaZk±jbZi+jur22.
F(r, θ)=F1,2(r, θ).
ΔWik=νpπ30π02 Re[F(H1-H2)]J1(rνp)drdθ,
f1,2(ν, ξ)=|F[P1,2f(r, θ)]|4,
P1,2f(r, θ)=expjaZ˜k±jbZ˜i+jur22.
W1,2=limνp 02π0νpf1,2νdνdξ.
W1,2=2π3-16π/30π02|F1,2|2rdrdθ,
F1,2(r, θ)=P1,2f(r, θ)P1,2f(r, θ)*.
ΔWik=2π3-16π/30π02[|F1|2-|F2|2]rdrdθ,
SVol,ik=-Sik(u)du,
A(x, y) * B(x, y)=--A(x, y)B(x-x, y-y)dxdy.
A(x, y)B(x, y)=--A(x, y)B(x-x, y-y)dxdy.

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