Abstract

In modern high-NA optical scanning instruments, like scanning microscopes, the refractive-index mismatch between the sample and the immersion medium introduces a significant amount of spherical aberration when imaging deep inside the specimen, spreading out the impulse response. Since such aberration depends on the focalization depth, it is not possible to achieve a static global compensation for the whole 3D sample in scanning microscopy. Therefore a depth-variant impulse response is generated. Consequently, the design of pupil elements that increase the tolerance to this aberration is of great interest. In this paper we report a hybrid technique that provides a focal spot that remains almost invariant in the depth-scanning processing of thick samples. This invariance allows the application of 3D deconvolution techniques to that provide an improved recovery of the specimen structure when imaging thick samples.

© 2009 OSA

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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  17. The highly corrected objectives are equipped with a correction collar to allow adjustment of the central lens group position to coincide with fluctuations in cover-glass thickness.
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  26. S. V. King, A. R. Libertun, R. Piestun, C. J. Cogswell, and C. Preza, “Quantitative phase microscopy through differential interference imaging,” J. Biomed. Opt. 13(2), 024020 (2008).
    [CrossRef] [PubMed]

2008

C. Mauclair, A. Mermillod-Blondin, N. Huot, E. Audouard, and R. Stoian, “Ultrafast laser writing of homogeneous longitudinal waveguides in glasses using dynamic wavefront correction,” Opt. Express 16(8), 5481–5492 (2008).
[CrossRef] [PubMed]

S. V. King, A. R. Libertun, R. Piestun, C. J. Cogswell, and C. Preza, “Quantitative phase microscopy through differential interference imaging,” J. Biomed. Opt. 13(2), 024020 (2008).
[CrossRef] [PubMed]

2006

M. J. Booth, M. Schwertner, T. Wilson, M. Nakano, Y. Kawata, M. Nakabayashi, and S. Miyata, “Predictive aberration correction for multilayer optical data storage,” Appl. Phys. Lett. 88(3), 031109 (2006).
[CrossRef]

V. N. Mahajan, “Gaussian apodization and beam propagation,” Prog. Opt. 49, 1–95 (2006).
[CrossRef]

I. Escobar, G. Saavedra, M. Martínez-Corral, and J. Lancis, “Reduction of the spherical aberration effect in high-numerical-aperture optical scanning instruments,” J. Opt. Soc. Am. A 23(12), 3150–3155 (2006).
[CrossRef]

2005

2004

2003

2002

M. J. Booth, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. U.S.A. 99(9), 5788–5792 (2002).
[CrossRef] [PubMed]

W. T. Cathey and E. R. Dowski, “New paradigm for imaging systems,” Appl. Opt. 41(29), 6080–6092 (2002).
[CrossRef] [PubMed]

1995

1991

C. J. R. Sheppard and M. Gu, “Aberration compensation in confocal microscopy,” Appl. Opt. 30(25), 3563–3568 (1991).
[CrossRef] [PubMed]

C. J. R. Sheppard and C. J. Cogswell, “Effects of aberrating layers and the tube length on confocal imaging properties,” Optik (Stuttg.) 87, 34–38 (1991).

1988

1986

1974

1965

R. Barakat and A. Houston, “Transfer function of an annular aperture in the presence of spherical aberration,” J. Opt. Soc. Am. A 55(5), 538–541 (1965).
[CrossRef]

1963

J. Tsujiuchi, “Correction of optical images by compensation of aberrations and by spatial frequency filtering,” Prog. Opt. 2, 131–180 (1963).
[CrossRef]

Andrés, P.

Audouard, E.

Barakat, R.

R. Barakat and A. Houston, “Transfer function of an annular aperture in the presence of spherical aberration,” J. Opt. Soc. Am. A 55(5), 538–541 (1965).
[CrossRef]

Booker, G. R.

Booth, M. J.

M. J. Booth, M. Schwertner, T. Wilson, M. Nakano, Y. Kawata, M. Nakabayashi, and S. Miyata, “Predictive aberration correction for multilayer optical data storage,” Appl. Phys. Lett. 88(3), 031109 (2006).
[CrossRef]

M. J. Booth, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. U.S.A. 99(9), 5788–5792 (2002).
[CrossRef] [PubMed]

Cathey, W. T.

Cogswell, C. J.

S. V. King, A. R. Libertun, R. Piestun, C. J. Cogswell, and C. Preza, “Quantitative phase microscopy through differential interference imaging,” J. Biomed. Opt. 13(2), 024020 (2008).
[CrossRef] [PubMed]

C. J. R. Sheppard and C. J. Cogswell, “Effects of aberrating layers and the tube length on confocal imaging properties,” Optik (Stuttg.) 87, 34–38 (1991).

Conchello, J. A.

Díaz, A.

Dowski, E. R.

Escamilla, H. M.

Escobar, I.

Gu, M.

Harvey, A. R.

Houston, A.

R. Barakat and A. Houston, “Transfer function of an annular aperture in the presence of spherical aberration,” J. Opt. Soc. Am. A 55(5), 538–541 (1965).
[CrossRef]

Huot, N.

Juskaitis, R.

M. J. Booth, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. U.S.A. 99(9), 5788–5792 (2002).
[CrossRef] [PubMed]

Kawata, Y.

M. J. Booth, M. Schwertner, T. Wilson, M. Nakano, Y. Kawata, M. Nakabayashi, and S. Miyata, “Predictive aberration correction for multilayer optical data storage,” Appl. Phys. Lett. 88(3), 031109 (2006).
[CrossRef]

King, S. V.

S. V. King, A. R. Libertun, R. Piestun, C. J. Cogswell, and C. Preza, “Quantitative phase microscopy through differential interference imaging,” J. Biomed. Opt. 13(2), 024020 (2008).
[CrossRef] [PubMed]

Laczik, Z.

Lancis, J.

Landgrave, J. E. A.

Libertun, A. R.

S. V. King, A. R. Libertun, R. Piestun, C. J. Cogswell, and C. Preza, “Quantitative phase microscopy through differential interference imaging,” J. Biomed. Opt. 13(2), 024020 (2008).
[CrossRef] [PubMed]

Lowenthal, D. D.

Mahajan, V. N.

V. N. Mahajan, “Gaussian apodization and beam propagation,” Prog. Opt. 49, 1–95 (2006).
[CrossRef]

Martínez-Corral, M.

Mauclair, C.

Mermillod-Blondin, A.

Mezouari, S.

Mills, J. P.

Miyata, S.

M. J. Booth, M. Schwertner, T. Wilson, M. Nakano, Y. Kawata, M. Nakabayashi, and S. Miyata, “Predictive aberration correction for multilayer optical data storage,” Appl. Phys. Lett. 88(3), 031109 (2006).
[CrossRef]

Nakabayashi, M.

M. J. Booth, M. Schwertner, T. Wilson, M. Nakano, Y. Kawata, M. Nakabayashi, and S. Miyata, “Predictive aberration correction for multilayer optical data storage,” Appl. Phys. Lett. 88(3), 031109 (2006).
[CrossRef]

Nakano, M.

M. J. Booth, M. Schwertner, T. Wilson, M. Nakano, Y. Kawata, M. Nakabayashi, and S. Miyata, “Predictive aberration correction for multilayer optical data storage,” Appl. Phys. Lett. 88(3), 031109 (2006).
[CrossRef]

Neil, M. A. A.

M. J. Booth, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. U.S.A. 99(9), 5788–5792 (2002).
[CrossRef] [PubMed]

Noyola-Isgleas, A.

Ojeda-Castaneda, J.

Ojeda-Castañeda, J.

Piestun, R.

S. V. King, A. R. Libertun, R. Piestun, C. J. Cogswell, and C. Preza, “Quantitative phase microscopy through differential interference imaging,” J. Biomed. Opt. 13(2), 024020 (2008).
[CrossRef] [PubMed]

Preza, C.

S. V. King, A. R. Libertun, R. Piestun, C. J. Cogswell, and C. Preza, “Quantitative phase microscopy through differential interference imaging,” J. Biomed. Opt. 13(2), 024020 (2008).
[CrossRef] [PubMed]

C. Preza and J. A. Conchello, “Depth-variant maximum likelihood restoration for three-dimensional fluorescence microscopy,” J. Opt. Soc. Am. A 21(9), 1593–1601 (2004).
[CrossRef]

Ramos, R.

Saavedra, G.

Schwertner, M.

M. J. Booth, M. Schwertner, T. Wilson, M. Nakano, Y. Kawata, M. Nakabayashi, and S. Miyata, “Predictive aberration correction for multilayer optical data storage,” Appl. Phys. Lett. 88(3), 031109 (2006).
[CrossRef]

Sheppard, C. J. R.

C. J. R. Sheppard and M. Gu, “Aberration compensation in confocal microscopy,” Appl. Opt. 30(25), 3563–3568 (1991).
[CrossRef] [PubMed]

C. J. R. Sheppard and C. J. Cogswell, “Effects of aberrating layers and the tube length on confocal imaging properties,” Optik (Stuttg.) 87, 34–38 (1991).

Stoian, R.

Thompson, B. J.

Török, P.

Tsujiuchi, J.

J. Tsujiuchi, “Correction of optical images by compensation of aberrations and by spatial frequency filtering,” Prog. Opt. 2, 131–180 (1963).
[CrossRef]

Varga, P.

Wilson, T.

M. J. Booth, M. Schwertner, T. Wilson, M. Nakano, Y. Kawata, M. Nakabayashi, and S. Miyata, “Predictive aberration correction for multilayer optical data storage,” Appl. Phys. Lett. 88(3), 031109 (2006).
[CrossRef]

M. J. Booth, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. U.S.A. 99(9), 5788–5792 (2002).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. Lett.

M. J. Booth, M. Schwertner, T. Wilson, M. Nakano, Y. Kawata, M. Nakabayashi, and S. Miyata, “Predictive aberration correction for multilayer optical data storage,” Appl. Phys. Lett. 88(3), 031109 (2006).
[CrossRef]

J. Biomed. Opt.

S. V. King, A. R. Libertun, R. Piestun, C. J. Cogswell, and C. Preza, “Quantitative phase microscopy through differential interference imaging,” J. Biomed. Opt. 13(2), 024020 (2008).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

Opt. Express

Opt. Lett.

Optik (Stuttg.)

C. J. R. Sheppard and C. J. Cogswell, “Effects of aberrating layers and the tube length on confocal imaging properties,” Optik (Stuttg.) 87, 34–38 (1991).

Proc. Natl. Acad. Sci. U.S.A.

M. J. Booth, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. U.S.A. 99(9), 5788–5792 (2002).
[CrossRef] [PubMed]

Prog. Opt.

V. N. Mahajan, “Gaussian apodization and beam propagation,” Prog. Opt. 49, 1–95 (2006).
[CrossRef]

J. Tsujiuchi, “Correction of optical images by compensation of aberrations and by spatial frequency filtering,” Prog. Opt. 2, 131–180 (1963).
[CrossRef]

Other

M. Gu, Advanced Optical Imaging Theory, (Springer-Verlag, Berlin) 2000.

In a real microscopy experiments there is, still, a coverslip between the immersion liquid and the sample medium. Such slab may induce a constant amount of SA that does not depend on the focusing depth. This SA can be compensated statically either with the correction collar, or with a proper index-matching immersion medium. Therefore it is not necessary to consider it in the calculations.

The highly corrected objectives are equipped with a correction collar to allow adjustment of the central lens group position to coincide with fluctuations in cover-glass thickness.

M. Born, and E. Wolf, Principles of Optics. (University Press, Cambrigde) 1999, Ch 13.

C. J. Cogswell, S. V. King, S. R. Prasanna Pavani, D. B. Conkey, and R. H. Cormack, “Microscope imaging capabilities improve using computational optics,” Proc. Focus on Microscopy 09 ( http://focusonmicroscopy.org/2009/PDF/341_Cogswell.pdf )

Supplementary Material (1)

» Media 1: AVI (7850 KB)     

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Figures (6)

Fig. 1.
Fig. 1.

Scheme for the evaluation of the phase distortions occurred in the tight focusing through a refractive-index interface. Definition of nomenclature: focusing depth, d 0, and penetration depth, d0(θ).

Fig. 2.
Fig. 2.

Intensity distribution in the focal spot calculated for the axial displacements: zS=0, 5.0µm, 9.7µm, and 15.0µm (which correspond to the focusing depths: z S=0, 6.6µm, 12.7µm, and 19.1µm).

Fig. 3.
Fig. 3.

Images of the spot target when set at axial displacements: zS=0, 5.0µm, 9.7µm, and 15.0µm.

Fig. 4.
Fig. 4.

Axial intensity distribution in the focal spot calculated for zS=0 and other six equally-spaced scanning positions. In the video (Media 1) we compare, for varying penetration depth, the focal spots produced by the circular aperture (CA) and by the cubic filter (CF).

Fig. 5.
Fig. 5.

The synthetic 3D object used for the numerical experiment is composed by 8 equidistant plates.

Fig. 6.
Fig. 6.

Five sections of the 3D image obtained with: (a) The clear circular pupil as the aperture stop; (b) The clear circular pupil and 3D deconvolution; (c) The cubic phase filter as the aperture stop; (d) The proposed hybrid method in which the cubic filter is inserted and a 3D deconvolution algorithm is applied.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

I(r,z)=0αP(θ)cosθJ0(krsinθ)exp[i2πW(θ)]exp(ikzcosθ)sinθdθ2.
W(θ;zS)=1λ[n2l2(θ;zS)n1l1(θ;zS)]W20(zS)sin2(θ2)sin2(α2)+W40(zS)sin4(θ2)sin4(α2).
w20(zS)=2n1n2(n2n1)sin2(α2)zSλ,
w40(zs)=2n12n23 (n22n12)sin4(α2)zSλ.
zN=2zn1λsin2(α2)w20(zS)w40(zs)
ζ=sin2(θ2)sin2(α2)0.5;q(ζ)=P(θ)cosθ,
I (r=0,zN;zS)=0.50.5q(ζ)exp(i2πw40(zS)ζ2)exp(i2πzNζ)dζ2.
I(x;z)=0.50.5P(x0)exp(+i2πw20,xx02)exp(i2πΔλfxxx0)dx02,
w20,x=zΔ22λfx2,

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