Abstract

We present a method for increasing the lateral resolution and detection efficiency of scanning fluorescence microscopes by adding an interferometer with partial image inversion to the detection pathway. We show that the resulting detection transfer function is essentially the absolute square of the system’s amplitude transfer function enlarged to twice its spatial frequency range. Simulations for a confocal system yield a lateral FWHM resolution of 168 nm (135 nm after image subtraction) as compared to 218 nm for confocal detection without an interferometer. Furthermore we demonstrate how this method is suitable for extended focus imaging. Here simulations for Bessel beam excitation and interferometric detection yield a resolution of 146 nm (116 nm after image subtraction) as compared to 199 nm for integrating detection without an interferometer.

© 2007 Optical Society of America

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References

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  1. A. Egner, S. Verrier, A. Goroshkov, H.-D. Söling and S. Hell, "4Pi-microscopy of the Golgi apparatus in live mammalian cells," J. Struct. Biol. 147, 70-76 (2004).
    [CrossRef] [PubMed]
  2. N. Sandeau and H. Giovannini, "Increasing the lateral resolution of 4Pi fluorescence microscopes," J. Opt. Soc. Am. A 23, 1089-1095 (2006).
    [CrossRef]
  3. N. Sandeau and H. Giovannini, "Arrangement of a 4Pi microscope for reducing the confocal detection volume with two-photon excitation," Opt. Commun. 264, 123-129 (2006).
    [CrossRef]
  4. R. Heintzmann and K. Wicker, UK patent (filed 2 Feb. 2007).
  5. N. Sandeau, H. Rigneault and H. Giovannini, "Increasing the lateral resolution in confocal fluorescence and bio-luminescence microscopes," Abstract book Focus on Microscopy 2007, Valencia, Spain, 248 (2007).
  6. N. Sandeau, H. Rigneault and H. Giovannini, French Patent (filed 8 Jun. 2006).
  7. N. Sandeau and H. Giovannini, "Influence of the pinhole size on the resolution of the 4Pi’ microscope studied by means of the optical transfer function," Nucl. Instrum. Methods Phys. Res. A 571, 404-406 (2007).
    [CrossRef]
  8. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, (Wiley-Interscience 1991).
    [CrossRef]
  9. W. Denk, J. H. Strickler and W. W. Webb, "Two-photon laser scanning fluorescence microscopy," Science 248, 73-76 (1990).
    [CrossRef] [PubMed]
  10. R. Heintzmann, V. Sarafis, P. Munroe, J. Nailon, Q. S. Hanley and T. M. Jovin, "Resolution enhancement by subtraction of confocal signals taken at different pinhole sizes," Micron. 34, 293-300 (2003).
    [CrossRef] [PubMed]
  11. B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems - II. Structure of the image field in an aplanatic system," Proc. Roy. Soc. 253 A, 358-379 (1959).
  12. J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, "Diffraction-free Beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
    [CrossRef] [PubMed]

2007 (1)

N. Sandeau and H. Giovannini, "Influence of the pinhole size on the resolution of the 4Pi’ microscope studied by means of the optical transfer function," Nucl. Instrum. Methods Phys. Res. A 571, 404-406 (2007).
[CrossRef]

2006 (2)

N. Sandeau and H. Giovannini, "Arrangement of a 4Pi microscope for reducing the confocal detection volume with two-photon excitation," Opt. Commun. 264, 123-129 (2006).
[CrossRef]

N. Sandeau and H. Giovannini, "Increasing the lateral resolution of 4Pi fluorescence microscopes," J. Opt. Soc. Am. A 23, 1089-1095 (2006).
[CrossRef]

2004 (1)

A. Egner, S. Verrier, A. Goroshkov, H.-D. Söling and S. Hell, "4Pi-microscopy of the Golgi apparatus in live mammalian cells," J. Struct. Biol. 147, 70-76 (2004).
[CrossRef] [PubMed]

2003 (1)

R. Heintzmann, V. Sarafis, P. Munroe, J. Nailon, Q. S. Hanley and T. M. Jovin, "Resolution enhancement by subtraction of confocal signals taken at different pinhole sizes," Micron. 34, 293-300 (2003).
[CrossRef] [PubMed]

1990 (1)

W. Denk, J. H. Strickler and W. W. Webb, "Two-photon laser scanning fluorescence microscopy," Science 248, 73-76 (1990).
[CrossRef] [PubMed]

1987 (1)

J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, "Diffraction-free Beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef] [PubMed]

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

J. Struct. Biol. (1)

A. Egner, S. Verrier, A. Goroshkov, H.-D. Söling and S. Hell, "4Pi-microscopy of the Golgi apparatus in live mammalian cells," J. Struct. Biol. 147, 70-76 (2004).
[CrossRef] [PubMed]

Micron. (1)

R. Heintzmann, V. Sarafis, P. Munroe, J. Nailon, Q. S. Hanley and T. M. Jovin, "Resolution enhancement by subtraction of confocal signals taken at different pinhole sizes," Micron. 34, 293-300 (2003).
[CrossRef] [PubMed]

Nucl. Instrum. Methods Phys. Res. A (1)

N. Sandeau and H. Giovannini, "Influence of the pinhole size on the resolution of the 4Pi’ microscope studied by means of the optical transfer function," Nucl. Instrum. Methods Phys. Res. A 571, 404-406 (2007).
[CrossRef]

Opt. Commun. (1)

N. Sandeau and H. Giovannini, "Arrangement of a 4Pi microscope for reducing the confocal detection volume with two-photon excitation," Opt. Commun. 264, 123-129 (2006).
[CrossRef]

Phys. Rev. Lett. (1)

J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, "Diffraction-free Beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef] [PubMed]

Science (1)

W. Denk, J. H. Strickler and W. W. Webb, "Two-photon laser scanning fluorescence microscopy," Science 248, 73-76 (1990).
[CrossRef] [PubMed]

Other (5)

R. Heintzmann and K. Wicker, UK patent (filed 2 Feb. 2007).

N. Sandeau, H. Rigneault and H. Giovannini, "Increasing the lateral resolution in confocal fluorescence and bio-luminescence microscopes," Abstract book Focus on Microscopy 2007, Valencia, Spain, 248 (2007).

N. Sandeau, H. Rigneault and H. Giovannini, French Patent (filed 8 Jun. 2006).

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, (Wiley-Interscience 1991).
[CrossRef]

B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems - II. Structure of the image field in an aplanatic system," Proc. Roy. Soc. 253 A, 358-379 (1959).

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Figures (7)

Fig. 1.
Fig. 1.

Lateral resolution can be improved using an interferometer. Light coming from a microscope is split, inverted in one arm of the interferometer and recombined.

Fig. 2.
Fig. 2.

Comparison of PSFs (a) and OTFs (b). The resolution improvement is strongest for the difference signal ΔI=I +-I -. The interferometric OTFs do not fall off towards the edge of the support region, therefore enhancing high frequency components. Note that the interferometric signals were calculated for detection without pinhole, in which case the detection PSF (OTF) of a confocal system would be constant (a δ-peak) and not contribute to the overall resolution at all.

Fig. 3.
Fig. 3.

PSFs for the constructive (a) and destructive (b) interferometer outputs C ±, for the confocal case without an interferometer C (c) and the difference in signal in the two interferometric outputs ΔC (d). Interferometric detection yields an improvement in lateral resolution: Lateral FWHM are 218 nm for C, 168 nm for C+ and 135 nm for ΔC. ΔC exhibits small negative values of about -2.9%. For simulation parameters see section 4. In all cases the pinhole has the size of one Airy disc.

Fig. 4.
Fig. 4.

Capability of the various methods for sectioning fluorescent planes. (a) The interferometer has an increased sectioning capability, with the difference signal surpassing the constructive output. (b) The logarithmic plot shows a z -2-dependance far away from the focal plane for all methods. However, the intensities of the interferometric measurements fall off more quickly close to the focus.

Fig. 5.
Fig. 5.

Radial plots of the extended focus PSFs. The simulation used circular polarisation and high NA vector theory. It is visible that the signal for Bessel beam excitation with integral detection decays much slower than for the difference term, for which it quickly reaches zero when the emitter is off axis. The FWHMs of the respective PSFs are 199 nm (integral detection), 146 nm (constructive) and 116 nm (difference).

Fig. 6.
Fig. 6.

Simulated extended focus images using scanning Bessel beam excitation. The synthetic sample (a) consists of a wagon wheel noodle, a solid and a hollow sphere and a point-like structure. The scalebar indicates a length of 2 µm. (c) and (d) are the constructive (I +) and destructive (I -) outputs respectively. The constructive image already exhibits a slight improvement in contrast over the non-interferometric integrating detection (b). The difference (e) of the two interferometric outputs ∆I shows a significant improvement in performance. (f) shows a contrast enhanced version of (e), where negative values were clipped. Maximum photon numbers of 15,000 per pixel were assumed in all simulations.

Fig. 7.
Fig. 7.

Simulated extended focus images using scanning Bessel beam excitation. (a) shows a sum projection image of the sample data used for the simulation, a 4Pi data set of a cardiac fibroblast. (b) shows the simulated image for non-interferometric integrating detection. While the constructive (I +) image, (c), only exhibits a slight improvement in contrast, the difference (d) of the two interferometric outputs ∆I (negative values clipped) shows a significant improvement in performance. Maximum photon numbers of 15,000 per pixel were assumed. The scalebar in (a) shows a length of 2 µm. We thank Elisabeth Ehler for the cardiac fibroblast sample.

Equations (10)

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g ± ( r , d ) = 1 2 ( a ( r d ) ± a ( r + d ) )
= 1 2a ( r ) ( δ ( r d ) ± δ ( r + d ) ) ,
g ˜ ± ( k , d ) = 1 / 2 a ˜ ( k )    ( exp ( ι k d ) ± exp ( ι k d ) ) ,
I ± ( d )= | g ± ( r , d ) | 2 dx  dy.
I ± ( d ) = | g ˜ ± ( k , d ) | 2 d k x    d k y = 1 4 | a ˜ ( k ) | 2 ( 2 ± e ι 2 k d ± e ι 2 k d ) d k x    d k y I ± ( d ) = 1 2 I 0 ± 1 16 | a ˜ ( k 2 ) | 2 e ι k d d k x d k y ± 1 16 | a ˜ ( k 2 ) | 2 e ι k d d k x d k y " ,
I ˜ ± ( k ) = 2 π ( I 0 2 δ ( k ) ± 1 16 [ a ˜ ( k 2 ) 2 + a ˜ ( k 2 ) 2 ] ) .
I ˜ ± ( k ) = { π I 0 δ ( k ) ± I 0 4 k c 2 , k 2 k c 0 , k > 2 k c
I ± ( r ) = I 0 ( 1 2 ± J 1 ( 2 k c r ) ( 2 k c r ) ) .
I B ( r , z ) J 0 2 ( k B r ) ,
C ef , ± ( r , z ) = I B ( r , z ) · I ± ( r , z ) J 0 2 ( k B r ) ( 1 2 ± J 1 ( 2 k c r ) 2 k c r ) .

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