Abstract

Wavefront sensing in the presence of background light sources is complicated by the need to restrict the effective depth of field of the wavefront sensor. This problem is particularly significant in direct wavefront sensing adaptive optic (AO) schemes for correcting imaging aberrations in biological microscopy. In this paper we investigate how a confocal pinhole can be used to reject out of focus light whilst still allowing effective wavefront sensing. Using a scaled set of phase screens with statistical properties derived from measurements of wavefront aberrations induced by C. elegans specimens, we investigate and quantify how the size of the pinhole and the aberration amplitude affect the transmitted wavefront. We suggest a lower bound for the pinhole size for a given aberration strength and quantify the optical sectioning provided by the system. For our measured aberration data we find that a pinhole of size approximately 3 Airy units represents a good compromise, allowing effective transmission of the wavefront and thin optical sections. Finally, we discuss some of the practical implications of confocal wavefront sensing for AO systems in microscopy.

© 2013 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. J. Booth, “Adaptive optics in microscopy,” Philos Trans A Math Phys Eng Sci365(1861), 2829–2843 (2007).
    [CrossRef] [PubMed]
  2. M. J. Booth, “Wavefront sensorless adaptive optics for large aberrations,” Opt. Lett.32(1), 5–7 (2007).
    [CrossRef] [PubMed]
  3. D. Debarre, M. J. Booth, and T. Wilson, “Image based adaptive optics through optimisation of low spatial frequencies,” Opt. Express15(13), 8176–8190 (2007).
    [CrossRef] [PubMed]
  4. N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods7(2), 141–147 (2010).
    [CrossRef] [PubMed]
  5. J. W. Cha, J. Ballesta, and P. T. C. So, “Shack-Hartmann wavefront-sensor-based adaptive optics system for multiphoton microscopy,” J. Biomed. Opt.15(4), 046022 (2010).
    [CrossRef] [PubMed]
  6. M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. U.S.A.103(46), 17137–17142 (2006).
    [CrossRef] [PubMed]
  7. O. Azucena, J. Crest, S. Kotadia, W. Sullivan, X. Tao, M. Reinig, D. Gavel, S. Olivier, and J. Kubby, “Adaptive optics wide-field microscopy using direct wavefront sensing,” Opt. Lett.36(6), 825–827 (2011).
    [CrossRef] [PubMed]
  8. X. Tao, B. Fernandez, O. Azucena, M. Fu, D. Garcia, Y. Zuo, D. C. Chen, and J. Kubby, “Adaptive optics confocal microscopy using direct wavefront sensing,” Opt. Lett.36(7), 1062–1064 (2011).
    [CrossRef] [PubMed]
  9. M. Feierabend, M. Rückel, and W. Denk, “Coherence-gated wave-front sensing in strongly scattering samples,” Opt. Lett.29(19), 2255–2257 (2004).
    [CrossRef] [PubMed]
  10. J. Wang and A. G. Podoleanu, “Demonstration of real-time depth-resolved Shack-Hartmann measurements,” Opt. Lett.37(23), 4862–4864 (2012).
    [CrossRef] [PubMed]
  11. L. A. Poyneer and B. Macintosh, “Spatially filtered wave-front sensor for high-order adaptive optics,” J. Opt. Soc. Am. A21(5), 810–819 (2004).
    [CrossRef] [PubMed]
  12. R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media2(3), 209–224 (1992).
    [CrossRef]
  13. O. Azucena, J. Crest, J. Cao, W. Sullivan, P. Kner, D. Gavel, D. Dillon, S. Olivier, and J. Kubby, “Wavefront aberration measurements and corrections through thick tissue using fluorescent microsphere reference beacons,” Opt. Express18(16), 17521–17532 (2010).
    [CrossRef] [PubMed]
  14. A. Facomprez, E. Beaurepaire, and D. Débarre, “Accuracy of correction in modal sensorless adaptive optics,” Opt. Express20(3), 2598–2612 (2012).
    [CrossRef] [PubMed]
  15. M. Schwertner, M. J. Booth, and T. Wilson, “Characterizing specimen induced aberrations for high NA adaptive optical microscopy,” Opt. Express12(26), 6540–6552 (2004).
    [CrossRef] [PubMed]
  16. X. D. Tao, J. Crest, S. Kotadia, O. Azucena, D. C. Chen, W. Sullivan, and J. Kubby, “Live imaging using adaptive optics with fluorescent protein guide-stars,” Opt. Express20(14), 15969–15982 (2012).
    [CrossRef] [PubMed]
  17. J. Notaras and C. Paterson, “Point-diffraction interferometer for atmospheric adaptive optics in strong scintillation,” Opt. Commun.281(3), 360–367 (2008).
    [CrossRef]
  18. W. H. Southwell, “Wave-front estimation from wave-front slope measurements,” J. Opt. Soc. Am.70(8), 998–1006 (1980).
    [CrossRef]
  19. M. Shaw, S. Hall, S. Knox, R. Stevens, and C. Paterson, “Characterization of deformable mirrors for spherical aberration correction in optical sectioning microscopy,” Opt. Express18(7), 6900–6913 (2010).
    [CrossRef] [PubMed]
  20. X. D. Tao, B. Fernandez, O. Azucena, M. Fu, D. Garcia, Y. Zuo, D. C. Chen, and J. Kubby, “Adaptive optics confocal microscopy using direct wavefront sensing,” Opt. Lett.36(7), 1062–1064 (2011).
    [CrossRef] [PubMed]
  21. M. Schwertner, M. J. Booth, and T. Wilson, “Simulation of specimen-induced aberrations for objects with spherical and cylindrical symmetry,” J. Microsc.215(3), 271–280 (2004).
    [CrossRef] [PubMed]
  22. N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng.29(10), 1174–1180 (1990).
    [CrossRef]
  23. T. Wilson, “Resolution and optical sectioning in the confocal microscope,” J. Microsc.244(2), 113–121 (2011).
    [CrossRef] [PubMed]
  24. J. D. Barchers, D. L. Fried, and D. J. Link, “Evaluation of the performance of Hartmann sensors in strong scintillation,” Appl. Opt.41(6), 1012–1021 (2002).
    [CrossRef] [PubMed]
  25. C. Paterson and J. Notaras, “Demonstration of closed-loop adaptive optics with a point-diffraction interferometer in strong scintillation with optical vortices,” Opt. Express15(21), 13745–13756 (2007).
    [CrossRef] [PubMed]

2012 (3)

2011 (4)

2010 (4)

2008 (1)

J. Notaras and C. Paterson, “Point-diffraction interferometer for atmospheric adaptive optics in strong scintillation,” Opt. Commun.281(3), 360–367 (2008).
[CrossRef]

2007 (4)

2006 (1)

M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. U.S.A.103(46), 17137–17142 (2006).
[CrossRef] [PubMed]

2004 (4)

2002 (1)

1992 (1)

R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media2(3), 209–224 (1992).
[CrossRef]

1990 (1)

N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng.29(10), 1174–1180 (1990).
[CrossRef]

1980 (1)

Azucena, O.

Ballesta, J.

J. W. Cha, J. Ballesta, and P. T. C. So, “Shack-Hartmann wavefront-sensor-based adaptive optics system for multiphoton microscopy,” J. Biomed. Opt.15(4), 046022 (2010).
[CrossRef] [PubMed]

Barchers, J. D.

Beaurepaire, E.

Betzig, E.

N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods7(2), 141–147 (2010).
[CrossRef] [PubMed]

Booth, M. J.

Cao, J.

Cha, J. W.

J. W. Cha, J. Ballesta, and P. T. C. So, “Shack-Hartmann wavefront-sensor-based adaptive optics system for multiphoton microscopy,” J. Biomed. Opt.15(4), 046022 (2010).
[CrossRef] [PubMed]

Chen, D. C.

Crest, J.

Dainty, J. C.

R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media2(3), 209–224 (1992).
[CrossRef]

Debarre, D.

Débarre, D.

Denk, W.

M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. U.S.A.103(46), 17137–17142 (2006).
[CrossRef] [PubMed]

M. Feierabend, M. Rückel, and W. Denk, “Coherence-gated wave-front sensing in strongly scattering samples,” Opt. Lett.29(19), 2255–2257 (2004).
[CrossRef] [PubMed]

Dillon, D.

Facomprez, A.

Feierabend, M.

Fernandez, B.

Fried, D. L.

Fu, M.

Garcia, D.

Gavel, D.

Glindemann, A.

R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media2(3), 209–224 (1992).
[CrossRef]

Hall, S.

Ji, N.

N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods7(2), 141–147 (2010).
[CrossRef] [PubMed]

Kner, P.

Knox, S.

Kotadia, S.

Kubby, J.

Lane, R. G.

R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media2(3), 209–224 (1992).
[CrossRef]

Link, D. J.

Macintosh, B.

Mack-Bucher, J. A.

M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. U.S.A.103(46), 17137–17142 (2006).
[CrossRef] [PubMed]

Milkie, D. E.

N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods7(2), 141–147 (2010).
[CrossRef] [PubMed]

Notaras, J.

J. Notaras and C. Paterson, “Point-diffraction interferometer for atmospheric adaptive optics in strong scintillation,” Opt. Commun.281(3), 360–367 (2008).
[CrossRef]

C. Paterson and J. Notaras, “Demonstration of closed-loop adaptive optics with a point-diffraction interferometer in strong scintillation with optical vortices,” Opt. Express15(21), 13745–13756 (2007).
[CrossRef] [PubMed]

Olivier, S.

Paterson, C.

Podoleanu, A. G.

Poyneer, L. A.

Reinig, M.

Roddier, N.

N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng.29(10), 1174–1180 (1990).
[CrossRef]

Rückel, M.

Rueckel, M.

M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. U.S.A.103(46), 17137–17142 (2006).
[CrossRef] [PubMed]

Schwertner, M.

M. Schwertner, M. J. Booth, and T. Wilson, “Simulation of specimen-induced aberrations for objects with spherical and cylindrical symmetry,” J. Microsc.215(3), 271–280 (2004).
[CrossRef] [PubMed]

M. Schwertner, M. J. Booth, and T. Wilson, “Characterizing specimen induced aberrations for high NA adaptive optical microscopy,” Opt. Express12(26), 6540–6552 (2004).
[CrossRef] [PubMed]

Shaw, M.

So, P. T. C.

J. W. Cha, J. Ballesta, and P. T. C. So, “Shack-Hartmann wavefront-sensor-based adaptive optics system for multiphoton microscopy,” J. Biomed. Opt.15(4), 046022 (2010).
[CrossRef] [PubMed]

Southwell, W. H.

Stevens, R.

Sullivan, W.

Tao, X.

Tao, X. D.

Wang, J.

Wilson, T.

T. Wilson, “Resolution and optical sectioning in the confocal microscope,” J. Microsc.244(2), 113–121 (2011).
[CrossRef] [PubMed]

D. Debarre, M. J. Booth, and T. Wilson, “Image based adaptive optics through optimisation of low spatial frequencies,” Opt. Express15(13), 8176–8190 (2007).
[CrossRef] [PubMed]

M. Schwertner, M. J. Booth, and T. Wilson, “Simulation of specimen-induced aberrations for objects with spherical and cylindrical symmetry,” J. Microsc.215(3), 271–280 (2004).
[CrossRef] [PubMed]

M. Schwertner, M. J. Booth, and T. Wilson, “Characterizing specimen induced aberrations for high NA adaptive optical microscopy,” Opt. Express12(26), 6540–6552 (2004).
[CrossRef] [PubMed]

Zuo, Y.

Appl. Opt. (1)

J. Biomed. Opt. (1)

J. W. Cha, J. Ballesta, and P. T. C. So, “Shack-Hartmann wavefront-sensor-based adaptive optics system for multiphoton microscopy,” J. Biomed. Opt.15(4), 046022 (2010).
[CrossRef] [PubMed]

J. Microsc. (2)

T. Wilson, “Resolution and optical sectioning in the confocal microscope,” J. Microsc.244(2), 113–121 (2011).
[CrossRef] [PubMed]

M. Schwertner, M. J. Booth, and T. Wilson, “Simulation of specimen-induced aberrations for objects with spherical and cylindrical symmetry,” J. Microsc.215(3), 271–280 (2004).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

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

Nat. Methods (1)

N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods7(2), 141–147 (2010).
[CrossRef] [PubMed]

Opt. Commun. (1)

J. Notaras and C. Paterson, “Point-diffraction interferometer for atmospheric adaptive optics in strong scintillation,” Opt. Commun.281(3), 360–367 (2008).
[CrossRef]

Opt. Eng. (1)

N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng.29(10), 1174–1180 (1990).
[CrossRef]

Opt. Express (7)

M. Shaw, S. Hall, S. Knox, R. Stevens, and C. Paterson, “Characterization of deformable mirrors for spherical aberration correction in optical sectioning microscopy,” Opt. Express18(7), 6900–6913 (2010).
[CrossRef] [PubMed]

C. Paterson and J. Notaras, “Demonstration of closed-loop adaptive optics with a point-diffraction interferometer in strong scintillation with optical vortices,” Opt. Express15(21), 13745–13756 (2007).
[CrossRef] [PubMed]

D. Debarre, M. J. Booth, and T. Wilson, “Image based adaptive optics through optimisation of low spatial frequencies,” Opt. Express15(13), 8176–8190 (2007).
[CrossRef] [PubMed]

O. Azucena, J. Crest, J. Cao, W. Sullivan, P. Kner, D. Gavel, D. Dillon, S. Olivier, and J. Kubby, “Wavefront aberration measurements and corrections through thick tissue using fluorescent microsphere reference beacons,” Opt. Express18(16), 17521–17532 (2010).
[CrossRef] [PubMed]

A. Facomprez, E. Beaurepaire, and D. Débarre, “Accuracy of correction in modal sensorless adaptive optics,” Opt. Express20(3), 2598–2612 (2012).
[CrossRef] [PubMed]

M. Schwertner, M. J. Booth, and T. Wilson, “Characterizing specimen induced aberrations for high NA adaptive optical microscopy,” Opt. Express12(26), 6540–6552 (2004).
[CrossRef] [PubMed]

X. D. Tao, J. Crest, S. Kotadia, O. Azucena, D. C. Chen, W. Sullivan, and J. Kubby, “Live imaging using adaptive optics with fluorescent protein guide-stars,” Opt. Express20(14), 15969–15982 (2012).
[CrossRef] [PubMed]

Opt. Lett. (6)

Philos Trans A Math Phys Eng Sci (1)

M. J. Booth, “Adaptive optics in microscopy,” Philos Trans A Math Phys Eng Sci365(1861), 2829–2843 (2007).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (1)

M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. U.S.A.103(46), 17137–17142 (2006).
[CrossRef] [PubMed]

Waves Random Media (1)

R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media2(3), 209–224 (1992).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Schematic diagram of a generalized confocal wavefront sensor. Blue dashed lines show the object and intermediate image plane, red dashed lines show the pupil plane of lens L1 and its image at the wavefront sensing plane.

Fig. 2
Fig. 2

The effect of a circular confocal pinhole of diameter 2 AU on individual spatial frequencies in the wavefront at the WFS plane. Plots show the phase along a line (x axis) through the centre of the WFS plane for a field in the pupil plane with a sinusoidally varying wavefront (a sin(πx/l)) with an rms of (a) λ/13 and (b) λ/4 and a uniform amplitude. White lines show the geometrical cutoff frequency at 2.44 cycles / pupil.

Fig. 3
Fig. 3

Mean number of phase singularities in the WFS plane as a function of rms wavefront aberration for a 2 AU pinhole. Calculated from 100 pupil plane phase screens generated from a power spectral density function of the form.ckr−4 Error bars show +/− 1 standard deviation truncated at zero.

Fig. 4
Fig. 4

Mean magnitude (blue bars) and standard deviation (red bars) of Zernike coefficients for 40 wavefront measurements performed throughout two C. elegans specimens. The mean rms wavefront aberration was λ/10. Inset shows a differential interference contrast image of parts of two C. elegans specimens.

Fig. 5
Fig. 5

(a) Contour plot of the effective Strehl ratio due to differences in the wavefront between the WFS and pupil planes caused by the pinhole. Results shown are the mean over 100 phase screens. (b) Example showing the wavefront at the WFS plane for different pinhole sizes for a pupil plane wavefront (top) with an rms of λ/5.

Fig. 6
Fig. 6

(a) Mean optical section thickness versus pinhole size for pupil plane aberrations up to λ/2. (b) Example pinhole transmittance as a function of defocus for a phase screen with an rms of λ/2 (bold lines) and in the absence of aberrations in the pupil plane (faint lines).

Fig. 7
Fig. 7

Rms residual wavefront error for different pinhole sizes caused by axial translation of the guide star away from the focal plane for an ideal imaging system.

Equations (3)

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

Φ ϕ ( k r )={ C k r 4 ,                      k r >0   0,                      otherwise. 
S ϕ =  | pupil e i( ϕ WFS ϕ pupil ) dxdy | 2 | pupil dxdy | 2 .
p( x,y )=a( x,y ) e iϕ(x,y) e iu ρ 2 /2 ,

Metrics