Abstract

We investigate theoretically and experimentally the parameters governing the accuracy of correction in modal sensorless adaptive optics for microscopy. On the example of two-photon fluorescence imaging, we show that using a suitable number of measurements, precise correction can be obtained for up to 2 radians rms aberrations without optimising the aberration modes used for correction. We also investigate the number of photons required for accurate correction when signal acquisition is shot-noise limited. We show that only 104 to 105 photons are required for complete correction so that the correction process can be implemented with limited extra-illumination and associated photoperturbation. Finally, we provide guidelines for implementing an optimal correction algorithm depending on the experimental conditions.

© 2012 OSA

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  1. M. J. Booth, M. A. A. Neil, R. Juškaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Nat. Acad. Sci. 99, 5788–5792 (2002).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  6. R. Aviles-Espinosa, J. Andilla, R. Porcar-Guezenec, O. E. Olarte, M. Nieto, X. Levecq, D. Artigas, and P. Loza-Alvarez, “Measurement and correction of in vivo sample aberrations employing a nonlinear guide-star in two-photon excited fluorescence microscopy,” Biomed. Opt. Express 2, 3135–3149 (2011).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  10. M. A. A. Neil, M. J. Booth, and T. Wilson, “New modal wave-front sensor: a theoretical analysis,” J. Opt. Soc. Am. A 17, 1098–1107 (2000).
    [CrossRef]
  11. A. J. Wright, S. P. Poland, J. M. Girkin, C. W. Freudiger, C. L. Evans, and X. S. Xie, “Adaptive optics for enhanced signal in CARS microscopy,” Opt. Express 15, 18209–18219 (2007).
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2011 (3)

D. Débarre, T. Vieille, and E. Beaurepaire, “Simple characterisation of a deformable mirror inside a high numerical aperture microscope using phase diversity,” J. Microsc. 244, 136–143 (2011).
[CrossRef] [PubMed]

A. Thayil and M. J. Booth, “Self calibration of sensorless adaptive optical microscopes,” J. Eur. Opt. Soc. 6, 11045 (2011).

R. Aviles-Espinosa, J. Andilla, R. Porcar-Guezenec, O. E. Olarte, M. Nieto, X. Levecq, D. Artigas, and P. Loza-Alvarez, “Measurement and correction of in vivo sample aberrations employing a nonlinear guide-star in two-photon excited fluorescence microscopy,” Biomed. Opt. Express 2, 3135–3149 (2011).
[CrossRef] [PubMed]

2009 (3)

2008 (1)

2007 (1)

2006 (1)

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

2003 (1)

2002 (1)

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

2000 (1)

Andilla, J.

Artigas, D.

Aviles-Espinosa, R.

Beaurepaire, E.

D. Débarre, T. Vieille, and E. Beaurepaire, “Simple characterisation of a deformable mirror inside a high numerical aperture microscope using phase diversity,” J. Microsc. 244, 136–143 (2011).
[CrossRef] [PubMed]

N. Olivier, D. Débarre, and E. Beaurepaire, “Dynamic aberration correction for multiharmonic microscopy”, Opt. Lett. 34, 3145–3147 (2009).
[CrossRef] [PubMed]

Betzig, E.

N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods 7, 141–147 (2009).
[CrossRef] [PubMed]

Booth, M. J.

Botcherby, E. J.

Burns, D.

Débarre, D.

Denk, W.

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

Evans, C. L.

Freudiger, C. W.

Girkin, J. M.

Ji, N.

N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods 7, 141–147 (2009).
[CrossRef] [PubMed]

Juškaitis, R.

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

Levecq, X.

Loza-Alvarez, P.

Mack-Bucher, J.

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

Marsh, P. N.

Milkie, D. E.

N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods 7, 141–147 (2009).
[CrossRef] [PubMed]

Neil, M. A. A.

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

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

Nieto, M.

Olarte, O. E.

Olivier, N.

Poland, S. P.

Porcar-Guezenec, R.

Rueckel, M.

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

Srinivas, S.

Thayil, A.

A. Thayil and M. J. Booth, “Self calibration of sensorless adaptive optical microscopes,” J. Eur. Opt. Soc. 6, 11045 (2011).

Vieille, T.

D. Débarre, T. Vieille, and E. Beaurepaire, “Simple characterisation of a deformable mirror inside a high numerical aperture microscope using phase diversity,” J. Microsc. 244, 136–143 (2011).
[CrossRef] [PubMed]

Watanabe, T.

Wilson, T.

Wright, A. J.

Xie, X. S.

Biomed. Opt. Express (1)

J. Eur. Opt. Soc. (1)

A. Thayil and M. J. Booth, “Self calibration of sensorless adaptive optical microscopes,” J. Eur. Opt. Soc. 6, 11045 (2011).

J. Microsc. (1)

D. Débarre, T. Vieille, and E. Beaurepaire, “Simple characterisation of a deformable mirror inside a high numerical aperture microscope using phase diversity,” J. Microsc. 244, 136–143 (2011).
[CrossRef] [PubMed]

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. Methods 7, 141–147 (2009).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lett. (2)

Proc. Nat. Acad. Sci. (2)

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

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

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Figures (8)

Fig. 1
Fig. 1

Principle of model-based modal aberration correction. (a), experimental setup. A titanium-sapphire laser (Ti:S) is used for excitation. The beam is reflected on a deformable mirror (DM) and focussed using a 20x, 1.05NA, water immersion, coverslip-corrected Olympus objective (obj). The blue, green and red generated 2PEF signals are separated with dichroic beamsplitters (DBS) and emissions filters (EF) and collected on photon-counting photomultiplier tubes (PMT). (b), principle of the algorithms used for correction. The metric M is plotted as a function of the amount of aberrations in two modes (here coma and spherical aberration). Left, 2N+1 algorithm: starting from the initial aberration (blue dot), measurements (blue and green) are performed with two biases applied in each of these two modes, and the location of the maximum of M is subsequently calculated (purple and orange). Right, 3N algorithm: optimisation is performed in mode 11, and then in mode 5, starting from the new position (purple dot). The final position is marked in red. (c), example of inaccurate correction in the presence of crosstalk. Left, no crosstalk; centre, linear crosstalk; right, nonlinear crosstalk. The blue dot is the starting point, the orange dot is the outcome of the 2N+1 algorithm, the red dot that of the 3N algorithm.

Fig. 2
Fig. 2

Comparison of the accuracy of correction of a 2N+1 algorithm using 11 Zernike modes (black dots) and combinations of the same modes with no residual linear crosstalk (red dots). A smaller final aberration corresponds to a more accurate correction. The error bars show the standard deviation for the 100 trials. The dotted orange line corresponds to a Strehl ratio of 0.9, set here as the limit for diffraction-limited focussing. The dash-dotted orange line represents a final aberration equal to the initial aberration : below this line, the quality of focussing is improved after correction.

Fig. 3
Fig. 3

Influence of the bias on the correction accuracy. (a), mean, and (b), maximum value of the residual error over 100 trials for the 2N+1 algorithm and a bias set to 0.5 (green), 1 (blue), 1.5 (red) and 2 radians (black). The dotted orange line corresponds to a Strehl ratio of 0.9 and the dash-dotted orange line represents a final aberration equal to the initial aberration. (c), illustration of the position of the 3 measurements on the experimental metric curve for mode 11 (spherical aberration) in the absence of initial aberrations.

Fig. 4
Fig. 4

Accuracy of correction as a function of the number of measurements P. Black, P = 3 (2N+1 algorithm); red, P = 5 (4N+1 algorithm); orange, P = 9 (8N+1 algorithm). The change in bias between two measurements is 0.5 rad, so that the total probed range is respectively ± 0.5, 1 and 2 rad. Mean values over 100 trials are plotted as dots, and the coloured areas span from the minimum to the maximum value. Blue dotted line: Strehl ratio of 0.9; blue dash-dotted line: first diagonal (y = x).

Fig. 5
Fig. 5

Comparison of residual error for the 4N+1 (a) and 5N (b) algorithms using 1 (black), 2 (purple) or 3 (blue) iterations. The dots are the mean values over 100 trials and the coloured areas span from the minimum to the maximum value. Dotted orange curve: Strehl ratio of 0.9; orange dash-dotted line: first diagonal (y = x), above which no improvement is expected when using several iterations of the same correction algorithm.

Fig. 6
Fig. 6

Accuracy of correction as a function of the number of photons, Ntot, used for correction. Red dots, zero initial aberrations; blue circles, 1 rad initial aberrations corrected with 3 rounds of the 9N algorithm. The error bars correspond to the maximum and minimum values measured over 100 trials. Black solid line, theoretical curve from equation 6. Dotted orange curve: Strehl ratio of 0.9. Inset, experimental values of metric M for astigmatism (z=5) for all P values of biases (dots) and corresponding model for the function f.

Fig. 7
Fig. 7

(a) Lily pollen grain image before (top) and after (bottom) aberration correction. The 2PEF signal was excited at 820nm and detected on 3 PMTs with different emission filters (410–490nm, 500–550nm and 600–700nm). The 3 signals are recombined here using respectively blue, green and red to obtain a false colour RGB image. (b), zoom on the white rectangle in (a). The pixel dwell time was 7.5μs in both cases and the same colour scale was used for both images. (c), intensity profiles for the three colours in the corrected (plain lines) and the uncorrected (dotted lines) images, along the black line plotted in (b).

Fig. 8
Fig. 8

Illustration of the experimental removal of residual tip and tilt on the case of astigmatism (z=6). (a), images are acquired with and without aberration applied, and the cross-correlation plane is calculated. The displacement of the correlation peak with respect to the center of the plane is then calculated as a function of the amount of aberration, and the slope is extracted along the two lateral directions. The process is repeated for tip and tilt (b and c), and the appropriate amount of tip and tilt to add to astigmatism is calculated as the ratio of the previously measured slopes.

Tables (1)

Tables Icon

Table 1 Zernike modes 1 to 15 and numbering scheme. The modes are expressed over the unit disk as functions of r and θ with 0 < r < 1 and 0 < θ < 2π.

Equations (6)

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M ( a ) = M 0 a T A a ,
ε noise = N tot + P B ,
ε = j = 1 P ( f ( I 0 , w , B , c , a i = b j ) m j ( i ) ) 2 = j = 1 P ( f ( I 0 , w , B , c , b j ) f ( I 0 c , w c , B c , c c , b j ) ) 2
ε ( dc ) = j = 1 P ( [ f I 0 I 0 m c + f w w m c + f B B m c + f c ] dc ) 2 = Fd c 2
dc = N tot + P B F
E = 11 N tot + 9 B F + E 0

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