Abstract

Optical aberrations have detrimental effects in multiphoton microscopy. These effects can be curtailed by implementing model-based wavefront sensorless adaptive optics, which only requires the addition of a wavefront shaping device, such as a deformable mirror (DM) to an existing microscope. The aberration correction is achieved by maximizing a suitable image quality metric. We implement a model-based aberration correction algorithm in a second-harmonic microscope. The tip, tilt, and defocus aberrations are removed from the basis functions used for the control of the DM, as these aberrations induce distortions in the acquired images. We compute the parameters of a quadratic polynomial that is used to model the image quality metric directly from experimental input–output measurements. Finally, we apply the aberration correction by maximizing the image quality metric using the least-squares estimate of the unknown aberration.

© 2014 Optical Society of America

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2014 (1)

2013 (4)

2012 (5)

2011 (4)

2010 (4)

2009 (4)

D. Débarre, E. J. Botcherby, T. Watanabe, S. Srinivas, M. J. Booth, and T. Wilson, “Image-based adaptive optics for two-photon microscopy,” Opt. Lett. 34, 2495–2497 (2009).
[CrossRef]

A. Jesacher, A. Thayil, K. Grieve, D. Débarre, T. Watanabe, T. Wilson, S. Srinivas, and M. Booth, “Adaptive harmonic generation microscopy of mammalian embryos,” Opt. Lett. 34, 3154–3156 (2009).
[CrossRef]

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]

B. Wang and M. J. Booth, “Optimum deformable mirror modes for sensorless adaptive optics,” Opt. Commun. 282, 4467–4474 (2009).
[CrossRef]

2008 (2)

A. Beck, P. Stoica, and J. Li, “Exact and approximate solutions of source localization problems,” IEEE Trans. Signal Process. 56, 1770–1778 (2008).
[CrossRef]

D. Débarre, E. J. Botcherby, M. J. Booth, and T. Wilson, “Adaptive optics for structured illumination microscopy,” Opt. Express 16, 9290–9305 (2008).
[CrossRef]

2007 (3)

2006 (2)

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. USA 103, 17137–17142 (2006).
[CrossRef]

M. Booth, “Wave front sensor-less adaptive optics: a model-based approach using sphere packings,” Opt. Express 14, 1339–1352 (2006).
[CrossRef]

2005 (3)

L. Murray, J. C. Dainty, and E. Daly, “Wavefront correction through image sharpness maximization,” Proc. SPIE 5823, 40–47 (2005).
[CrossRef]

A. J. Wright, D. Burns, B. A. Patterson, S. P. Poland, G. J. Valentine, and J. M. Girkin, “Exploration of the optimisation algorithms used in the implementation of adaptive optics in confocal and multiphoton microscopy,” Microsc. Res. Tech. 67, 36–44 (2005).
[CrossRef]

M. Booth, T. Wilson, H.-B. Sun, T. Ota, and S. Kawata, “Methods for the characterization of deformable membrane mirrors,” Appl. Opt. 44, 5131–5139 (2005).
[CrossRef]

2003 (2)

2002 (2)

2001 (1)

P. J. Campagnola, A. Lewis, L. M. Loew, H. A. Clark, and W. A. Mohler, “Second-harmonic imaging microscopy of living cells,” J. Biomed. Opt. 6, 277–286 (2001).
[CrossRef]

2000 (3)

1998 (2)

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112–147 (1998).
[CrossRef]

G. Vdovin, “Optimization-based operation of micromachined deformable mirrors,” Proc. SPIE 3353, 902–909 (1998).
[CrossRef]

1995 (1)

1993 (1)

J. J. Moré, “Generalizations of the trust region problem,” Optim. Methods Softw. 2, 189–209 (1993).
[CrossRef]

1990 (1)

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

1984 (1)

D. Torrieri, “Statistical theory of passive location systems,” IEEE Trans. Aeros. Electron. Syst. AES-20, 183–198 (1984).
[CrossRef]

1976 (1)

Albert, O.

Andersen, M.

M. Andersen, J. Dahl, Z. Liu, and L. Vandenberghe, “Interior-point methods for large-scale cone programming,” in Optimization for Machine Learning, S. Sra, S. Nowozin, and S. J. Wright, eds. (MIT, 2011), pp. 55–83.

Andilla, J.

Antonello, J.

Artal, P.

Artigas, D.

Aviles-Espinosa, R.

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, 046022 (2010).
[CrossRef]

Beaurepaire, E.

Beck, A.

A. Beck, P. Stoica, and J. Li, “Exact and approximate solutions of source localization problems,” IEEE Trans. Signal Process. 56, 1770–1778 (2008).
[CrossRef]

Betzig, E.

D. E. Milkie, E. Betzig, and N. Ji, “Pupil-segmentation-based adaptive optical microscopy with full-pupil illumination,” Opt. Lett. 36, 4206–4208 (2011).
[CrossRef]

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]

Bodington, D.

Booth, M.

Booth, M. J.

Botcherby, E. J.

Bueno, J. M.

J. M. Bueno, E. J. Gualda, and P. Artal, “Adaptive optics multiphoton microscopy to study ex vivo ocular tissues,” J. Biomed. Opt. 15, 066004 (2010).
[CrossRef]

Burns, D.

A. J. Wright, D. Burns, B. A. Patterson, S. P. Poland, G. J. Valentine, and J. M. Girkin, “Exploration of the optimisation algorithms used in the implementation of adaptive optics in confocal and multiphoton microscopy,” Microsc. Res. Tech. 67, 36–44 (2005).
[CrossRef]

P. Marsh, D. Burns, and J. Girkin, “Practical implementation of adaptive optics in multiphoton microscopy,” Opt. Express 11, 1123–1130 (2003).
[CrossRef]

Campagnola, P. J.

P. J. Campagnola, A. Lewis, L. M. Loew, H. A. Clark, and W. A. Mohler, “Second-harmonic imaging microscopy of living cells,” J. Biomed. Opt. 6, 277–286 (2001).
[CrossRef]

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, 046022 (2010).
[CrossRef]

Chien, C.

Clark, H. A.

P. J. Campagnola, A. Lewis, L. M. Loew, H. A. Clark, and W. A. Mohler, “Second-harmonic imaging microscopy of living cells,” J. Biomed. Opt. 6, 277–286 (2001).
[CrossRef]

Crest, J.

Dahl, J.

M. Andersen, J. Dahl, Z. Liu, and L. Vandenberghe, “Interior-point methods for large-scale cone programming,” in Optimization for Machine Learning, S. Sra, S. Nowozin, and S. J. Wright, eds. (MIT, 2011), pp. 55–83.

Dainty, J.

Dainty, J. C.

L. Murray, J. C. Dainty, and E. Daly, “Wavefront correction through image sharpness maximization,” Proc. SPIE 5823, 40–47 (2005).
[CrossRef]

Daly, E.

L. Murray, J. C. Dainty, and E. Daly, “Wavefront correction through image sharpness maximization,” Proc. SPIE 5823, 40–47 (2005).
[CrossRef]

Dean, Z.

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. USA 103, 17137–17142 (2006).
[CrossRef]

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

Dillon, D.

Facomprez, A.

A. Facomprez, E. Beaurepaire, and D. Débarre, “Accuracy of correction in modal sensorless adaptive optics,” Opt. Express 20, 2598–2612 (2012).
[CrossRef]

D. Débarre, A. Facomprez, and E. Beaurepaire, “Assessing correction accuracy in image-based adaptive optics,” Proc. SPIE 8253, 82530F (2012).
[CrossRef]

Fernandez, E.

Fraanje, R.

Gavel, D.

Gerritsen, H.

T. van Werkhoven, H. Truong, J. Antonello, R. Fraanje, H. Gerritsen, M. Verhaegen, and C. Keller, “Coherence-gated wavefront sensing for microscopy using fringe analysis,” Proc. SPIE 8253, 82530E (2012).
[CrossRef]

Gerritsen, H. C.

Girkin, J.

Girkin, J. M.

A. J. Wright, D. Burns, B. A. Patterson, S. P. Poland, G. J. Valentine, and J. M. Girkin, “Exploration of the optimisation algorithms used in the implementation of adaptive optics in confocal and multiphoton microscopy,” Microsc. Res. Tech. 67, 36–44 (2005).
[CrossRef]

Grieve, K.

Gualda, E. J.

J. M. Bueno, E. J. Gualda, and P. Artal, “Adaptive optics multiphoton microscopy to study ex vivo ocular tissues,” J. Biomed. Opt. 15, 066004 (2010).
[CrossRef]

Hansen, P. C.

P. C. Hansen, Discrete Inverse Problems: Insight and Algorithms (SIAM, 2010), Vol. 7.

Jesacher, A.

Ji, N.

D. E. Milkie, E. Betzig, and N. Ji, “Pupil-segmentation-based adaptive optical microscopy with full-pupil illumination,” Opt. Lett. 36, 4206–4208 (2011).
[CrossRef]

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]

Kawata, S.

Keller, C.

T. van Werkhoven, H. Truong, J. Antonello, R. Fraanje, H. Gerritsen, M. Verhaegen, and C. Keller, “Coherence-gated wavefront sensing for microscopy using fringe analysis,” Proc. SPIE 8253, 82530E (2012).
[CrossRef]

Keller, C. U.

Kissel, M.

Kner, P.

Kroese, H.

Kubby, J.

Lagarias, J. C.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112–147 (1998).
[CrossRef]

Levecq, X.

Lewis, A.

P. J. Campagnola, A. Lewis, L. M. Loew, H. A. Clark, and W. A. Mohler, “Second-harmonic imaging microscopy of living cells,” J. Biomed. Opt. 6, 277–286 (2001).
[CrossRef]

Li, J.

A. Beck, P. Stoica, and J. Li, “Exact and approximate solutions of source localization problems,” IEEE Trans. Signal Process. 56, 1770–1778 (2008).
[CrossRef]

Linhai, H.

Liu, Z.

M. Andersen, J. Dahl, Z. Liu, and L. Vandenberghe, “Interior-point methods for large-scale cone programming,” in Optimization for Machine Learning, S. Sra, S. Nowozin, and S. J. Wright, eds. (MIT, 2011), pp. 55–83.

Loew, L. M.

P. J. Campagnola, A. Lewis, L. M. Loew, H. A. Clark, and W. A. Mohler, “Second-harmonic imaging microscopy of living cells,” J. Biomed. Opt. 6, 277–286 (2001).
[CrossRef]

Loktev, M.

G. Vdovin, O. Soloviev, M. Loktev, and V. Patlan, OKO Guide to Adaptive Optics, 4th ed. (Flexible Optical BV, 2013).

Loza-Alvarez, P.

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. USA 103, 17137–17142 (2006).
[CrossRef]

Mahou, P.

Marcos, S.

Marsh, P.

Milkie, D. E.

D. E. Milkie, E. Betzig, and N. Ji, “Pupil-segmentation-based adaptive optical microscopy with full-pupil illumination,” Opt. Lett. 36, 4206–4208 (2011).
[CrossRef]

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]

Mohler, W. A.

P. J. Campagnola, A. Lewis, L. M. Loew, H. A. Clark, and W. A. Mohler, “Second-harmonic imaging microscopy of living cells,” J. Biomed. Opt. 6, 277–286 (2001).
[CrossRef]

Moré, J. J.

J. J. Moré, “Generalizations of the trust region problem,” Optim. Methods Softw. 2, 189–209 (1993).
[CrossRef]

Mourou, G.

Munro, I.

Murray, L.

L. Murray, J. C. Dainty, and E. Daly, “Wavefront correction through image sharpness maximization,” Proc. SPIE 5823, 40–47 (2005).
[CrossRef]

Navarro, R.

Neil, M. A. A.

Nieto, M.

Noll, R. J.

Norris, T. B.

Norton, A.

O’Holleran, K.

Olarte, O. E.

Olivier, S.

Ota, T.

Paterson, C.

Patlan, V.

G. Vdovin, O. Soloviev, M. Loktev, and V. Patlan, OKO Guide to Adaptive Optics, 4th ed. (Flexible Optical BV, 2013).

Patterson, B. A.

A. J. Wright, D. Burns, B. A. Patterson, S. P. Poland, G. J. Valentine, and J. M. Girkin, “Exploration of the optimisation algorithms used in the implementation of adaptive optics in confocal and multiphoton microscopy,” Microsc. Res. Tech. 67, 36–44 (2005).
[CrossRef]

Poland, S. P.

A. J. Wright, D. Burns, B. A. Patterson, S. P. Poland, G. J. Valentine, and J. M. Girkin, “Exploration of the optimisation algorithms used in the implementation of adaptive optics in confocal and multiphoton microscopy,” Microsc. Res. Tech. 67, 36–44 (2005).
[CrossRef]

Porcar-Guezenec, R.

Rahman, S. A.

Rao, C.

Reeds, J. A.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112–147 (1998).
[CrossRef]

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. USA 103, 17137–17142 (2006).
[CrossRef]

Schanne-Klein, M.-C.

Schitter, G.

H. Song, R. Fraanje, G. Schitter, H. Kroese, G. Vdovin, and M. Verhaegen, “Model-based aberration correction in a closed-loop wavefront-sensor-less adaptive optics system,” Opt. Express 18, 24070–24084 (2010).
[CrossRef]

H. W. Yoo, M. Verhaegen, M. van Royen, and G. Schitter, “Automated adjustment of aberration correction in scanning confocal microscopy,” in IEEE International Instrumentation and Measurement Technology Conference (I2MTC) (IEEE, 2012), pp. 1083–1088.

Shaw, M.

Sherman, L.

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, 046022 (2010).
[CrossRef]

Soloviev, O.

G. Vdovin, O. Soloviev, M. Loktev, and V. Patlan, OKO Guide to Adaptive Optics, 4th ed. (Flexible Optical BV, 2013).

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Figures (10)

Fig. 1.
Fig. 1.

Contour plot of Eq. (13). In this example, f(x) is not convex and exhibits a local minimum. The parameters are c0=100 and Q=[1.250.4330.4331.25]. Four measurements of y˜, taken at r1=[0,0]T, r2=[1,0]T, r3=[0,1]T, and r4=[0,1]T are marked with × symbols. The global minimum xls=[1.2,1.2]T and the local minimum xloc[1.2582,0.3421]T are indicated with * symbols. Isolines with an elevation greater than 70 have been removed for clarity. A cross section along the dashed line is reported in the plot in the bottom.

Fig. 2.
Fig. 2.

Illustration of the optical setup. The components in black are used throughout the aberration correction experiments. The components in gray are used only for the initial characterization of the DM. A pulsed laser beam is expanded with lenses L1 and L2, clipped by aperture AP, and reflected by flat mirror M1 onto the DM. The DM is in an image of the back aperture of the microscope objective (OBJ), using lenses L3 and L4. The DM is illuminated under an angle of about 10° using the flat mirrors M1 and M2. The microscope objective (OBJ) focuses the light onto the specimen, which is supported by an xyz stage (XYZ). The second-harmonic signal emitted from the focal point inside the specimen is collected with the objective and separated from the illumination beam using a dichroic beam splitter (DBS). The emitted signal is focused by lens L5 onto a photomultiplier tube (PMT). For characterizing the DM, the surface of the DM is reimaged onto a CCD camera (CCD) using the flip mirror FM1, flat mirror M6, and lenses L6 and L7. A reference arm is created using beam splitter BS1, flat mirrors M3, M4, M5, and beam splitter BS2. A coherence-gated fringe analysis method described elsewhere [6] is applied to the fringe pattern generated onto the CCD.

Fig. 3.
Fig. 3.

Cross sections of rat tail collagen fiber used in our experiments. The smaller image on the right-hand side is an xz cross section (50μm×50μm, 128pixels×128pixels). The dashed line denotes an xy cross section (80μm×80μm, 256pixels×256pixels) approximately 33 μm deep, which is shown on the left-hand side. Three different 20μm×20μm regions are marked.

Fig. 4.
Fig. 4.

Validations and cross-validations of the computation of c0, c1, and Q using Eq. (20). The computation has been performed six times in region A in Fig. 3. Di denotes the input–output data taken during the ith time. Mi denotes the set of parameters [c0, c1, and Q in Eq. (20)] computed from Di. For each combination Mi and Dj, the ith random input subsequence and Mj are used to compute the predicted output o^R250. Each rectangle reports the goodness of fit [R2, see Eq. (21)] computed comparing o^ with the corresponding measured output oR250 of Dj. A value of one for the goodness of fit indicates that the model fits the data without error. High values of the goodness of fit are reported in all combinations, showing that Eq. (20) is a robust method to compute the parameters.

Fig. 5.
Fig. 5.

Summary of three aberration correction experiments. (a) Evolution of the normalized image quality metric. The experiments were performed in region A (curve with ○ markers), B (curve with □ markers), and C (curve with ⋆ markers), which are marked in Fig. 3. For each region, the corresponding parameters computed by solving Eq. (20) were used. y˜max is the maximum measurement of y˜ in each region. The estimated rms rad of each aberration is 0.38 for region A, 0.37 for region B, and 1.27 for region C. (b) 256pixels×256pixels image of region C at sample time k=0. (c) 256pixels×256pixels image of region C at sample time k=24. (d) cross sections taken along the arrows marked in (b) and (c), black for (b) and gray for (c).

Fig. 6.
Fig. 6.

Summary of the correction of 20 random aberrations induced by the DM in region A, which is marked in Fig. 3. The upper plot reports the normalized measurements of the image quality metric. The measurements are normalized using the maximum measurement y˜max that is recorded throughout the 20 experiments. At time k=0 the initial value of y˜ is reported; this data point is not supplied to the aberration correction algorithm. Between time k=1 and k=8, the data collection step is executed. From time k=9 onward, the aberration correction step is applied. A statistical analysis is made at each time instant using the function boxplot from MATLAB. The tops and bottoms of the rectangles denote the 25th and 75th percentiles, the horizontal lines in the middle of the rectangles denote the medians, and the whiskers extend to the furthest measurements not considered as outliers. The + symbols denote single outliers. The same statistical analysis is performed for the residual aberration, and the results are shown in the lower plot.

Fig. 7.
Fig. 7.

Summary of the correction of 20 random aberrations induced by the DM in region B. See the caption of Fig. 6 for a legend of the plots.

Fig. 8.
Fig. 8.

Summary of the correction of 20 random aberrations induced by the DM in region C. See the caption of Fig. 6 for a legend of the plots.

Fig. 9.
Fig. 9.

Two aberration correction experiments from the set of experiments reported in Fig. 7. These two experiments resulted, respectively, in (a) the maximum and (b) the minimum improvement of y˜. In both (a) and (b), a 256pixels×256pixels image is taken before (on the left, k=0) and after (on the right, k=24) the aberration correction. The graphs in the bottom of (a) and (b) show, respectively, the evolution of the normalized metric (on the left) and the cross sections indicated by the arrows in the images (on the right). In the cross section graphs, the dark and the light lines correspond, respectively, to k=0 and k=24.

Fig. 10.
Fig. 10.

Two aberration correction experiments from the set of experiments reported in Fig. 8. These two experiments resulted, respectively, in (a) the maximum and (b) the minimum improvement of y˜. Refer to the caption of Fig. 9 for a detailed legend.

Equations (21)

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

Φ(ξ)=i=1Nauiψi(ξ).
Φ(ξ)j=21+NzzjZj(ξ),
minHi=1DϕiZHui2.
ZTZH(i=1DuiuiT)=ZT(i=1DϕiuiT),
[zlzh][HlHh]u,
Hl=Ul[Σl0][Vl1TVl2T],
Φ(ξ)=i=1Nauiψi(ξ),s.t.u=Vl2p
Φ(ξ)=i=1Nppiωi(ξ),
y˜k=c0(x+rk)TQ(x+rk)+ϵk,
g(x)=[c0(x+r1)TQ(x+r1)c0(x+rm)TQ(x+rm)],
y˜=g(x)+ϵ.
minxf(x),
f(x)=y˜g(x)2.
minx,αk=1m(α2rkTQx+c0rkTQrky˜k)2s.t.α=xTQx.
minwAwb2s.t.wTDw+2fTw=0,
wT=[xTα],R=[r1rm],A=[2RTQ1],b=[r1TQr1+y˜1c0rmTQrm+y˜mc0],D=[Q000],fT=[01/2]T
(ATA+νD)w=ATbνfwTDw+2fTw=0ATA+νD0.
w(ν)=(ATA+νD)1(ATbνf)
w(ν)TDw(ν)+2fTw(ν)=0.
minx˜A˜x˜b˜s.t.A˜=[1r1Tr1Tr1T1r320Tr320Tr320T],b˜=[y˜1y˜320]T,x˜=[c0c1Tvec(Q)T]T,Q0,
R2=1Sr/St,Sr=oo^2,St=oo¯12,o¯=(1/250)1To,

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