Abstract

Adaptive optics (AO) strategies using optimization-based, sensorless approaches are widely used, especially for microscopy applications. To converge rapidly to the best correction, such approaches require that a quality metric and a set of modes be chosen optimally. Fluorescence fluctuations microscopy, a family of methods that provides quantitative measurements of molecular concentration and mobility in living specimen, is in particular need of adaptive optics, since its results can be strongly biased by optical aberrations. We examined two possible metrics for sensorless AO, measured in a solution of fluorophores diffusing in 3D: the fluorescence count rate and the molecular brightness (or number of photons detected per molecule in the observation volume). We studied their respective measurement noise and sensitivity to aberrations. Then, AO correction accuracy was experimentally assessed by measuring the residual aberration after correcting a known wavefront. We proposed a theoretical framework to predict the correction accuracy, knowing the metric measurement noise and sensitivity. In the small aberration range, the brightness allows more accurate corrections when fluorophores are few but bright, whereas the count rate performs better in more concentrated solutions. When correcting large aberrations, the count rate is expected to be a more reliable metric.

© 2017 Optical Society of America

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2014 (4)

K. Wang, D. E. Milkie, A. Saxena, P. Engerer, T. Misgeld, M. E. Bronner, J. Mumm, and E. Betzig, “Rapid adaptive optical recovery of optimal resolution over large volumes,” Nat. Methods 11, 625–628 (2014).
[Crossref] [PubMed]

J. Antonello, T. van Werkhoven, M. Verhaegen, H. H. Truong, C. U. Keller, and H. C. Gerritsen, “Optimization-based wavefront sensorless adaptive optics for multiphoton microscopy,” J. Opt. Soc. Am. A 31, 1337–1347 (2014).
[Crossref]

C.-E. Leroux, S. Monnier, I. Wang, G. Cappello, and A. Delon, “Fluorescent correlation spectroscopy measurements with adaptive optics in the intercellular space of spheroids,” Biomed. Opt. Express 5, 3730–3738 (2014).
[Crossref] [PubMed]

J. Gallagher, C.-E. Leroux, I. Wang, and A. Delon, “Accuracy of adaptive optics correction using fluorescence fluctuations,” Proc. SPIE 8978, 89780A (2014).
[Crossref]

2013 (1)

2012 (3)

2011 (3)

2009 (3)

2008 (1)

M. A. Digman, R. Dalal, A. F. Horwitz, and E. Gratton, “Mapping the number of molecules and brightness in the laser scanning microscope,” Biophys. J. 94, 2320–2332 (2008).
[Crossref]

2007 (1)

E. Haustein and P. Schwille, “Fluorescence correlation spectroscopy: Novel variations of an established technique,” Annu. Rev. Bioph. Biom. 36, 151–169 (2007).
[Crossref]

2004 (1)

J. D. Müller, “Cumulant analysis in fluorescence fluctuation spectroscopy,” Biophys. J. 86, 3981–3992 (2004).
[Crossref] [PubMed]

2003 (1)

S. Saffarian and E. L. Elson, “Statistical analysis of fluorescence correlation spectroscopy: The standard deviation and bias,” Biophys. J. 84, 2030–2042 (2003).
[Crossref] [PubMed]

2002 (1)

M. J. Booth, M. A. A. Neil, R. Jukaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” P. Natl. Acad. Sci. USA 99, 5788–5792 (2002).
[Crossref]

2000 (2)

1990 (1)

H. Qian, “On the statistics of fluorescence correlation spectroscopy,” Biophys. Chem. 38, 49–57 (1990).
[Crossref] [PubMed]

1974 (1)

D. E. Koppel, “Statistical accuracy in fluorescence correlation spectroscopy,” Phys. Rev. A 10, 1938–1945 (1974).
[Crossref]

Albert, O.

Andilla, J.

Antonello, J.

Artigas, D.

Aviles-Espinosa, R.

Azucena, O.

Beaurepaire, E.

Betzig, E.

K. Wang, D. E. Milkie, A. Saxena, P. Engerer, T. Misgeld, M. E. Bronner, J. Mumm, and E. Betzig, “Rapid adaptive optical recovery of optimal resolution over large volumes,” Nat. Methods 11, 625–628 (2014).
[Crossref] [PubMed]

N. Ji, T. R. Sato, and E. Betzig, “Characterization and adaptive optical correction of aberrations during in vivo imaging in the mouse cortex,” P. Natl. Acad. Sci. USA 109, 22–27 (2012).
[Crossref]

Booth, M.

Booth, M. J.

Botcherby, E. J.

Bronner, M. E.

K. Wang, D. E. Milkie, A. Saxena, P. Engerer, T. Misgeld, M. E. Bronner, J. Mumm, and E. Betzig, “Rapid adaptive optical recovery of optimal resolution over large volumes,” Nat. Methods 11, 625–628 (2014).
[Crossref] [PubMed]

Cappello, G.

Chen, D. C.

Dalal, R.

M. A. Digman, R. Dalal, A. F. Horwitz, and E. Gratton, “Mapping the number of molecules and brightness in the laser scanning microscope,” Biophys. J. 94, 2320–2332 (2008).
[Crossref]

Débarre, D.

Delon, A.

Derouard, J.

Digman, M. A.

M. A. Digman, R. Dalal, A. F. Horwitz, and E. Gratton, “Mapping the number of molecules and brightness in the laser scanning microscope,” Biophys. J. 94, 2320–2332 (2008).
[Crossref]

Elson, E. L.

S. Saffarian and E. L. Elson, “Statistical analysis of fluorescence correlation spectroscopy: The standard deviation and bias,” Biophys. J. 84, 2030–2042 (2003).
[Crossref] [PubMed]

Engerer, P.

K. Wang, D. E. Milkie, A. Saxena, P. Engerer, T. Misgeld, M. E. Bronner, J. Mumm, and E. Betzig, “Rapid adaptive optical recovery of optimal resolution over large volumes,” Nat. Methods 11, 625–628 (2014).
[Crossref] [PubMed]

Facomprez, A.

Fu, M.

Gallagher, J.

J. Gallagher, C.-E. Leroux, I. Wang, and A. Delon, “Accuracy of adaptive optics correction using fluorescence fluctuations,” Proc. SPIE 8978, 89780A (2014).
[Crossref]

Gerritsen, H. C.

Gratton, E.

M. A. Digman, R. Dalal, A. F. Horwitz, and E. Gratton, “Mapping the number of molecules and brightness in the laser scanning microscope,” Biophys. J. 94, 2320–2332 (2008).
[Crossref]

Grichine, A.

Grieve, K.

Haustein, E.

E. Haustein and P. Schwille, “Fluorescence correlation spectroscopy: Novel variations of an established technique,” Annu. Rev. Bioph. Biom. 36, 151–169 (2007).
[Crossref]

Horwitz, A. F.

M. A. Digman, R. Dalal, A. F. Horwitz, and E. Gratton, “Mapping the number of molecules and brightness in the laser scanning microscope,” Biophys. J. 94, 2320–2332 (2008).
[Crossref]

Jesacher, A.

Ji, N.

N. Ji, T. R. Sato, and E. Betzig, “Characterization and adaptive optical correction of aberrations during in vivo imaging in the mouse cortex,” P. Natl. Acad. Sci. USA 109, 22–27 (2012).
[Crossref]

Jukaitis, R.

M. J. Booth, M. A. A. Neil, R. Jukaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” P. Natl. Acad. Sci. USA 99, 5788–5792 (2002).
[Crossref]

Keller, C. U.

Koppel, D. E.

D. E. Koppel, “Statistical accuracy in fluorescence correlation spectroscopy,” Phys. Rev. A 10, 1938–1945 (1974).
[Crossref]

Kubby, J.

Leroux, C.-E.

Levecq, X.

Loza-Alvarez, P.

Mahou, P.

Milkie, D. E.

K. Wang, D. E. Milkie, A. Saxena, P. Engerer, T. Misgeld, M. E. Bronner, J. Mumm, and E. Betzig, “Rapid adaptive optical recovery of optimal resolution over large volumes,” Nat. Methods 11, 625–628 (2014).
[Crossref] [PubMed]

Misgeld, T.

K. Wang, D. E. Milkie, A. Saxena, P. Engerer, T. Misgeld, M. E. Bronner, J. Mumm, and E. Betzig, “Rapid adaptive optical recovery of optimal resolution over large volumes,” Nat. Methods 11, 625–628 (2014).
[Crossref] [PubMed]

Monnier, S.

Mourou, G.

Müller, J. D.

J. D. Müller, “Cumulant analysis in fluorescence fluctuation spectroscopy,” Biophys. J. 86, 3981–3992 (2004).
[Crossref] [PubMed]

Mumm, J.

K. Wang, D. E. Milkie, A. Saxena, P. Engerer, T. Misgeld, M. E. Bronner, J. Mumm, and E. Betzig, “Rapid adaptive optical recovery of optimal resolution over large volumes,” Nat. Methods 11, 625–628 (2014).
[Crossref] [PubMed]

Neil, M. A. A.

M. J. Booth, M. A. A. Neil, R. Jukaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” P. Natl. Acad. Sci. USA 99, 5788–5792 (2002).
[Crossref]

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.

Norris, T. B.

Olarte, O. E.

Olivier, N.

Porcar-Guezenec, R.

Qian, H.

H. Qian, “On the statistics of fluorescence correlation spectroscopy,” Biophys. Chem. 38, 49–57 (1990).
[Crossref] [PubMed]

Saffarian, S.

S. Saffarian and E. L. Elson, “Statistical analysis of fluorescence correlation spectroscopy: The standard deviation and bias,” Biophys. J. 84, 2030–2042 (2003).
[Crossref] [PubMed]

Sato, T. R.

N. Ji, T. R. Sato, and E. Betzig, “Characterization and adaptive optical correction of aberrations during in vivo imaging in the mouse cortex,” P. Natl. Acad. Sci. USA 109, 22–27 (2012).
[Crossref]

Saxena, A.

K. Wang, D. E. Milkie, A. Saxena, P. Engerer, T. Misgeld, M. E. Bronner, J. Mumm, and E. Betzig, “Rapid adaptive optical recovery of optimal resolution over large volumes,” Nat. Methods 11, 625–628 (2014).
[Crossref] [PubMed]

Schanne-Klein, M.-C.

Schwille, P.

E. Haustein and P. Schwille, “Fluorescence correlation spectroscopy: Novel variations of an established technique,” Annu. Rev. Bioph. Biom. 36, 151–169 (2007).
[Crossref]

Sherman, L.

Srinivas, S.

Tao, X.

Thayil, A.

Truong, H. H.

van Werkhoven, T.

Vdovin, G.

Verhaegen, M.

Wang, I.

Wang, K.

K. Wang, D. E. Milkie, A. Saxena, P. Engerer, T. Misgeld, M. E. Bronner, J. Mumm, and E. Betzig, “Rapid adaptive optical recovery of optimal resolution over large volumes,” Nat. Methods 11, 625–628 (2014).
[Crossref] [PubMed]

Watanabe, T.

Wilson, T.

Zeng, J.

Zuo, Y.

Annu. Rev. Bioph. Biom. (1)

E. Haustein and P. Schwille, “Fluorescence correlation spectroscopy: Novel variations of an established technique,” Annu. Rev. Bioph. Biom. 36, 151–169 (2007).
[Crossref]

Biomed. Opt. Express (3)

Biophys. Chem. (1)

H. Qian, “On the statistics of fluorescence correlation spectroscopy,” Biophys. Chem. 38, 49–57 (1990).
[Crossref] [PubMed]

Biophys. J. (3)

S. Saffarian and E. L. Elson, “Statistical analysis of fluorescence correlation spectroscopy: The standard deviation and bias,” Biophys. J. 84, 2030–2042 (2003).
[Crossref] [PubMed]

J. D. Müller, “Cumulant analysis in fluorescence fluctuation spectroscopy,” Biophys. J. 86, 3981–3992 (2004).
[Crossref] [PubMed]

M. A. Digman, R. Dalal, A. F. Horwitz, and E. Gratton, “Mapping the number of molecules and brightness in the laser scanning microscope,” Biophys. J. 94, 2320–2332 (2008).
[Crossref]

J. Opt. Soc. Am. A (2)

Nat. Methods (1)

K. Wang, D. E. Milkie, A. Saxena, P. Engerer, T. Misgeld, M. E. Bronner, J. Mumm, and E. Betzig, “Rapid adaptive optical recovery of optimal resolution over large volumes,” Nat. Methods 11, 625–628 (2014).
[Crossref] [PubMed]

Opt. Express (2)

Opt. Lett. (6)

P. Natl. Acad. Sci. USA (2)

M. J. Booth, M. A. A. Neil, R. Jukaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” P. Natl. Acad. Sci. USA 99, 5788–5792 (2002).
[Crossref]

N. Ji, T. R. Sato, and E. Betzig, “Characterization and adaptive optical correction of aberrations during in vivo imaging in the mouse cortex,” P. Natl. Acad. Sci. USA 109, 22–27 (2012).
[Crossref]

Phys. Rev. A (1)

D. E. Koppel, “Statistical accuracy in fluorescence correlation spectroscopy,” Phys. Rev. A 10, 1938–1945 (1974).
[Crossref]

Proc. SPIE (1)

J. Gallagher, C.-E. Leroux, I. Wang, and A. Delon, “Accuracy of adaptive optics correction using fluorescence fluctuations,” Proc. SPIE 8978, 89780A (2014).
[Crossref]

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Figures (6)

Fig. 1
Fig. 1

Fluorescence time trace (left) and photon count histogram (right) measured on two solutions of Sulforhodamine B in a water/glycerol mixture: the 20 nM solution (blue) exhibits dilute and bright molecules, while the 200 nM solution (red) is characterized by concentrated but dimmer molecules. FCS fits (not shown) yield average numbers of molecules of 8 and 68, and brightness values of 18 kHz/molecule and 2.5 kHz/molecules respectively for the 20 nM and 200 nM solutions, while the diffusion time is 11 ms for both solutions. The brightness is varied by adjusting the excitation power.

Fig. 2
Fig. 2

Signal-to-noise ratio (S/N) of measured count rate and molecular brightness in different experimental conditions. (A) S/N measured (symbols) and calculated (solid lines) as a function of integration time T for both metrics estimated on two solutions of Sulforhodamine B of different concentrations. (B) Calculated S/N for count rate measurements and (C) calculated S/N for brightness measurements, as a function of the average number of molecules and brightness (integration time set at T = 0.1 s). The two solutions shown in (A) are depicted as crosses in the 2D maps.

Fig. 3
Fig. 3

Sensitivity to aberrations (A) Measured value of both metrics (count rate and brightness) as a function of aberration magnitude for random combinations of 11 Zernike modes introduced by the deformable mirror. The sample is a aqueous 10 nM solution of Sulforhodamine B (Nmol=1.6). The Strehl ratio squared is plotted as a solid line. Quadratic fits in the small aberration range for both metrics give sensitivity values of 0.37 rad−2 for CR and 1.5 rad −2 for brightness (B) Variation of other parameters extracted from fluctuation analysis, the number of molecules (top) and the diffusion time (bottom) as a function of aberration amplitude. For each rms, the parameters are measured with 20 random aberrations. The graphs depict the mean and standard deviation of these measurements.

Fig. 4
Fig. 4

Comparison of AO correction using either the count rate or the molecular brightness as optimization metric. (A) Examples of optimization in either a dilute sample with relatively bright molecules (top) or a more concentrated solution with dim molecules (bottom). The left graphs depict the count rate measured during AO optimization using the count rate as metric. The right graphs depict the measured brightness during AO optimization using the brightness as metric. (B) Residual aberrations after correcting with the count rate (red circles) or the brightness (blue triangles) as metric, in four samples with different concentrations (corresponding to Nmol=30, 8, 2 and 0.5 molecules in the observation volume) at various laser power. The error bars are the standard deviation of 50 optimizations per point for each metric. The continuous line are residuals calculated with the method presented in the text. The correction is performed on 10 modes using 3 measurements per mode for bias −b, 0 and +b (b=0.54 rad) and an initial aberration of 0.54 rad.

Fig. 5
Fig. 5

Predicted AO correction accuracy. (A) Calculated 2D maps of residual aberrations in rad as a function of the molecular brightness and the number of molecules, when using the count rate (left) or the brightness (right) as metric. The black dashed lines show the concentrations of the solutions used in the experiments. The correction accuracy needed for a Strehl ration of 0.9 is shown by a dashed white line. (B) Ratio of the calculated residual with the brightness metric to the one obtained with the count rate metric. When this ratio is smaller than 1, brightness leads to more accurate correction. When it is larger than 1, count rate yields more accurate correction.

Fig. 6
Fig. 6

Performance of the two metrics in case of large aberrations. (A) Expected signal-to-noise ratio of Count Rate (red circles) and Brightness (blue triangles) measurements as a function of total aberration amplitude. These S/N are calculated from measured values of CR, brightness and τD (Fig. 3) obtained for 20 random aberrations at each total rms amplitude. (B) Expected error on each mode estimation as a function of the total aberration amplitude, calculated with 3 measurements per mode and 0.5 rad bias, using either the Count Rate (red circles) or the Brightness (blue triangles) as metric. If the aberration is uniformly distributed over Nmodes modes, an improvement can only be obtained if the uncertainty for one mode is below rms = N modes. The corresponding area is shown for Nmodes = 10 (left) and Nmodes = 50 (right). For all graphs in this figure, the number of molecules is Nmol=1.6 and the brightness is 37 kHz/molecule without aberration.

Equations (10)

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

W = T / 2 T / 2 I ( t ) d t
Δ W 2 = 2 N mol B ( T )
Δ 2 = Δ S 2 k 2 + S 2 k 4 Δ k 2 + 2 S 2 k 3 Δ S Δ k
Δ 2 = 1 K 2 ( δ t / T ) 2 ( Δ S 2 + S 2 K 2 Δ K 2 )
M = M 0 ( 1 β σ 2 )
J ( δ p δ q δ a m ) = δ y i
J = [ f p ( x i , p , q , a m ) f q ( x i , p , q , a m ) f a m ( x i , p , q , a m ) ]
L = ( J T J ) 1 J T
Σ α = L Σ y L T
Δ a m 2 = i = 1 N mes L 3 i 2 Δ y i 2

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