## Adaptive optics for fluorescence correlation spectroscopy |

Optics Express, Vol. 19, Issue 27, pp. 26839-26849 (2011)

http://dx.doi.org/10.1364/OE.19.026839

Acrobat PDF (1074 KB)

### Abstract

Fluorescence Correlation Spectroscopy (FCS) yields measurement parameters (number of molecules, diffusion time) that characterize the concentration and kinetics of fluorescent molecules within a supposedly known observation volume. Absolute derivation of concentrations and diffusion constants therefore requires preliminary calibrations of the confocal Point Spread Function with phantom solutions under perfectly controlled environmental conditions. In this paper, we quantify the influence of optical aberrations on single photon FCS and demonstrate a simple Adaptive Optics system for aberration correction. Optical aberrations are gradually introduced by focussing the excitation laser beam at increasing depths in fluorescent solutions with various refractive indices, which leads to drastic depth-dependent bias in the estimated FCS parameters. Aberration correction with a Deformable Mirror stabilizes these parameters within a range of several tens of *μ*m into the solution. We also demonstrate, both theoretically and experimentally, that the molecular brightness scales as the Strehl ratio squared.

© 2011 OSA

## 1. Introduction

*μ*M range) [1

1. M. A. Digman and E. Gratton, “Lessons in fluctuation correlation spectroscopy,” Annu. Rev. Phys. Chem . **62**, 645–668 (2011). [CrossRef] [PubMed]

*N*and the diffusion time,

*τ*, through the observation volume [2

_{D}2. E. Haustein and P. Schwille, “Fluorescence correlation spectroscopy: novel variations of an established technique,” Annu. Rev. Biophys. Biomol. Struct . **36**, 151–169 (2007). [CrossRef] [PubMed]

3. E. L. Elson, “Quick tour of fluorescence correlation spectroscopy,” J. Biomed. Opt . **9**, 857–864 (2004). [CrossRef] [PubMed]

4. S. T. Hess and W. W. Webb, “Focal volume optics and experimental artifacts in confocal fluorescence correlation spectroscopy,” Biophys J . **83**, 2300–2317 (2002). [CrossRef] [PubMed]

6. B. Huang, T. D. Perroud, and R. N. Zare, “Photon counting histogram: one-photon excitation,” ChemPhysChem **5**, 1523–1531 (2004). [CrossRef] [PubMed]

*N*and

*τ*, that scale with the observation volume, which makes it difficult to compare measurements obtained with different samples (solutions, cells, tissues,

_{D}*etc.*) and in different environments (temperature, substrates). Preliminary calibrations of the observation volume are usually performed with fluorophore solutions, with well known diffusion constant and concentration [7

7. S. Rüttinger, V. Buschmann, B. Krämer, R. Erdmann, R. Macdonald, and F. Koberling, “Comparison and accuracy of methods to determine the confocal volume for quantitative fluorescence correlation spectroscopy,” J. Microsc . **232**, 343–352 (2008). [CrossRef] [PubMed]

*etc.*, these calibrations are unusable if not performed under the exact same conditions as the experiment of interest. The key role of refractive index mismatches in FCS samples has been stressed by Enderlein

*et al.*[8

8. T. Dertinger, A. Loman, B. Ewers, C. Müller, B. Krämer, and J. Enderlein, “The optics and performance of dual-focus fluorescence correlation spectroscopy,” Opt. Express **16**, 14353–14368 (2008). [CrossRef] [PubMed]

9. C. B. Müller, T. Eckert, A. Loman, J. Enderlein, and W. Richtering, “Dual-focus fluorescence correlation spectroscopy: a robust tool for studying molecular crowding,” Soft Matter **5**, 1358–1366 (2009). [CrossRef]

*τ*,

_{D}*N*) and conventional images. The field dependence of optical aberrations can lead to a twofold increase in diffusion times and even more in molecular brightness, while the effects on the confocal image are barely noticeable [10

10. N. Dross, C. Spriet, M. Zwerger, G. Müller, W. Waldeck, and J. Langowski, “Mapping eGFP oligomer mobility in living cell nuclei,” PLoS ONE **4**, e5041 1–13 (2009). [CrossRef]

11. P. Ferrand, M. Pianta, A. Kress, A. Aillaud, and H. Rigneault, “A versatile dual spot laser scanning confocal microscopy system for advanced fuorescence correlation spectroscopy analysis in living cell,” Rev. Sci. Instrum . **80**, 083702 (2009). [CrossRef] [PubMed]

*μ*m RMS), dependent upon the observation depth, that dramatically affect the FCS outputs (

*e.g.*the number of molecules is multiplied by more than a factor 4). The DM will be used in this case to correct the aberrations.

## 2. FCS and aberration modeling

*τ*and the triplet fraction,

_{T}*f*, that is the average fraction of molecules in the triplet state [12

_{T}12. J. Widengren, U. Mets, and R. Rigler, “Fluorescence correlation spectroscopy of triplet states in solution: a theoretical and experimental study,” J. Phys. Chem . **99**, 13368–13379 (1995). [CrossRef]

*N*, is the less model dependent one. Its estimated value depends on aberrations but not on the exact analytical form of the

*G*(

*τ*) model. The reason is that, for time lag tending to zero, the amplitude of the ACF is proportional to 1

*/N*, the proportionality factor depending only on the triplet fraction,

*f*, which is, for a fixed laser power, constant.

_{T}*etc.*, so that the Molecular Detection Efficiency function, used in FCS [4

4. S. T. Hess and W. W. Webb, “Focal volume optics and experimental artifacts in confocal fluorescence correlation spectroscopy,” Biophys J . **83**, 2300–2317 (2002). [CrossRef] [PubMed]

*PSF*, and the FCS observation volume,

_{con}*V*, reads [13

_{fcs}13. J. Mertz, “Molecular photodynamics involved in multi-photon excitation fluorescence microscopy,” Eur. Phys. J. D **3**, 53–66 (1998). [CrossRef]

*CR*, is proportional to the integral of the product of the illumination intensity profile times the collection efficiency profile. In presence of aberrations, both illumination and collection profiles are expected to show a lower peak value and enlarged width. The Strehl ratio accounts, by definition, for the attenuation of the peak intensity. Introducing

*S*as the single-pass Strehl ratio, which is assumed to have the same value for the illumination and collection paths [14

_{tr}14. M. Schwertner, M. Booth, and T. Wilson, “Characterizing specimen induced aberrations for high NA adaptive optical microscopy,” Opt. Express **12**, 6540–6552 (2004). [CrossRef] [PubMed]

*η*takes into account the laser power in the sample, the absorption cross section, the fluorescence quantum yield and the overall detection efficiency (including lenses, fluorescence filters and efficiency of the photon detector). Note that, still under the assumption of a Gaussian profile, the integral of the confocal PSF reads

*CRM*=

*CR/*(

*C*×

*V*), reads:

_{fcs}*σ*is the Root Mean Square (RMS) amplitude of the aberrations (of both the illumination and detection beams) and

_{wf}*λ*is the mean value of the excitation and fluorescence wavelengths. In practice, the amplitudes of Zernike aberrations introduced by the sample can be estimated, by assuming that the aberrations are perfectly corrected by the DM. For each Zernike mode

*i*, we denote with

*a*the amplitude of the aberration mode

_{i}*i*. Piston, tilts and defocus terms are ignored in our work, because, to first order, they have no impact on the shape of the confocal PSF. Thanks to the orthonormal property of Zernike aberrations, the overall RMS amplitude of all the modes reads:

*a*

_{4},

*a*

_{5}), comas (

*a*

_{6},

*a*

_{7}), trefoils (

*a*

_{8},

*a*

_{9}), and primary spherical aberration (

*a*

_{10}). Our analysis of the impact of aberrations on the estimated FCS parameters ignored other Zernike modes, but nevertheless describes our experimental results accurately.

## 3. Experimental setup and materials

### 3.1. Adaptive optics

*μ*m core radius coupled to an Avalanche Photodiode (APD) from PerkinElmer) and a ×5.3 imager (lenses

*L*5 and

*L*6). The overall magnification of this confocal microscope being 276, the detector radius corresponds to 2.15 optical units. The laser beam at 633 nm (HeNe, from Thorlabs) has a uniform intensity profile in the pupil plane of the microscope objective, which is required to have a uniform signal to noise ratio on the Shack-Hartmann Wavefront Sensor (SHWFS) when performing the calibration of the DM.

16. 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. Express **18**, 17521–17532 (2010). [CrossRef] [PubMed]

19. X. Tao, O. Azucena, M. Fu, Y. Zuo, D. Chen, and J. Kubby, “Adaptive optics microscopy with direct wavefront sensing using fluorescent protein guide stars,” Opt. Lett . **36**, 3389–3391 (2011). [CrossRef] [PubMed]

*i*of amplitude

*a*, one can quantify the departure from the target aberration using the RMS error of the open-loop,

_{i}*ɛ*, which is measured by the SHWFS, using 75 Zernike modes. Results are shown in Fig. 2 for astigmatism

_{i}*a*

_{4}, coma

*a*

_{6}, and spherical aberration

*a*

_{10}. The error is smaller than 25 nm in the range of aberrations that we corrected in the present study (|

*a*

_{10}| < 0.1

*μ*m). It is worthwhile noting that the error is larger for spherical aberration, because the linear model of the open-loop DM control is less accurate for higher order aberrations.

20. M. Neil, M. Booth, and T. Wilson, “Closed-loop aberration correction by use of a modal Zernike wave-front sensor,” Opt. Lett . **25**, 1083–1085 (2000). [CrossRef]

21. M. Booth, M. Neil, and T. Wilson, “New modal wave-front sensor: application to adaptive confocal fluorescence microscopy and two-photon excitation fluorescence microscopy,” J. Opt. Soc. Am. A **19**, 2112–2120 (2002). [CrossRef]

*i*, with the DM biased at

*a*= −0.1,0,0.1

_{i}*μ*m. A parabolic interpolation of the corresponding measurements of the count rate yielded the optimal amplitude

*â*that will be retained for each mode

_{i}*i*. Final correction was obtained after cycling twice through all the 7 Zernike modes and thus took 42 s.

### 3.2. Fluorescence excitation, data acquisition and treatment

*μ*W, in order to avoid any saturation effect that would affect the shape of the PSF. In case of no aberration, this leads to a typical count rate per molecule of 7 kHz. The digital signal of the APD was sent to a homemade data acquisition system based on a PCI 6602 card from National Instrument, which provides real time evaluation of the count rate and raw data saving. Each ACF curve, with its mean value and standard error of the mean, was computed using Eq. (1) with 10 acquisitions

*I*(

*t*) of 10 seconds. Raw data processing (ACF calculations and fits) were performed using MatLab (Mathworks) and Origin (OriginLab Corp.). Since, in case of aberrations (

*i.e.*for glycerol solutions), the value of the structure parameter,

*S*, is ill defined, the corresponding fits were performed by setting

*S*to its estimated value after aberration corrections (typically found, by fitting

*S*with Eq. (4), between 5 and 7).

### 3.3. Fluorophores

*C*, with Alexa Fluor 647 (A647), purchased from Invitrogen Molecular Probe. Stock solutions were prepared without further purification. The molecular concentration of the A647 solutions was 80 nM, unless specified. We used A647 in pure water and in two aqueous solutions of glycerol: 50% (v/v) and 70.4% (v/v). Using a rheometer (Anton Paar, model MCR 301), we controlled the viscosities of the glycerol solutions and found 7.86 mPa.s for the 50% glycerol solution and 30.7 mPa.s for the 70.4% one. These values are in good agreement with the tabulated values of water-glycerol mixtures [22]. In addition, we estimated the refraction indices to their tabulated values: 1.407 for the 50% glycerol solution and 1.435 for the 70.4% one [23].

## 4. Experimental results and discussion

### 4.1. Calibration at the cover slide - sample interface

*a*

_{5}≃ 0.2

*μ*m), which is probably introduced by the dichroic mirror and the surface of the DM that is non-flat when no commands are applied. The correction collar of the objective was also manually optimized before starting aberration corrections and then set to this adjustment for the entire experiment. These optimized set of Zernike aberrations was then systematically applied to the DM before any FCS measurement. Henceforth, in the case of glycerol solutions, the outcome of our experiments only depends on whether we corrected the remaining aberrations introduced by the sample or not. The reference depth was taken at

*z*= 10

*μ*m, to avoid any artifact due to the cover slide - solution interface.

24. P. Kapusta, “Absolute diffusion coefficients: compilation of reference data for FCS calibration,” http://www.picoquant.com/technotes/appnote_diffusion_coefficients.pdf.

*C*) [23], we derive a reference value

*D*= 304.5

_{water}*μ*m

^{2}.s

^{−1}. From the measured diffusion time of A647 in pure water,

*τ*= 48

_{D}*μ*s (data not shown), we use Eq. (3) to deduce the radial width of the confocal PSF and found

*w*= 0.242

_{r}*μ*m. In addition, using the measured structure parameter and number of molecules,

*S*= 10 and

*N*= 34.6, we obtain, using Eq. (2), a concentration of 73 nM, in good agreement with the one we intended to prepare (80 nM). Our measured diffusion time of A647 in pure water can now be compared with the corresponding values in aqueous solutions of glycerol. Using the viscosities of water at 22°

*C*(0.955 mPa.s [23]) and of our glycerol solutions (7.86 and 30.7 mPa.s, see above), we derive a diffusion time

*τ*= 395

_{D}*μ*s in the 50% glycerol solution and

*τ*= 1545

_{D}*μ*s in the 70.4% one. Of course, these derivations assume that the confocal radial waist,

*w*, is the same in water and in the glycerol solutions, so that the diffusion time is proportional to the viscosity. In other words, the calculated diffusion times in the aqueous solutions of glycerol correspond to perfectly corrected optical aberrations. Experimentally, we measured, at the reference depth of

_{r}*z*= 10

*μ*m,

*τ*= 410

_{D}*μ*s for the 50% glycerol solution (data not shown) and

*τ*= 1391

_{D}*μ*s for the 70.4% one (see the corresponding ACF in Fig. 3, red curve in the left graph). The 10% discrepancy of

*τ*from its expected value, in the case of the 70.4% glycerol solution, can be attributed to the non perfect aberration corrections at the interface.

_{D}### 4.2. Measurements as a function of the focussing depth

*N*(Eq. (4)) due to the increase in the FCS observation volume (Eq. (2)). Our AO system provides an efficient aberration correction, and the differences between the ACF curves are greatly reduced (right graph). The AO correction was clearly less efficient at

*z*= 45

*μ*m focussing depth and we therefore did not acquire data deeper into the 70.4% glycerol solution. In contrast, with the 50% solution, we obtained an efficient aberration correction down to

*z*= 80

*μ*m (data not shown). This is because the refraction index mismatch is lower with this solution.

*N*and

*τ*at each focussing depth, for the two glycerol solutions. Fig. 4 show results that are normalized to the values obtained at the reference depth of

_{D}*z*= 10

*μ*m, without and with AO switched on (left and right graph respectively). Without AO,

*N*and

*τ*are more sensitive to the focussing depth with the 70.4% glycerol solution, because the larger refraction index mismatch the larger the aberrations. Note that

_{D}*τ*depends only upon the lateral size,

_{D}*w*, of the confocal PSF (Eq. (3)), while

_{r}*N*depends upon the volume (Eq. (2)), which explains why the relative increase of

*N*is more pronounced than that of

*τ*. The right panel of Fig. 4 exemplifies the very efficient aberration correction.

_{D}*a*

_{10}, open circles) and residual RMS of all the other modes (

*r*

_{10}, open squares) generated by the DM for the two glycerol solutions. As expected, the refractive index mismatch introduces a spherical aberration, the amplitude of which is proportional to the focussing depth [25

25. M. Booth, M. Neil, and T. Wilson, “Aberration correction for confocal imaging in refractive-index-mismatched media,” J. Microsc . **192**, 90–98 (1998). [CrossRef]

*CRM*and the amplitude of the Zernike aberrations, we can compare the experimental data with the modeling presented in Section 2, which shows that the molecular brightness scales as the Strehl ratio squared (see Eq. (7)).

*z*= 10

*μ*m depth taken as reference:

*σ*(black solid line), using Eq. (8) and the brightness obtained in the two glycerol solutions. Brightness values are computed using the fit values of

_{wf}*N*(Fig. 4, left panel) and the corresponding count rate,

*CR*(data not shown) without AO correction. They are normalized with the value measured at

*z*= 10

*μ*m. The agreement between experimental data and the predictions of Eq. (7) is good, even though the Gaussian approximation of an aberrated confocal PSF is probably inaccurate.

*σ*, used to compute the Strehl ratio squared (with Eq. (8)), equates to the amplitude of the single Zernike mode,

_{wf}*a*. We performed the experiments for Zernike astigmatism

_{i}*a*

_{4}and spherical aberration

*a*

_{10}. The molecular brightness, normalized with the value measured for

*a*= 0, is shown in Fig. 6 (right panel). We observe a good agreement with the model, although there is a slight discrepancy for astigmatism. Two reasons could explain that the modeling is less accurate with the astigmatism mode: i) the image of the microscope objective exit pupil in the plane of the DM is elongated, because of a 15° incidence angle on the DM; ii) the lack of radial symmetry of the confocal PSF when astigmatism is introduced, which is not taken into account with the ACF modeling of Eq. (4), since only one lateral diffusion time

_{i}*τ*is defined. Curves very similar to the ones of the right panel of Fig. 6 have been obtained with a A647 8 nM pure water solution (data not shown).

_{D}## 5. Conclusion

*n*up to 0.1) can have a dramatic impact on FCS data, when focusing at a few tens of

*μ*m above the cover slide - solution interface. Although the wavefront is weakly distorted (aberration amplitude has a RMS smaller than 0.1

*μ*m), the FCS parameters are strongly biased (the diffusion time is multiplied by up to a factor 2 and the number of molecules by more than a factor 4). Such effects constitute a technical bottleneck, since an ideal FCS experiment requires a perfectly controlled observation volume, in order to compare FCS parameters obtained with different samples of interest. We showed that Adaptive Optics makes it possible to stabilize the observation volume in solutions of fluorescent molecules of nM concentrations. Interestingly, the count rate per molecule (or molecular brightness), as provided by FCS, scales as the square of the Strehl ratio. It is remarkable that, thanks to FCS, this key quantity can be obtained without acquiring an image. We demonstrated this idea in homogeneous media, but it could be extended to weakly contrasted samples. Thus, we suggest that the count rate per molecule could be used as an optimization metric for Adaptive Optics. More importantly for biological applications of FCS, after aberration corrections, the count rate per molecule would more confidently reflect environmental conditions, such as fluorescent probe aggregation, pH variations,

*etc*. In the near future, our AO system should improve significantly the robustness of FCS measurements in environments of various optical properties (crowded solutions, cellular media, tissues, etc.).

## Acknowledgments

## References and links

1. | M. A. Digman and E. Gratton, “Lessons in fluctuation correlation spectroscopy,” Annu. Rev. Phys. Chem . |

2. | E. Haustein and P. Schwille, “Fluorescence correlation spectroscopy: novel variations of an established technique,” Annu. Rev. Biophys. Biomol. Struct . |

3. | E. L. Elson, “Quick tour of fluorescence correlation spectroscopy,” J. Biomed. Opt . |

4. | S. T. Hess and W. W. Webb, “Focal volume optics and experimental artifacts in confocal fluorescence correlation spectroscopy,” Biophys J . |

5. | J. D. Müller, “Cumulant analysis in fluorescence fluctuation spectroscopy,” Biophys. J . |

6. | B. Huang, T. D. Perroud, and R. N. Zare, “Photon counting histogram: one-photon excitation,” ChemPhysChem |

7. | S. Rüttinger, V. Buschmann, B. Krämer, R. Erdmann, R. Macdonald, and F. Koberling, “Comparison and accuracy of methods to determine the confocal volume for quantitative fluorescence correlation spectroscopy,” J. Microsc . |

8. | T. Dertinger, A. Loman, B. Ewers, C. Müller, B. Krämer, and J. Enderlein, “The optics and performance of dual-focus fluorescence correlation spectroscopy,” Opt. Express |

9. | C. B. Müller, T. Eckert, A. Loman, J. Enderlein, and W. Richtering, “Dual-focus fluorescence correlation spectroscopy: a robust tool for studying molecular crowding,” Soft Matter |

10. | N. Dross, C. Spriet, M. Zwerger, G. Müller, W. Waldeck, and J. Langowski, “Mapping eGFP oligomer mobility in living cell nuclei,” PLoS ONE |

11. | P. Ferrand, M. Pianta, A. Kress, A. Aillaud, and H. Rigneault, “A versatile dual spot laser scanning confocal microscopy system for advanced fuorescence correlation spectroscopy analysis in living cell,” Rev. Sci. Instrum . |

12. | J. Widengren, U. Mets, and R. Rigler, “Fluorescence correlation spectroscopy of triplet states in solution: a theoretical and experimental study,” J. Phys. Chem . |

13. | J. Mertz, “Molecular photodynamics involved in multi-photon excitation fluorescence microscopy,” Eur. Phys. J. D |

14. | M. Schwertner, M. Booth, and T. Wilson, “Characterizing specimen induced aberrations for high NA adaptive optical microscopy,” Opt. Express |

15. | M. Booth, A. Kubasik-Thayil, A. Jesacher, D. Débarre, K. Grieve, and T. Wilson, “Adaptive optics in biomedical microscopy,” in Novel Techniques in Microscopy, OSA Technical Digest (CD) (Optical Society of America, 2009), paper NWA1. |

16. | 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. Express |

17. | 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 . |

18. | X. Tao, B. Fernandez, O. Azucena, M. Fu, D. Garcia, Y. Zuo, D. Chen, and J. Kubby, “Adaptive optics confocal microscopy using direct wavefront sensing,” Opt. Lett . |

19. | X. Tao, O. Azucena, M. Fu, Y. Zuo, D. Chen, and J. Kubby, “Adaptive optics microscopy with direct wavefront sensing using fluorescent protein guide stars,” Opt. Lett . |

20. | M. Neil, M. Booth, and T. Wilson, “Closed-loop aberration correction by use of a modal Zernike wave-front sensor,” Opt. Lett . |

21. | M. Booth, M. Neil, and T. Wilson, “New modal wave-front sensor: application to adaptive confocal fluorescence microscopy and two-photon excitation fluorescence microscopy,” J. Opt. Soc. Am. A |

22. | N. E. Dorsey, |

23. | D. R. Lide, ed., |

24. | P. Kapusta, “Absolute diffusion coefficients: compilation of reference data for FCS calibration,” http://www.picoquant.com/technotes/appnote_diffusion_coefficients.pdf. |

25. | M. Booth, M. Neil, and T. Wilson, “Aberration correction for confocal imaging in refractive-index-mismatched media,” J. Microsc . |

**OCIS Codes**

(010.1080) Atmospheric and oceanic optics : Active or adaptive optics

(170.6280) Medical optics and biotechnology : Spectroscopy, fluorescence and luminescence

(180.1790) Microscopy : Confocal microscopy

**ToC Category:**

Adaptive Optics

**History**

Original Manuscript: October 11, 2011

Revised Manuscript: November 25, 2011

Manuscript Accepted: December 2, 2011

Published: December 15, 2011

**Virtual Issues**

Vol. 7, Iss. 2 *Virtual Journal for Biomedical Optics*

**Citation**

Charles-Edouard Leroux, Irène Wang, Jacques Derouard, and Antoine Delon, "Adaptive optics for fluorescence correlation spectroscopy," Opt. Express **19**, 26839-26849 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-27-26839

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### References

- M. A. Digman and E. Gratton, “Lessons in fluctuation correlation spectroscopy,” Annu. Rev. Phys. Chem. 62, 645–668 (2011). [CrossRef] [PubMed]
- E. Haustein and P. Schwille, “Fluorescence correlation spectroscopy: novel variations of an established technique,” Annu. Rev. Biophys. Biomol. Struct. 36, 151–169 (2007). [CrossRef] [PubMed]
- E. L. Elson, “Quick tour of fluorescence correlation spectroscopy,” J. Biomed. Opt. 9, 857–864 (2004). [CrossRef] [PubMed]
- S. T. Hess and W. W. Webb, “Focal volume optics and experimental artifacts in confocal fluorescence correlation spectroscopy,” Biophys J. 83, 2300–2317 (2002). [CrossRef] [PubMed]
- J. D. Müller, “Cumulant analysis in fluorescence fluctuation spectroscopy,” Biophys. J. 86, 3981–3992 (2004). [CrossRef] [PubMed]
- B. Huang, T. D. Perroud, and R. N. Zare, “Photon counting histogram: one-photon excitation,” ChemPhysChem5, 1523–1531 (2004). [CrossRef] [PubMed]
- S. Rüttinger, V. Buschmann, B. Krämer, R. Erdmann, R. Macdonald, and F. Koberling, “Comparison and accuracy of methods to determine the confocal volume for quantitative fluorescence correlation spectroscopy,” J. Microsc. 232, 343–352 (2008). [CrossRef] [PubMed]
- T. Dertinger, A. Loman, B. Ewers, C. Müller, B. Krämer, and J. Enderlein, “The optics and performance of dual-focus fluorescence correlation spectroscopy,” Opt. Express16, 14353–14368 (2008). [CrossRef] [PubMed]
- C. B. Müller, T. Eckert, A. Loman, J. Enderlein, and W. Richtering, “Dual-focus fluorescence correlation spectroscopy: a robust tool for studying molecular crowding,” Soft Matter5, 1358–1366 (2009). [CrossRef]
- N. Dross, C. Spriet, M. Zwerger, G. Müller, W. Waldeck, and J. Langowski, “Mapping eGFP oligomer mobility in living cell nuclei,” PLoS ONE4, e5041 1–13 (2009). [CrossRef]
- P. Ferrand, M. Pianta, A. Kress, A. Aillaud, and H. Rigneault, “A versatile dual spot laser scanning confocal microscopy system for advanced fuorescence correlation spectroscopy analysis in living cell,” Rev. Sci. Instrum. 80, 083702 (2009). [CrossRef] [PubMed]
- J. Widengren, U. Mets, and R. Rigler, “Fluorescence correlation spectroscopy of triplet states in solution: a theoretical and experimental study,” J. Phys. Chem. 99, 13368–13379 (1995). [CrossRef]
- J. Mertz, “Molecular photodynamics involved in multi-photon excitation fluorescence microscopy,” Eur. Phys. J. D3, 53–66 (1998). [CrossRef]
- M. Schwertner, M. Booth, and T. Wilson, “Characterizing specimen induced aberrations for high NA adaptive optical microscopy,” Opt. Express12, 6540–6552 (2004). [CrossRef] [PubMed]
- M. Booth, A. Kubasik-Thayil, A. Jesacher, D. Débarre, K. Grieve, and T. Wilson, “Adaptive optics in biomedical microscopy,” in Novel Techniques in Microscopy, OSA Technical Digest (CD) (Optical Society of America, 2009), paper NWA1.
- 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, 17521–17532 (2010). [CrossRef] [PubMed]
- 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, 825–827 (2011). [CrossRef] [PubMed]
- X. Tao, B. Fernandez, O. Azucena, M. Fu, D. Garcia, Y. Zuo, D. Chen, and J. Kubby, “Adaptive optics confocal microscopy using direct wavefront sensing,” Opt. Lett. 36, 1062–1064 (2011). [CrossRef] [PubMed]
- X. Tao, O. Azucena, M. Fu, Y. Zuo, D. Chen, and J. Kubby, “Adaptive optics microscopy with direct wavefront sensing using fluorescent protein guide stars,” Opt. Lett. 36, 3389–3391 (2011). [CrossRef] [PubMed]
- M. Neil, M. Booth, and T. Wilson, “Closed-loop aberration correction by use of a modal Zernike wave-front sensor,” Opt. Lett. 25, 1083–1085 (2000). [CrossRef]
- M. Booth, M. Neil, and T. Wilson, “New modal wave-front sensor: application to adaptive confocal fluorescence microscopy and two-photon excitation fluorescence microscopy,” J. Opt. Soc. Am. A19, 2112–2120 (2002). [CrossRef]
- N. E. Dorsey, Properties of Ordinary Water-Substance in All Its Phases (New York, Reinhold Pub. Corp., 1940), p. 184.
- D. R. Lide, ed., Handbook of Chemistry and Physics (CRC Press, Cleveland, 2006).
- P. Kapusta, “Absolute diffusion coefficients: compilation of reference data for FCS calibration,” http://www.picoquant.com/technotes/appnote_diffusion_coefficients.pdf .
- M. Booth, M. Neil, and T. Wilson, “Aberration correction for confocal imaging in refractive-index-mismatched media,” J. Microsc. 192, 90–98 (1998). [CrossRef]

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