Abstract

In the presence of strong light scattering, as often encountered in biological tissue, optical microscopy becomes challenging and technical demanding. Beside image quality, the quantitative determination of molecular properties is also strongly affected by scattering. We have carried out fluorescence correlation spectroscopy (FCS) experiments, in a solution of fluorophores, through a sparse scattering layer made of dielectric beads. We observe that the fluorescence signal steadily decreases as the focus is moved away from the scattering layer. By contrast, the estimated number of molecules recovers its normal value beyond a characteristic distance of about twice the bead diameters, below which it is strongly biased. Accompanying theoretical modeling demonstrates how diffraction and refraction by the scattering layer and their impact on FCS measurements depend on size and refractive index of the beads.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (1)

2017 (1)

F. Ingremeau, M. E. Dolega, J. Gallagher, I. Wang, G. Cappello, and A. Delon, “Optical sensing of mechanical pressure based on diffusion measurement in polyacrylamide cell-like barometers,” Soft Matter 13(23), 4210–4213 (2017).
[Crossref] [PubMed]

2016 (1)

2015 (2)

2014 (2)

2013 (2)

C.-E. Leroux, A. Grichine, I. Wang, and A. Delon, “Correction of cell-induced optical aberrations in a fluorescence fluctuation microscope,” Opt. Lett. 38(14), 2401–2403 (2013).
[Crossref] [PubMed]

M. L. Byron and E. A. Variano, “Refractive-index-matched hydrogel materials for measuring flow-structure interactions,” Exp. Fluids 54(2), 1456 (2013).
[Crossref]

2012 (2)

S. Zustiak, J. Riley, H. Boukari, A. Gandjbakhche, and R. Nossal, “Effects of multiple scattering on fluorescence correlation spectroscopy measurements of particles moving within optically dense media,” J. Biomed. Opt. 17(12), 125004 (2012).
[Crossref] [PubMed]

Y. Chen, D. Wang, and J. T. C. Liu, “Assessing the tissue-imaging performance of confocal microscope architectures via Monte Carlo simulations,” Opt. Lett. 37(21), 4495–4497 (2012).
[Crossref] [PubMed]

2011 (1)

2007 (1)

E. Haustein and P. Schwille, “Fluorescence correlation spectroscopy: novel variations of an established technique,” Annu. Rev. Biophys. Biomol. Struct. 36(1), 151–169 (2007).
[Crossref] [PubMed]

2005 (1)

J. Enderlein, I. Gregor, D. Patra, T. Dertinger, and U. B. Kaupp, “Performance of fluorescence correlation spectroscopy for measuring diffusion and concentration,” ChemPhysChem 6(11), 2324–2336 (2005).
[Crossref] [PubMed]

2004 (1)

E. L. Elson, “Quick tour of fluorescence correlation spectroscopy from its inception,” J. Biomed. Opt. 9(5), 857–864 (2004).
[Crossref] [PubMed]

1998 (1)

1988 (1)

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61(20), 2328–2331 (1988).
[Crossref] [PubMed]

1986 (1)

1963 (1)

1959 (1)

B. Richards, E. Wolf, and D. Gabor, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanetic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Bertolotti, J.

Bixler, J. N.

Blanca, C. M.

Boukari, H.

S. Zustiak, J. Riley, H. Boukari, A. Gandjbakhche, and R. Nossal, “Effects of multiple scattering on fluorescence correlation spectroscopy measurements of particles moving within optically dense media,” J. Biomed. Opt. 17(12), 125004 (2012).
[Crossref] [PubMed]

Bourdieu, L.

Byron, M. L.

M. L. Byron and E. A. Variano, “Refractive-index-matched hydrogel materials for measuring flow-structure interactions,” Exp. Fluids 54(2), 1456 (2013).
[Crossref]

Cappello, G.

F. Ingremeau, M. E. Dolega, J. Gallagher, I. Wang, G. Cappello, and A. Delon, “Optical sensing of mechanical pressure based on diffusion measurement in polyacrylamide cell-like barometers,” Soft Matter 13(23), 4210–4213 (2017).
[Crossref] [PubMed]

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(10), 3730–3738 (2014).
[Crossref] [PubMed]

Chen, Y.

Davis, M. A.

Delon, A.

Dertinger, T.

J. Enderlein, I. Gregor, D. Patra, T. Dertinger, and U. B. Kaupp, “Performance of fluorescence correlation spectroscopy for measuring diffusion and concentration,” ChemPhysChem 6(11), 2324–2336 (2005).
[Crossref] [PubMed]

Dolega, M. E.

F. Ingremeau, M. E. Dolega, J. Gallagher, I. Wang, G. Cappello, and A. Delon, “Optical sensing of mechanical pressure based on diffusion measurement in polyacrylamide cell-like barometers,” Soft Matter 13(23), 4210–4213 (2017).
[Crossref] [PubMed]

Dunn, A. K.

Edrei, E.

Elpers, G.

Elson, E. L.

E. L. Elson, “Quick tour of fluorescence correlation spectroscopy from its inception,” J. Biomed. Opt. 9(5), 857–864 (2004).
[Crossref] [PubMed]

Enderlein, J.

J. Enderlein, I. Gregor, D. Patra, T. Dertinger, and U. B. Kaupp, “Performance of fluorescence correlation spectroscopy for measuring diffusion and concentration,” ChemPhysChem 6(11), 2324–2336 (2005).
[Crossref] [PubMed]

Farone, W. A.

Feng, S.

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61(20), 2328–2331 (1988).
[Crossref] [PubMed]

Freund, I.

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61(20), 2328–2331 (1988).
[Crossref] [PubMed]

Gabor, D.

B. Richards, E. Wolf, and D. Gabor, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanetic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Gallagher, J.

F. Ingremeau, M. E. Dolega, J. Gallagher, I. Wang, G. Cappello, and A. Delon, “Optical sensing of mechanical pressure based on diffusion measurement in polyacrylamide cell-like barometers,” Soft Matter 13(23), 4210–4213 (2017).
[Crossref] [PubMed]

Gandjbakhche, A.

S. Zustiak, J. Riley, H. Boukari, A. Gandjbakhche, and R. Nossal, “Effects of multiple scattering on fluorescence correlation spectroscopy measurements of particles moving within optically dense media,” J. Biomed. Opt. 17(12), 125004 (2012).
[Crossref] [PubMed]

Gigan, S.

Gregor, I.

J. Enderlein, I. Gregor, D. Patra, T. Dertinger, and U. B. Kaupp, “Performance of fluorescence correlation spectroscopy for measuring diffusion and concentration,” ChemPhysChem 6(11), 2324–2336 (2005).
[Crossref] [PubMed]

Grichine, A.

Haustein, E.

E. Haustein and P. Schwille, “Fluorescence correlation spectroscopy: novel variations of an established technique,” Annu. Rev. Biophys. Biomol. Struct. 36(1), 151–169 (2007).
[Crossref] [PubMed]

Hayakawa, C. K.

Hokr, B. H.

Ingremeau, F.

F. Ingremeau, M. E. Dolega, J. Gallagher, I. Wang, G. Cappello, and A. Delon, “Optical sensing of mechanical pressure based on diffusion measurement in polyacrylamide cell-like barometers,” Soft Matter 13(23), 4210–4213 (2017).
[Crossref] [PubMed]

Ishimaru, A.

Kaupp, U. B.

J. Enderlein, I. Gregor, D. Patra, T. Dertinger, and U. B. Kaupp, “Performance of fluorescence correlation spectroscopy for measuring diffusion and concentration,” ChemPhysChem 6(11), 2324–2336 (2005).
[Crossref] [PubMed]

Kerker, M.

Kuga, Y.

Lee, S. Y.

Léger, J.-F.

Leroux, C.-E.

Liu, J. T. C.

Matijevic, E.

Monnier, S.

Mycek, M. A.

Nossal, R.

S. Zustiak, J. Riley, H. Boukari, A. Gandjbakhche, and R. Nossal, “Effects of multiple scattering on fluorescence correlation spectroscopy measurements of particles moving within optically dense media,” J. Biomed. Opt. 17(12), 125004 (2012).
[Crossref] [PubMed]

Patra, D.

J. Enderlein, I. Gregor, D. Patra, T. Dertinger, and U. B. Kaupp, “Performance of fluorescence correlation spectroscopy for measuring diffusion and concentration,” ChemPhysChem 6(11), 2324–2336 (2005).
[Crossref] [PubMed]

Potma, E. O.

Ranasinghesagara, J. C.

Richards, B.

B. Richards, E. Wolf, and D. Gabor, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanetic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Riley, J.

S. Zustiak, J. Riley, H. Boukari, A. Gandjbakhche, and R. Nossal, “Effects of multiple scattering on fluorescence correlation spectroscopy measurements of particles moving within optically dense media,” J. Biomed. Opt. 17(12), 125004 (2012).
[Crossref] [PubMed]

Rosenbluh, M.

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61(20), 2328–2331 (1988).
[Crossref] [PubMed]

Saloma, C.

Scarcelli, G.

Schott, S.

Schwille, P.

E. Haustein and P. Schwille, “Fluorescence correlation spectroscopy: novel variations of an established technique,” Annu. Rev. Biophys. Biomol. Struct. 36(1), 151–169 (2007).
[Crossref] [PubMed]

Scully, M. O.

Thomas, R. J.

Variano, E. A.

M. L. Byron and E. A. Variano, “Refractive-index-matched hydrogel materials for measuring flow-structure interactions,” Exp. Fluids 54(2), 1456 (2013).
[Crossref]

Venugopalan, V.

Wang, D.

Wang, I.

Wolf, E.

B. Richards, E. Wolf, and D. Gabor, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanetic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Yakovlev, V. V.

Zollars, B.

Zustiak, S.

S. Zustiak, J. Riley, H. Boukari, A. Gandjbakhche, and R. Nossal, “Effects of multiple scattering on fluorescence correlation spectroscopy measurements of particles moving within optically dense media,” J. Biomed. Opt. 17(12), 125004 (2012).
[Crossref] [PubMed]

Annu. Rev. Biophys. Biomol. Struct. (1)

E. Haustein and P. Schwille, “Fluorescence correlation spectroscopy: novel variations of an established technique,” Annu. Rev. Biophys. Biomol. Struct. 36(1), 151–169 (2007).
[Crossref] [PubMed]

Appl. Opt. (2)

Biomed. Opt. Express (2)

ChemPhysChem (1)

J. Enderlein, I. Gregor, D. Patra, T. Dertinger, and U. B. Kaupp, “Performance of fluorescence correlation spectroscopy for measuring diffusion and concentration,” ChemPhysChem 6(11), 2324–2336 (2005).
[Crossref] [PubMed]

Exp. Fluids (1)

M. L. Byron and E. A. Variano, “Refractive-index-matched hydrogel materials for measuring flow-structure interactions,” Exp. Fluids 54(2), 1456 (2013).
[Crossref]

J. Biomed. Opt. (2)

S. Zustiak, J. Riley, H. Boukari, A. Gandjbakhche, and R. Nossal, “Effects of multiple scattering on fluorescence correlation spectroscopy measurements of particles moving within optically dense media,” J. Biomed. Opt. 17(12), 125004 (2012).
[Crossref] [PubMed]

E. L. Elson, “Quick tour of fluorescence correlation spectroscopy from its inception,” J. Biomed. Opt. 9(5), 857–864 (2004).
[Crossref] [PubMed]

J. Opt. Soc. Am. (1)

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

Opt. Express (2)

Opt. Lett. (3)

Optica (1)

Phys. Rev. Lett. (1)

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61(20), 2328–2331 (1988).
[Crossref] [PubMed]

Proc. R. Soc. Lond. A Math. Phys. Sci. (1)

B. Richards, E. Wolf, and D. Gabor, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanetic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Soft Matter (1)

F. Ingremeau, M. E. Dolega, J. Gallagher, I. Wang, G. Cappello, and A. Delon, “Optical sensing of mechanical pressure based on diffusion measurement in polyacrylamide cell-like barometers,” Soft Matter 13(23), 4210–4213 (2017).
[Crossref] [PubMed]

Other (3)

C. F. Bohren and D. R. Huffmann, Absorption and Scattering of Light by Small particles (Wiley, 2007)

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press, 2012).

Physics Forum, “Code of the Angular Spectrum Method,” https://www.physicsforums.com/threads/code-of-the-angular-spectrum-method.823494/

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Figures (10)

Fig. 1
Fig. 1 a) Scheme of the optical configuration, showing the illumination and detection beams scattered by the 2D layer of beads within a disk of diameter ϕ, which depends upon the observation depth, D; b) segmented image of a 2D layer of beads with coverage fraction 17%, where the superimposed circles correspond to observation depths, D = 10, 50 and 100 µm.
Fig. 2
Fig. 2 Scheme of the illumination and fluorescence collection optics used in the numerical modelling
Fig. 3
Fig. 3 a) Image of a sample of 6 µm silica beads deposited on a glass coverslip used for FCS measurements; b) Representation of the corresponding 2D phase object used in the numerical simulations
Fig. 4
Fig. 4 FCS metrics (fluorescence count rate, CR and number of molecules, N) normalized to the value with no scattering substrate as a function of the distance D between the scattering substrate and the focus. Experimental values averaged over 18 configurations of 3 µm silica beads (average coverage fraction 17%), 16 configurations of 6 µm silica beads (average coverage fraction 8%), 19 configurations of 15 µm silica beads (average coverage fraction 7.5%) and 22 configurations of PAA beads of diameter 14.5 µm (average coverage fraction 17%). The error bars represent one standard deviation of the measurements.
Fig. 5
Fig. 5 Same as Fig. 4, but with the horizontal axis z scaled with respect to the size of the beads.
Fig. 6
Fig. 6 Numerical simulations of FCS metrics (fluorescence count rate, CR and number of molecules, N) normalized to the value with no scattering substrate as a function of the distance D between the scattering substrate and the focus. The numerical simulations correspond to the conditions of Figs. 4, 5. The data are the result of an average over 15 random configurations; error bars represent one standard deviation.
Fig. 7
Fig. 7 Normalized FCS metrics (fluorescence count rate, CR and number of molecules, N), as a function of the distance D between the scattering substrate and the focus. The plots correspond to different configurations of the scattering substrate as shown on the top of the figure. Numerical simulations (bottom) refer to the same scattering substrate configurations as the measurements. The substrate is covered by 6 µm silica beads.
Fig. 8
Fig. 8 a) Graph of the local coverage fraction, cov, of the optical beams (illumination and fluorescence) by the beads, corresponding to the configurations of Fig. 7; b) Graph of the quantity (1-q × cov)2, where q is the Mie scattering efficiency (see below, Fig. 10): this quantity correlates with the attenuation of the count rate displayed in Fig. 7.
Fig. 9
Fig. 9 Molecular Detection Function calculated using our numerical model. a) Without scattering beads, water immersion objective / NA = 1.2, λ0 = 0.56 µm. b) With an aberrating phase object placed at distance corresponding to 12 µm from the focus. The phase distribution of the scattering object is represented below.
Fig. 10
Fig. 10 Mie theory calculations of the total and differential scattering cross section. a) Scattering efficiency of light, q, by a spherical dielectric particle as a function of the phase delay Δϕ. Three plots are superimposed corresponding to the variation of Δϕ induced by the variation of one of the three parameters rbead (particle radius), Δn (refractive index contrast between the particle and the surrounding medium) and λ0 (wavelength of light in vacuum). When one of these three parameters is varied, the others stay at the reference values. The two green dots correspond to two particles of same diameter (6.12 µm), but different refractive indices at λ0 = 0.56 µm, 1.3625 for the model material and 1.458 for silica, such that they have the same scattering efficiency, q = 1.94. Their respective phase delays are 0.71π and 2.8π. b) Plots of the differential cross section vs the deflection angle for these two particles, averaged over polarizations and weighted by the sine of the scattering angle.

Tables (1)

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Table 1 Correlation of the Mie scattering efficiency and coverage fraction with asymptotic count rate

Equations (9)

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A(x,y,L)= 1 x 2 + y 2 + L 2 exp[ ik x 2 + y 2 + L 2 ] for θ   θ max
A(x,y,L)=0 for θ >  θ max
A em ( x 0 , y 0 , z 0 ;x,y,z )= 1 ( x x 0 ) 2 + ( y y 0 ) 2 + ( z+ z 0 ) 2 ×exp[ ik ( x x 0 ) 2 + ( y y 0 ) 2 + ( z+ z 0 ) 2 ]
T coll ( x,y )=exp[ 2ik x 2 + y 2 +  L 2 ]
I fluo ( x 0 , y 0 , z 0 ; x , y ,z' ) I ill ( x 0 + x , y 0 + y , z 0 +z' )
MDF( x 0 , y 0 , z 0 )  I ill ( x 0 , y 0 , z 0 ) 0 r pin I ill ( x 0 + x , y 0 + y ,z )dx'dy'
 CR  MDF( x 0 , y 0 , z 0 )d x 0 d y 0 d z 0
 N [ MDF( x 0 , y 0 , z 0 )d x 0 d y 0 d z 0 ] 2 /MD F 2 ( x 0 , y 0 , z 0 )d x 0 d y 0 d z 0
  ( CR C R 0 ) D   ( 1q×cov ) 2

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