Abstract

We present a new method called optical coherence correlation spectroscopy (OCCS) using nanoparticles as reporters of kinetic processes at the single particle level. OCCS is a spectral interferometry based method, thus giving simultaneous access to several sampling volumes along the optical axis. Based on an auto-correlation analysis, we extract the diffusion coefficients and concentrations of nanoparticles over a large concentration range. The cross-correlation analysis between adjacent sampling volumes allows to measure flow parameters. This shows the potential of OCCS for spatially resolved diffusion and flow measurements.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Magde, E. Elson, W. Webb, “Thermodynamic fluctuations in a reacting system measurement by fluorescence correlation spectroscopy,” Phys. Rev. Lett. 29, 705–708 (1972).
    [CrossRef]
  2. R. Rigler, E. Elson, Fluorescence Correlation Spectroscopy: Theory and Applications (Springer, 2001).
    [CrossRef]
  3. K. Hassler, P. Rigler, H. Blom, R. Rigler, J. Widengren, T. Lasser, “Dynamic disorder in horseradish peroxidase observed with total internal reflection fluorescence correlation spectroscopy,” Opt. Express 15, 5366–5375 (2007).
    [CrossRef] [PubMed]
  4. P. Schwille, U. Haupts, S. Maiti, W. Webb, “Molecular dynamics in living cells observed by fluorescence correlation spectroscopy with one- and two-photon excitation,” Biophys. J. 77, 2251–2265 (1999).
    [CrossRef] [PubMed]
  5. D. Schaeffel, R. Staff, H.-J. Butt, K. Landfester, D. Crespy, K. Koynov, “Fluorescence correlation spectroscopy directly monitors coalescence during nanoparticle preparation,” Nano Lett. 12, 6012–6017 (2012).
    [CrossRef] [PubMed]
  6. K. Jaskiewicz, A. Larsen, D. Schaeffel, K. Koynov, I. Lieberwirth, G. Fytas, K. Landfester, A. Kroeger, “Incorporation of nanoparticles into polymersomes: Size and concentration effects,” ACS Nano 6, 7254–7262 (2012).
    [CrossRef] [PubMed]
  7. P. Dittrich, P. Schwille, “Spatial two-photon fluorescence cross-correlation spectroscopy for controlling molecular transport in microfluidic structures,” Anal. Chem. 74, 4472–4479 (2002).
    [CrossRef] [PubMed]
  8. W. Schrof, J. Klingler, S. Rozouvan, D. Horn, “Raman correlation spectroscopy: A method for studying chemical composition and dynamics of disperse systems,” Phys. Rev. E. 57, R2523–R2526 (1998).
    [CrossRef]
  9. T. Hellerer, A. Schiller, G. Jung, A. Zumbusch, “Coherent anti-stokes raman scattering (cars) correlation spectroscopy,” Chem. Phys. Chem. 3, 630–633 (2002).
    [CrossRef] [PubMed]
  10. J. Cheng, E. Potma, S. Xie, “Coherent anti-stokes raman scattering correlation spectroscopy: Probing dynamical processes with chemical selectivity,” J. Phys. Chem. A 106, 8561–8568 (2002).
    [CrossRef]
  11. M. Geissbuehler, L. Bonacina, V. Shcheslavskiy, N. Bocchio, S. Geissbuehler, M. Leutenegger, I. Maerki, J. Wolf, T. Lasser, “Nonlinear correlation spectroscopy (nlcs),” Nano Lett. 12, 1668–1672 (2012).
    [CrossRef] [PubMed]
  12. T. Liedl, S. Keller, F. Simmel, J. Radler, W. Parak, “Fluorescent nanocrystals as colloidal probes in complex fluids measured by fluorescence correlation spectroscopy,” Small 1, 997–1003 (2005).
    [CrossRef]
  13. V. Octeau, L. Cognet, L. Duchesne, D. Lasne, N. Schaeffer, D. Fernig, B. Lounis, “Photothermal absorption correlation spectroscopy,” ACS Nano 3, 345–350 (2009).
    [CrossRef] [PubMed]
  14. P. Paulo, A. Gaiduk, F. Kulzer, S. Gabby Krens, H. Spaink, T. Schmidt, M. Orrit, “Photothermal correlation spectroscopy of gold nanoparticles in solution,” J. Phys. Chem. C 113, 11451–11457 (2009).
    [CrossRef]
  15. J. Yguerabide, E. Yguerabide, “Light-scattering submicroscopic particles as highly fluorescent analogs and their use as tracer labels in clinical and biological applications i. theory,” Anal. Biochem. 262, 137–156 (1998).
    [CrossRef] [PubMed]
  16. B. Berne, R. Pecora, Dynamic Light Scattering with Applications to Chemistry, Biology and Physics (John Wiley and Sons, New-York, 1976).
  17. D. Boas, K. Bizheva, A. Siegel, “Using dynamic low-coherence interferometry to image brownian motion within highly scattering media,” Opt. Lett. 23, 319–321 (1998).
    [CrossRef]
  18. S. Dominguez-Medina, S. McDonough, P. Swanglap, C. Landes, S. Link, “In situ measurement of bovine serum albumin interaction with gold nanospheres,” Langmuir 28, 9131–9139 (2012).
    [CrossRef] [PubMed]
  19. S. Wennmalm, J. Widengren, “Interferometry and fluorescence detection for simultaneous analysis of labeled and unlabeled nanoparticles in solution,” J. Am. Chem. Soc. 134, 19516–19519 (2012).
    [CrossRef] [PubMed]
  20. J. Chen, J. Irudayaraj, “Quantitative investigation of compartmentalized dynamics of erbb2 targeting gold nanorods in live cells by single molecule spectroscopy,” ACS Nano 3, 4071–4079 (2009).
    [CrossRef] [PubMed]
  21. M. Digman, C. Brown, P. Sengupta, P. Wiseman, A. Horwitz, E. Gratton, “Measuring fast dynamics in solutions and cells with a laser scanning microscope,” Biophys. J. 89, 1317–1327 (2005).
    [CrossRef] [PubMed]
  22. M. Brinkmeier, K. Doerre, J. Stephan, M. Eigen, “Two-beam cross-correlation: A method to characterize transport phenomena in micrometer-sized structures,” Anal. Chem. 71, 609–616 (1999).
    [CrossRef] [PubMed]
  23. M. Gosch, H. Blom, S. Anderegg, K. Korn, P. Thyberg, M. Wells, T. Lasser, R. Rigler, A. Magnusson, S. Hard, “Parallel dual-color fluorescence cross-correlation spectroscopy using diffractive optical elements,” J. Biomed. Opt. 10, 054008 (2005).
    [CrossRef] [PubMed]
  24. T. Dertinger, V. Pacheco, I. Von Der Hocht, R. Hartmann, I. Gregor, J. Enderlein, “Two-focus fluorescence correlation spectroscopy: A new tool for accurate and absolute diffusion measurements,” Chem. Phys. Chem. 8, 433–443 (2007).
    [CrossRef] [PubMed]
  25. J. Izatt, M. Choma, Optical Coherence Tomography: Technology and Applications (Springer Verlag, Berlin, 2008).
  26. P. Schwille, “Fluorescence correlation spectroscopy and its potential for intracellular applications,” Cell Biochem. Biophys. 34, 383–408 (2001).
    [CrossRef]
  27. M. Leutenegger, C. Ringemann, T. Lasser, S. Hell, C. Eggeling, “Fluorescence correlation spectroscopy with a total internal reflection fluorescence sted microscope (tirf-sted-fcs),” Opt. Express 20, 5243–5263 (2012).
    [CrossRef] [PubMed]
  28. T. Wohland, R. Rigler, H. Vogel, “The standard deviation in fluorescence correlation spectroscopy,” Biophys. J. 80, 2987–2999 (2001).
    [CrossRef] [PubMed]
  29. J. Kalkman, R. Sprik, T. Van Leeuwen, “Path-length-resolved diffusive particle dynamics in spectral-domain optical coherence tomography,” Phys. Rev. Lett. 105, 198302 (2010).
    [CrossRef]
  30. R. A. Leitgeb, M. Villiger, A. H. Bachmann, L. Steinmann, T. Lasser, “Extended focus depth for fourier domain optical coherence microscopy,” Opt. Lett. 31, 2450–2452 (2006).
    [CrossRef] [PubMed]
  31. M. Villiger, C. Pache, T. Lasser, “Dark-field optical coherence microscopy,” Opt. Lett. 35, 3489–3491 (2010).
    [CrossRef] [PubMed]
  32. C. Pache, N. Bocchio, A. Bouwens, M. Villiger, C. Berclaz, J. Goulley, M. Gibson, C. Santschi, T. Lasser, “Fast three-dimensional imaging of gold nanoparticles in living cells with photothermal optical lock-in optical coherence microscopy,” Opt. Express 20, 21385–21399 (2012).
    [CrossRef] [PubMed]
  33. M. Villiger, T. Lasser, “Image formation and tomogram reconstruction in optical coherence microscopy,” J. Opt. Soc. Am. A 27, 2216–2228 (2010).
    [CrossRef]
  34. M. Leutenegger, R. Rao, R. Leitgeb, T. Lasser, “Fast focus field calculations,” Opt. Express 14, 11277–11291 (2006).
    [CrossRef] [PubMed]
  35. M. A. van Dijk, A. L. Tchebotareva, M. Orrit, M. Lippitz, S. Berciaud, D. Lasne, L. Cognet, B. Lounis, “Absorption and scattering microscopy of single metal nanoparticles,” Phys. Chem. Chem. Phys. 8, 3486–3495 (2006).
    [CrossRef] [PubMed]
  36. A. Tcherniak, J. Ha, S. Dominguez-Medina, L. Slaughter, S. Link, “Probing a century old prediction one plasmonic particle at a time,” Nano Lett. 10, 1398–1404 (2010).
    [CrossRef] [PubMed]
  37. N. Cheng, “Formula for the viscosity of a glycerol-water mixture,” Ind. Eng. Chem. Res. 47, 3285–3288 (2008).
    [CrossRef]
  38. S. Hess, W. Webb, “Focal volume optics and experimental artifacts in confocal fluorescence correlation spectroscopy,” Biophys. J. 83, 2300–2317 (2002).
    [CrossRef] [PubMed]
  39. D. Koppel, “Statistical accuracy in fluorescence correlation spectroscopy,” Phys. Rev. A 10, 1938–1945 (1974).
    [CrossRef]
  40. W. Wright, G. Sonek, M. Berns, “Parametric study of the forces on microspheres held by optical tweezers,” Appl. Opt. 33, 1735–1748 (1994).
    [CrossRef] [PubMed]
  41. M. Dienerowitz, M. Mazilu, K. Dholakia, “Optical manipulation of nanoparticles: A review,” J. Nanophotonics 2, 021875 (2008).
    [CrossRef]
  42. W. Singer, M. Totzeck, H. Gross, Handbook of Optical Systems: Vol. 2 Physical Image Formation (Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2005).
  43. S. Broillet, A. Sato, S. Geissbuehler, C. Pache, A. Bouwens, T. Lasser, M. Leutenegger, “Matlab OCCS Experiment,” http://lob.epfl.ch/page-103066.html .

2012 (7)

D. Schaeffel, R. Staff, H.-J. Butt, K. Landfester, D. Crespy, K. Koynov, “Fluorescence correlation spectroscopy directly monitors coalescence during nanoparticle preparation,” Nano Lett. 12, 6012–6017 (2012).
[CrossRef] [PubMed]

K. Jaskiewicz, A. Larsen, D. Schaeffel, K. Koynov, I. Lieberwirth, G. Fytas, K. Landfester, A. Kroeger, “Incorporation of nanoparticles into polymersomes: Size and concentration effects,” ACS Nano 6, 7254–7262 (2012).
[CrossRef] [PubMed]

M. Geissbuehler, L. Bonacina, V. Shcheslavskiy, N. Bocchio, S. Geissbuehler, M. Leutenegger, I. Maerki, J. Wolf, T. Lasser, “Nonlinear correlation spectroscopy (nlcs),” Nano Lett. 12, 1668–1672 (2012).
[CrossRef] [PubMed]

S. Dominguez-Medina, S. McDonough, P. Swanglap, C. Landes, S. Link, “In situ measurement of bovine serum albumin interaction with gold nanospheres,” Langmuir 28, 9131–9139 (2012).
[CrossRef] [PubMed]

S. Wennmalm, J. Widengren, “Interferometry and fluorescence detection for simultaneous analysis of labeled and unlabeled nanoparticles in solution,” J. Am. Chem. Soc. 134, 19516–19519 (2012).
[CrossRef] [PubMed]

M. Leutenegger, C. Ringemann, T. Lasser, S. Hell, C. Eggeling, “Fluorescence correlation spectroscopy with a total internal reflection fluorescence sted microscope (tirf-sted-fcs),” Opt. Express 20, 5243–5263 (2012).
[CrossRef] [PubMed]

C. Pache, N. Bocchio, A. Bouwens, M. Villiger, C. Berclaz, J. Goulley, M. Gibson, C. Santschi, T. Lasser, “Fast three-dimensional imaging of gold nanoparticles in living cells with photothermal optical lock-in optical coherence microscopy,” Opt. Express 20, 21385–21399 (2012).
[CrossRef] [PubMed]

2010 (4)

J. Kalkman, R. Sprik, T. Van Leeuwen, “Path-length-resolved diffusive particle dynamics in spectral-domain optical coherence tomography,” Phys. Rev. Lett. 105, 198302 (2010).
[CrossRef]

A. Tcherniak, J. Ha, S. Dominguez-Medina, L. Slaughter, S. Link, “Probing a century old prediction one plasmonic particle at a time,” Nano Lett. 10, 1398–1404 (2010).
[CrossRef] [PubMed]

M. Villiger, T. Lasser, “Image formation and tomogram reconstruction in optical coherence microscopy,” J. Opt. Soc. Am. A 27, 2216–2228 (2010).
[CrossRef]

M. Villiger, C. Pache, T. Lasser, “Dark-field optical coherence microscopy,” Opt. Lett. 35, 3489–3491 (2010).
[CrossRef] [PubMed]

2009 (3)

J. Chen, J. Irudayaraj, “Quantitative investigation of compartmentalized dynamics of erbb2 targeting gold nanorods in live cells by single molecule spectroscopy,” ACS Nano 3, 4071–4079 (2009).
[CrossRef] [PubMed]

V. Octeau, L. Cognet, L. Duchesne, D. Lasne, N. Schaeffer, D. Fernig, B. Lounis, “Photothermal absorption correlation spectroscopy,” ACS Nano 3, 345–350 (2009).
[CrossRef] [PubMed]

P. Paulo, A. Gaiduk, F. Kulzer, S. Gabby Krens, H. Spaink, T. Schmidt, M. Orrit, “Photothermal correlation spectroscopy of gold nanoparticles in solution,” J. Phys. Chem. C 113, 11451–11457 (2009).
[CrossRef]

2008 (2)

M. Dienerowitz, M. Mazilu, K. Dholakia, “Optical manipulation of nanoparticles: A review,” J. Nanophotonics 2, 021875 (2008).
[CrossRef]

N. Cheng, “Formula for the viscosity of a glycerol-water mixture,” Ind. Eng. Chem. Res. 47, 3285–3288 (2008).
[CrossRef]

2007 (2)

T. Dertinger, V. Pacheco, I. Von Der Hocht, R. Hartmann, I. Gregor, J. Enderlein, “Two-focus fluorescence correlation spectroscopy: A new tool for accurate and absolute diffusion measurements,” Chem. Phys. Chem. 8, 433–443 (2007).
[CrossRef] [PubMed]

K. Hassler, P. Rigler, H. Blom, R. Rigler, J. Widengren, T. Lasser, “Dynamic disorder in horseradish peroxidase observed with total internal reflection fluorescence correlation spectroscopy,” Opt. Express 15, 5366–5375 (2007).
[CrossRef] [PubMed]

2006 (3)

2005 (3)

M. Gosch, H. Blom, S. Anderegg, K. Korn, P. Thyberg, M. Wells, T. Lasser, R. Rigler, A. Magnusson, S. Hard, “Parallel dual-color fluorescence cross-correlation spectroscopy using diffractive optical elements,” J. Biomed. Opt. 10, 054008 (2005).
[CrossRef] [PubMed]

M. Digman, C. Brown, P. Sengupta, P. Wiseman, A. Horwitz, E. Gratton, “Measuring fast dynamics in solutions and cells with a laser scanning microscope,” Biophys. J. 89, 1317–1327 (2005).
[CrossRef] [PubMed]

T. Liedl, S. Keller, F. Simmel, J. Radler, W. Parak, “Fluorescent nanocrystals as colloidal probes in complex fluids measured by fluorescence correlation spectroscopy,” Small 1, 997–1003 (2005).
[CrossRef]

2002 (4)

T. Hellerer, A. Schiller, G. Jung, A. Zumbusch, “Coherent anti-stokes raman scattering (cars) correlation spectroscopy,” Chem. Phys. Chem. 3, 630–633 (2002).
[CrossRef] [PubMed]

J. Cheng, E. Potma, S. Xie, “Coherent anti-stokes raman scattering correlation spectroscopy: Probing dynamical processes with chemical selectivity,” J. Phys. Chem. A 106, 8561–8568 (2002).
[CrossRef]

P. Dittrich, P. Schwille, “Spatial two-photon fluorescence cross-correlation spectroscopy for controlling molecular transport in microfluidic structures,” Anal. Chem. 74, 4472–4479 (2002).
[CrossRef] [PubMed]

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

2001 (2)

P. Schwille, “Fluorescence correlation spectroscopy and its potential for intracellular applications,” Cell Biochem. Biophys. 34, 383–408 (2001).
[CrossRef]

T. Wohland, R. Rigler, H. Vogel, “The standard deviation in fluorescence correlation spectroscopy,” Biophys. J. 80, 2987–2999 (2001).
[CrossRef] [PubMed]

1999 (2)

M. Brinkmeier, K. Doerre, J. Stephan, M. Eigen, “Two-beam cross-correlation: A method to characterize transport phenomena in micrometer-sized structures,” Anal. Chem. 71, 609–616 (1999).
[CrossRef] [PubMed]

P. Schwille, U. Haupts, S. Maiti, W. Webb, “Molecular dynamics in living cells observed by fluorescence correlation spectroscopy with one- and two-photon excitation,” Biophys. J. 77, 2251–2265 (1999).
[CrossRef] [PubMed]

1998 (3)

J. Yguerabide, E. Yguerabide, “Light-scattering submicroscopic particles as highly fluorescent analogs and their use as tracer labels in clinical and biological applications i. theory,” Anal. Biochem. 262, 137–156 (1998).
[CrossRef] [PubMed]

W. Schrof, J. Klingler, S. Rozouvan, D. Horn, “Raman correlation spectroscopy: A method for studying chemical composition and dynamics of disperse systems,” Phys. Rev. E. 57, R2523–R2526 (1998).
[CrossRef]

D. Boas, K. Bizheva, A. Siegel, “Using dynamic low-coherence interferometry to image brownian motion within highly scattering media,” Opt. Lett. 23, 319–321 (1998).
[CrossRef]

1994 (1)

1974 (1)

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

1972 (1)

D. Magde, E. Elson, W. Webb, “Thermodynamic fluctuations in a reacting system measurement by fluorescence correlation spectroscopy,” Phys. Rev. Lett. 29, 705–708 (1972).
[CrossRef]

Anderegg, S.

M. Gosch, H. Blom, S. Anderegg, K. Korn, P. Thyberg, M. Wells, T. Lasser, R. Rigler, A. Magnusson, S. Hard, “Parallel dual-color fluorescence cross-correlation spectroscopy using diffractive optical elements,” J. Biomed. Opt. 10, 054008 (2005).
[CrossRef] [PubMed]

Bachmann, A. H.

Berciaud, S.

M. A. van Dijk, A. L. Tchebotareva, M. Orrit, M. Lippitz, S. Berciaud, D. Lasne, L. Cognet, B. Lounis, “Absorption and scattering microscopy of single metal nanoparticles,” Phys. Chem. Chem. Phys. 8, 3486–3495 (2006).
[CrossRef] [PubMed]

Berclaz, C.

Berne, B.

B. Berne, R. Pecora, Dynamic Light Scattering with Applications to Chemistry, Biology and Physics (John Wiley and Sons, New-York, 1976).

Berns, M.

Bizheva, K.

Blom, H.

K. Hassler, P. Rigler, H. Blom, R. Rigler, J. Widengren, T. Lasser, “Dynamic disorder in horseradish peroxidase observed with total internal reflection fluorescence correlation spectroscopy,” Opt. Express 15, 5366–5375 (2007).
[CrossRef] [PubMed]

M. Gosch, H. Blom, S. Anderegg, K. Korn, P. Thyberg, M. Wells, T. Lasser, R. Rigler, A. Magnusson, S. Hard, “Parallel dual-color fluorescence cross-correlation spectroscopy using diffractive optical elements,” J. Biomed. Opt. 10, 054008 (2005).
[CrossRef] [PubMed]

Boas, D.

Bocchio, N.

Bonacina, L.

M. Geissbuehler, L. Bonacina, V. Shcheslavskiy, N. Bocchio, S. Geissbuehler, M. Leutenegger, I. Maerki, J. Wolf, T. Lasser, “Nonlinear correlation spectroscopy (nlcs),” Nano Lett. 12, 1668–1672 (2012).
[CrossRef] [PubMed]

Bouwens, A.

Brinkmeier, M.

M. Brinkmeier, K. Doerre, J. Stephan, M. Eigen, “Two-beam cross-correlation: A method to characterize transport phenomena in micrometer-sized structures,” Anal. Chem. 71, 609–616 (1999).
[CrossRef] [PubMed]

Brown, C.

M. Digman, C. Brown, P. Sengupta, P. Wiseman, A. Horwitz, E. Gratton, “Measuring fast dynamics in solutions and cells with a laser scanning microscope,” Biophys. J. 89, 1317–1327 (2005).
[CrossRef] [PubMed]

Butt, H.-J.

D. Schaeffel, R. Staff, H.-J. Butt, K. Landfester, D. Crespy, K. Koynov, “Fluorescence correlation spectroscopy directly monitors coalescence during nanoparticle preparation,” Nano Lett. 12, 6012–6017 (2012).
[CrossRef] [PubMed]

Chen, J.

J. Chen, J. Irudayaraj, “Quantitative investigation of compartmentalized dynamics of erbb2 targeting gold nanorods in live cells by single molecule spectroscopy,” ACS Nano 3, 4071–4079 (2009).
[CrossRef] [PubMed]

Cheng, J.

J. Cheng, E. Potma, S. Xie, “Coherent anti-stokes raman scattering correlation spectroscopy: Probing dynamical processes with chemical selectivity,” J. Phys. Chem. A 106, 8561–8568 (2002).
[CrossRef]

Cheng, N.

N. Cheng, “Formula for the viscosity of a glycerol-water mixture,” Ind. Eng. Chem. Res. 47, 3285–3288 (2008).
[CrossRef]

Choma, M.

J. Izatt, M. Choma, Optical Coherence Tomography: Technology and Applications (Springer Verlag, Berlin, 2008).

Cognet, L.

V. Octeau, L. Cognet, L. Duchesne, D. Lasne, N. Schaeffer, D. Fernig, B. Lounis, “Photothermal absorption correlation spectroscopy,” ACS Nano 3, 345–350 (2009).
[CrossRef] [PubMed]

M. A. van Dijk, A. L. Tchebotareva, M. Orrit, M. Lippitz, S. Berciaud, D. Lasne, L. Cognet, B. Lounis, “Absorption and scattering microscopy of single metal nanoparticles,” Phys. Chem. Chem. Phys. 8, 3486–3495 (2006).
[CrossRef] [PubMed]

Crespy, D.

D. Schaeffel, R. Staff, H.-J. Butt, K. Landfester, D. Crespy, K. Koynov, “Fluorescence correlation spectroscopy directly monitors coalescence during nanoparticle preparation,” Nano Lett. 12, 6012–6017 (2012).
[CrossRef] [PubMed]

Dertinger, T.

T. Dertinger, V. Pacheco, I. Von Der Hocht, R. Hartmann, I. Gregor, J. Enderlein, “Two-focus fluorescence correlation spectroscopy: A new tool for accurate and absolute diffusion measurements,” Chem. Phys. Chem. 8, 433–443 (2007).
[CrossRef] [PubMed]

Dholakia, K.

M. Dienerowitz, M. Mazilu, K. Dholakia, “Optical manipulation of nanoparticles: A review,” J. Nanophotonics 2, 021875 (2008).
[CrossRef]

Dienerowitz, M.

M. Dienerowitz, M. Mazilu, K. Dholakia, “Optical manipulation of nanoparticles: A review,” J. Nanophotonics 2, 021875 (2008).
[CrossRef]

Digman, M.

M. Digman, C. Brown, P. Sengupta, P. Wiseman, A. Horwitz, E. Gratton, “Measuring fast dynamics in solutions and cells with a laser scanning microscope,” Biophys. J. 89, 1317–1327 (2005).
[CrossRef] [PubMed]

Dittrich, P.

P. Dittrich, P. Schwille, “Spatial two-photon fluorescence cross-correlation spectroscopy for controlling molecular transport in microfluidic structures,” Anal. Chem. 74, 4472–4479 (2002).
[CrossRef] [PubMed]

Doerre, K.

M. Brinkmeier, K. Doerre, J. Stephan, M. Eigen, “Two-beam cross-correlation: A method to characterize transport phenomena in micrometer-sized structures,” Anal. Chem. 71, 609–616 (1999).
[CrossRef] [PubMed]

Dominguez-Medina, S.

S. Dominguez-Medina, S. McDonough, P. Swanglap, C. Landes, S. Link, “In situ measurement of bovine serum albumin interaction with gold nanospheres,” Langmuir 28, 9131–9139 (2012).
[CrossRef] [PubMed]

A. Tcherniak, J. Ha, S. Dominguez-Medina, L. Slaughter, S. Link, “Probing a century old prediction one plasmonic particle at a time,” Nano Lett. 10, 1398–1404 (2010).
[CrossRef] [PubMed]

Duchesne, L.

V. Octeau, L. Cognet, L. Duchesne, D. Lasne, N. Schaeffer, D. Fernig, B. Lounis, “Photothermal absorption correlation spectroscopy,” ACS Nano 3, 345–350 (2009).
[CrossRef] [PubMed]

Eggeling, C.

Eigen, M.

M. Brinkmeier, K. Doerre, J. Stephan, M. Eigen, “Two-beam cross-correlation: A method to characterize transport phenomena in micrometer-sized structures,” Anal. Chem. 71, 609–616 (1999).
[CrossRef] [PubMed]

Elson, E.

D. Magde, E. Elson, W. Webb, “Thermodynamic fluctuations in a reacting system measurement by fluorescence correlation spectroscopy,” Phys. Rev. Lett. 29, 705–708 (1972).
[CrossRef]

R. Rigler, E. Elson, Fluorescence Correlation Spectroscopy: Theory and Applications (Springer, 2001).
[CrossRef]

Enderlein, J.

T. Dertinger, V. Pacheco, I. Von Der Hocht, R. Hartmann, I. Gregor, J. Enderlein, “Two-focus fluorescence correlation spectroscopy: A new tool for accurate and absolute diffusion measurements,” Chem. Phys. Chem. 8, 433–443 (2007).
[CrossRef] [PubMed]

Fernig, D.

V. Octeau, L. Cognet, L. Duchesne, D. Lasne, N. Schaeffer, D. Fernig, B. Lounis, “Photothermal absorption correlation spectroscopy,” ACS Nano 3, 345–350 (2009).
[CrossRef] [PubMed]

Fytas, G.

K. Jaskiewicz, A. Larsen, D. Schaeffel, K. Koynov, I. Lieberwirth, G. Fytas, K. Landfester, A. Kroeger, “Incorporation of nanoparticles into polymersomes: Size and concentration effects,” ACS Nano 6, 7254–7262 (2012).
[CrossRef] [PubMed]

Gabby Krens, S.

P. Paulo, A. Gaiduk, F. Kulzer, S. Gabby Krens, H. Spaink, T. Schmidt, M. Orrit, “Photothermal correlation spectroscopy of gold nanoparticles in solution,” J. Phys. Chem. C 113, 11451–11457 (2009).
[CrossRef]

Gaiduk, A.

P. Paulo, A. Gaiduk, F. Kulzer, S. Gabby Krens, H. Spaink, T. Schmidt, M. Orrit, “Photothermal correlation spectroscopy of gold nanoparticles in solution,” J. Phys. Chem. C 113, 11451–11457 (2009).
[CrossRef]

Geissbuehler, M.

M. Geissbuehler, L. Bonacina, V. Shcheslavskiy, N. Bocchio, S. Geissbuehler, M. Leutenegger, I. Maerki, J. Wolf, T. Lasser, “Nonlinear correlation spectroscopy (nlcs),” Nano Lett. 12, 1668–1672 (2012).
[CrossRef] [PubMed]

Geissbuehler, S.

M. Geissbuehler, L. Bonacina, V. Shcheslavskiy, N. Bocchio, S. Geissbuehler, M. Leutenegger, I. Maerki, J. Wolf, T. Lasser, “Nonlinear correlation spectroscopy (nlcs),” Nano Lett. 12, 1668–1672 (2012).
[CrossRef] [PubMed]

Gibson, M.

Gosch, M.

M. Gosch, H. Blom, S. Anderegg, K. Korn, P. Thyberg, M. Wells, T. Lasser, R. Rigler, A. Magnusson, S. Hard, “Parallel dual-color fluorescence cross-correlation spectroscopy using diffractive optical elements,” J. Biomed. Opt. 10, 054008 (2005).
[CrossRef] [PubMed]

Goulley, J.

Gratton, E.

M. Digman, C. Brown, P. Sengupta, P. Wiseman, A. Horwitz, E. Gratton, “Measuring fast dynamics in solutions and cells with a laser scanning microscope,” Biophys. J. 89, 1317–1327 (2005).
[CrossRef] [PubMed]

Gregor, I.

T. Dertinger, V. Pacheco, I. Von Der Hocht, R. Hartmann, I. Gregor, J. Enderlein, “Two-focus fluorescence correlation spectroscopy: A new tool for accurate and absolute diffusion measurements,” Chem. Phys. Chem. 8, 433–443 (2007).
[CrossRef] [PubMed]

Gross, H.

W. Singer, M. Totzeck, H. Gross, Handbook of Optical Systems: Vol. 2 Physical Image Formation (Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2005).

Ha, J.

A. Tcherniak, J. Ha, S. Dominguez-Medina, L. Slaughter, S. Link, “Probing a century old prediction one plasmonic particle at a time,” Nano Lett. 10, 1398–1404 (2010).
[CrossRef] [PubMed]

Hard, S.

M. Gosch, H. Blom, S. Anderegg, K. Korn, P. Thyberg, M. Wells, T. Lasser, R. Rigler, A. Magnusson, S. Hard, “Parallel dual-color fluorescence cross-correlation spectroscopy using diffractive optical elements,” J. Biomed. Opt. 10, 054008 (2005).
[CrossRef] [PubMed]

Hartmann, R.

T. Dertinger, V. Pacheco, I. Von Der Hocht, R. Hartmann, I. Gregor, J. Enderlein, “Two-focus fluorescence correlation spectroscopy: A new tool for accurate and absolute diffusion measurements,” Chem. Phys. Chem. 8, 433–443 (2007).
[CrossRef] [PubMed]

Hassler, K.

Haupts, U.

P. Schwille, U. Haupts, S. Maiti, W. Webb, “Molecular dynamics in living cells observed by fluorescence correlation spectroscopy with one- and two-photon excitation,” Biophys. J. 77, 2251–2265 (1999).
[CrossRef] [PubMed]

Hell, S.

Hellerer, T.

T. Hellerer, A. Schiller, G. Jung, A. Zumbusch, “Coherent anti-stokes raman scattering (cars) correlation spectroscopy,” Chem. Phys. Chem. 3, 630–633 (2002).
[CrossRef] [PubMed]

Hess, S.

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

Horn, D.

W. Schrof, J. Klingler, S. Rozouvan, D. Horn, “Raman correlation spectroscopy: A method for studying chemical composition and dynamics of disperse systems,” Phys. Rev. E. 57, R2523–R2526 (1998).
[CrossRef]

Horwitz, A.

M. Digman, C. Brown, P. Sengupta, P. Wiseman, A. Horwitz, E. Gratton, “Measuring fast dynamics in solutions and cells with a laser scanning microscope,” Biophys. J. 89, 1317–1327 (2005).
[CrossRef] [PubMed]

Irudayaraj, J.

J. Chen, J. Irudayaraj, “Quantitative investigation of compartmentalized dynamics of erbb2 targeting gold nanorods in live cells by single molecule spectroscopy,” ACS Nano 3, 4071–4079 (2009).
[CrossRef] [PubMed]

Izatt, J.

J. Izatt, M. Choma, Optical Coherence Tomography: Technology and Applications (Springer Verlag, Berlin, 2008).

Jaskiewicz, K.

K. Jaskiewicz, A. Larsen, D. Schaeffel, K. Koynov, I. Lieberwirth, G. Fytas, K. Landfester, A. Kroeger, “Incorporation of nanoparticles into polymersomes: Size and concentration effects,” ACS Nano 6, 7254–7262 (2012).
[CrossRef] [PubMed]

Jung, G.

T. Hellerer, A. Schiller, G. Jung, A. Zumbusch, “Coherent anti-stokes raman scattering (cars) correlation spectroscopy,” Chem. Phys. Chem. 3, 630–633 (2002).
[CrossRef] [PubMed]

Kalkman, J.

J. Kalkman, R. Sprik, T. Van Leeuwen, “Path-length-resolved diffusive particle dynamics in spectral-domain optical coherence tomography,” Phys. Rev. Lett. 105, 198302 (2010).
[CrossRef]

Keller, S.

T. Liedl, S. Keller, F. Simmel, J. Radler, W. Parak, “Fluorescent nanocrystals as colloidal probes in complex fluids measured by fluorescence correlation spectroscopy,” Small 1, 997–1003 (2005).
[CrossRef]

Klingler, J.

W. Schrof, J. Klingler, S. Rozouvan, D. Horn, “Raman correlation spectroscopy: A method for studying chemical composition and dynamics of disperse systems,” Phys. Rev. E. 57, R2523–R2526 (1998).
[CrossRef]

Koppel, D.

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

Korn, K.

M. Gosch, H. Blom, S. Anderegg, K. Korn, P. Thyberg, M. Wells, T. Lasser, R. Rigler, A. Magnusson, S. Hard, “Parallel dual-color fluorescence cross-correlation spectroscopy using diffractive optical elements,” J. Biomed. Opt. 10, 054008 (2005).
[CrossRef] [PubMed]

Koynov, K.

K. Jaskiewicz, A. Larsen, D. Schaeffel, K. Koynov, I. Lieberwirth, G. Fytas, K. Landfester, A. Kroeger, “Incorporation of nanoparticles into polymersomes: Size and concentration effects,” ACS Nano 6, 7254–7262 (2012).
[CrossRef] [PubMed]

D. Schaeffel, R. Staff, H.-J. Butt, K. Landfester, D. Crespy, K. Koynov, “Fluorescence correlation spectroscopy directly monitors coalescence during nanoparticle preparation,” Nano Lett. 12, 6012–6017 (2012).
[CrossRef] [PubMed]

Kroeger, A.

K. Jaskiewicz, A. Larsen, D. Schaeffel, K. Koynov, I. Lieberwirth, G. Fytas, K. Landfester, A. Kroeger, “Incorporation of nanoparticles into polymersomes: Size and concentration effects,” ACS Nano 6, 7254–7262 (2012).
[CrossRef] [PubMed]

Kulzer, F.

P. Paulo, A. Gaiduk, F. Kulzer, S. Gabby Krens, H. Spaink, T. Schmidt, M. Orrit, “Photothermal correlation spectroscopy of gold nanoparticles in solution,” J. Phys. Chem. C 113, 11451–11457 (2009).
[CrossRef]

Landes, C.

S. Dominguez-Medina, S. McDonough, P. Swanglap, C. Landes, S. Link, “In situ measurement of bovine serum albumin interaction with gold nanospheres,” Langmuir 28, 9131–9139 (2012).
[CrossRef] [PubMed]

Landfester, K.

K. Jaskiewicz, A. Larsen, D. Schaeffel, K. Koynov, I. Lieberwirth, G. Fytas, K. Landfester, A. Kroeger, “Incorporation of nanoparticles into polymersomes: Size and concentration effects,” ACS Nano 6, 7254–7262 (2012).
[CrossRef] [PubMed]

D. Schaeffel, R. Staff, H.-J. Butt, K. Landfester, D. Crespy, K. Koynov, “Fluorescence correlation spectroscopy directly monitors coalescence during nanoparticle preparation,” Nano Lett. 12, 6012–6017 (2012).
[CrossRef] [PubMed]

Larsen, A.

K. Jaskiewicz, A. Larsen, D. Schaeffel, K. Koynov, I. Lieberwirth, G. Fytas, K. Landfester, A. Kroeger, “Incorporation of nanoparticles into polymersomes: Size and concentration effects,” ACS Nano 6, 7254–7262 (2012).
[CrossRef] [PubMed]

Lasne, D.

V. Octeau, L. Cognet, L. Duchesne, D. Lasne, N. Schaeffer, D. Fernig, B. Lounis, “Photothermal absorption correlation spectroscopy,” ACS Nano 3, 345–350 (2009).
[CrossRef] [PubMed]

M. A. van Dijk, A. L. Tchebotareva, M. Orrit, M. Lippitz, S. Berciaud, D. Lasne, L. Cognet, B. Lounis, “Absorption and scattering microscopy of single metal nanoparticles,” Phys. Chem. Chem. Phys. 8, 3486–3495 (2006).
[CrossRef] [PubMed]

Lasser, T.

M. Geissbuehler, L. Bonacina, V. Shcheslavskiy, N. Bocchio, S. Geissbuehler, M. Leutenegger, I. Maerki, J. Wolf, T. Lasser, “Nonlinear correlation spectroscopy (nlcs),” Nano Lett. 12, 1668–1672 (2012).
[CrossRef] [PubMed]

M. Leutenegger, C. Ringemann, T. Lasser, S. Hell, C. Eggeling, “Fluorescence correlation spectroscopy with a total internal reflection fluorescence sted microscope (tirf-sted-fcs),” Opt. Express 20, 5243–5263 (2012).
[CrossRef] [PubMed]

C. Pache, N. Bocchio, A. Bouwens, M. Villiger, C. Berclaz, J. Goulley, M. Gibson, C. Santschi, T. Lasser, “Fast three-dimensional imaging of gold nanoparticles in living cells with photothermal optical lock-in optical coherence microscopy,” Opt. Express 20, 21385–21399 (2012).
[CrossRef] [PubMed]

M. Villiger, T. Lasser, “Image formation and tomogram reconstruction in optical coherence microscopy,” J. Opt. Soc. Am. A 27, 2216–2228 (2010).
[CrossRef]

M. Villiger, C. Pache, T. Lasser, “Dark-field optical coherence microscopy,” Opt. Lett. 35, 3489–3491 (2010).
[CrossRef] [PubMed]

K. Hassler, P. Rigler, H. Blom, R. Rigler, J. Widengren, T. Lasser, “Dynamic disorder in horseradish peroxidase observed with total internal reflection fluorescence correlation spectroscopy,” Opt. Express 15, 5366–5375 (2007).
[CrossRef] [PubMed]

M. Leutenegger, R. Rao, R. Leitgeb, T. Lasser, “Fast focus field calculations,” Opt. Express 14, 11277–11291 (2006).
[CrossRef] [PubMed]

R. A. Leitgeb, M. Villiger, A. H. Bachmann, L. Steinmann, T. Lasser, “Extended focus depth for fourier domain optical coherence microscopy,” Opt. Lett. 31, 2450–2452 (2006).
[CrossRef] [PubMed]

M. Gosch, H. Blom, S. Anderegg, K. Korn, P. Thyberg, M. Wells, T. Lasser, R. Rigler, A. Magnusson, S. Hard, “Parallel dual-color fluorescence cross-correlation spectroscopy using diffractive optical elements,” J. Biomed. Opt. 10, 054008 (2005).
[CrossRef] [PubMed]

Leitgeb, R.

Leitgeb, R. A.

Leutenegger, M.

Lieberwirth, I.

K. Jaskiewicz, A. Larsen, D. Schaeffel, K. Koynov, I. Lieberwirth, G. Fytas, K. Landfester, A. Kroeger, “Incorporation of nanoparticles into polymersomes: Size and concentration effects,” ACS Nano 6, 7254–7262 (2012).
[CrossRef] [PubMed]

Liedl, T.

T. Liedl, S. Keller, F. Simmel, J. Radler, W. Parak, “Fluorescent nanocrystals as colloidal probes in complex fluids measured by fluorescence correlation spectroscopy,” Small 1, 997–1003 (2005).
[CrossRef]

Link, S.

S. Dominguez-Medina, S. McDonough, P. Swanglap, C. Landes, S. Link, “In situ measurement of bovine serum albumin interaction with gold nanospheres,” Langmuir 28, 9131–9139 (2012).
[CrossRef] [PubMed]

A. Tcherniak, J. Ha, S. Dominguez-Medina, L. Slaughter, S. Link, “Probing a century old prediction one plasmonic particle at a time,” Nano Lett. 10, 1398–1404 (2010).
[CrossRef] [PubMed]

Lippitz, M.

M. A. van Dijk, A. L. Tchebotareva, M. Orrit, M. Lippitz, S. Berciaud, D. Lasne, L. Cognet, B. Lounis, “Absorption and scattering microscopy of single metal nanoparticles,” Phys. Chem. Chem. Phys. 8, 3486–3495 (2006).
[CrossRef] [PubMed]

Lounis, B.

V. Octeau, L. Cognet, L. Duchesne, D. Lasne, N. Schaeffer, D. Fernig, B. Lounis, “Photothermal absorption correlation spectroscopy,” ACS Nano 3, 345–350 (2009).
[CrossRef] [PubMed]

M. A. van Dijk, A. L. Tchebotareva, M. Orrit, M. Lippitz, S. Berciaud, D. Lasne, L. Cognet, B. Lounis, “Absorption and scattering microscopy of single metal nanoparticles,” Phys. Chem. Chem. Phys. 8, 3486–3495 (2006).
[CrossRef] [PubMed]

Maerki, I.

M. Geissbuehler, L. Bonacina, V. Shcheslavskiy, N. Bocchio, S. Geissbuehler, M. Leutenegger, I. Maerki, J. Wolf, T. Lasser, “Nonlinear correlation spectroscopy (nlcs),” Nano Lett. 12, 1668–1672 (2012).
[CrossRef] [PubMed]

Magde, D.

D. Magde, E. Elson, W. Webb, “Thermodynamic fluctuations in a reacting system measurement by fluorescence correlation spectroscopy,” Phys. Rev. Lett. 29, 705–708 (1972).
[CrossRef]

Magnusson, A.

M. Gosch, H. Blom, S. Anderegg, K. Korn, P. Thyberg, M. Wells, T. Lasser, R. Rigler, A. Magnusson, S. Hard, “Parallel dual-color fluorescence cross-correlation spectroscopy using diffractive optical elements,” J. Biomed. Opt. 10, 054008 (2005).
[CrossRef] [PubMed]

Maiti, S.

P. Schwille, U. Haupts, S. Maiti, W. Webb, “Molecular dynamics in living cells observed by fluorescence correlation spectroscopy with one- and two-photon excitation,” Biophys. J. 77, 2251–2265 (1999).
[CrossRef] [PubMed]

Mazilu, M.

M. Dienerowitz, M. Mazilu, K. Dholakia, “Optical manipulation of nanoparticles: A review,” J. Nanophotonics 2, 021875 (2008).
[CrossRef]

McDonough, S.

S. Dominguez-Medina, S. McDonough, P. Swanglap, C. Landes, S. Link, “In situ measurement of bovine serum albumin interaction with gold nanospheres,” Langmuir 28, 9131–9139 (2012).
[CrossRef] [PubMed]

Octeau, V.

V. Octeau, L. Cognet, L. Duchesne, D. Lasne, N. Schaeffer, D. Fernig, B. Lounis, “Photothermal absorption correlation spectroscopy,” ACS Nano 3, 345–350 (2009).
[CrossRef] [PubMed]

Orrit, M.

P. Paulo, A. Gaiduk, F. Kulzer, S. Gabby Krens, H. Spaink, T. Schmidt, M. Orrit, “Photothermal correlation spectroscopy of gold nanoparticles in solution,” J. Phys. Chem. C 113, 11451–11457 (2009).
[CrossRef]

M. A. van Dijk, A. L. Tchebotareva, M. Orrit, M. Lippitz, S. Berciaud, D. Lasne, L. Cognet, B. Lounis, “Absorption and scattering microscopy of single metal nanoparticles,” Phys. Chem. Chem. Phys. 8, 3486–3495 (2006).
[CrossRef] [PubMed]

Pache, C.

Pacheco, V.

T. Dertinger, V. Pacheco, I. Von Der Hocht, R. Hartmann, I. Gregor, J. Enderlein, “Two-focus fluorescence correlation spectroscopy: A new tool for accurate and absolute diffusion measurements,” Chem. Phys. Chem. 8, 433–443 (2007).
[CrossRef] [PubMed]

Parak, W.

T. Liedl, S. Keller, F. Simmel, J. Radler, W. Parak, “Fluorescent nanocrystals as colloidal probes in complex fluids measured by fluorescence correlation spectroscopy,” Small 1, 997–1003 (2005).
[CrossRef]

Paulo, P.

P. Paulo, A. Gaiduk, F. Kulzer, S. Gabby Krens, H. Spaink, T. Schmidt, M. Orrit, “Photothermal correlation spectroscopy of gold nanoparticles in solution,” J. Phys. Chem. C 113, 11451–11457 (2009).
[CrossRef]

Pecora, R.

B. Berne, R. Pecora, Dynamic Light Scattering with Applications to Chemistry, Biology and Physics (John Wiley and Sons, New-York, 1976).

Potma, E.

J. Cheng, E. Potma, S. Xie, “Coherent anti-stokes raman scattering correlation spectroscopy: Probing dynamical processes with chemical selectivity,” J. Phys. Chem. A 106, 8561–8568 (2002).
[CrossRef]

Radler, J.

T. Liedl, S. Keller, F. Simmel, J. Radler, W. Parak, “Fluorescent nanocrystals as colloidal probes in complex fluids measured by fluorescence correlation spectroscopy,” Small 1, 997–1003 (2005).
[CrossRef]

Rao, R.

Rigler, P.

Rigler, R.

K. Hassler, P. Rigler, H. Blom, R. Rigler, J. Widengren, T. Lasser, “Dynamic disorder in horseradish peroxidase observed with total internal reflection fluorescence correlation spectroscopy,” Opt. Express 15, 5366–5375 (2007).
[CrossRef] [PubMed]

M. Gosch, H. Blom, S. Anderegg, K. Korn, P. Thyberg, M. Wells, T. Lasser, R. Rigler, A. Magnusson, S. Hard, “Parallel dual-color fluorescence cross-correlation spectroscopy using diffractive optical elements,” J. Biomed. Opt. 10, 054008 (2005).
[CrossRef] [PubMed]

T. Wohland, R. Rigler, H. Vogel, “The standard deviation in fluorescence correlation spectroscopy,” Biophys. J. 80, 2987–2999 (2001).
[CrossRef] [PubMed]

R. Rigler, E. Elson, Fluorescence Correlation Spectroscopy: Theory and Applications (Springer, 2001).
[CrossRef]

Ringemann, C.

Rozouvan, S.

W. Schrof, J. Klingler, S. Rozouvan, D. Horn, “Raman correlation spectroscopy: A method for studying chemical composition and dynamics of disperse systems,” Phys. Rev. E. 57, R2523–R2526 (1998).
[CrossRef]

Santschi, C.

Schaeffel, D.

D. Schaeffel, R. Staff, H.-J. Butt, K. Landfester, D. Crespy, K. Koynov, “Fluorescence correlation spectroscopy directly monitors coalescence during nanoparticle preparation,” Nano Lett. 12, 6012–6017 (2012).
[CrossRef] [PubMed]

K. Jaskiewicz, A. Larsen, D. Schaeffel, K. Koynov, I. Lieberwirth, G. Fytas, K. Landfester, A. Kroeger, “Incorporation of nanoparticles into polymersomes: Size and concentration effects,” ACS Nano 6, 7254–7262 (2012).
[CrossRef] [PubMed]

Schaeffer, N.

V. Octeau, L. Cognet, L. Duchesne, D. Lasne, N. Schaeffer, D. Fernig, B. Lounis, “Photothermal absorption correlation spectroscopy,” ACS Nano 3, 345–350 (2009).
[CrossRef] [PubMed]

Schiller, A.

T. Hellerer, A. Schiller, G. Jung, A. Zumbusch, “Coherent anti-stokes raman scattering (cars) correlation spectroscopy,” Chem. Phys. Chem. 3, 630–633 (2002).
[CrossRef] [PubMed]

Schmidt, T.

P. Paulo, A. Gaiduk, F. Kulzer, S. Gabby Krens, H. Spaink, T. Schmidt, M. Orrit, “Photothermal correlation spectroscopy of gold nanoparticles in solution,” J. Phys. Chem. C 113, 11451–11457 (2009).
[CrossRef]

Schrof, W.

W. Schrof, J. Klingler, S. Rozouvan, D. Horn, “Raman correlation spectroscopy: A method for studying chemical composition and dynamics of disperse systems,” Phys. Rev. E. 57, R2523–R2526 (1998).
[CrossRef]

Schwille, P.

P. Dittrich, P. Schwille, “Spatial two-photon fluorescence cross-correlation spectroscopy for controlling molecular transport in microfluidic structures,” Anal. Chem. 74, 4472–4479 (2002).
[CrossRef] [PubMed]

P. Schwille, “Fluorescence correlation spectroscopy and its potential for intracellular applications,” Cell Biochem. Biophys. 34, 383–408 (2001).
[CrossRef]

P. Schwille, U. Haupts, S. Maiti, W. Webb, “Molecular dynamics in living cells observed by fluorescence correlation spectroscopy with one- and two-photon excitation,” Biophys. J. 77, 2251–2265 (1999).
[CrossRef] [PubMed]

Sengupta, P.

M. Digman, C. Brown, P. Sengupta, P. Wiseman, A. Horwitz, E. Gratton, “Measuring fast dynamics in solutions and cells with a laser scanning microscope,” Biophys. J. 89, 1317–1327 (2005).
[CrossRef] [PubMed]

Shcheslavskiy, V.

M. Geissbuehler, L. Bonacina, V. Shcheslavskiy, N. Bocchio, S. Geissbuehler, M. Leutenegger, I. Maerki, J. Wolf, T. Lasser, “Nonlinear correlation spectroscopy (nlcs),” Nano Lett. 12, 1668–1672 (2012).
[CrossRef] [PubMed]

Siegel, A.

Simmel, F.

T. Liedl, S. Keller, F. Simmel, J. Radler, W. Parak, “Fluorescent nanocrystals as colloidal probes in complex fluids measured by fluorescence correlation spectroscopy,” Small 1, 997–1003 (2005).
[CrossRef]

Singer, W.

W. Singer, M. Totzeck, H. Gross, Handbook of Optical Systems: Vol. 2 Physical Image Formation (Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2005).

Slaughter, L.

A. Tcherniak, J. Ha, S. Dominguez-Medina, L. Slaughter, S. Link, “Probing a century old prediction one plasmonic particle at a time,” Nano Lett. 10, 1398–1404 (2010).
[CrossRef] [PubMed]

Sonek, G.

Spaink, H.

P. Paulo, A. Gaiduk, F. Kulzer, S. Gabby Krens, H. Spaink, T. Schmidt, M. Orrit, “Photothermal correlation spectroscopy of gold nanoparticles in solution,” J. Phys. Chem. C 113, 11451–11457 (2009).
[CrossRef]

Sprik, R.

J. Kalkman, R. Sprik, T. Van Leeuwen, “Path-length-resolved diffusive particle dynamics in spectral-domain optical coherence tomography,” Phys. Rev. Lett. 105, 198302 (2010).
[CrossRef]

Staff, R.

D. Schaeffel, R. Staff, H.-J. Butt, K. Landfester, D. Crespy, K. Koynov, “Fluorescence correlation spectroscopy directly monitors coalescence during nanoparticle preparation,” Nano Lett. 12, 6012–6017 (2012).
[CrossRef] [PubMed]

Steinmann, L.

Stephan, J.

M. Brinkmeier, K. Doerre, J. Stephan, M. Eigen, “Two-beam cross-correlation: A method to characterize transport phenomena in micrometer-sized structures,” Anal. Chem. 71, 609–616 (1999).
[CrossRef] [PubMed]

Swanglap, P.

S. Dominguez-Medina, S. McDonough, P. Swanglap, C. Landes, S. Link, “In situ measurement of bovine serum albumin interaction with gold nanospheres,” Langmuir 28, 9131–9139 (2012).
[CrossRef] [PubMed]

Tchebotareva, A. L.

M. A. van Dijk, A. L. Tchebotareva, M. Orrit, M. Lippitz, S. Berciaud, D. Lasne, L. Cognet, B. Lounis, “Absorption and scattering microscopy of single metal nanoparticles,” Phys. Chem. Chem. Phys. 8, 3486–3495 (2006).
[CrossRef] [PubMed]

Tcherniak, A.

A. Tcherniak, J. Ha, S. Dominguez-Medina, L. Slaughter, S. Link, “Probing a century old prediction one plasmonic particle at a time,” Nano Lett. 10, 1398–1404 (2010).
[CrossRef] [PubMed]

Thyberg, P.

M. Gosch, H. Blom, S. Anderegg, K. Korn, P. Thyberg, M. Wells, T. Lasser, R. Rigler, A. Magnusson, S. Hard, “Parallel dual-color fluorescence cross-correlation spectroscopy using diffractive optical elements,” J. Biomed. Opt. 10, 054008 (2005).
[CrossRef] [PubMed]

Totzeck, M.

W. Singer, M. Totzeck, H. Gross, Handbook of Optical Systems: Vol. 2 Physical Image Formation (Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2005).

van Dijk, M. A.

M. A. van Dijk, A. L. Tchebotareva, M. Orrit, M. Lippitz, S. Berciaud, D. Lasne, L. Cognet, B. Lounis, “Absorption and scattering microscopy of single metal nanoparticles,” Phys. Chem. Chem. Phys. 8, 3486–3495 (2006).
[CrossRef] [PubMed]

Van Leeuwen, T.

J. Kalkman, R. Sprik, T. Van Leeuwen, “Path-length-resolved diffusive particle dynamics in spectral-domain optical coherence tomography,” Phys. Rev. Lett. 105, 198302 (2010).
[CrossRef]

Villiger, M.

Vogel, H.

T. Wohland, R. Rigler, H. Vogel, “The standard deviation in fluorescence correlation spectroscopy,” Biophys. J. 80, 2987–2999 (2001).
[CrossRef] [PubMed]

Von Der Hocht, I.

T. Dertinger, V. Pacheco, I. Von Der Hocht, R. Hartmann, I. Gregor, J. Enderlein, “Two-focus fluorescence correlation spectroscopy: A new tool for accurate and absolute diffusion measurements,” Chem. Phys. Chem. 8, 433–443 (2007).
[CrossRef] [PubMed]

Webb, W.

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

P. Schwille, U. Haupts, S. Maiti, W. Webb, “Molecular dynamics in living cells observed by fluorescence correlation spectroscopy with one- and two-photon excitation,” Biophys. J. 77, 2251–2265 (1999).
[CrossRef] [PubMed]

D. Magde, E. Elson, W. Webb, “Thermodynamic fluctuations in a reacting system measurement by fluorescence correlation spectroscopy,” Phys. Rev. Lett. 29, 705–708 (1972).
[CrossRef]

Wells, M.

M. Gosch, H. Blom, S. Anderegg, K. Korn, P. Thyberg, M. Wells, T. Lasser, R. Rigler, A. Magnusson, S. Hard, “Parallel dual-color fluorescence cross-correlation spectroscopy using diffractive optical elements,” J. Biomed. Opt. 10, 054008 (2005).
[CrossRef] [PubMed]

Wennmalm, S.

S. Wennmalm, J. Widengren, “Interferometry and fluorescence detection for simultaneous analysis of labeled and unlabeled nanoparticles in solution,” J. Am. Chem. Soc. 134, 19516–19519 (2012).
[CrossRef] [PubMed]

Widengren, J.

S. Wennmalm, J. Widengren, “Interferometry and fluorescence detection for simultaneous analysis of labeled and unlabeled nanoparticles in solution,” J. Am. Chem. Soc. 134, 19516–19519 (2012).
[CrossRef] [PubMed]

K. Hassler, P. Rigler, H. Blom, R. Rigler, J. Widengren, T. Lasser, “Dynamic disorder in horseradish peroxidase observed with total internal reflection fluorescence correlation spectroscopy,” Opt. Express 15, 5366–5375 (2007).
[CrossRef] [PubMed]

Wiseman, P.

M. Digman, C. Brown, P. Sengupta, P. Wiseman, A. Horwitz, E. Gratton, “Measuring fast dynamics in solutions and cells with a laser scanning microscope,” Biophys. J. 89, 1317–1327 (2005).
[CrossRef] [PubMed]

Wohland, T.

T. Wohland, R. Rigler, H. Vogel, “The standard deviation in fluorescence correlation spectroscopy,” Biophys. J. 80, 2987–2999 (2001).
[CrossRef] [PubMed]

Wolf, J.

M. Geissbuehler, L. Bonacina, V. Shcheslavskiy, N. Bocchio, S. Geissbuehler, M. Leutenegger, I. Maerki, J. Wolf, T. Lasser, “Nonlinear correlation spectroscopy (nlcs),” Nano Lett. 12, 1668–1672 (2012).
[CrossRef] [PubMed]

Wright, W.

Xie, S.

J. Cheng, E. Potma, S. Xie, “Coherent anti-stokes raman scattering correlation spectroscopy: Probing dynamical processes with chemical selectivity,” J. Phys. Chem. A 106, 8561–8568 (2002).
[CrossRef]

Yguerabide, E.

J. Yguerabide, E. Yguerabide, “Light-scattering submicroscopic particles as highly fluorescent analogs and their use as tracer labels in clinical and biological applications i. theory,” Anal. Biochem. 262, 137–156 (1998).
[CrossRef] [PubMed]

Yguerabide, J.

J. Yguerabide, E. Yguerabide, “Light-scattering submicroscopic particles as highly fluorescent analogs and their use as tracer labels in clinical and biological applications i. theory,” Anal. Biochem. 262, 137–156 (1998).
[CrossRef] [PubMed]

Zumbusch, A.

T. Hellerer, A. Schiller, G. Jung, A. Zumbusch, “Coherent anti-stokes raman scattering (cars) correlation spectroscopy,” Chem. Phys. Chem. 3, 630–633 (2002).
[CrossRef] [PubMed]

ACS Nano (3)

K. Jaskiewicz, A. Larsen, D. Schaeffel, K. Koynov, I. Lieberwirth, G. Fytas, K. Landfester, A. Kroeger, “Incorporation of nanoparticles into polymersomes: Size and concentration effects,” ACS Nano 6, 7254–7262 (2012).
[CrossRef] [PubMed]

V. Octeau, L. Cognet, L. Duchesne, D. Lasne, N. Schaeffer, D. Fernig, B. Lounis, “Photothermal absorption correlation spectroscopy,” ACS Nano 3, 345–350 (2009).
[CrossRef] [PubMed]

J. Chen, J. Irudayaraj, “Quantitative investigation of compartmentalized dynamics of erbb2 targeting gold nanorods in live cells by single molecule spectroscopy,” ACS Nano 3, 4071–4079 (2009).
[CrossRef] [PubMed]

Anal. Biochem. (1)

J. Yguerabide, E. Yguerabide, “Light-scattering submicroscopic particles as highly fluorescent analogs and their use as tracer labels in clinical and biological applications i. theory,” Anal. Biochem. 262, 137–156 (1998).
[CrossRef] [PubMed]

Anal. Chem. (2)

P. Dittrich, P. Schwille, “Spatial two-photon fluorescence cross-correlation spectroscopy for controlling molecular transport in microfluidic structures,” Anal. Chem. 74, 4472–4479 (2002).
[CrossRef] [PubMed]

M. Brinkmeier, K. Doerre, J. Stephan, M. Eigen, “Two-beam cross-correlation: A method to characterize transport phenomena in micrometer-sized structures,” Anal. Chem. 71, 609–616 (1999).
[CrossRef] [PubMed]

Appl. Opt. (1)

Biophys. J. (4)

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

M. Digman, C. Brown, P. Sengupta, P. Wiseman, A. Horwitz, E. Gratton, “Measuring fast dynamics in solutions and cells with a laser scanning microscope,” Biophys. J. 89, 1317–1327 (2005).
[CrossRef] [PubMed]

T. Wohland, R. Rigler, H. Vogel, “The standard deviation in fluorescence correlation spectroscopy,” Biophys. J. 80, 2987–2999 (2001).
[CrossRef] [PubMed]

P. Schwille, U. Haupts, S. Maiti, W. Webb, “Molecular dynamics in living cells observed by fluorescence correlation spectroscopy with one- and two-photon excitation,” Biophys. J. 77, 2251–2265 (1999).
[CrossRef] [PubMed]

Cell Biochem. Biophys. (1)

P. Schwille, “Fluorescence correlation spectroscopy and its potential for intracellular applications,” Cell Biochem. Biophys. 34, 383–408 (2001).
[CrossRef]

Chem. Phys. Chem. (2)

T. Dertinger, V. Pacheco, I. Von Der Hocht, R. Hartmann, I. Gregor, J. Enderlein, “Two-focus fluorescence correlation spectroscopy: A new tool for accurate and absolute diffusion measurements,” Chem. Phys. Chem. 8, 433–443 (2007).
[CrossRef] [PubMed]

T. Hellerer, A. Schiller, G. Jung, A. Zumbusch, “Coherent anti-stokes raman scattering (cars) correlation spectroscopy,” Chem. Phys. Chem. 3, 630–633 (2002).
[CrossRef] [PubMed]

Ind. Eng. Chem. Res. (1)

N. Cheng, “Formula for the viscosity of a glycerol-water mixture,” Ind. Eng. Chem. Res. 47, 3285–3288 (2008).
[CrossRef]

J. Am. Chem. Soc. (1)

S. Wennmalm, J. Widengren, “Interferometry and fluorescence detection for simultaneous analysis of labeled and unlabeled nanoparticles in solution,” J. Am. Chem. Soc. 134, 19516–19519 (2012).
[CrossRef] [PubMed]

J. Biomed. Opt. (1)

M. Gosch, H. Blom, S. Anderegg, K. Korn, P. Thyberg, M. Wells, T. Lasser, R. Rigler, A. Magnusson, S. Hard, “Parallel dual-color fluorescence cross-correlation spectroscopy using diffractive optical elements,” J. Biomed. Opt. 10, 054008 (2005).
[CrossRef] [PubMed]

J. Nanophotonics (1)

M. Dienerowitz, M. Mazilu, K. Dholakia, “Optical manipulation of nanoparticles: A review,” J. Nanophotonics 2, 021875 (2008).
[CrossRef]

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

J. Phys. Chem. A (1)

J. Cheng, E. Potma, S. Xie, “Coherent anti-stokes raman scattering correlation spectroscopy: Probing dynamical processes with chemical selectivity,” J. Phys. Chem. A 106, 8561–8568 (2002).
[CrossRef]

J. Phys. Chem. C (1)

P. Paulo, A. Gaiduk, F. Kulzer, S. Gabby Krens, H. Spaink, T. Schmidt, M. Orrit, “Photothermal correlation spectroscopy of gold nanoparticles in solution,” J. Phys. Chem. C 113, 11451–11457 (2009).
[CrossRef]

Langmuir (1)

S. Dominguez-Medina, S. McDonough, P. Swanglap, C. Landes, S. Link, “In situ measurement of bovine serum albumin interaction with gold nanospheres,” Langmuir 28, 9131–9139 (2012).
[CrossRef] [PubMed]

Nano Lett. (3)

M. Geissbuehler, L. Bonacina, V. Shcheslavskiy, N. Bocchio, S. Geissbuehler, M. Leutenegger, I. Maerki, J. Wolf, T. Lasser, “Nonlinear correlation spectroscopy (nlcs),” Nano Lett. 12, 1668–1672 (2012).
[CrossRef] [PubMed]

D. Schaeffel, R. Staff, H.-J. Butt, K. Landfester, D. Crespy, K. Koynov, “Fluorescence correlation spectroscopy directly monitors coalescence during nanoparticle preparation,” Nano Lett. 12, 6012–6017 (2012).
[CrossRef] [PubMed]

A. Tcherniak, J. Ha, S. Dominguez-Medina, L. Slaughter, S. Link, “Probing a century old prediction one plasmonic particle at a time,” Nano Lett. 10, 1398–1404 (2010).
[CrossRef] [PubMed]

Opt. Express (4)

Opt. Lett. (3)

Phys. Chem. Chem. Phys. (1)

M. A. van Dijk, A. L. Tchebotareva, M. Orrit, M. Lippitz, S. Berciaud, D. Lasne, L. Cognet, B. Lounis, “Absorption and scattering microscopy of single metal nanoparticles,” Phys. Chem. Chem. Phys. 8, 3486–3495 (2006).
[CrossRef] [PubMed]

Phys. Rev. A (1)

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

Phys. Rev. E. (1)

W. Schrof, J. Klingler, S. Rozouvan, D. Horn, “Raman correlation spectroscopy: A method for studying chemical composition and dynamics of disperse systems,” Phys. Rev. E. 57, R2523–R2526 (1998).
[CrossRef]

Phys. Rev. Lett. (2)

D. Magde, E. Elson, W. Webb, “Thermodynamic fluctuations in a reacting system measurement by fluorescence correlation spectroscopy,” Phys. Rev. Lett. 29, 705–708 (1972).
[CrossRef]

J. Kalkman, R. Sprik, T. Van Leeuwen, “Path-length-resolved diffusive particle dynamics in spectral-domain optical coherence tomography,” Phys. Rev. Lett. 105, 198302 (2010).
[CrossRef]

Small (1)

T. Liedl, S. Keller, F. Simmel, J. Radler, W. Parak, “Fluorescent nanocrystals as colloidal probes in complex fluids measured by fluorescence correlation spectroscopy,” Small 1, 997–1003 (2005).
[CrossRef]

Other (5)

R. Rigler, E. Elson, Fluorescence Correlation Spectroscopy: Theory and Applications (Springer, 2001).
[CrossRef]

B. Berne, R. Pecora, Dynamic Light Scattering with Applications to Chemistry, Biology and Physics (John Wiley and Sons, New-York, 1976).

J. Izatt, M. Choma, Optical Coherence Tomography: Technology and Applications (Springer Verlag, Berlin, 2008).

W. Singer, M. Totzeck, H. Gross, Handbook of Optical Systems: Vol. 2 Physical Image Formation (Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2005).

S. Broillet, A. Sato, S. Geissbuehler, C. Pache, A. Bouwens, T. Lasser, M. Leutenegger, “Matlab OCCS Experiment,” http://lob.epfl.ch/page-103066.html .

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1
Fig. 1

A typical OCCS experiment. (a) Particles diffusing in a liquid. The trajectory rp(t) of a particle is exemplified. (b) Bessel illumination of the particles and detection of the backscattered light W (rp,k). (c) The interference signal generated by the backscattered sample field and the reference field is recorded via a spectrometer. (d) The sample spectrum is then re-sampled at equidistant wavenumbers (λ to k mapping) (e), and the depth profile containing a sequence of sampling volumes is extracted by computing the fast Fourier transform of the spectrum. (f) Auto-correlations of these time-dependent signals and cross-correlations of time traces between different sampling volumes are calculated.

Fig. 2
Fig. 2

Normalized OCCS curves for ∅100nm gold NPs in water at 9.3pM in the sampling volume V0 (N ≪ 1). The auto-correlation curves are obtained by averaging 10 measurements. The illumination power was 2mW and each measurement lasted 100s. The measured autocorrelation is compared to different model functions: calculation from the brightness profile W (r), from a full Monte-Carlo (MC) simulation, from an analytical model considering a 3D Gaussian volume, and from an analytical model considering a 3D Bessel-Gaussian (BG) volume.

Fig. 3
Fig. 3

Schematic of the OCCS setup. The interferometer in in a Bessel-Gauss configuration [33]: an axicon generates the Bessel beam illumination, whereas the detection mode is Gaussian. The complementary apertures Fill and Fdet are placed in conjugated planes of the objective back-aperture, ensuring the dark-field effect [31].

Fig. 4
Fig. 4

Brightness profiles characterization. (a) ∅100nm single gold NP en-face view. (b) Cross-section of the same particle along the y-axis. Scalebars: 1 μm. (c) Radial brightness profiles of ∅100nm, ∅80nm, ∅50nm, ∅30nm gold NPs and ∅109nm PSs MSs (averaged for at least ten particles of each type) compared with calculation. (d) Axial brightness profiles of the same particles compared with the coherence gate. The ∅30nm gold NPs axial brightness profile seems to be larger due to a lower signal-to-noise ratio (SNR). (e) Depth of field characterization with ∅100nm gold NPs freely diffusing in water (concentration: 9.3pM; illumination power: 2mW; average on 10 measurements of 100 seconds). The useful DOF is indicated by the dashed lines showing the FWHM. V0 corresponds to the focal sampling volume.

Fig. 5
Fig. 5

OCCS signal scaling versus gold NP diameter. The OCCS signals were taken from the center of the measured brightness profiles (Fig. 4(c), illumination power of 9mW).

Fig. 6
Fig. 6

(a) Normalized OCCS curves from gold NPs of different diameters in water in the single particle regime. Thin lines with markers show the average auto-correlations in V0 of 10 measurements lasting 100 seconds each. Thick lines show the fits using Eq. (11) and the residuals. (b) The extracted diffusion coefficients compared to the theoretical values. (c) The extracted lateral diffusion time τxy of ∅80nm gold NPs versus viscosity in various glycerin/water solutions.

Fig. 7
Fig. 7

(a) OCCS autocorrelations of 109nm polystyrene MSs at different concentrations in 80% glycerol/water mixtures in the focal sampling volume for a measurement of 50 seconds (thin lines with markers), along with the fit using Eq. (13) (thick lines) and the fit residuals. (b) The extracted Ac and N along with the number of particles calculated from the brightness profile (red line). Each value is averaged over 10 measurements lasting 50 seconds each. (c) OCCS autocorrelations of 109nm polystyrene MSs in glycerol/water mixtures in V0 (thin lines with markers).Thick lines show the fits using Eq. (13). (d) The extracted τc as compared to the theoretical values. Each data point is averaged on 10 measurements lasting 100 seconds each.

Fig. 8
Fig. 8

The three concentrations regimes in OCCS with their corresponding fit model. Left: in the single particle regime the starting amplitude is γ/N and the decay is modeled using Eq. (11). Middle: the few particles regime is modeled according to Eq. (13). Right: the many particles regime fit model has a starting amplitude of γ and a single exponential decay according to Eq. (15).

Fig. 9
Fig. 9

(a) Cross-correlation between sampling volume V0 and V2, different illumination powers on a sample of ∅100nm gold NPs. Blue cross markers indicate the mean transit time between the sampling volumes. (b) Cross-correlation between sampling volume V0 and V2, additional pushing laser 532nm, illumination laser at 2mW. (c) The extracted mean transition speed from the cross-correlations in (b).

Fig. 10
Fig. 10

Cross-correlations between sampling volumes with a sample of ∅100nm gold NPs at a concentration of 9.3pM. (a) Illumination laser set at 2mW. (b) Illumination laser set at 20mW. (c) Illumination laser set at 2mW, while an additional laser (20mW, 532nm, Gaussian shape, NA=0.19) is used to push the particles. The legends indicate the sampling volume’s relative positions from the observation focus (increasing index means further away from objective).

Fig. 11
Fig. 11

Monte-Carlo simulation with two kinds of ∅100nm NPs that were given the brightnesses of ∅100nm and ∅30nm gold NPs, which modeled high and low SNR, respectively, along with fits (thick lines).

Equations (23)

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

l c = 2 ln ( 2 ) n π λ 0 2 Δ λ ,
Δ z = 2 π 2 Δ k s ,
I D ( k , t ) = | E r + E s | 2 = S ( k ) | α r exp ( 2 i k z r ) + p = 1 N α p exp ( 2 i k z p ( t ) ) | 2 = S ( k ) ( α r 2 + p = 1 N α p 2 ) + ( i ) 2 S ( k ) p = 1 N α r α p cos ( 2 k ( z r z p ( t ) ) ) + ( ii ) 2 S ( k ) p = 1 q > p N α p α q cos ( 2 k ( z p ( t ) z q ( t ) ) ) , ( iii )
I d , m ( t ) = α r α s g ( 2 n ( z 1 ( t ) z m ) ) = α r α s | g ( 2 n ( z 1 ( t ) z m ) | exp ( i 2 n k 0 ( z 1 ( t ) z m ) ) ,
I d , m ( t ) = α r α s W m ( ρ 1 ( t ) , z 1 ( t ) ) exp ( i 2 n k 0 ( z 1 ( t ) z m ) ) .
I m ( t ) = α r α s W m ( ρ 1 ( t ) , z 1 ( t ) ) .
G m n ( τ ) = ( T τ ) 0 T τ I m ( t ) I n ( t + τ ) d t 0 T τ I m ( t ) d t τ T I n ( t ) d t 1 ,
G S , m ( τ ) = 1 C ( 4 π D τ ) 3 2 W m ( r ) W m ( r ¯ ) ) exp ( ( r r ¯ ) 2 4 D τ ) d r d r ¯ ( W m ( r ) d r ) 2 ,
G S , m ( τ ) = γ N [ ( 1 + τ τ xy ) 1 + τ τ z ] 1 ,
N = C V eff = C ( W ( r ) d r ) 2 W 2 ( r ) d r = C γ 1 W ( r ) d r ,
G S , m ( τ ) = γ N [ ( 1 + τ τ xy ) 1 + τ τ z ] 1 ( 1 + A b exp ( τ τ b ) )
I d , m ( t ) = p = 1 N α r α s W m ( ρ p ( t ) , z p ( t ) ) exp ( i 2 n k 0 ( z p ( t ) z m ) ) .
G F , m ( τ ) = γ N [ ( 1 + τ τ xy ) 1 + τ τ z ] 1 ( 1 + A b exp ( τ τ b ) ) ( 1 + A c exp ( τ τ c ) ) ,
τ c = 1 8 n 2 k 0 2 D
G M , m ( τ ) = γ ( 1 + A b ) exp ( τ τ c ) ,
W m ( x , y , z ) = | E ill ( x , y , z ) E det ( x , y , z ) g ( 2 n ( z z m ) ) |
E ill ( ρ , z , k ) = J 0 ( 2.404 k ρ k c ρ 0 ) max ( 0 , v ( z ) ) exp ( 1 v 2 ( z ) 2 i k z cos θ ) ,
E det ( ρ , z , k ) = w ( 0 , k ) w ( z , k ) exp ( ρ 2 w 2 ( z , k ) + i arctan ( z Z ( k ) ) i k ρ 2 2 R ( z , k ) i k z )
R ( z , k ) = z ( 1 + Z 2 ( k ) z 2 ) w ( z , k ) = w 0 k c k 1 + z 2 Z 2 ( k ) Z ( k ) = w 0 2 k c 2 2 k
W ( ρ , z , k ) J 0 ( 2.404 ρ ρ 0 ) max ( 0 , v ( z ) ) exp ( 1 v 2 ( z ) 2 ) × w ( 0 , k c ) w ( z , k c ) exp ( ρ 2 w 2 ( z , k c ) ) × exp ( i k z ( 1 + cos θ ) ) .
E s ( k ) = p = 1 N α p W ( ρ p , z p , k ) ,
I ( k ) = S ( k ) | E r ( k ) + E s ( k ) | 2 ,
I D ( k ) = [ s poissrnd ( I ( k ) ) + o + normrnd ( 0 , σ ) ] [ 0 , 2 bits 1 ]

Metrics