- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Expanding the reach of diffusing wave spectroscopy and tracer bead microrheology

M. Helfer, C. Zhang, and F. Scheffold*

  • *Contact author: Frank.Scheffold@unifr.ch
PDF

Phys. Rev. Research 7, 043274 – Published 9 December, 2025

DOI: https://doi.org/10.1103/k34t-ghws

Abstract

Diffusing wave spectroscopy (DWS) is an extension of standard dynamic light scattering, applied to soft materials that are turbid or opaque. The propagation of light is modeled using light diffusion, characterized by a light diffusion coefficient that depends on the transport mean free path ℓ* of the medium. DWS is highly sensitive to small particle displacements or other local fluctuations in the scattering properties and can probe subnanometer displacements. Analyzing the motion of beads in a viscoelastic matrix, known as one-bead microrheology, is one of the most common applications of DWS. Despite significant advancements since its invention in the late 1980s, including two-cell and multispeckle DWS, challenges such as merging single- and multispeckle data and limited accuracy for short correlation times persist. Here, we address these issues by improving the two-cell echo DWS scheme. We propose a calibration-free method to blend and merge echo and two-cell DWS data and demonstrate the use of an exponential basis fit to enhance data quality, in particular at very short times. Building on this, we introduce stable corrections for bead and fluid inertia, significantly improving the quality of microrheology data at high frequencies.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (81)

  1. D. Weitz, J. Zhu, D. Durian, H. Gang, and D. Pine, Diffusing-wave spectroscopy: The technique and some applications, Phys. Scr. T49B, 610 (1993).
  2. D. J. Pine, D. A. Weitz, J. Zhu, and E. Herbolzheimer, Diffusing-wave spectroscopy: Dynamic light scattering in the multiple scattering limit, J. Phys. 51, 2101 (1990).
  3. D. J. Pine and D. A. Weitz, Diffusing-wave spectroscopy, in Dynamic Light Scattering: The Method and Some Applications, edited by W. Brown (Oxford University Press, Oxford, Wyn Brown, Uppsala, Sweden, 1993), pp. 652–720.
  4. G. Maret, Diffusing-wave spectroscopy, Curr. Opin. Colloid Interface Sci. 2, 251 (1997).
  5. J. Harden and V. Viasnoff, Recent advances in DWS-based micro-rheology, Curr. Opin. Colloid Interface Sci. 6, 438 (2001).
  6. B. R. Dasgupta, S.-Y. Tee, J. C. Crocker, B. Frisken, and D. Weitz, Microrheology of polyethylene oxide using diffusing wave spectroscopy and single scattering, Phys. Rev. E 65, 051505 (2002).
  7. N. Willenbacher, C. Oelschlaeger, M. Schopferer, P. Fischer, F. Cardinaux, and F. Scheffold, Broad bandwidth optical and mechanical rheometry of wormlike micelle solutions, Phys. Rev. Lett. 99, 068302 (2007).
  8. J. Galvan-Miyoshi, J. Delgado, and R. Castillo, Diffusing wave spectroscopy in Maxwellian fluids, Eur. Phys. J. E 26, 369 (2008).
  9. Z. Fahimi, F. J. Aangenendt, P. Voudouris, J. Mattsson, and H. M. Wyss, Diffusing-wave spectroscopy in a standard dynamic light scattering setup, Phys. Rev. E 96, 062611 (2017).
  10. Z. Xing, A. Caciagli, T. Cao, I. Stoev, M. Zupkauskas, T. O’Neill, T. Wenzel, R. Lamboll, D. Liu, and E. Eiser, Microrheology of DNA hydrogels, Proc. Natl. Acad. Sci. USA 115, 8137 (2018).
  11. V. Lorusso, D. Orsi, F. Salerni, L. Liggieri, F. Ravera, R. McMillin, J. Ferri, and L. Cristofolini, Recent developments in emulsion characterization: Diffusing wave spectroscopy beyond average values, Adv. Colloid Interface Sci. 288, 102341 (2021).
  12. K. A. Dennis, Q. Li, N. Sbalbi, S. C. Brown, and E. M. Furst, Diffusing wave spectroscopy measurements of colloidal suspension dynamics, Langmuir 40, 6129 (2024).
  13. F. Scheffold, Light scattering and propagation in turbid media, in Neutrons, X-rays, and light: Scattering Methods Applied to Soft Condensed Matter, edited by P. Lindner and J. Oberdisse (Elsevier, France, 2024), pp. 581–610.
  14. G. Maret and P. Wolf, Multiple light scattering from disordered media. The effect of Brownian motion of scatterers, Z. Phys. B 65, 409 (1987).
  15. D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, Diffusing wave spectroscopy, Phys. Rev. Lett. 60, 1134 (1988).
  16. B. J. Berne and R. Pecora, Dynamic Light Scattering: With Applications to Chemistry, Biology, and Physics (Dover Publications, Inc. Mineoloa, New York, 2000).
  17. F. Scheffold, S. Skipetrov, S. Romer, and P. Schurtenberger, Diffusing-wave spectroscopy of nonergodic media, Phys. Rev. E 63, 061404 (2001).
  18. D. A. Boas, L. Campbell, and A. G. Yodh, Scattering and imaging with diffusing temporal field correlations, Phys. Rev. Lett. 75, 1855 (1995).
  19. D. A. Boas and A. G. Yodh, Spatially varying dynamical properties of turbid media probed with diffusing temporal light correlation, J. Opt. Soc. Am. A 14, 192 (1997).
  20. X. Qiu, X. Wu, J. Xue, D. Pine, D. Weitz, and P. M. Chaikin, Hydrodynamic interactions in concentrated suspensions, Phys. Rev. Lett. 65, 516 (1990).
  21. L. Rojas-Ochoa, S. Romer, F. Scheffold, and P. Schurtenberger, Diffusing wave spectroscopy and small-angle neutron scattering from concentrated colloidal suspensions, Phys. Rev. E 65, 051403 (2002).
  22. Q. Li, K. A. Dennis, Y.-F. Lee, and E. M. Furst, Two-point microrheology and diffusing wave spectroscopy, J. Rheol. 67, 1107 (2023).
  23. H. S. Kim, N. Şenbil, C. Zhang, F. Scheffold, and T. G. Mason, Diffusing wave microrheology of highly scattering concentrated monodisperse emulsions, Proc. Natl. Acad. Sci. USA 116, 7766 (2019).
  24. Y. Xu and T. G. Mason, Jamming and depletion in extremely bidisperse mixtures of microscale emulsions and nanoemulsions, Sci. Adv. 9, eadh3715 (2023).
  25. T. G. Mason and D. A. Weitz, Optical measurements of frequency-dependent linear viscoelastic moduli of complex fluids, Phys. Rev. Lett. 74, 1250 (1995).
  26. M. L. Gardel, M. T. Valentine, and D. A. Weitz, Microrheology, in Microscale Diagnostic Techniques (Springer, Berlin, Heidelberg, 2004), pp. 1–49.
  27. T. A. Waigh, Microrheology of complex fluids, Rep. Prog. Phys. 68, 685 (2005).
  28. E. M. Furst and T. M. Squires, Microrheology (Oxford University Press, Oxford, UK, 2017).
  29. C. Zhang, M. Reufer, D. Gaudino, and F. Scheffold, Improved diffusing wave spectroscopy based on the automatized determination of the optical transport and absorption mean free path, Korea-Aust. Rheol. J. 29, 241 (2017).
  30. I. D. Block and F. Scheffold, Modulated 3D cross-correlation light scattering: Improving turbid sample characterization, Rev. Sci. Instrum. 81, 123107 (2010).
  31. D. A. Weitz, D. J. Pine, P. N. Pusey, and R. J. A Tough, Nondiffusive Brownian motion studied by diffusing-wave spectroscopy, Phys. Rev. Lett. 63, 1747 (1989).
  32. H. M. Wyss, S. Romer, F. Scheffold, P. Schurtenberger, and L. J. Gauckler, Diffusing-wave spectroscopy of concentrated alumina suspensions during gelation, J. Colloid Interface Sci. 241, 89 (2001).
  33. F. Gittes and F. C. MacKintosh, Dynamic shear modulus of a semiflexible polymer network, Phys. Rev. E 58, R1241 (1998).
  34. F. Gittes, B. Schnurr, P. Olmsted, F. C. MacKintosh, and C. F. Schmidt, Microscopic viscoelasticity: Shear moduli of soft materials determined from thermal fluctuations, Phys. Rev. Lett. 79, 3286 (1997).
  35. A. J. Levine and T. Lubensky, Response function of a sphere in a viscoelastic two-fluid medium, Phys. Rev. E 63, 041510 (2001).
  36. S. Romer, F. Scheffold, and P. Schurtenberger, Sol-gel transition of concentrated colloidal suspensions, Phys. Rev. Lett. 85, 4980 (2000).
  37. P. N. Pusey and W. Van Megen, Dynamic light scattering by non-ergodic media, Physica A 157, 705 (1989).
  38. J.-Z. Xue, D. Pine, S. Milner, X.-L. Wu, and P. Chaikin, Nonergodicity and light scattering from polymer gels, Phys. Rev. A 46, 6550 (1992).
  39. G. Nisato, P. Hebraud, J.-P. Munch, and S. Candau, Diffusing-wave-spectroscopy investigation of latex particle motion in polymer gels, Phys. Rev. E 61, 2879 (2000).
  40. A. Knaebel, M. Bellour, J.-P. Munch, V. Viasnoff, F. Lequeux, and J. Harden, Aging behavior of laponite clay particle suspensions, Europhys. Lett. 52, 73 (2000).
  41. F. Cardinaux, L. Cipelletti, F. Scheffold, and P. Schurtenberger, Microrheology of giant-micelle solutions, Europhys. Lett. 57, 738 (2002).
  42. V. Viasnoff, F. Lequeux, and D. Pine, Multispeckle diffusing-wave spectroscopy: A tool to study slow relaxation and time-dependent dynamics, Rev. Sci. Instrum. 73, 2336 (2002).
  43. P. Zakharov, F. Cardinaux, and F. Scheffold, Multispeckle diffusing-wave spectroscopy with a single-mode detection scheme, Phys. Rev. E 73, 011413 (2006).
  44. K. Pham, S. Egelhaaf, A. Moussaíd, and P. Pusey, Ensemble-averaging in dynamic light scattering by an echo technique, Rev. Sci. Instrum. 75, 2419 (2004).
  45. S. Zhang, J. Peuser, C. Zhang, F. Cardinaux, P. Zakharov, S. E. Skipetrov, R. Cerbino, and F. Scheffold, Echo speckle imaging of dynamic processes in soft materials, Opt. Express 30, 30991 (2022).
  46. M. Alexander and D. G. Dalgleish, Diffusing wave spectroscopy of aggregating and gelling systems, Curr. Opin. Colloid Interface Sci. 12, 179 (2007).
  47. X. Xue, X. Miao, J. Liu, Y. Ding, Y. Zhang, Y. Sun, W. Huang, Q. Jiang, B. Jiang, and S. Komarneni, Investigating the pH-dependence of gelation process in chitosan-glutaraldehyde hydrogels with diffusing wave spectroscopy, Polymer 316, 127827 (2025).
  48. E. J. Sie, H. Chen, E.-F. Saung, R. Catoen, T. Tiecke, M. A. Chevillet, and F. Marsili, High-sensitivity multispeckle diffuse correlation spectroscopy, Neurophotonics 7, 035010 (2020).
  49. M. A. Wayne, E. J. Sie, A. C. Ulku, P. Mos, A. Ardelean, F. Marsili, C. Bruschini, and E. Charbon, Massively parallel, real-time multispeckle diffuse correlation spectroscopy using a 500×500 SPAD camera, Biomed. Opt. Express 14, 703 (2023).
  50. S. E. Skipetrov, J. Peuser, R. Cerbino, P. Zakharov, B. Weber, and F. Scheffold, Noise in laser speckle correlation and imaging techniques, Opt. Express 18, 14519 (2010).
  51. See Supplemental Material at http://link.aps.org/supplemental/10.1103/k34t-ghws for additional characterization data and figures.
  52. B. Schroyen, D. Vlassopoulos, P. Van Puyvelde, and J. Vermant, Bulk rheometry at high frequencies: A review of experimental approaches, Rheol. Acta 59, 1 (2020).
  53. G. Fritz, W. Pechhold, N. Willenbacher, and N. J. Wagner, Characterizing complex fluids with high frequency rheology using torsional resonators at multiple frequencies, J. Rheol. 47, 303 (2003).
  54. K. Schätzel, Noise in photon correlation and photon structure functions, Opt. Acta: Int. J. Opt. 30, 155 (1983).
  55. J. Yoon, F. Cardinaux, C. Lapointe, C. Zhang, T. G. Mason, K. H. Ahn, and F. Scheffold, Brownian dynamics of colloidal microspheres with tunable elastic properties from soft to hard, Colloids Surf. A 546, 360 (2018).
  56. P.-A. Lemieux, M. Vera, and D. J. Durian, Diffusing-light spectroscopies beyond the diffusion limit: The role of ballistic transport and anisotropic scattering, Phys. Rev. E 57, 4498 (1998).
  57. T. G. Mason, Estimating the viscoelastic moduli of complex fluids using the generalized Stokes–Einstein equation, Rheol. Acta 39, 371 (2000).
  58. R. Evans, M. Tassieri, D. Auhl, and T. A. Waigh, Direct conversion of rheological compliance measurements into storage and loss moduli, Phys. Rev. E 80, 012501 (2009).
  59. M. Tassieri, R. Evans, R. L. Warren, N. J. Bailey, and J. M. Cooper, Microrheology with optical tweezers: Data analysis, New J. Phys. 14, 115032 (2012).
  60. M. Tassieri, Comment on “A symmetrical method to obtain shear moduli from microrheology” by K. Nishi, M. L. Kilfoil, C. F. Schmidt, and F. C. Mackintosh, Soft Matter, 2018, 14, 3716, Soft Matter 14, 8666 (2018).
  61. A. Einstein et al., On the motion of small particles suspended in liquids at rest required by the molecular-kinetic theory of heat, Ann. Phys. 17, 549 (1905).
  62. E. J. Hinch, Application of the Langevin equation to fluid suspensions, J. Fluid Mech. 72, 499 (1975).
  63. R. Huang, I. Chavez, K. M. Taute, B. Lukić, S. Jeney, M. G. Raizen, and E.-L. Florin, Direct observation of the full transition from ballistic to diffusive Brownian motion in a liquid, Nat. Phys. 7, 576 (2011).
  64. I. Madrid et al., Ballistic Brownian motion of nanoconfined DNA, ACS Nano 17, 17031 (2023).
  65. D. Coglitore, S. P. Edwardson, P. Macko, E. A. Patterson, and M. Whelan, Transition from fractional to classical Stokes–Einstein behaviour in simple fluids, R. Soc. Open Sci. 4, 170507 (2017).
  66. P. Domínguez-García, F. Cardinaux, E. Bertseva, L. Forró, F. Scheffold, and S. Jeney, Accounting for inertia effects to access the high-frequency microrheology of viscoelastic fluids, Phys. Rev. E 90, 060301 (2014).
  67. T. Indei, J. D. Schieber, and A. Córdoba, Competing effects of particle and medium inertia on particle diffusion in viscoelastic materials, and their ramifications for passive microrheology, Phys. Rev. E 85, 041504 (2012).
  68. D. Mizuno, D. Head, F. MacKintosh, and C. Schmidt, Active and passive microrheology in equilibrium and nonequilibrium systems, Macromolecules 41, 7194 (2008).
  69. Mathematica, Version 14.0 (Wolfram Research, Inc., Champaign, IL, 2024).
  70. Python Language Reference, version 3.10, Python Software Foundation (Wilmington, Delaware, 2021).
  71. P. Fischer and H. Rehage, Rheological master curves of viscoelastic surfactant solutions by varying the solvent viscosity and temperature, Langmuir 13, 7012 (1997).
  72. C. Oelschlaeger, M. Schopferer, F. Scheffold, and N. Willenbacher, Linear-to-branched micelles transition: A rheometry and diffusing wave spectroscopy (DWS) study, Langmuir 25, 716 (2009).
  73. K. Schaetzel and R. Peters, Noise on multiple-tau photon correlation data, in Photon Correlation Spectroscopy: Multicomponent Systems, edited by K. S. Schmitz (SPIE, Bellingham, Washington, 1991), Vol. 1430, pp. 109–115.
  74. P. Virtanen, R. Gommers, T. E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S. J. van der Walt, M. Brett, J. Wilson, K. J. Millman, N. Mayorov, A. R. J. Nelson, E. Jones, R. Kern, E. Larson, C. J. Carey et al., SciPy 1.0: Fundamental algorithms for scientific computing in Python, Nat. Methods 17, 261 (2020).
  75. CRC Handbook of Chemistry and Physics, edited by J. Rumble, 106th ed. (CRC Press/Taylor & Francis Group, Boca Raton, FL, 2025).
  76. M. Bergman, Y. Xu, J. Muñéton Díaz, C. Zhang, T. G. Mason, and F. Scheffold, A free energy model for the plateau shear modulus in thermosensitive microgel suspensions, Langmuir 41, 4084 (2025).
  77. Y. Hertle, M. Zeiser, P. Fouquet, M. Maccarini, and T. Hellweg, The internal network dynamics of poly (NIPAM) based copolymer micro- and macrogels: A comparative neutron spin-echo study, Z. Phys. Chem. 228, 1053 (2014).
  78. A. Rao, B. R. Carrick, H. Yao, and B. D. Olsen, Hindered segmental dynamics in associative protein hydrogels studied by neutron spin-echo spectroscopy, Phys. Rev. Mater. 7, 075602 (2023).
  79. H. Manuel, Z. Chi, S. Frank, Expanding the reach of diffusing wave spectroscopy and tracer bead microrheology, [Data set], Zenodo (2025), https://doi.org/10.5281/zenodo.17426137.
  80. https://github.com/ManuelH26/pyDWS.
  81. https://pypi.org/project/pyDWS/.

Outline

Information

Phys. Rev. Research 7, 043274– Published 9 December, 2025
  • Received 30 January 2025
  • Accepted 12 October 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation