Diffusing-wave spectroscopy: Difference between revisions

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'''Diffusing-wave spectroscopy''' ('''DWS''') is an optical technique derived from [[dynamic light scattering]] (DLS) that studies the dynamics of scattered light in the limit of strong multiple scattering.<ref>

{{cite journal

<ref>G. Maret and P. E. Wolf, Z. Phys. B: Condens. Matter 65, 409 1987</ref>

|author1=G. Maret |author2=P. E. Wolf |year=1987

<ref>D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, Phys. Rev. Lett. 60, 1134 1988</ref>

|title=Multiple light scattering from disordered media. The effect of brownian motion of scatterers

It has been widely used in the past to study colloidal [[suspension]]s, [[emulsions]],[[foams]], gels, biological media and other forms of [[soft matter]]. If carefully calibrated, DWS allows the quantitative measurement of microscopic motion in a soft material, from which the [[rheological]] properties of the complex medium can be extracted ''via'' the so-called [[microrheology]] approach.

|journal=[[Zeitschrift für Physik B]]

|volume=65 |pages=409

|doi=10.1007/BF01303762

|bibcode = 1987ZPhyB..65..409M

|issue=4 |s2cid=121962976 }}</ref><ref>

{{cite journal

<ref> |author1=D. J. Pine, |author2=D. A. Weitz, |author3=P. M. Chaikin, and |author4=E. Herbolzheimer, Phys. Rev. Lett. 60, 1134 |year=1988</ref>

|title=Diffusing wave spectroscopy

|journal=[[Physical Review Letters]]

|volume=60 |pages=1134–1137

|doi=10.1103/PhysRevLett.60.1134

|bibcode=1988PhRvL..60.1134P

|issue=12

|pmid=10037950 }}</ref> It has been widely used in the past to study colloidal [[Suspension (chemistry)|suspension]]s, [[emulsions]], [[foams]], gels, biological media and other forms of [[soft matter]]. If carefully calibrated, DWS allows the quantitative measurement of microscopic motion in a soft material, from which the [[rheological]] properties of the complex medium can be extracted ''via'' the so-called [[microrheology]] approach.

==One-speckle diffusing-wave spectroscopy==

Laser light is sent to the sample and the outcoming transmitted or backscattered light is detected by an optoelectric sensor. The light intensity detected is the result of the interference of all the optical waves coming from the different light paths.

<gallery>

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The signal is analysed by calculating the intensity [[autocorrelation]] function called g₂.

<math>g_2(\tau)=\frac{<\langle I(t)I(t+\tau)>_t\rangle_t}{<\langle I(t)>_t\rangle_t^2}</math>

For the case of non-interacting particles suspended in a (complex) fluid a direct relation between g₂-1 and the [[mean squaresquared displacement]] of the particles <Δr²> can be established. Let's us note P(s) the probability density function (PDF) of the photon path length s. The relation can be written as follows:<ref>F. Scheffold, S. Romer, F. Cardinaux, H. Bissig, A. Stradner, L. F. Rojas-Ochoa1, V. Trappe, C. Urban, S. E. Skipetrov, L. Cipelletti and P. Schurtenberger, New trends in optical microrheology of complex fluids and gels, Progress in Colloid and Polymer Science, vol 123/2004, pp 141-146</ref> <br />

{{cite journal

|author=F. Scheffold

|author-link=Frank Scheffold

|year=2004

|title=New trends in optical microrheology of complex fluids and gels

|url=http://w3.lcvn.univ-montp2.fr/~lucacip/NewTrendsMicroRheology.pdf

|journal=[[Progress in Colloid and Polymer Science]]

|volume=123

|pages=141–146

|doi=10.1007/b11748

|isbn=978-3-540-00553-7

|display-authors=etal

|url-status=dead

|archiveurl=https://web.archive.org/web/20110721023401/http://w3.lcvn.univ-montp2.fr/~lucacip/NewTrendsMicroRheology.pdf

|archivedate=2011-07-21

}}</ref>

<math>g_2(\tau)-1=[\int {ds P(s) \exp(-(s/l*)k_0^2 <\langle\Delta r^2(\tau)>\rangle) }]^2</math><br />

For the case of non-interacting particles suspended in a (complex) fluid a direct relation between g₂-1 and the mean square displacement of the particles <Δr²> can be established. Let's note P(s) the probability density function (PDF) of the photon path length s. The relation can be written as follows:<ref>F. Scheffold, S. Romer, F. Cardinaux, H. Bissig, A. Stradner, L. F. Rojas-Ochoa1, V. Trappe, C. Urban, S. E. Skipetrov, L. Cipelletti and P. Schurtenberger, New trends in optical microrheology of complex fluids and gels, Progress in Colloid and Polymer Science, vol 123/2004, pp 141-146</ref> <br />

<math>g_2(\tau)-1=[\int {ds P(s) exp(-(s/l*)k_0^2 <\Delta r^2(\tau)>) }]^2</math><br />

with <math>k_0=\frac{2\pi n}{\lambda}</math> and <math>l*</math> is the transport mean free path of scattered light.

For simple cell geometries, it is thus possible to calculate the mean squaresquared displacement of the particles <Δr²> from the measured g₂-1 values analytically. For example, for the backscattering geometry, an infinitely thick cell, large laser spot illumination and detection of photons coming from the center of the spot, the relation shiprelationship between g₂-1 and <Δr²> is :<br />

<math>g_2(\tau)-1=exp[-2 \gamma \sqrt{<\Delta r^2(\tau)>k_0^2}]</math>, γ value is around 2.

<math>g_2(\tau)-1=\exp[\left(-2 \gamma \sqrt{<\langle\Delta r^2(\tau)>\rangle k_0^2}]\right)</math>, γ value is around 2.

For less thick cells and in transmission, the relationship depends also on l* (the transport length)<ref>D. A. Weitz and D. J. Pine, “Diffusing-wave spectroscopy,” in Dynamic Light scattering, W. Brown, ed., Clarendon Press, Oxford (1993) 652–720</ref>.

For less thick cells and in transmission, the relationship depends also on l* (the transport length)<ref>D. A. Weitz and D. J. Pine, “Diffusing-wave spectroscopy,” in Dynamic Light scattering, W. Brown, ed., Clarendon Press, Oxford (1993) 652–720</ref>.

==Multispeckle Diffusing-Wave Spectroscopy (MSDWS)==

{{cite book

|author1=D. A. Weitz |author2=D. J. Pine |year=1993

|chapter=Diffusing-wave spectroscopy

|editor=W. Brown

|title=Dynamic Light scattering

|pages=652–720

|publisher=[[Clarendon Press]]

|isbn=978-0-19-853942-1

}}</ref>

For quasi-transparent cells, an angle-independent variant method called cavity amplified scattering spectroscopy<ref>{{Cite journal |last1=Graciani |first1=Guillaume |last2=King |first2=John T. |last3=Amblard |first3=François |date=2022-08-30 |title=Cavity-Amplified Scattering Spectroscopy Reveals the Dynamics of Proteins and Nanoparticles in Quasi-transparent and Miniature Samples |url=https://pubs.acs.org/doi/10.1021/acsnano.2c06471 |journal=ACS Nano |volume=16 |issue=10 |language=en |pages=16796–16805 |doi=10.1021/acsnano.2c06471 |pmid=36039927 |arxiv=2111.09616 |s2cid=244345602 |issn=1936-0851}}</ref> makes use of an [[integrating sphere]] to isotropically probe samples from all directions, elongating photon paths through the sample in the process, allowing for the study of low turbidity samples under the DWS formalism.

This technique either uses a camera to detect many speckle grains (see [[speckle pattern]]) or a ground glass to create a large number of speckle realizations (Echo-DWS <ref>http://spie.org/x8591.xml?highlight=x2404&ArticleID=x8591</ref>). In both cases an average over a large number of statistically independent intensity values is obtained, allowing a much faster data acquisition time.

==Multispeckle Diffusingdiffusing-Wavewave Spectroscopyspectroscopy (MSDWS)==

This technique either uses a camera to detect many speckle grains (see [[speckle pattern]]) or a ground glass to create a large number of speckle realizations (Echo-DWS <ref>{{Cite web|url=http://spie.org/x8591.xml?highlight=x2404&ArticleID=x8591|title=Light scattering technique reveals properties of soft solids}}</ref>). In both cases an average over a large number of statistically independent intensity values is obtained, allowing a much faster data acquisition time.

<gallery>

Image:figureMSDWS.png|Typical setup of Multispeckle Diffusing-wave spectroscopy

</gallery>

<math>g_2(\tau)=\frac{<\langle I(t)I(t+\tau)>_p\rangle_p}{<\langle I(t)>_p\rangle_p^2}</math>

MSDWS is particularly adapted for the study of slow dynamics and non ergodic media. Echo-DWS allows seamless integration of MSDWS in a traditional DWS-scheme with superior [[temporal resolution]] down to 12ns <ref>Multispeckle diffusing-wave spectroscopy with a single-mode detection scheme, P12&nbsp;ns. Zakharov, F. Cardinaux, and F. Scheffold, Phys. Rev. E 73, 011413 (2006) http://link.aps.org/doi/10.1103/PhysRevE.73.011413]</ref>. Camera based adaptive image processing

{{cite journal

<ref>L. Brunel, A. Brun, P. Snabre, and L. Cipelletti, Optics Express, Vol. 15, Issue 23, pp. 15250-15259 [http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-15-23-15250]</ref> [http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-15-23-15250]

|author1=P. Zakharov |author2=F. Cardinaux |author3=F. Scheffold |year=2006

allows online measurement of particle dynamics for example during drying.

|title=Multispeckle diffusing-wave spectroscopy with a single-mode detection scheme

|journal=[[Physical Review E]]

|volume=73 |issue=1 |pages=011413

|doi=10.1103/PhysRevE.73.011413

|pmid=16486146 |arxiv = cond-mat/0509637 |bibcode = 2006PhRvE..73a1413Z |s2cid=6251182 }}</ref> Camera based adaptive image processing allows online measurement of particle dynamics for example during drying.<ref>

{{cite journal

|author1=L. Brunel |author2=A. Brun |author3=P. Snabre |author4=L. Cipelletti |title=Adaptive Speckle Imaging Interferometry: a new technique for the analysis of microstructure dynamics, drying processes and coating formation

|url=http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-15-23-15250

|journal=[[Optics Express]]

|volume=15 |issue=23 |pages=15250–15259

|year=2007

|doi=10.1364/OE.15.015250

|bibcode = 2007OExpr..1515250B

|pmid=19550809|arxiv = 0711.1219 |s2cid=5753232 }}</ref>

==References==

{{Reflist}}

<references/>

==External links==

*[https://web.archive.org/web/20110930154856/http://www.formulaction.com/technology_dws.html Diffusing Wave Spectroscopy Overview with video]

* Formulation SA, France [http://www.formulaction.com/]

*[http://www.lsinstruments.ch/technology/diffusing_wave_spectroscopy_dws/ Diffusing Wave Spectroscopy Overview with Animations] {{Webarchive|url=https://web.archive.org/web/20140520215951/http://www.lsinstruments.ch/technology/diffusing_wave_spectroscopy_dws |date=2014-05-20 }}

*LSInstruments GmbH, Switzerland [http://www.lsinstruments.ch/]

*[http://www.lsinstruments.ch/technology/diffusing_wave_spectroscopy_dws/dws_particle_sizing/ Particle Sizing using Diffusing Wave Spectroscopy] {{Webarchive|url=https://web.archive.org/web/20140520220247/http://www.lsinstruments.ch/technology/diffusing_wave_spectroscopy_dws/dws_particle_sizing/ |date=2014-05-20 }}

[[Category:Physics]]

[[Category:Optics]]

[[Category:PhysicsSpectroscopy]]

[[Category:Soft matter]]