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 lightscattered scattererslight in the caselimit of strong multiple scattering.<ref>

{{Nolead|date=October 2009}}

{{cite journal

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

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

|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 suspensions[[Suspension (chemistry)|suspension]]s, [[emulsions]], [[foams]], gels, biological media, etcand other forms of [[soft matter]]. If carefully calibrated, DWS allows the quantitative measurement of particlemicroscopic motion in a soft material, from which the [[rheological]] properties of the complex medium andcan thenbe itsextracted rheologyvia the ([[Microrheologymicrorheology]]) approach.

==One-speckle diffusing-wave spectroscopy==

A laserLaser light is sent insideto the productsample 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.

Diffusing-wave spectroscopy is an optical technique derived from [[dynamic light scattering]] (DLS) that studies the dynamics of light scatterers in the case of strong multiple scattering.

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

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

It has been widely used to study colloidal suspensions, emulsions, foams, gels, biological media, etc. If carefully calibrated, DWS allows the measurement of particle motion in a complex medium and then its rheology ([[Microrheology]]).

A laser light is sent inside the product 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.

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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>

<br /><br />

For the case of non-interacting particles suspended in a (complex) fluid a direct relation between g₂-1 and the [[mean squared displacement]] of the particles <Δr²> can be established. Let us note P(s) the probability density function (PDF) of the photon path length s. The relation can be written as follows:<ref>

{{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 />

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

For simple cell geometries, it is thus possible to calculate the mean squaresquared displacement of the particles <Δr²> withfrom respectthe tomeasured 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[\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>

In general the relation between g₂-1 and the mean square displacement of the particles <Δr²> depends on the photons trajectories. Let's note P(s) the probability density function (PDF) of the photon path length s. The relation can be written as following:<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 book

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

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

with <math>k_0=\frac{2\pi n}{\lambda}</math> and <math>l*</math>: the transport length.

|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.

For simple cell geometries, it is possible to calculate the mean square displacement of the particles <Δr²> with respect to g₂-1. 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 ship 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.

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

For less thick cells and transmission, the relationship depends 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>.

The multiple scattering implies a high dependence on the cell geometry and . An advantage is that the control of the geometry allows to control the studied length scale.

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.

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

This technique uses a camera to detect many speckle grains (see [[speckle pattern]]) at the same time. In this case the averaging is done among the camera pixels, allowing a much faster 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>

This 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 12&nbsp;ns.<ref>

{{cite journal

An adaptive image processing

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

<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]

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

allows online measurement of particle dynamics for example drying.

|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/tech_dws_gbtechnology_dws.html Diffusing Illustrated descriptionWave ofSpectroscopy DWSOverview with moviesvideo]

*[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 }}

*[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:PhysicsSpectroscopy]]

[[Category:Optics]]

[[Category:Soft matter]]