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>

==One speckle Diffusing-wave_spectroscopy==

{{cite journal

Diffusing-wave spectroscopy is an optical technique derivated from [[Dynamic light scattering]] (DLS) that study the dynamics of light scatterers in the case of strong multiple scattering

<ref> |author1=G. Maret and |author2=P. E. Wolf, Z. Phys. B: Condens. Matter 65, 409 |year=1987</ref>

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

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

|journal=[[Zeitschrift für Physik B]]

. 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]])<br />

|volume=65 |pages=409

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. <br />

|doi=10.1007/BF01303762

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

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

{{cite journal

|author1=D. J. Pine |author2=D. A. Weitz |author3=P. M. Chaikin |author4=E. Herbolzheimer |year=1988

|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 [[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>

Image:figureDWS.png|Typical setup of Diffusingdiffusing-wave spectroscopy

</gallery>

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

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

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

{{cite journal

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

|author=F. Scheffold

<br /><br />

|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>

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 />

<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>: the transport length.<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> 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[-2 \gamma \sqrt{<\Delta r^2(\tau)>k_0^2}]</math>, γ value is around 2.<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 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 dependance on the cell geometry and . An advantage is that the control of the geometry allows to control the studied length scale.<br /><br />

For less thick cells and in transmission, the relationship depends also on l* (the transport length).<ref>

{{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.

==Multispeckle diffusing-wave spectroscopy (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.

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

This technique use a camera to detects 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>

<br />

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]]