Spatially resolved measurements of micro-deformations in granular materials using diffusing wave spectroscopy

Abstract

This article is a tutorial on the practical implementation of a method of measurement of minute deformations based on multiple scattering. This technique has been recently developed and has proven to give new insights on the spatial repartition of strain in a granular material. We provide here the basics to understand the method by giving a synthetic review on Diffusing Wave Spectroscopy and multiple scattering in granular materials. We detail a simple experiment using standard lab equipment to pedagogically demonstrate the implementation of the method. Finally we give a few examples of measurements that have been obtained in other works to discuss the potential of the method.

Preface: Focus on imaging methods in granular physics

“…34 Alternatively, it is possible to embrace the multiple scattering effects and use coherent light to gather information from the resulting speckle pattern. 35 Finally, we can abandon the range of visible light entirely and instead use penetrating radiation to obtain the data from the bulk of the sample. A variety of such methods are extensively covered in this focus edition, covering terahertz electromagnetic radiation, 36 radar, 37 positron emission, 38 nuclear magnetic resonance, 39 and X-ray tomography.…”

“…These techniques are reviewed in an article of this Focus Issue. 35 Finally, as discussed in the introduction, acoustic echo 42 or Doppler measurement 41 can be used to measure velocities in the limit of single scattering of the acoustic waves. The usefulness of such methods is rapidly limited by multiple scattering in granular piles.…”

Self-consistent quantum field theory for the characterization of complex random media by short laser pulses

“…where a represents the amplification or absorption length of the intensity and osc marks the length over which the intensity oscillates, where ξ 2 a has already been defined in Eq. (34 ). The corresponding time scales may then be defined as…”

“…Non-invasive and non-destructive methods of optical analysis and medical imaging that can detect reflected signals as small as 10 −10 of the incident intensity and beyond [9,[11][12][13][14] might be improved again by orders of magnitude. Their application range could be systematically improved in the fields of dynamic and non-conserving media, nematic liquid crystals, semiconductors for telecom applications, glasses and tissue [34,[50][51][52][53]. In this article we develop a quantum field theory for photonic transport in dense multiple scattering complex random media, see Fig.…”

Laser Speckle Strain Imaging reveals the origin of delayed fracture in a soft solid

“…In principle, the d 2 function measures a convolution of both types of motion. To disentangle these contributions, we first convert d 2 to the electric field correlation function g 1 (see Materials and Methods), which we can subsequently express as ( 20 , 34 ) where k 0 = 2π n /λ is the wave vector with n = 1.5 the refractive index of poly(dimethylsiloxane) (PDMS), h = 5 mm is the sample thickness, with U the strain tensor and Tr its trace, l * = 50 μm is the photon transport mean free path determined independently by means of coherent backscattering (see Materials and Methods), and 〈Δ r 2 〉 is the Brownian mean-square displacement of the tracer particles. We consider the latter constant (at fixed τ) and set it at the mean-square displacement of the nanoparticles in the quiescent material (see Materials and Methods).…”