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Radiative transfer and diffusion limits for wave field correlations in locally shifted random media

Habib Ammari Department of Mathematics and Applications, Ecole Normale Supérieure, 45 Rue d’Ulm, 75005 Paris, France Emmanuel Bossy Institut Langevin, ESPCI ParisTech, CNRS UMR 7587, 10 rue Vauquelin, 75231 Paris Cedex 05, France Josselin Garnier Laboratoire de Probabilités et Modèles Aléatoires & Laboratoire Jacques-Louis Lions, Université Paris VII, 75205 Paris Cedex 13, France Wenjia Jing Department of Mathematics and Applications, Ecole Normale Supérieure, 45 Rue d’Ulm, 75005 Paris, France Laurent Seppecher Department of Mathematics and Applications, Ecole Normale Supérieure, 45 Rue d’Ulm, 75005 Paris, France

Analysis of PDEs Mathematical Physics mathscidoc:2206.03007

Journal of Mathematical Physics, 54, (2), 021501, 2013.2
The aim of this paper is to develop a mathematical framework for opto-elastography. In opto-elastography, a mechanical perturbation of the medium produces a decorrelation of optical speckle patterns due to the displacements of optical scatterers. To model this, we consider two optically random media, with the second medium obtained by shifting the first medium in some local region. We derive the radiative transfer equation for the cross-correlation of the wave fields in the media. Then we derive its diffusion approximation. In both the radiative transfer and the diffusion regimes, we relate the correlation of speckle patterns to the solutions of the radiative transfer and the diffusion equations. We present numerical simulations based on our model which are in agreement with recent experimental measurements.
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@inproceedings{habib2013radiative,
  title={Radiative transfer and diffusion limits for wave field correlations in locally shifted random media},
  author={Habib Ammari, Emmanuel Bossy, Josselin Garnier, Wenjia Jing, and Laurent Seppecher},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220622160258489025455},
  booktitle={Journal of Mathematical Physics},
  volume={54},
  number={2},
  pages={021501},
  year={2013},
}
Habib Ammari, Emmanuel Bossy, Josselin Garnier, Wenjia Jing, and Laurent Seppecher. Radiative transfer and diffusion limits for wave field correlations in locally shifted random media. 2013. Vol. 54. In Journal of Mathematical Physics. pp.021501. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220622160258489025455.
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