- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access
  • Access by Xinjiang University

Light-scattering reconstruction of transparent shapes using neural networks

Tymoteusz Miara1,*,†, Draga Pihler-Puzović1, Matthias Heil2, and Anne Juel1,‡

  • 1Department of Physics & Astronomy, School of Natural Sciences, University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
  • 2Department of Mathematics, School of Natural Sciences, University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom

  • *Present address: School of Biological and Behavioural Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom.
  • †Contact author: tymoteuszmiara@gmail.com
  • ‡Contact author: anne.juel@manchester.ac.uk
PDF

Phys. Rev. Fluids 11, 064901 – Published 18 June, 2026

DOI: https://doi.org/10.1103/n2kn-zkqv

Abstract

The accurate characterization of the three-dimensional deformations of slender fibers and thin sheets in flow is a key experimental challenge in the study of particle-laden flows. We propose a high-resolution, single-camera method to visualize nonintrusively the shape of a transparent crumpled sheet, as it translates, rotates, and deforms. We perform periodic scans of the crumpled shape by illuminating it with a sequence of stacked light sheets at a rate much faster than its deformation and image the scattered light signal in a plane near orthogonal to the plane of lighting. Processing of the data using a pinhole camera model yields a noisy spatiotemporal dataset of the strongly deformed time-evolving surface of the sheet, which we reconstruct in three dimensions using a neural autoencoder. We validate the robustness of the shape reconstruction algorithm to noise using synthetic data sets, and demonstrate the accurate reconstruction of laboratory sedimentation experiments with elastic disks. We find that the inclusion of isometricity-enforcing penalties into the cost function of the autoencoder enables us to robustly reconstruct highly folded shapes, where different regions of the sheet overlap.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (33)

  1. M. Tavallaeinejad, M. F. Salinas, M. P. Païdoussis, M. Legrand, M. Kheiri, and R. M. Botez, Dynamics of inverted flags: Experiments and comparison with theory, J. Fluids Struct. 101, 103199 (2021).
  2. M. H. DiBenedetto, The fluid mechanics of ocean microplastics, Annu. Rev. Fluid Mech. 58, 355 (2025).
  3. Y. Liu, B. Chakrabarti, D. Saintillan, A. Lindner, and O. du Roure, Morphological transitions of elastic filaments in shear flow, Proc. Natl. Acad. Sci. USA 115, 9438 (2018).
  4. K. S. Silmore, M. S. Strano, and J. W. Swan, Buckling, crumpling, and tumbling of semiflexible sheets in simple shear flow, Soft Matter 17, 4707 (2021).
  5. B. Marchetti, V. Raspa, A. Lindner, O. du Roure, L. Bergougnoux, E. Guazzelli, and C. Duprat, Deformation of a flexible fiber settling in a quiescent viscous fluid, Phys. Rev. Fluids 3, 104102 (2018).
  6. Y. Yu and M. D. Graham, Free-space and near-wall dynamics of a flexible sheet sedimenting in Stokes flow, Phys. Rev. Fluids 9, 054104 (2024).
  7. M. Sugathapala, T. Capuano, L. Brandt, D. Iudicone, and G. Sardina, Vertical transport of buoyant microplastic particles in the ocean: The role of turbulence and biofouling, Environ. Pollut. 369, 125819 (2025).
  8. B. Cyganek and J. P. Siebert, An Introduction to 3D Computer Vision Techniques and Algorithms (John Wiley & Sons, New York, 2009).
  9. H. Li, A. Juel, F. Box, and D. Pihler-Puzović, Propagation of air fingers into an elasto-rigid Y-bifurcation, Phys. Rev. Fluids 8, 094001 (2023).
  10. J. R. Lister, G. G. Peng, and J. A. Neufeld, Viscous control of peeling an elastic sheet by bending and pulling, Phys. Rev. Lett. 111, 154501 (2013).
  11. N. Ben-Shachar, D. R. Brumley, A. J. Hogg, and E. M. Hinton, Viscoplastic slumps supported by a barrier, J. Fluid Mech. 1017, A14 (2025).
  12. S. Wildeman, Real-time quantitative Schlieren imaging by fast Fourier demodulation of a checkered backdrop, Exp. Fluids 59, 97 (2018).
  13. W.-E. Khatla, Écoulements modéles de films minces géo-inspirés : Étalement et coalescence de cloques visqueuses, Ph.D. thesis, ESPCI, Universite Paris PSL, 2024.
  14. H. Aharoni and E. Sharon, Direct observation of the temporal and spatial dynamics during crumpling, Nat. Mater. 9, 993 (2010).
  15. Y. C. Lin, J. M. Sun, J. H. Hsiao, Y. Hwu, C. L. Wang, and T. M. Hong, Spontaneous emergence of ordered phases in crumpled sheets, Phys. Rev. Lett. 103, 263902 (2009).
  16. B. Chakrabarti, Y. Liu, J. LaGrone, R. Cortez, L. Fauci, O. du Roure, D. Saintillan, and A. Lindner, Flexible filaments buckle into helicoidal shapes in strong compressional flows, Nat. Phys. 16, 689 (2020).
  17. G. A. Voth and A. Soldati, Anisotropic particles in turbulence, Annu. Rev. Fluid Mech. 49, 249 (2017).
  18. C. Brouzet, G. Verhille, and P. LeGal, Flexible fiber in a turbulent flow: A macroscopic polymer, Phys. Rev. Lett. 112, 074501 (2014).
  19. C. Marchioli, M. E. Rosti, and G. Verhille, Flexible fibers in turbulence, Annu. Rev. Fluid. Mech. 58, 167 (2026).
  20. G. Verhille and A. Bartoli, 3D conformation of a flexible fiber in a turbulent flow, Exp. Fluids 57, 117 (2016).
  21. K.-M. Cheung, S. Baker, and T. Kanade, Shape-from-silhouette across time. Part I: Theory and algorithms, Int. J. Comput. Vis. 62, 221 (2005).
  22. G. Verhille, Deformability of discs in turbulence, J. Fluid Mech. 933, A3 (2022).
  23. E. Ibarra, B. Adrien, and V. Gautier, 3d reconstruction of a thin flexible disc in a vortical flow, Exp. Fluids 64, 172 (2023).
  24. Y. A. LeCun, L. Bottou, G. B. Orr, and K.-R. Müller, Efficient backprop, in Neural Networks: Tricks of the Trade: Second Edition, edited by G. Montavon, G. B. Orr, and K.-R. Müller (Springer, Berlin, 2012), pp. 9–48.
  25. S. Arora, N. Cohen, and E. Hazan, On the optimization of deep networks: Implicit acceleration by overparameterization, in 35th International Conference Machine Learning (ICML), Stockholm, Sweden (International Machine Learning Society, 2018), pp. 372–389.
  26. D. P. Kingma and J. Ba, Adam: A method for stochastic optimization, in International Conference on Learning Representations (ICLR), San Diego, CA (University of Amsterdam, 2015).
  27. K. He, X. Zhang, S. Ren, and J. Sun, Delving deep into rectifiers: Surpassing human-level performance on ImageNet classification, in 2015 IEEE International Conference on Computer Vision (ICCV), Santiago, Chile (IEEE, Piscataway, NJ, 2015), pp. 1026–1034.
  28. S. Kubota, H. Hayashi, T. Hayase, and S. Uchida, Layer-wise interpretation of deep neural networks using identity initialization, in ICASSP 2021-2021 IEEE International Conference on Acoustics, Speech and Signal Processing, Toronto, Ontario, Canada (IEEE, Piscataway, NJ, 2021), pp. 3945–3949.
  29. https://github.com/TymoteuszMiara/Light-scattering-reconstruction-of-transparent-shapes-using-neural-networks.
  30. T. Miara, Folding flakes: The deformation of elastic sheets in viscous flow, Ph.D. thesis, University of Manchester, 2024.
  31. J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics (Martinus Nijhoff Publishers, The Hague, 1983).
  32. L. D. Landau, E. M. Lifshitz, A. M. Kosevich, and L. P. Pitaevskii, Theory of Elasticity, 3rd ed., Course of Theoretical Physics Vol. 7 (Butterworth-Heinemann, Oxford, 1986).
  33. Z. Wang, D. Tonderys, S. E. Leggett, E. K. Williams, M. T. Kiani, R. Spitz Steinberg, Y. Qiu, I. Y. Wong, and R. H. Hurt, Wrinkled, wavelength-tunable graphene-based surface topographies for directing cell alignment and morphology, Carbon 97, 14 (2016).

Outline

Information

Phys. Rev. Fluids 11, 064901– Published 18 June, 2026
  • Received 29 October 2025
  • Accepted 6 May 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation