The vanishing distance: a practical range boundary for dynamic wavefront shaping
Abstract
Optical imaging and transmission through scattering media conventionally rely on ballistic light, whose power decays exponentially with the optical thickness. Although ballistic light cannot be exploited beyond a certain depth, no simple criterion currently identifies this limit. Therefore, we introduce here the vanishing distance that is defined as the propagation length at which the ballistic power equals the power carried by a single diffuse optical mode. Beyond the vanishing distance, multiply scattered light dominates, which can be harnessed by optical wavefront shaping or by computational reconstructions. We present a simple semi-analytical model for radiance propagation, validated by Monte Carlo simulations and by experiments in both monodisperse and heterogeneous scattering media. From these data, we estimate the vanishing distance and the associated minimum source power. Across representative scattering environments, ballistic light vanishes after about 20 to 40 scattering mean free paths. Unlike the transport mean free path that characterizes the angular randomization of the scattered light, the vanishing distance identifies the loss of the ballistic channel on a modal-power basis. The vanishing distance is thus a two-sided bound: ballistic approaches cannot be efficiently applied beyond it, whereas wavefront shaping of scattered light offers no advantage below it.
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BibTeX
@misc{lassiette2026vanishing,
title = {{The vanishing distance: a practical range boundary for dynamic wavefront shaping}},
author = {Hugo Lassiette and Léa Testé and Léa Krafft and Geoffrey Maulion and Vincent Michau and Romain Pierrat and Sébastien Popoff and Willem L. Vos and Serge Meimon},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.17551},
eprint = {2608.17551},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05740350v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - The vanishing distance: a practical range boundary for dynamic wavefront shaping
AU - Hugo Lassiette
AU - Léa Testé
AU - Léa Krafft
AU - Geoffrey Maulion
AU - Vincent Michau
AU - Romain Pierrat
AU - Sébastien Popoff
AU - Willem L. Vos
AU - Serge Meimon
PY - 2026
DA - 2026/09/07
PB - HAL
DO - 10.48550/arxiv.2608.17551
UR - https://hal.science/hal-05740350v1
AB - Optical imaging and transmission through scattering media conventionally rely on ballistic light, whose power decays exponentially with the optical thickness. Although ballistic light cannot be exploited beyond a certain depth, no simple criterion currently identifies this limit. Therefore, we introduce here the vanishing distance that is defined as the propagation length at which the ballistic power equals the power carried by a single diffuse optical mode. Beyond the vanishing distance, multiply scattered light dominates, which can be harnessed by optical wavefront shaping or by computational reconstructions. We present a simple semi-analytical model for radiance propagation, validated by Monte Carlo simulations and by experiments in both monodisperse and heterogeneous scattering media. From these data, we estimate the vanishing distance and the associated minimum source power. Across representative scattering environments, ballistic light vanishes after about 20 to 40 scattering mean free paths. Unlike the transport mean free path that characterizes the angular randomization of the scattered light, the vanishing distance identifies the loss of the ballistic channel on a modal-power basis. The vanishing distance is thus a two-sided bound: ballistic approaches cannot be efficiently applied beyond it, whereas wavefront shaping of scattered light offers no advantage below it.
ER -