Abstract
The propagation of monochromatic light through a scattering medium produces speckle patterns in reflection and transmission, and the apparent randomness of these patterns prevents direct imaging through thick turbid media. Yet, since elastic multiple scattering is fundamentally a linear and deterministic process, information is not lost but distributed among many degrees of freedom that can be resolved and manipulated. Here, we demonstrate experimentally that the reflected and transmitted speckle patterns are robustly correlated, and we unravel all the complex and unexpected features of this fundamentally non-Gaussian and long-range correlation. In particular, we show that it is preserved even for opaque media with thickness much larger than the scattering mean free path, proving that information survives the multiple scattering process and can be recovered. The existence of correlations between the two sides of a scattering medium opens up new possibilities for the control of transmitted light without any feedback from the target side, but using only information gathered from the reflected speckle.
9 More- Received 1 December 2017
- Revised 8 March 2018
DOI:https://doi.org/10.1103/PhysRevX.8.021041
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
Physics Subject Headings (PhySH)
Popular Summary
When coherent light (like a laser) passes through or reflects off most materials, it scatters and creates what is known as a speckle pattern, a seemingly random intensity pattern. These speckles limit the precision of many types of imaging applications, including microscopic images of biological processes and ground-based telescopic views of space. Common sense suggests that reflected and transmitted light are completely uncorrelated—no information can be obtained regarding the transmitted light by measuring the reflected one and vice versa. However, some of our team recently predicted that interference effects should lead to such correlations. We experimentally investigate this prediction, and we find that this correlation not only exists but is much richer and more complicated than expected.
We shine a helium-neon laser at a 45-degree angle onto a slab of glycerol with suspended particles of titanium dioxide and look for correlations between the speckle patterns of the transmitted and reflected light. By exploring a large range of sample thicknesses and scattering mean-free paths, we show that for large optical densities, the reflected and transmitted intensity profiles exhibit a long-range anticorrelation. For thinner systems, this is accompanied by a previously unforeseen long-range positive correlation. We develop a perturbative theory that describes both contributions and accurately represents the experimental results.
The presence of correlations between the reflected and transmitted light proves that information of what is happening on the far side of an opaque medium can, in principle, be obtained by only measuring reflected light, thus opening the way to novel noninvasive imaging techniques.