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 correlated, even for opaque media with thickness much larger than the transport mean free path, proving that information survives the multiple scattering process and can be recovered. The existence of mutual information 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.
Highlights
In multiply scattering materials, the random inhomogeneities in the refractive index scramble the incident wavefront, mixing colors and spatial degrees of freedom, resulting in a white and opaque appearance [1]
We show that this correlation is robust and we provide a complete understanding of all its complex features, for scattering materials with thickness L and scattering mean free path l covering the entire range from single scattering (L ≲ l) to diffusive transport (L ≫ l)
We have demonstrated experimentally the existence of a cross-correlation between the speckle patterns measured in reflection and transmission on the surface of a disordered medium
Summary
The random inhomogeneities in the refractive index scramble the incident wavefront, mixing colors and spatial degrees of freedom, resulting in a white and opaque appearance [1]. A recent theoretical study suggested that a long-range correlation should survive even for thick (opaque) scattering media [18] The existence of this reflection-transmission (R-T) correlation suggests that one could noninvasively extract information on the transmitted speckle from a measurement restricted to the reflection half-space. We will identify a regime of moderate optical thickness, where the correlation function becomes anisotropic and keeps a memory of the illumination angle This memory effect, due to long-range correlations, has never been detected before and is fundamentally different from the well-known memory effect observed in transmission or reflection and resulting from Gaussian statistics [15]
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