Non-Gaussian Correlations between Reflected and Transmitted Intensity Patterns Emerging from Opaque Disordered Media

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.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]. Under illumination with coherent light and for elastic scattering, interference produces large intensity fluctuations that is not averaged out by a single realization of the disorder, resulting in a seemingly random speckle pattern [2]. In principle the speckle pattern encodes all the information on the sample and the incident light [3]. A complete knowledge of the scattering matrix allows one to reverse the multiple scattering process and to recover the initial wavefront, thus permitting imaging through turbid materials [4,5]. Conversely, if the scattering matrix is not known, a multiply scattering material effectively behaves as an opaque screen.Speckle patterns are not as random as they appear at first sight. Interference between the possible scattering paths in the medium are known to produce spatial correlations between the intensity measured at different positions [6][7][8], and correlations of different ranges have been identified [9]. Short-range correlations determine the size of a speckle spot. Long-range correlations emerge as a consequence of constraints such as energy conservation or reciprocity [10][11][12]. Spatial correlations have not been used for imaging, a notable exception being the optical memory effect [13], a correlation of purely geometrical origin that has been exploited for non-invasive imaging through an opaque scattering layer [14,15].At first glance, as transmitted and reflected waves are expected to undergo very different multiple scattering sequences, correlations between transmitted and reflected wavefronts are expected to quickly average to zero. Very little attention has been given to cross-correlations between transmitted and reflected speckles, their existence being only mentionned in passing [16,17]. However, a recent theoretical study suggested that a long-range correlation should survive even for thick (opaque) scattering media [18]. Th...

Localization of scattering resonances in aperiodic Vogel spirals

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