Focusing Waves Through a Randomly Scattering Medium in the White-Noise Paraxial Regime

Abstract

When waves propagate through a complex or heterogeneous medium the wave field is corrupted by the heterogeneities. Such corruption limits the performance of imaging or communication schemes. One may then ask the question, Is there an optimal way of encoding a signal so as to counteract the corruption by the medium? In the ideal situation the answer is given by time reversal: for a given target or focusing point, in a first step let the target emit a signal and then record the signal transmitted to the source antenna, time reverse this, and use it as the source trace at the source antenna in a second step. This source will give a sharply focused wave at the target location if the source aperture is large enough. Here we address this scheme in the more practical situation with a limited aperture, time-harmonic signal, and finite-sized elements in the source array. Central questions are then the focusing resolution and signal-to-noise ratio at the target, their dependence on the physical parameters, and the capacity to focus selectively in the neighborhood of the target point and therefore to transmit images. Sharp results are presented for these questions.

Speckle Memory Effect in the Frequency Domain and Stability in Time-Reversal Experiments

“…If we consider the case when y = 0, then we find that the variance of the refocused wave has the form Var ûtr x; 0 = 1 1 + DL This result has already been obtained (when Ω = 0) in [16]. When DL 3 ≫ r 2 0 , ρ 2 0 , we find that the SNR varies as r 2 0 /ρ 2 0 , that is to say, as the number of elements of the TRM.…”

Partially Coherent Electromagnetic Beam Propagation in Random Media

“…where ρ tr corresponds to the refocusing resolution one obtains when a point source emits a wave which is captured on a time reversal mirror at distance L and reemitted (after time reversal) toward the source. Then it will refocus at the original source location with a resolution of the order of the lateral correlation range ρ tr (L) essentially independently of the actual physical aperture [22]. This can be understood in that the propagator of the transmitted wave decorrelates (laterally) on this scale and the refocused wave is essentially the convolution of the propagator with itself.…”

Scintillation of Partially Coherent Light in Time Varying Complex Media

“…For convenience we use here a Gaussian correlation function for the spatial source correlations, but we remark that we could have used a more general form. A more detailed model for the source, in particular a discussion of realization via Spatial Light Modulators (SLMs) can be found in [24,2]. For other approaches to the generation of the partially coherent source we refer to [34] for instance.…”

“…The kernel (24) depends on the two-point statistics of the random medium fluctuations and reflects cumulative scattering effects over the propagation distance L. Note that g = 0 corresponds to the situation with intensities of wave fields having propagated through uncorrelated random media and that indeed Q 0 (L) = 0. The first term in the square brackets in (23) corresponds to the scintillation contribution from the fluctuations of the source and this contribution is damped by temporal decorrelation of the medium fluctuations as well as temporal averaging at the detector.…”