Imaging In Random Media Research Articles

Imaging in Random Media by Two-Point Coherent Interferometry

This paper considers wave-based imaging through a heterogeneous (random) scattering medium. The goal is to estimate the support of the reflectivity function of a remote scene from measurements of t...

Passive Array Imaging in Random Media

We present a novel algorithm for a high-resolution coherent imaging of sound sources in random scattering media using time-resolved measurements of the acoustic pressure at an array of receivers. The sound waves travel a long distance between the sources and receivers so that they are significantly affected by scattering in the random medium. We model the scattering effects by large random wavefront distortions, but the results extend to stronger effects, as long as the waves retain some coherence, i.e., before the onset of wave diffusion. It is known that scattering in random media can be mitigated in imaging using coherent interferometry (CINT). This method introduces a statistical stabilization in the image formation, at the cost of image blur. We show how to modify the CINT method in order to image wave sources that are too close to each other to be distinguished by CINT alone. We introduce the algorithm from first principles and demonstrate its performance with numerical simulations.

Wavefront shaping of acoustic waves in scattering media

As an essential necessity for fundamental study and a broad variety of technological applications, it is important to control the propagation of acoustic waves and select their particular wavefronts. This work is to achieve effective wavefront shaping of acoustic waves along specific paths in strongly scattering media including phononic periodic structures and random media. In the phononic crystal, a kind of artificial phononic structures, wavefront shaping, and super-resolution imaging have been achieved by designing the geometry and material parameters. Furthermore, the confocal technique of the optical beam and acoustic beam has been improved to achieve sub-wavelength imaging in random media with strongly scattering. The presented results of wavefront shaping have implications for tailoring phonon dynamics in scattering media, which offers further possibilities of controllable acoustic waves in complex materials and enlightens the interaction of multi-physics fields.

Second-harmonic imaging in random media

We consider the problem of optical imaging of small nonlinear scatterers in random media. We propose an extension of coherent interferometric imaging (CINT) that applies to scatterers that emit second-harmonic light. We compare this method to a nonlinear version of migration imaging and find that the images obtained by CINT are more robust to statistical fluctuations. This finding is supported by a resolution analysis that is carried out in the setting of geometrical optics in random media. It is also consistent with numerical simulations for which the assumptions of the geometrical optics model do not hold.

Imaging in Random Media with Convex Optimization

We study an inverse problem for the wave equation where localized wave sources in random scattering media are to be determined from time resolved measurements of the waves at an array of receivers. The sources are far from the array, so the measurements are affected by cumulative scattering in the medium, but they are not further than a transport mean free path, which is the length scale characteristic of the onset of wave diffusion that prohibits coherent imaging. The inversion is based on the coherent interferometric (CINT) imaging method, which mitigates the scattering effects by introducing an appropriate smoothing operation in the image formation. This smoothing stabilizes the images statistically, at the expense of their resolution. We complement the CINT method with a convex ($l_1$) optimization in order to improve the source localization and obtain quantitative estimates of the source intensities. We analyze the method in a regime where scattering can be modeled by large random wavefront distortio...

Statistical Stability of Ultrawideband Time-Reversal Imaging in Random Media

We carry out a study on the statistical stability of ultrawideband (UWB) time-reversal (TR) imaging in random media under different combinations of random medium parameters and interrogating signal properties. We examine conditions under which frequency decorrelation in random media provides a more effective “self-averaging” and, therefore, better statistical stability. We also present a new frequency-synthesized technique for UWB TR-based imaging. This technique is employed to construct TR-operator-decomposition and multiple-signal-classification images using either linear or full-aspect transceiver array configurations. The proposed technique automatically provides the best images of desired target(s) in terms of focusing resolution without the need for (synthetic) propagation of TR signals and ad hoc determination of the optimal focusing time instant. In addition, information about the imaging domain (background) can be stored and reused to reconstruct different targets.

Limits to the representation capacity of imaging in random media

The information capacity of an image in the atmosphere, ocean, or biological media does not grow indefinitely with increasing light power but has well defined limits. Here, the exact effects of the propagation of light in random inhomogeneous media are elucidated and upper bounds to the capacity of image pixels to represent a corresponding point in the object are described.

Subspace projection filters for imaging in random media

We consider the problem of selective imaging extended reflectors in cluttered media. We propose a random travel time model for simulating the array response matrix in clutter and we compare it with the full wave solution. Our simplified model captures very well the full wave random medium behavior as this is illustrated by our numerical results. The algorithm for selective array imaging uses coherent interferometry on a filtered version of the data. The filter, which is based on the singular value decomposition of the response matrix, enhances the signal reflected by the edges of the reflector. We illustrate the performance of the imaging algorithm with numerical simulations in the regime of ultrasonic non-destructive testing in concrete.

From angle-resolved ellipsometry of light scattering to imaging in random media

A procedure is described to allow selective cancellation of polarized scattering within optical substrates and multilayers. It is shown how bulk scattering (respectively surface) can be directly eliminated while the remaining roughness (respectively bulk) signal is still measurable. The same procedure can be applied to isolate a single interface or bulk within a stack or to detect slight departure from perfect correlation within multilayers. Experiments and a procedure for selective imaging in random media are described.

Transport-Based Imaging in Random Media

This paper generalizes well-established derivations of the radiative transfer equation from first principles to model the energy density of time-dependent and monochromatic high frequency waves pro...

Optimal illumination and wave form design for imaging in random media

The problem of optimal illumination for selective array imaging of small and not well separated scatterers in clutter is considered. The imaging algorithms introduced are based on the coherent interferometric (CINT) imaging functional, which can be viewed as a smoothed version of travel-time migration. The smoothing gives statistical stability to the image but it also causes blurring. The trade-off between statistical stability and blurring is optimized with an adaptive version of CINT. The algorithm for optimal illumination and for selective array imaging uses CINT. It is a constrained optimization problem that is based on the quality of the image obtained with adaptive CINT. The resulting optimal illuminations and selectivity improve the resolution of the images significantly, as can be seen in the numerical simulations presented in the paper.

Selective probing and imaging in random media based on the elimination of polarized scattering

An ellipsometric technique based on angle-resolved light scattering is addressed to open applications in the field of imaging in random media. The first experimental demonstration is given to prove the selective extinction of different scattering sources such as surface roughness and bulk heterogeneity in optical components and liquids. The results are compared with theory.

Kinetic Models for Imaging in Random Media

We derive kinetic models for the correlations and the energy densities of wave fields propagating in random media. These models take the form of radiative transfer and diffusion equations. We use these macroscopic models to address the detection and imaging of small objects buried in highly heterogeneous media. More specifically, we quantify the influence of small objects on (i) the energy density measured at an array of detectors and (ii) the correlation between the wave field measured in the absence of the object and the wave field measured in the presence of the object. We analyze the advantages and disadvantages of such measurements as a function of the level of disorder in the random media. Numerical simulations verify the theoretical predictions.

Propagation of terahertz pulses in random media.

We describe measurements of single-cycle terahertz pulse propagation in a random medium. The unique capabilities of terahertz time-domain spectroscopy permit the characterization of a multiply scattered field with unprecedented spatial and temporal resolution. With these results, we can develop a framework for understanding the statistics of broadband laser speckle. Also, the ability to extract information on the phase of the field opens up new possibilities for characterizing multiply scattered waves. We illustrate this with a simple example, which involves computing a time-windowed temporal correlation between fields measured at different spatial locations. This enables the identification of individual scattering events, and could lead to a new method for imaging in random media.

Statistically stable ultrasonic imaging in random media.

Analysis of array data from acoustic scattering in a random medium with a small number of isolated targets is performed in order to image and, thereby, localize the spatial position of each target. Because the host medium has random fluctuations in wave speed, the background medium is itself a source of scattered energy. It is assumed, however, that the targets are sufficiently larger and/or more reflective than the background fluctuations so that a clear distinction can be made between targets and background scatterers. In numerical simulations nonreflective boundary conditions are used so as to isolate the effects of the host randomness from those of the spatial boundaries, which can then be treated in a separate analysis. It is shown that the key to successful imaging is finding statistically stable functionals of the data whose extreme values provide estimates of scatterer locations. The best ones are related to the eigenfunctions and eigenvalues of the array response matrix, just as one might expect from prior work on array data processing in complex scattering media having homogeneous backgrounds. The specific imaging functionals studied include matched-field processing and linear subspace methods, such as MUSIC (MUtiple SIgnal Classification). But statistical stability is not characteristic of the frequency domain, which is often the province of these methods. By transforming back into the time domain after first diagonalizing the array data in the frequency domain, one can take advantage of both the time-domain stability and the frequency-domain orthogonality of the relevant eigenfunctions.

Imaging and time reversal in random media

Time reversal in random media can result in refocusing on the source with a resolution that is better than the diffraction limit. This is because of the multipathing that occurs in the random medium, making the time reversal array appear to be wider than it is. What is not clear, however, is why this phenomenon is statistically stable. That is, why the refocused spot size does not fluctuate in the random medium. The reason for this statistical stability is that it is a time domain phenomenon and does not occur with narrow band signals. I will explain this effect analytically and will also show how it can be used for imaging in random media.

Long distance time reversal and imaging in random media: Numerical simulations

We have conducted a careful time reversal and imaging study for long distance wave propagation in random media in the underwater acoustics regime. In this talk we briefly describe the computational technology, which is based on a phase-screen propagation code for the paraxial wave equation. The advantages and limitations of the code are discussed. We show some time reversal results which demonstrate the super-resolution phenomenon and its statistical stability in the time domain. We also show results of imaging in random media using an array of active transducers.

Imaging in random media

We present a general method for estimating the location of small scatterers buried in a random, weakly scattering medium, using an active antenna array. The main features of this method are (i) an arrival time analysis of the echo received from the scatterers, (ii) a singular value decomposition of the array response matrix in the frequency domain, and (iii) the construction of an objective function in the time domain that is statistically stable and peaks on the scatterers. By statistically stable we mean that the objective function is self-averaging over different realizations of the medium. This is a new approach to array imaging that is motivated by recent studies of time reversal in a random medium. It combines features from seismic imaging like arrival time analysis with frequency domain radar signal subspace methodology like MUSIC (MUltiple SIgnal Classification).

Modeling of high-frequency wave propagation with application to the double-passage imaging in random media

It is shown that uncertainty considerations play an important role in the construction of high-frequency propagators in randomly fluctuating media. A paired field measure and its spectral transforms known as Wigner and ambiguity functions have been defined in order to account for the uncertainty in the spatial location and the slope of geometrical ray trajectories. The values of these functions at the source plane and the observation plane are related by mixed space-spectral propagators. Writing these propagators in the path integral form and replacing the multiple trajectories by straight ray trajectories leads to solutions that correctly represent intensity correlation characteristics. The fact that the above propagators contain information about the random refractive-index variation along the propagation path allows their application to double-passage analysis when the scattered backward radiation traverses the same random inhomogeneities as the incident one. The resolution effects arising as a result of backward reflection of a spherical wave from a two-point-scatterer target are considered