Retrieving time-dependent Green's functions in optics with low-coherence interferometry

Harnessing forward multiple scattering for optical imaging deep inside an opaque medium

As light travels through a disordered medium such as biological tissues, it undergoes multiple scattering events. This phenomenon is detrimental to in-depth optical microscopy, as it causes a drastic degradation of contrast, resolution and brightness of the resulting image beyond a few scattering mean free paths. However, the information about the inner reflectivity of the sample is not lost; only scrambled. To recover this information, a matrix approach of optical imaging can be fruitful. Here, we report on a de-scanned measurement of a high-dimension reflection matrix R via low coherence interferometry. Then, we show how a set of independent focusing laws can be extracted for each medium voxel through an iterative multi-scale analysis of wave distortions contained in R. It enables an optimal and local compensation of forward multiple scattering paths and provides a three-dimensional confocal image of the sample as the latter one had become digitally transparent. The proof-of-concept experiment is performed on a human opaque cornea and an extension of the penetration depth by a factor five is demonstrated compared to the state-of-the-art.

Towards passive non-line-of-sight acoustic localization around corners using uncontrolled random noise sources

Non-line-of-sight (NLoS) imaging is an important challenge in many fields ranging from autonomous vehicles and smart cities to defense applications. Several recent works in optics and acoustics tackle the challenge of imaging targets hidden from view (e.g. placed around a corner) by measuring time-of-flight information using active SONAR/LiDAR techniques, effectively mapping the Green functions (impulse responses) from several controlled sources to an array of detectors. Here, leveraging passive correlations-based imaging techniques (also termed 'acoustic daylight imaging'), we study the possibility of acoustic NLoS target localization around a corner without the use of controlled active sources. We demonstrate localization and tracking of a human subject hidden around a corner in a reverberating room using Green functions retrieved from correlations of broadband uncontrolled noise sources recorded by multiple detectors. Our results demonstrate that for NLoS localization controlled active sources can be replaced by passive detectors as long as a sufficiently broadband noise is present in the scene.

Diffuse field cross-correlations: Scattering theory and electromagnetic experiments

The passive estimation of impulse responses from ambient noise correlations arouses increasing interest in seismology, acoustics, optics, and electromagnetism. Assuming the equipartition of the noise field, the cross-correlation function measured with noninvasive receiving probes converges towards the difference of the causal and anticausal Green's functions. Here, we consider the case when the receiving field probes are antennas which are well coupled to a complex medium-a scenario of practical relevance in electromagnetism. We propose a general approach based on the scattering matrix formalism to explore the convergence of the cross-correlation function. The analytically derived theoretical results for chaotic systems are confirmed in microwave measurements within a mode-stirred reverberation chamber. This study provides fundamental insight into the Green's function retrieval technique and paves the way for a new technique to characterize electromagnetic antennas.

Distortion matrix concept for deep optical imaging in scattering media

In optical imaging, light propagation is affected by the inhomogeneities of the medium. Sample-induced aberrations and multiple scattering can strongly degrade the image resolution and contrast. On the basis of a dynamic correction of the incident and/or reflected wavefronts, adaptive optics has been used to compensate for those aberrations. However, it only applies to spatially invariant aberrations or to thin aberrating layers. Here, we propose a global and noninvasive approach based on the distortion matrix concept. This matrix basically connects any focusing point of the image with the distorted part of its wavefront in reflection. A singular value decomposition of the distortion matrix allows to correct for high-order aberrations and forward multiple scattering over multiple isoplanatic modes. Proof-of-concept experiments are performed through biological tissues including a turbid cornea. We demonstrate a Strehl ratio enhancement up to 2500 and recover a diffraction-limited resolution until a depth of 10 scattering mean free paths.

Passive optical time-of-flight for non line-of-sight localization

Optical imaging through diffusive, visually-opaque barriers and around corners is an important challenge in many fields, ranging from defense to medical applications. Recently, novel techniques that combine time-of-flight (TOF) measurements with computational reconstruction have allowed breakthrough imaging and tracking of objects hidden from view. These light detection and ranging (LiDAR)-based approaches require active short-pulsed illumination and ultrafast time-resolved detection. Here, bringing notions from passive radio detection and ranging (RADAR) and passive geophysical mapping approaches, we present an optical TOF technique that allows passive localization of light sources and reflective objects through diffusive barriers and around corners. Our approach retrieves TOF information from temporal cross-correlations of scattered light, via interferometry, providing temporal resolution that surpasses state-of-the-art ultrafast detectors by three orders of magnitude. While our passive approach is limited by signal-to-noise to relatively sparse scenes, we demonstrate passive localization of multiple white-light sources and reflective objects hidden from view using a simple setup.

Far-field probing of leaky topological states in all-dielectric metasurfaces

Topological phase transitions in condensed matter systems give rise to exotic states of matter such as topological insulators, superconductors, and superfluids. Photonic topological systems open a whole new realm of research and technological opportunities, exhibiting a number of important distinctions from their condensed matter counterparts. Photonic modes can leak into free space, which makes it possible to probe topological photonic phases by spectroscopic means via Fano resonances. Based on this idea, we develop a technique to retrieve the topological properties of all-dielectric metasurfaces from the measured far-field scattering characteristics. Collected angle-resolved spectra provide the momentum-dependent frequencies and lifetimes of the photonic modes that enable the retrieval of the effective Hamiltonian and extraction of the topological invariant. Our results demonstrate how the topological states of open non-Hermitian systems can be explored via far-field measurements, thus paving a way to the design of metasurfaces with unique scattering characteristics controlled via topological effects.

Photoacoustic imaging in scattering media by combining a correlation matrix filter with a time reversal operator

Acoustic scattering medium is a fundamental challenge for photoacoustic imaging. In this study, we reveal the different coherent properties of the scattering photoacoustic waves and the direct photoacoustic waves in a matrix form. Direct waves show a particular coherence on the antidiagonals of the matrix, whereas scattering waves do not. Based on this property, a correlation matrix filter combining with a time reversal operator is proposed to preserve the direct waves and recover the image behind a scattering layer. Both numerical simulations and photoacoustic imaging experiments demonstrate that the proposed approach effectively increases the image contrast and decreases the background speckles in a scattering medium. This study might improve the quality of photoacoustic imaging in an acoustic scattering environment and extend its applications.

Robust source localization from wavefield separation including prior information

Strong reverberation is a challenge for narrowband source localization, as most of the existing methods are based on times-of-arrival measurements, that is affected by boundaries. Amongst the methods that explicitly take into account the reverberation, wavefield separation projector processing (WSPP) splits the acoustic wave field into the direct path of the sources and the reverberation. However, WSPP requires a very large number of microphones, making this method impractical. This article studies three ways of alleviating this constraint, extending WSPP by adding different prior information on the wavefield. The first method is based on using the knowledge of the critical distance of the room to decrease the selectivity of the field separation. The second method adds constraints called "virtual measurements" when the room geometry is partially known. Finally, the last method requires a simple calibration step to estimate the Green's functions between each pair of microphones; this also extends the model to weakly inhomogeneous propagation media. It is shown numerically and experimentally that these methods allow a precise source localization, with a reduced number of microphones.

Smart optical coherence tomography for ultra-deep imaging through highly scattering media

Multiple scattering of waves in disordered media is a nightmare whether it is for detection or imaging purposes. So far, the best approach to get rid of multiple scattering is optical coherence tomography. This basically combines confocal microscopy and coherence time gating to discriminate ballistic photons from a predominant multiple scattering background. Nevertheless, the imaging-depth range remains limited to 1 mm at best in human soft tissues because of aberrations and multiple scattering. We propose a matrix approach of optical imaging to push back this fundamental limit. By combining a matrix discrimination of ballistic waves and iterative time reversal, we show, both theoretically and experimentally, an extension of the imaging-depth limit by at least a factor of 2 compared to optical coherence tomography. In particular, the reported experiment demonstrates imaging through a strongly scattering layer from which only 1 reflected photon out of 1000 billion is ballistic. This approach opens a new route toward ultra-deep tissue imaging.

Green's Function Retrieval with Absorbing Probes in Reverberating Cavities

The cross-correlation of a diffuse wave field converges toward the difference between the anticausal and causal Green's functions between two points. This property has paved the way to passive imaging using ambient noise sources. In this Letter, we investigate Green's function retrieval in electromagnetism. Using a model based on the fluctuation dissipation theorem, we demonstrate theoretically that the cross-correlation function strongly depends on the absorption properties of the receivers. This is confirmed in measurements within a reverberation chamber. In contrast to measurements with noninvasive probes, we show that only the anticausal Green's function can be retrieved with a matched antenna. Finally, we interpret this result as an equivalent time-reversal experiment with an electromagnetic sink.