When imaging with classical waves, multiple scattering (MS) is often seen as an unavoidable obstacle. The diffraction-limited resolution obtainable with methods such as microscopy requires that single-scattering (SS) dominates; for depths where MS processes become important, such methods result in an image without any connection to the reflectivity of the medium. Conversely, techniques such as diffuse optical tomography take advantage of the diffuse nature of light, but their resolution power is limited. To do better, methods such as wavefront shaping and adaptive optics have been developed. Focussing through a thick diffusive layer was demonstrated using a transmission matrix approach consisting of the measurement of Green’s functions between each pixel of a spatial light modulator (SLM) and of a charge-coupled device (CCD) camera across the medium. To image inside a multiple-scattering medium, we present a matrix approach based on the experimental measurement of a reflection matrix from the medium. An analysis based on the geometric and statistical properties of this reflection matrix can enhance the SS contribution which would otherwise be swamped by MS at large depths, and correct the resulting image for aberration effects induced by the turbid medium itself. The correction does not require the presence of bright scatterers, does not rely on any feedback loop and works even at depths where the field-of-view contains several isoplanatic patches. Here we present the application of our reflection matrix approach to optical imaging in biological tissues. Compared to OCT and related methods, we demonstrate an extension of the current imaging-depth limit.
Optical imaging through turbid media and around corner is a difficult challenge. Even a very thin layer of a turbid media, which randomly scatters the probe light, can appear opaque and hide any objects behind it. Despite many recent advances, no current method can image the object behind turbid media with single record using coherent laser illumination. Here we report a method that allows non-invasive single-shot optical imaging through turbid media and around corner via speckle correlation. Instead of being as an obstacle in forming diffractionlimited images, speckle actually can be a carrier that encodes sufficient information to imaging through visually opaque layers. Optical imaging through turbid media and around corner is experimentally demonstrated using traditional imaging system with the aid of iterative phase retrieval algorithm. Our method require neither scan of illumination nor two-arm interferometry or long-time exposure in acquisition, which has new implications in optical sensing through common obscurants such as fog, smoke and haze.
Our approach first consists in measuring a time-gated reflection matrix associated to a scattering medium using a spatial light modulator at the input and a CCD camera at the output. An interferometric arm allows to discriminate the scattered photons as a function of their time of flight. Inspired by previous works in acoustics, a random matrix approach then allows to get rid of multiple scattering. This improves by far the detection and imaging of targets embedded in or hidden behind a highly scattering medium. As proof of concept, we tackle with the issue of imaging ZnO micrometric beads across a highly scattering paper sheet whose optical thickness is of 12.5 ls, with ls the scattering mean free path. This experimental situation is particularly extreme, even almost desperate for imaging. The ballistic wave has to go through 25 ls back and forth, thus undergoing an attenuation of 10^-11 in intensity. For an incident plane wave, 1 scattered photon over 1000 billions is associated to the target beads. In optical coherence tomography, the single-to-multiple scattering ratio is of 5×10^-4 which prevents from any target detection and imaging. On the contrary, our approach allows to get rid of most of the multiple scattering contribution in this extreme situation. By means of the time-reversal operator, the ballistic echoes associated to each bead are extracted and allow to reconstruct a satisfying image of the targets. The perspective of this work is to apply this promising approach to in-depth imaging of biological tissues.
We recently showed how the correlations of a broadband and incoherent wave-field can directly yield the time-dependent Green's functions between scatterers of a complex medium [Badon et al., Phys. Rev. Lett., 2015]. In this study, we apply this approach to the imaging of optical transport properties in complex media. A parallel measurement of millions of Green's functions at the surface of several strongly scattering samples (ZnO, TiO2, Teflon tape) is performed. A statistical analysis of this Green’s matrix allows to investigate locally the spatio-temporal evolution of the diffusive halo within the scattering sample. An image of diffusion tensor is then obtained. It allows to map quantitatively the local concentration of scatterers and their anisotropy within the scattering medium. The next step of this work is to test this approach on biological tissues and illustrate how it can provide an elegant and powerful alternative to diffuse optical imaging techniques.
Measurement of the refractive index of regular shaped glass by speckle correlation is reported. One intensity image in the diffraction field of a speckle-illuminated sample is captured by a CCD before the presence of glass sample and another intensity image is captured after the presence of glass sample. As the position of peak correlation coefficient is quantitatively related to the change in optical path length arising due to the presence of glass, the refractive index of the glass can be evaluated by the correlation of the intensity images before and after the glass insertion. The theoretical correlation function is first derived that describes the relationship between optical path length change and speckle decorrelation. In experiment, various regular shaped glasses are measured to demonstrate the accuracy and robustness of the proposed technique.
Speckle fields are formed when quasi-monochromatic light is scattered by an optically rough surface. These fields
are usually described by reference to their first and second order statistical properties. In this paper we review
and extend some of these fundamental properties and propose a novel technique for estimating the refractive
index of a smooth sample. Theoretical and experimental results are presented. Separately, we also report on
a preliminary experiment to determine some characteristics of speckle fields formed in free space by a rotating
compound diffuser. Some initial measurements are made where we examine how the speckle intensity pattern in
the output plane changes as a function of the relative rotation angle.
Access to both the phase and intensity of an image can be provided using digital holographic (DH) imaging techniques. Recently, the difference of two holograms captured with two appropriately related wavelengths was demonstrated to produce the Laplacian of an object field. Applying telecommunication lasers the feasibility of infrared (IR) DH and DH Laplacian reconstruction and the associated theoretical analyses are presented. This is achieved by combining a tunable mid-IR laser source and mid-IR sensitive InGaAs-based digital camera.
Quasi-monochromatic light reflected from an optically rough surface produces a complicated 3D speckle field. This
speckle field is often described using a correlation function from which the 3D speckle properties can be examined. The
derivation of the correlation function is based on a physical model where several critical assumptions about the input and
output fields in the model are made. However, experimental works verifying this correlation function are rare and
sometimes produce inconsistent results. In this paper, we examine some practical issues encountered when
experimentally measuring this correlation function, including: The realization of the ensemble average between speckle
fields at two point positions; and, The pixel integrating effect of the recording camera and the implications this has for
the statistics of the measured speckle field. Following verification of the correlation function and examining the speckle
decorrelation properties in 3D space, two practical applications are proposed, one is the aligning of the system optical
axis with the camera center and the other is the measurement of the out-of-plane displacement of an object surface.
Simulation and experimental results that support our analysis are presented.
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