Imaging with optical resolution through and inside complex samples is a difficult challenge with important applications in many fields. The fundamental problem is that inhomogeneous samples, such as biological tissues, randomly scatter and diffuse light, impeding conventional image formation. Despite many advancements, no current method enables to noninvasively image in real-time using diffused light. Here, we show that owing to the 'memory-effect' for speckle correlations, a single image of the scattered light, captured with a standard high-resolution camera, encodes all the information that is required to image through the medium or around a corner. We experimentally demonstrate single-shot imaging through scattering media and around corners using incoherent light and various samples, from white paint to dynamic biological samples. Our lensless technique is simple, does not require laser sources, wavefront-shaping, nor time-gated detection, and is realized here using a camera-phone. It has the potential to enable imaging in currently inaccessible scenarios.

We describe an advanced image reconstruction algorithm for pseudothermal ghost imaging, reducing the number of measurements required for image recovery by an order of magnitude. The algorithm is based on compressed sensing, a technique that enables the reconstruction of an N -pixel image from much less than N measurements. We demonstrate the algorithm using experimental data from a pseudothermal ghost-imaging setup. The algorithm can be applied to data taken from past pseudothermal ghost-imaging experiments, improving the reconstruction's quality.Ghost imaging (GI) has emerged a decade ago as an imaging technique which exploits the quantum nature of light, and has been in the focus of many studies since [1, and references therin]. In GI an object is imaged even though the light which illuminates it is collected by a single-pixel detector which has no spatial resolution (a bucket detector). This is done by correlating the intensities measured by the bucket detector with an image of the eld which impinges upon the object. GI was originally performed using entangled photon pairs [2], and later on was realized with classical light sources [3,4,5,6]. The demonstrations of GI with classical light sources, and especially pseudothermal sources, triggered an ongoing e ort to implement GI for various sensing applications [4,7]. However, one of the main drawbacks of pseudothermal GI is the long acquisition times required for reconstructing images with a good signal-to-noise ratio (SNR) [1,8].In this work we propose an advanced reconstruction algorithm for pseudothermal GI, which reduces signicantly the required acquisition times. The algorithm is based on compressed sensing (or compressive sampling, CS) [9,10], an advanced sampling and reconstruction technique which has been recently implemented in several elds of imaging. Examples for such are magnetic resonance imaging [11], astronomy [12], THz imaging [13], and single-pixel cameras [14]. The main idea behind CS is to exploit the redundancy in the structure of most natural signals/objects to reduce the number of measurements required for faithful reconstruction. Here we show that applying a CS-based reconstruction algorithm to data taken from conventional pseudothermal GI measurements dramatically improves the SNR of the reconstructed images and thus allows for shorter acquisition times.In conventional pseudothermal GI, an object is illuminated by a speckle eld generated by passing a laser beam through a rotating di user [ Fig. 1(a)]. For each phase realization r of the di user, the speckle eld I r (x, y) which impinges on the object is imaged. This is done by splitting the beam before the object to an 'object arm' and a 'reference arm', and placing a CCD camera at the refer- * Electronic address: ori.katz@weizmann.ac.il Figure 1: (Color online) (a) Standard pseudothermal GI twodetectors setup. A copy of the speckle eld which impinges on the object is imaged with a CCD camera, and correlated with the intensity measured by a bucket detector. (b) The computational GI singl...

We experimentally demonstrate pseudothermal ghost imaging and ghost diffraction using only a single single-pixel detector. We achieve this by replacing the high resolution detector of the reference beam with a computation of the propagating field, following a recent proposal by Shapiro [J. H. Shapiro, arXiv:0807.2614 (2008)]. Since only a single detector is used, this provides an experimental evidence that pseudothermal ghost imaging does not rely on non-local quantum correlations. In addition, we show the depth-resolving capability of this ghost imaging technique.Comment: See video at http://www.weizmann.ac.il/home/feori/Misc.html Comments are welcom

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Abstract:Light scattering in inhomogeneous media induces wavefront distortions which pose an inherent limitation in many optical applications. Examples range from microscopy and nanosurgery to astronomy. In recent years, ongoing efforts have made the correction of spatial distortions possible by wavefront shaping techniques. However, when ultrashort pulses are employed scattering induces temporal distortions which hinder their use in nonlinear processes such as in multiphoton microscopy and quantum control experiments. Here we show that correction of both spatial and temporal distortions can be attained by manipulating only the spatial degrees of freedom of the incident wavefront. Moreover, by optimizing a nonlinear signal the refocused pulse can be shorter than the input pulse. We demonstrate focusing of 100fs pulses through a 1mm thick brain tissue, and 1000-fold enhancement of a localized two-photon fluorescence signal. Our results open up new possibilities for optical manipulation and nonlinear imaging in scattering media. 2The propagation of light in inhomogeneous media results in scattering and distortions of the propagating wavefront. Such distortions limit the effective focusing of optical intensity and degrade imaging quality through disordered or scattering media 1 . The problem of focusing light through inhomogeneous media is even more challenging when ultrashort pulses are considered, as in addition to the spatial distortions scattering also distorts the pulse shape in time [2][3][4][5] . The challenge of correcting the spatial distortions induced by scattering has been in the focus of many recent works [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] . Weak wavefront aberrations, such as those occurring in astronomical observations through the atmosphere, have been efficiently corrected using adaptive optics techniques [6][7][8] . These techniques, however, were considered inadequate for correcting distortions in highly scattering and turbid samples, which lead to diffusive light propagation and result in complex speckle patterns with no simple relation to the incident wavefront 1,20 . Recently, in a pioneering work, Vellekoop et al. have shown that adaptive optimization of the incident wavefront can increase the focused intensity of multiply scattered light by a factor that is roughly equivalent to the number of degrees of control [9][10][11][12] . Using a spatial light modulator (SLM) with 1000 degrees of control enabled a 1000-fold enhancement in the focused brightness after a turbid medium 9 . Following Vellekoop's works, other approaches for determining the optimal corrections were demonstrated either by measurement of the optical transmission matrix 13,14 or the complex-valued relation between spatial modes 15 , or alternatively by directly recording the distorted wavefront using optical phase conjugation 16,17 . These results, however, were only relevant for quasi-continuous light, and in spite of these remarkable achievements in the correction of spatial distortions, no work to date h...

† These authors contributed equally to this work Optical wavefront-shaping has emerged as a powerful tool to manipulate light in strongly scattering media 1, 2 . It enables diffraction-limited focusing 3 and imaging 4, 5 at depths where conventional microscopy techniques fail 6 . However, while most wavefront-shaping works to-date exploited direct access to the target 2-5, 7-11 or implanted probes 12, 13 , the challenge is to apply it non-invasively inside complex samples. Ultrasonic-tagging techniques have been recently demonstrated 14-18 but these require a sequential point-bypoint acquisition, a major drawback for imaging applications. Here, we introduce a novel approach to non-invasively measure the optical transmission-matrix 5 inside a scattering medium, exploiting the photo-acoustic effect 19-23 . Our approach allows for the first time to simultaneously discriminate, localize, and selectively focus light on multiple targets inside a scattering sample, as well as to recover and exploit the scattering medium properties. Combining the powerful approach of the transmission-matrix with the advantages of photoacoustic imaging 19-21 opens the path towards deep-tissue imaging and light-delivery utilizing endogenous optical contrast.

The recent theory of compressive sensing leverages upon the structure of signals to acquire them with much fewer measurements than was previously thought necessary, and certainly well below the traditional Nyquist-Shannon sampling rate. However, most implementations developed to take advantage of this framework revolve around controlling the measurements with carefully engineered material or acquisition sequences. Instead, we use the natural randomness of wave propagation through multiply scattering media as an optimal and instantaneous compressive imaging mechanism. Waves reflected from an object are detected after propagation through a well-characterized complex medium. Each local measurement thus contains global information about the object, yielding a purely analog compressive sensing method. We experimentally demonstrate the effectiveness of the proposed approach for optical imaging by using a 300-micrometer thick layer of white paint as the compressive imaging device. Scattering media are thus promising candidates for designing efficient and compact compressive imagers.

Diffraction-limited imaging through complex scattering media is a long sought after goal with important applications in biomedical research. In recent years, high resolution wavefront-shaping has emerged as a powerful approach to generate a sharp focus through highly scattering, visually opaque samples. However, it requires a localized feedback signal from the target point of interest, which necessitates an invasive procedure in all-optical techniques. Here, we show that by exploiting optical nonlinearities, a diffraction-limited focus can be formed inside or through a complex sample, even when the feedback signal is not localized. We prove our approach theoretically and numerically, and experimentally demonstrate it with a two-photon fluorescence signal through highly scattering biological samples. We use the formed focus to perform two-photon microscopy through highly scattering, visually opaque layers.