Singularities in forward scattering through random media

Abstract

We consider a random medium in which scattering is exclusively in the forward direction. Waves are emitted by an object in the medium and Fourier components of the intensity are shown to propagate independently. At small wavevectors the intensity propagates very simply through increasing thickness, z, of medium, as λ ^z , and Fourier components of the object can easily be reconstructed. For wavevectors greater than a critical value, q _c , the intensity changes with z in a more complex fashion making it very difficult to reconstruct the object. They develop a simple model for the singularity and apply it to the reconstruction of an object degraded by passage through a random medium.     

Multiple scattering in random media

The paper is an application of a general microscopic approach to the theory of the average scattering matrix for a particle interacting with random scatterers. We present a detailed treatment for the case of uncorrelated positions of the scatterers. First, the general two-body additive approximation is used to truncate the hierarchy of correlation functions for fluctuations. It is shown that the self-energy is accurate through the fourth power of the individual scattering amplitude. Second, the hierarchy is terminated at the next stage. The self-energy is correct to the sixth power of the scattering amplitude.Work supported in part by the National Science Foundation under Contract No. NSF DMR 79-23213.     

Parallel wavefront optimization method for focusing light through random scattering media

A parallel wavefront optimization method is demonstrated experimentally to focus light through random scattering media. The simultaneous modulation of multiple phase elements, each at a unique frequency, enables a parallel determination of the optimal wavefront. Compared to a pixel-by-pixel measurement, the reported parallel method uses the target signal in a highly efficient way. With 441 phase elements, a high-quality focus was formed through a glass diffuser with a peak-to-background ratio of ～270. The accuracy and repeatability of the system were tested through experiments.     

Low-coherence enhanced backscattering from highly forward scattering media

We present a theoretical basis for calculation of the angular profile of the coherent backscattering intensity under low spatial coherence illumination. We take into account two contributions to the intensity, namely, the diffusion contribution and the contribution from the waves that experience the small-angle multiple scattering before and after single deflection in the backward direction. The latter contribution describes transport of light at subdiffusion length scales and is responsible for the wings of the backscattering angular profile. Our results are in good agreement with data of Monte-Carlo simulations and experiment.     

Stereoscopic imaging through scattering media

We develop and experimentally test a method for three-dimensional imaging of hidden objects in a scattering medium. In our scheme, objects hidden between two biological tissues at different depths from the viewing system are recovered, and their three-dimensional locations are computed. Analogous to a fly's two eyes, two microlens arrays are used to observe the hidden objects from different perspectives. At the output of each lens array we construct the objects from several sets of many speckled images with a previously suggested technique that uses a reference point. The differences of the reconstructed images in both arrays with respect to the reference point yield the information regarding the relative depth among the various objects.     

Tissue structure study through ultrasonic forward scattering

A procedure is demonstrated for characterization of biological tissues at small scattering angles. The power spectra of ultrasonic pulses transmitted through excised tissue samples were measured and compared to the spectra of signals transmitted through a water path. The specimens were examined in two spatial-frequency bands by acquiring data at scattering angles of 10 degrees and 20 degrees using 2.25 MHz transducers. Peaks in the measured power spectra are interpreted using two signal models. The medium is modelled either as a periodic structure producing a single spectral peak, or by two discrete targets producing a periodic modulation of the spectrum. The periodic structure model appears to be the more promising method for interpretation of forward-scattered signals. Data acquired from hyperplastic spleen and atheromatous aorta specimens both exhibited increases in pulse-tissue interaction at low spatial frequencies compared to normal specimens of those tissues. This observation is tentatively linked to increases in the size or separation of distributed scattering structures resulting from those pathologies.     

Anomalous polarization effects during light scattering in random media

The dependence of the intensity of light backscattered from a layer of a randomly inhomogeneous medium on the polarization of incident light and the size of scatterers has been investigated. The results of numerical simulation have demonstrated that the direction of rotation of the plane of polarization is different in systems with small- and large-scale inhomogeneities. It is shown for the first time that the dependence of the sign of the residual circular polarization on the size of scatterers can be observed in systems described by the Henyey-Greenstein phase function used in simulating biological tissues. A similar anomalous polarization effect, which consists in changing the direction of rotation of the plane of polarization of backscattered light with an increase in the scattering angle, is revealed in studying the coherent backscattering component. These polarization effects are observed in light backscattering from optically active media.     

超短THz脉冲在随机散射介质中的传播

用Monte-Carlo方法模拟了超短THz脉冲在随机散射介质中的传播.根据Mie理论计算出随机散射介质的散射系数和各向异性因子，研究了随机散射颗粒及介质厚度的大小对透射脉冲的影响.结果表明在Mie散射范围内，在相同的浓度下，颗粒尺寸越小，散射介质越厚，THz散射越严重，对透射脉冲的影响越大.散射同时降低了THz脉冲在随机散射介质中的成像分辨率. 关键词： 超短THz脉冲 随机散射介质 Mie理论 Monte-Carlo方法     

Numerical study of the characterization of forward scattering Mueller matrix patterns of turbid media with triple forward scattering assumption

We propose a triple forward scattering model to numerically investigate the forward scattering Mueller matrix of a turbid medium. The calculated results show that the Mueller matrix based on the triple scattering model can completely describe the basic symmetries and azimuthal structures of the forward scattering Mueller matrix of a turbid medium. The results show that the forward scattering Mueller matrix is characterized with special symmetric structure compared with backscattering Mueller matrix patterns. The method will extend the investigation to light scattering mechanism from cells and to diagnosis of diabetes and other blood related diseases.     

Transport of quantum noise through random media

We present an experimental study of the propagation of quantum noise in a multiple scattering random medium. Both static and dynamic scattering measurements are performed: the total transmission of noise is related to the mean free path for scattering, while the noise frequency correlation function determines the diffusion constant. The quantum noise observables are found to scale markedly differently with scattering parameters compared to classical noise observables. The measurements are explained with a full quantum model of multiple scattering.     

Optimal beams for propagation through random media

The problem of maximizing the intensity that is transferred from a transmitter aperture to a receiver aperture is considered in which the propagation medium is random. Two optimization criteria are considered: maximal expected intensity transfer and minimal scintillation index. The beam that maximizes the expected intensity is shown to be fully coherent. Its coherent mode is determined as the principal eigenfunction for a kernel that is determined through the second-order moments of the propagation Green's function. The beam that minimizes the scintillation index is shown to be partially coherent in general, with its coherent modes determined by minimizing a quadratic form that has nonlinear dependence on the coherent-mode fields, and on the second- and fourth-order moments of the propagation Green's function.     

Singular value distribution of the propagation matrix in random scattering media

The distribution of singular values of the propagation operator in a random medium is investigated, in a backscattering configuration. Experiments are carried out with pulsed ultrasonic waves around 3 MHz, using an array of 64 programmable transducers placed in front of a random scattering medium. The impulse responses between each pair of transducers are measured and form the response matrix. The evolution of its singular values with time and frequency is computed by means of a short-time Fourier analysis. The mean distribution of singular values exhibits a very different behaviour in the single and multiple scattering regimes. The results are compared with random matrix theory. Once the experimental matrix coefficients are renormalized, experimental results and theoretical predictions are found to be in a very good agreement. Two kinds of random media have been investigated: a highly scattering medium in which multiple scattering predominates and a weakly scattering medium. In both cases, residual correlations that may exist between matrix elements are shown to be a key parameter. Finally, the possibility of detecting a target embedded in a random scattering medium based on the statistical properties of the strongest singular value is discussed.     

Multiple scattering in random media I. Restricted two-body additive approximation

We present a microscopic theory of the problem of finding the properties of a particle interacting with potentials located at random sites. The sites are governed by a general probability distribution. The starting point is the multiple scattering equations for the amplitude k ₁|T |k ₂ in terms of the individual scattering amplitudes k ₁|T |k ₂. We work with quantitiesA defined by k ₁|T |k ₂=k ₁|T |k ₂exp[i(k ₁–k ₂)R ]. The theory is based on a splitting of the fundamental equation forA into equations for the mean A and the fluctuationsAA . Neglect of the fluctuations yields the quasicrystalline approximation. We rearrange the equation forAA to isolate the collective part of the fluctuations. We then make the simplest microscopic truncation which is thatAA is a restricted two-body additive function of the site positions. With the contribution of the collective fluctuations, this yields results forA that are accurate to ordert ⁴.Work supported in part by the National Science Foundation under Contract No. NSF DMRWork supported in part by the National Science Foundation under Contract No. NSF DMR     

Photon density wave for imaging through random media

The passage of a photon density wave through random media has been investigated extensively for medical imaging based on the diffusion approximation. In this paper, the photon density wave is studied based on the exact time-dependent vector radiative transfer theory. Both continuous and pulse photon density waves are analysed in a plane parallel medium using Mie scattering and the discrete ordinates method. The photon density wave shows superior properties over regular waves in several aspects. It has a narrower angular spectrum and maintains the original pulse shape. It also preserves the degree of polarization and increases the cross-polarization discrimination. These properties of a photon density wave suggest its potential for improving imaging. Thus, we apply the photon density wave to an imaging problem and show that it improves the quality of the images compared to other conventional imaging techniques.     

Controlling single-photon Fock-state propagation through opaque scattering media

The control of light scattering is essential in many quantum optical experiments. Wavefront shaping is a technique used for ultimate control over wave propagation through multiple-scattering media by adaptive manipulation of incident waves. We control the propagation of single-photon Fock states through opaque scattering media by spatial phase modulation of the incident wavefront. We enhance the probability that a single photon arrives in a target output mode with a factor 30. Our proof-of-principle experiment shows that the propagation of quantum light through multiple-scattering media can be controlled, with prospective applications in quantum communication and quantum cryptography.     

Focusing coherent light through opaque strongly scattering media

We report focusing of coherent light through opaque scattering materials by control of the incident wavefront. The multiply scattered light forms a focus with a brightness that is up to a factor of 1000 higher than the brightness of the normal diffuse transmission.     

Generation of Lommel beams through highly scattering media

Lommel beams have been potential candidates for optical communication and optical manipulation, due to their adjustable symmetry of transverse intensity distribution and continuously variable orbital angular momentum. However, the wavefront of the Lommel beam is scrambled when it transmits through highly scattering media. Here, we explore the construction of Lommel beams through highly scattering media with a transmission matrix-based point spread function engineering method. Experimentally, var...     

基于压缩感知的动态散射成像

利用基于压缩感知的成像系统可以透过静态的散射介质获得高质量的重建图像. 但是当散射介质动态变化时, 因为采样所得的测量值受到散射介质衰减系数非线性变化的影响, 重建图像质量会大大下降. 针对上述情况, 本文提出基于压缩感知成像系统的测量值线性拉伸算法, 该算法能够对所得到的非线性测量值进行分析, 根据测量值大小的不同将测量值划分成数个区域并计算补偿系数, 从而根据补偿系数进行测量值线性拉伸变换, 使测量值线性化. 最后再对变换后的测量值进行压缩感知重建计算. 通过理论分析、计算机仿真和实验证明了所提算法能够有效地应对动态的散射介质, 提高基于压缩感知成像系统在透过动态散射介质时的图像重建质量.