A singular-value method for reconstruction of nonradial and lossy objects

Efficient inverse scattering algorithms for nonradial lossy objects are presented using singular-value decomposition to form reduced-rank representations of the scattering operator. These algorithms extend eigenfunction methods that are not applicable to nonradial lossy scattering objects because the scattering operators for these objects do not have orthonormal eigenfunction decompositions. A method of local reconstruction by segregation of scattering contributions from different local regions is also presented. Scattering from each region is isolated by forming a reduced-rank representation of the scattering operator that has domain and range spaces comprised of far-field patterns with retransmitted fields that focus on the local region. Methods for the estimation of the boundary, average sound speed, and average attenuation slope of the scattering object are also given. These methods yielded approximations of scattering objects that were sufficiently accurate to allow residual variations to be reconstructed in a single iteration. Calculated scattering from a lossy elliptical object with a random background, internal features, and white noise is used to evaluate the proposed methods. Local reconstruction yielded images with spatial resolution that is finer than a half wavelength of the center frequency and reproduces sound speed and attenuation slope with relative root-mean-square errors of 1.09% and 11.45%, respectively.     

Extended focused imaging for digital holograms of macroscopic three-dimensional objects

When a digital hologram is reconstructed, only points located at the reconstruction distance are in focus. We have developed a novel technique for creating an in-focus image of the macroscopic objects encoded in a digital hologram. This extended focused image is created by combining numerical reconstructions with depth information extracted by using our depth-from-focus algorithm. To our knowledge, this is the first technique that creates extended focused images of digital holograms encoding macroscopic objects. We present results for digital holograms containing low- and high-contrast macroscopic objects.     

A frame-based approach for wideband correlation-inversion of lossless scatterers

Presented here is an ultra-wideband-correlation-based scheme for imaging and inversion of an unknown weak and lossless scatterer embedded in a known background medium. The scheme uses an excitation and reception of ultra wideband/short-pulsed fields by an array of transducers located outside the imaging domain. The scatterer image is formed by cross correlating (in the short-pulsed domain or via spectral integration in the ultra wideband domain) the numerically/ analytically back-propagated, measured, and scattered data set with the forward-propagation excitations. It is shown that in the ultra wideband domain, the forward-backward propagation functions form a frame set in a finite Hilbert space. Within the weak scattering assumption (Born approximation) the scatterer's image and object function (velocity profile) are related via the corresponding frame operator. Therefore, an exact inversion scheme of the frame operator is readily available to yield the object function via an iterative scheme or using the dual frame set. Numerical examples that demonstrate the performance of the imaging and inversion schemes for scatterers with various velocity profiles are presented. It is shown that the scatterer image is generally of poor resolution. However, on inversion, a high-quality velocity profile is obtained that captures the scatterer fine details.     

UWB Short-Range Bifocusing Tomographic Imaging

In this paper, the capability of ultra-wideband (UWB) sensor arrays for tomographic imaging of electrically large objects in 2-D and 3-D environments is presented. One of the main concerns when imaging extended real objects is the capability of the system to correctly reconstruct the object cross-section electric properties. An imaging method using a UWB multifrequency bifocusing (UWB-MFBF) operator with good tomographic imaging capabilities is presented, and numerical simulations are conducted to obtain the basic geometry and sampling parameters for a good-quality image reconstruction for geometrical and electrical parameters. Canonical-shape experimental reconstructions are performed to validate the established criteria.     

Ultrasonic inverse scattering of multidimensional objects buried in multilayered elastic background structures

The authors focus on the multidimensional inverse scattering of objects buried in an inhomogeneous elastic background structure. The medium is probed by an ultrasonic force and the scattered field is observed along a receiver array. The goal is to retrieve both the geometry (imaging problem) and the constitutive parameters (inverse problem) of the object through an appropriate multiparameter direct linear inversion. The problem is cast in terms of a vector integral equation elastic scattering framework. The multidimensional inverse scattering problem, being nonlinear and ill-posed, is linearized within the Born approximation for inhomogeneous background, and a minimum-norm least-square solution to the discretized version of the vector integral formulation is sought. The solution is based on a singular value decomposition of the forward operator matrix. The method is illustrated on a 2-D problem where constrained least-square inversion of the object is performed from synthetic data. A Tikhonov regularization scheme is examined and compared to the minimum-norm least-square estimate.     

Generalized Lorenz–Mie scattering theory for focused radiation and finite solids of revolution: case I: symmetrically polarized beams

Interaction of focused radiation with spherical and finite cylindrical homogeneous particles is considered. The aim of this investigation is to calculate the structure of the electromagnetic (EM) fields scattered by and propagated within the scattering objects. The incident EM fields are assumed to be focused fields in the image space of an aplanatic system with or without aberrations of category one. The radiation in the object space is assumed to be symmetrically polarized. The incident fields in the neighbourhood of the focus are calculated using the well-known theory of Richards and Wolf and a methodology developed by the author. At the interface between the homogeneous and the image space of the aplanatic system, the continuity conditions of the tangential components of the electric displacement and magnetic moment vectors are satisfied. The procedure results in dual discretized-Fredholm integral equations that are solved using orthogonal expansions. It is assumed that the scattered field, at large distances from the focus, is a spherical wave propagating away from the focus. Scattering by objects of various materials ranging from dielectric to perfect conductor is studied. The theory and its solution developed here allow for the scattering objects to be located anywhere along the optical axis in the image space. One of the main objectives is to calculate the energy distribution at the tip of the cylindrical homogeneous particle. Numerical calculations suggest that energy density at the tip is further enhanced if the cylindrical homogeneous particle is placed away from focus.     

Computation of electromagnetic wave scattering from an arbitrarythree-dimensional inhomogeneous dielectric object

A scattering matrix formulation for scattering of electromagnetic fields by an arbitrary three-dimensional dielectric objects is presented. It is based on an extended moment method that digitizes the scattering equation by dividing the scatterer as well as the measurement region into small cells. The Green's function within each cell is derived analytically by integrating over the cell. The accuracy of the method is demonstrated by computing vector scattering fields from a uniform dielectric sphere and comparing the results with those calculated using the Mie scattering formula. The formulation also provides an inverse solution, namely, determination of the dielectric profile of the scatterer from the scattering field measured in a finite region outside the scatterer     

Image formation with regard to object shadow for objects inside a scattering medium

The conventional theory of image transfer through a scattering medium treats objects located upon reflecting surfaces. It is shown that, when an object is located inside a scattering medium and shields a part of space, ignoring the shadowing leads to incorrect results, especially for modern time-gating systems. We develop a general theory of image formation including the shadowing effect when an object is located inside a scattering medium. The example of the observation of a submerged object through a windy ocean surface is chosen to illustrate this theory. A few unexpected effects in imaging of a submerged object are found and discussed, including contrast conversion for a sinking object and higher contrast in the shadow image than in the image of the object itself. The conclusion that using the shadow image for detection of a submerged object can be more efficient than using the image of the object itself is of practical significance.     

Signal-to-noise ratio for astronomical imaging by deconvolution from wave-front sensing

One method for improving the quality of astronomical images measured through a atmospheric turbulence uses simultaneous short-exposure measurements of both an image and the output of a wave-front sensor exposed to an image of the telescope pupil. The wave-front sensor measurements are used to reconstruct an estimate of the instantaneous generalized pupil function of the telescope, which is used to compute an estimate of the instantaneous optical transfer function, which is then used in a deconvolution procedure. This imaging method has been called both deconvolution from wave-front sensor (DWFS) measurements and self-referenced speckle holography. We analyze the signal-to-noise ratio (SNR) behavior of this imaging method in the spatial frequency domain. The analysis includes effects arising from differences in the correlation properties of the incident and the estimated pupil phases and the fact that the object-spectrum estimator is a randomly filtered doubly stochastic Poisson random process. SNR resultsobtained for the DWFS method are compared with the speckle-imaging powerspectrum SNR for equivalent seeing conditions and light levels. It is shown that for unresolved stars the power-spectrum SNR is superior to the DWFS SNR. However, for extended objects the power-spectrum SNR and the DWFS SNR are similar. Since speckle imaging uses a separate Fourier phasereconstruction process not required by the DWFS method, the DWFS method provides an alternative to speckle imaging that uses simple postprocessing at the cost of a wave-front sensor measurement but with no loss of SNR performance for extended objects.     

Illusion Optics: Disguising with Ordinary Dielectric Materials

Illusion devices are usually designed using transformation optics. Here, a new method is proposed to achieve optical illusions without external devices by elaborately manipulating the scattering potential of an object. In contrast to the conventional transformation optics method, which completely replaces one object by the image of another object using complementary\restoring media and a superlens, the method described here is more of a cosmetic operation for an object, which modifies the scattering pattern of the object to mimic another object by exchanging their scattering potentials in two symmetrical areas in the wave vector domain. Only positive isotropic nonmagnetic materials are introduced in the present method, which is impossible using the conventional method because superlenses require negative‐index materials. Both numerical simulations and experimental demonstrations are used to verify the performance of the illusion devices of this method.     

Improving closely spaced dim object detection through multiframe blind deconvolution of near stellar neighbourhoods

A new iterative algorithm is proposed to improve the detection of dim stellar objects that are in the neighbourhood of a bright object, using short-exposure images. This method separates data functions into the primary bright object function, the neighbourhood system function, and the background function. This approach uses the principles of the Expectation-Maximization algorithm with the Gerchberg-Saxton phase retrieval algorithm to overcome the image degradation caused by the photon counting noise from the charge-coupled devices and the turbulent atmospheric conditions. The performance of this new neighbourhood system algorithm is compared with that of the multiframe blind deconvolution algorithm, using laboratory data and computer-simulated data. This paper provides an improved technique to image closely spaced dim objects.     

Harmonic vibro-acoustography

Vibro-acoustography is an imaging method that uses the radiation force of two interfering ultrasound beams of slightly different frequency to probe an object. An image is made using the acoustic emission resulted from the object vibration at the difference frequency. In this paper, the feasibility of imaging objects at twice the difference frequency (harmonic acoustic emission) is studied. Several possible origins of harmonic acoustic emission are explored. As an example, it is shown that microbubbles close to resonance can produce significant harmonic acoustic emission due to its high nonlinearity. Experiments demonstrate that, compared to the fundamental acoustic emission, harmonic acoustic emission greatly improves the contrast between microbubbles and other objects in vibro-acoustography (an improvement of 17-23 dB in these experiments). Applications of this technique include imaging the nonlinearity of the object and selective detection of microbubbles for perfusion imaging. The impact of microbubble destruction during the imaging process also is discussed.     

An efficient method of solving the Navier–Stokes equations for flow control

A new method of solving the Navier–Stokes equations efficiently by reducing their number of modes is proposed in the present paper. It is based on the Karhunen–Loève decomposition which is a technique of obtaining empirical eigenfunctions from the experimental or numerical data of a system. Employing these empirical eigenfunctions as basis functions of a Galerkin procedure, one can a priori limit the function space considered to the smallest linear subspace that is sufficient to describe the observed phenomena, and consequently reduce the Navier–Stokes equation defined on a complicated geometry to a set of ordinary differential equations with a minimum degree of freedom. The present algorithm is well suited for the problems of flow control or optimization, where one has to compute the flow field repeatedly using the Navier–Stokes equation but one can also estimate the approximate solution space of the flow field based on the range of control variables. The low-dimensional dynamic model of viscous fluid flow derived by the present method is shown to produce accurate flow fields at a drastically reduced computational cost when compared with the finite difference solution of the Navier–Stokes equation. © 1998 John Wiley & Sons, Ltd.     

Ultrasound imaging using variations of the iterative Born technique [biomedical diagnosis

The iterative Born method is an inverse technique that has been used successfully in ultrasound imaging. However, the calculation cost of the standard iterative Born method is high, and parallel computation is limited to the forward problem. In this work, two methods are introduced to increase the rate of convergence of the iterative Born algorithm. These methods are tested on three different objects. The results are promising, with both algorithms giving accurate results at lower computational cost. The first method, referred to as the coarse resolution initial value (CRIV) method, uses the iterative Born algorithm for a coarse grid to quickly estimate the initial value of the object to be reconstructed. From this initial value, the final image is obtained for a finer grid with additional iterations. The cost of this method is 40% less than that of the iterative Born technique. The second method, the quadriphase source (QS) method, simultaneously uses four single sources, and object reconstruction for each is performed in parallel; the reconstruction results for all four sources then are averaged to obtain the final image. The cost of this method is 20% less than that of the standard iterative Born method. When the object to be reconstructed is of low contrast and/or has a small phase shift, the QS method is very promising because parallel computation can be used to solve both the forward and inverse problems. However, the QS method fails for high contrast objects.     

Ultrafast, cross-correlated harmonic imaging through scattering media

A simple upconversion scheme utilizing 40-fs pulses is shown to permit high-contrast imaging of objects obscured by a highly scattering medium when no ballistic component is evident in the scattered light and imaging is performed with any portion of the scattered light pulse. We present a time-gated, inherently low-pass spatially filtered imaging method that minimizes signal-averaging requirements and greatly facilitates imaging under severe scattering (turbid) conditions.     

超声层析成像的迭代重建

利用变形Born迭代方法,建立了超声衍射重建算法。在迭代过程中,为了解决超声逆散射问题中的非线性性,需要反复地求解前向散射方程和逆散射方程,以达到全场和未知函数的近似,较好地重建物体内部的断层图象。由于逆散射方程是一个不适定性的方程组,要用正则化方法处理方程的不适定性问题,使迭代方法收敛于问题的真实解,才能成功地应用于较高对比度物体的图象重建问题。用Picard准则对不适定问题进行了分析,给出了通过简单图形．确定模型受噪声污染情况以及正则化方法适用范围的方法。在重建实验中。对建立的图像重建算法进行了实验仿真。达到了较好的效果。     

Solution of convergence problem in ultrasound inverse scattering tomography

When the product of contrast and size of an object, which is to be reconstructed by using the ultrasound inverse scattering tomography algorithm, is large, it is well known that those algorithms fail to converge to a unique global minimum. In order to solve this well known and difficult convergence problem, in this paper we present a new method, which converges to the true solution, for obtaining the scattering potential without using the Born or Rytov approximation. This method converts the nonlinear nature of the problem into a linear one. Through computer simulations we will show the validity of the new approach for high contrast two-dimensional scattering objects which are insonified by an incident ultrasound plane wave. Numerical results show that the reconstruction error is very small for circularly symmetric two-dimensional cylindrical objects whose refractive indices range from small to even sufficiently large values for which the previous inverse scattering algorithms fail to converge.     

Spatial Periodicities in Coherent and Partially Coherent Fields

The propagation of light in free space yields images of a certain class of objects. This effect, discovered 150 years ago by Talbot, is known as ‘self-imaging’. The self-imaging phenomenon, or the periodic properties of coherent and partially coherent fields, are described in this paper as eigenfunctions of the operator that represents the solution of the Helmholtz equation. Using this simple treatment, we state the necessary and sufficient conditions for self-imaging in coherent and partially coherent fields. We indicate that certain laterally aperiodical, partially coherent fields also exhibit self-imaging properties. Our treatment is exact, but it disregards evanescent waves.     

In-line hologram reconstruction using Hartley transform

In reconstruction of in-line recorded holograms, zero-order and conjugate images appear on the same physical location as the object image. Here we propose a method, new to our knowledge, to separate the object image from the others by using two quadrature phase-shifted holograms. The method uses the Hartley transform and a phase retrieval type of algorithm on the difference hologram.     

扩展目标高分辨力斑点成象的模拟

介绍了扩展目标高分辨力斑点成象过程的计算机模拟,内容包括大气湍波的模拟、目标短曝光象的形成、目标功率谱的估计、目标傅里叶相位的恢复以及克服大气湍流影响后目标高分瘁力图象的重建。模拟结果显示,斑点成象技术可以克服大气湍流的影响,获得了望远镜口径决定的衍射极限的成象分辨力。模拟所建立的系统,也为进一步深入研究扩展目标的高分辨力斑点成象技术打下了基础。