Three-Dimensional Diffraction Tomography Using Filtered Backpropagation and Multiple Illumination Planes

In this paper, a three-dimensional (3-D) extension of the well-known filtered-backpropagation (FBP) algorithm is presented with the aim of taking into account scattered-field-data measurements obtained using incident directions not restricted in a single plane. The FBP algorithm has been extensively used to solve the two-dimensional inverse-scattering problem under the first-order Born and Rytov approximations for weak scatterers. The extension of this algorithm in three dimensions is not straightforward, because the task of collecting the data needed to obtain a low-pass filtered version of the scattering object, taking into account all spatial frequencies within a radius of radic2k₀, and of incorporating these data to the FBP algorithm, needs to be addressed. A simple extension using incident field directions restricted to a single plane (illumination plane) leaves a region of spatial frequencies of the sphere of radius radic2k ₀ undetermined. The locus of these spatial frequencies may be crucial for the accurate reconstruction of objects which do not vary slowly along the axis perpendicular to the illumination plane. The proposed 3-D FBP algorithm presented here is able to incorporate the data collected from more than one illumination plane and to ensure the reliability of the reconstruction results     

Transmission of a two-dimensional Gaussian beam into a uniaxial crystal.

We study the transmission of a two-dimensional (2-D) TM Gaussian beam through a plane interface between an isotropic medium (e.g., air) and a uniaxially anisotropic crystal. The optic axis of the crystal is taken to be in the plane of incidence but is arbitrarily oriented relative to the interface normal. We show that, in the paraxial approximation, a nontruncated transmitted 2-D TM Gaussian beam inside a uniaxial crystal can be expressed in a form similar to that of a scalar Gaussian beam that propagates in a homogeneous medium. We also show that the transmitted beam corresponding to an incident 2-D TM Gaussian beam with its main propagation direction along the interface normal is tilted inside the crystal by the same angle as is the transmitted axial ray that corresponds to a normally incident ray.     

Three-dimensional image sensing and reconstruction with time-division multiplexed computational integral imaging

A method to compute high-resolution three-dimensional images based on integral imaging is presented. A sequence of integral images (IIs) is captured by means of time-division multiplexing with a moving lenslet array technique. For the acquisition of each II, the location of the lenslet array is shifted periodically within the lenslet pitch in a plane perpendicular to the optical axis. The II sequence obtained by the detector array is processed digitally with superresolution reconstruction algorithms to obtain a reconstructed image, appropriate to a viewing direction, which has a spatial resolution beyond the optical limitation.     

Time-resolved Fourier optical diffuse tomography.

Time-resolved Fourier optical diffuse tomography is a novel approach for imaging of objects in a highly scattering turbid medium with use of an incident (near) plane wave. The theory of the propagation of spatial Fourier components of the scattered wave field is presented, along with a fast algorithm for three-dimensional reconstruction in a parallel planar geometry. Examples of successful reconstructions of simulated hidden absorptive or scattering objects embedded inside a human-tissue-like semi-infinite turbid medium are provided.     

Position‐dependent defocus processing for acoustic holography images

Acoustic holography is a transmission‐based ultrasound imaging method that uses optical image reconstruction and provides a larger field of view than pulse‐echo ultrasound imaging. A focus parameter controls the position of the focal plane along the optical axis, and the images obtained contain defocused content from objects not near the focal plane. Moreover, it is not always possible to bring all objects of interest into simultaneous focus. In this article, digital image processing techniques are presented to (1) identify a “best focused” image from a sequence of images taken with different focus settings and (2) simultaneously focus every pixel in the image through fusion of pixels from different frames in the sequence. Experiments show that the three‐dimensional image information provided by acoustic holography requires position‐dependent filtering for the enhancement step. It is found that filtering in the spatial domain is more computationally efficient than in the frequency domain. In addition, spatial domain processing gives the best performance. © 2002 Wiley Periodicals, Inc. Int J Imaging Syst Technol 12, 101–111, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.10017     

Super resolution in CT

The general framework of super resolution in computed tomography (CT) system is introduced. Two data acquisition ways before or after the reconstruction respectively are described. Three models including the sinogram model, the in‐plane model and the z‐axis model, are addressed to adapt super resolution to CT system. The improved iterative back projection algorithm is used in this work. Experimental results based on simulated data, GE performance phantom scanned by GE LightSpeed VCT system, one patient volunteer scanned by TOSHIBA Aquilion system, and a special experimental apparatus demonstrate that super resolution is effective to improve the resolution of CT images. The sinogram model is suitable for future CT system; the in‐plane model is restricted to some special clinical diagnoses; and the z‐axis model is practicable for current general clinical CT images. © 2015 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 25, 92–101, 2015     

Approach to 3-d ultrasound high resolution imaging for mechanically moving large-aperture transducer based upon Fourier transform

A new three-dimensional (3-D) acoustic image formation technique is proposed that is based on the transmission of wide bandwidth pulse signals and the application of the 3-D fast Fourier transform. A solution to the Helmholtz wave equation has been obtained using the Born approximation. The solution contains analytical expressions for the spatial spectra of the transmit and receive radiation patterns for transducers of various geometries with lenses of fixed focal distances. It has been shown that the proposed algorithms allow for radiation patterns with constant widths at depths both behind and in front of the focal point, starting practically from the plane of the transducer. The theoretical and experimental investigations and computer simulation for both spherical and rectangular transducer shapes have been performed. The results were used to estimate the beamwidths and the side lobe levels. A variant of the linear array has been studied for a cylindrical lens of a fixed focal distance moving in a lateral direction. It has been shown that, in this case, a high resolution (of the order of a few wavelengths) can be achieved along all three Cartesian coordinates at a very high scanning velocity. The influence of the moving scatterers' velocity in inhomogeneous medium on the spatial radiation pattern characteristics has been estimated.     

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.     

Three-dimensional polarization states of monochromatic light fields

The 3×1 generalized Jones vectors (GJVs) [E(x) E(y) E(z)](t) (t indicates the transpose) that describe the linear, circular, and elliptical polarization states of an arbitrary three-dimensional (3-D) monochromatic light field are determined in terms of the geometrical parameters of the 3-D vibration of the time-harmonic electric field. In three dimensions, there are as many distinct linear polarization states as there are points on the surface of a hemisphere, and the number of distinct 3-D circular polarization states equals that of all two-dimensional (2-D) polarization states on the Poincaré sphere, of which only two are circular states. The subset of 3-D polarization states that results from the superposition of three mutually orthogonal x, y, and z field components of equal amplitude is considered as a function of their relative phases. Interesting contours of equal ellipticity and equal inclination of the normal to the polarization ellipse with respect to the x axis are obtained in 2-D phase space. Finally, the 3×3 generalized Jones calculus, in which elastic scattering (e.g., by a nano-object in the near field) is characterized by the 3-D linear transformation E(s)=T E(i), is briefly introduced. In such a matrix transformation, E(i) and E(s) are the 3×1 GJVs of the incident and scattered waves and T is the 3×3 generalized Jones matrix of the scatterer at a given frequency and for given directions of incidence and scattering.     

Wavelet-based image enhancement in x-ray imaging and tomography

We consider an application of the wavelet transform to image processing in x-ray imaging and three-dimensional (3-D) tomography aimed at industrial inspection. Our experimental setup works in two operational modes-digital radiography and 3-D cone-beam tomographic data acquisition. Although the x-ray images measured have a large dynamic range and good spatial resolution, their noise properties and contrast are often not optimal. To enhance the images, we suggest applying digital image processing by using wavelet-based algorithms and consider the wavelet-based multiscale edge representation in the framework of the Mallat and Zhong approach [IEEE Trans. Pattern Anal. Mach. Intell. 14, 710 (1992)]. A contrast-enhancement method by use of equalization of the multiscale edges is suggested. Several denoising algorithms based on modifying the modulus and the phase of the multiscale gradients and several contrast-enhancement techniques applying linear and nonlinear multiscale edge stretching are described and compared by use of experimental data. We propose the use of a filter bank of wavelet-based reconstruction filters for the filtered-backprojection reconstruction algorithm. Experimental results show a considerable increase in the performance of the whole x-ray imaging system for both radiographic and tomographic modes in the case of the application of the wavelet-based image-processing algorithms.     

斜入射下水下地基场地地震输入的一维化时域方法

地震波斜入射下水下地基场地地震动输入问题,是涉及水层、饱和多孔介质和基岩三种不同性质介质耦合的复杂问题,目前理论成果还很匮乏。该文在现有的成层饱和多孔介质平面波斜入射的一维化时域方法的基础上,建立了水下地基场地的一维化时域计算方法。该计算方法依据Snell定理,将地震波斜入射下水层波动的空间二维问题转化为简单的一维问题,通过考虑水层与饱和多孔介质层交界面、不同饱和多孔介质交界面以及基岩与饱和多孔介质层交界面的边界条件,将已有的成层饱和土的一维化有限元方程与水层的一维化有限元方程组装,采用单相弹性介质精确人工边界条件模拟基岩半空间的波动辐射和输入特征,形成了水下地基场地的整体有限元方程,借助于中心差分法和Newmark法相结合的时步积分法,推导了地震波斜入射下水下地基场地各节点动力响应时程的显式表达式。通过与傅里叶变换得到的理论解和现有的文献进行了对比,初步验证了该文时域算法的有效性和精度,为地震波斜入射下水下地基场地地震动输入提供了一种新型高效的研究方法。     

Residual Stress Analysis Using Multiparameter Tomographic Reconstruction

In this work, the potential application of acoustic tomography to determine the distribution of residual stresses is discussed. Multiparameter reconstruction techniques are presented for both 2-D and 3-D residual stress states along with results from synthetic data. The effect of measurement errors on the accuracy of the reconstruction is also presented.     

Potential and limits of holographic reconstruction algorithms

For the purpose of ultrasonic nondestructive testing of materials, holography in connection with digital reconstruction algorithms has been proposed as a modern tool to extract crack sizes from ultrasonic scattering data. Defining the typical holographic reconstruction algorithm as the application of the scalar Kirchhoff diffraction theory to backward wave propagation, we demonstrate its general incapability of reconstructing equivalent sources, and hence, geometries of scattering bodies. Only the special case of a planar measurement recording surface, that is to say, a hologram plane, and a planar crack with perfectly rigid boundary conditions parallel to the hologram plane and perpendicular to the incident field yields a nearly perfect correlation between crack size and reconstructed image; the reconstruction algorithm is then referred to as the Rayleigh-Sommerfeld formula; it therefore represents the optimal case matched to that special geometrical situation and, hence, may be interpreted as a quasi-matched spatial filter. Using integral equation theory and physical optics, we compute synthetic holographic data for a linear cracklike scatterer for both plane and spherical wave incidence, the latter case simulating a synthetic aperture impulse echo situation, thus illustrating how the Rayleigh-Sommerfeld algorithm or its Fresnel approximation increasingly fail for cracks inclined to the hologram plane and excited nonperpendicularly. Furthermore, we point out how the physical data recording process may additionally influence the reconstruction accuracy, and, finally, guidelines for a careful and serious application of these holographic reconstruction algorithms are given. The theoretical results are supported by measurements.     

Damping of the dipole vortex

When a circular electric dipole moment, rotating in the x-y plane, is embedded in a material with relative permittivity ε(r) and relative permeability μ(r), the field lines of energy flow of the emitted radiation are dramatically influenced by the surrounding material. For emission in free space, the field lines swirl around the z axis and lie on a cone. The direction of rotation of the field lines around the z axis is the same as the direction of rotation of the dipole moment. We found that when the real part of ε(r) is negative, the rotation of the field lines changes direction, and hence the energy counter-rotates the dipole moment. When there is damping in the material, due to an imaginary part of ε(r), the cone turns into a funnel, and the density of the field lines diminishes near the location of the source. In addition, all radiation is emitted along the z axis and the x-y plane, whereas for emission in free space, the radiation is emitted in all directions. It is also shown that the displacement of the dipole image in the far field depends on the material parameters and that the shift can be much larger than the shift of the image in free space.     

Finite-element-based photoacoustic tomography: phantom and chicken bone experiments

We describe a photoacoustic image reconstruction algorithm that is based on the finite-element solution to the photoacoustic wave equation in the frequency domain. Our reconstruction approach is an iterative Newton method coupled with combined Marquardt and Tikhonov regularizations that can extract the spatial distribution of optical-absorption property in heterogeneous media. We demonstrate this algorithm by using phantom and chicken bone measurements from a circular scanning photoacoustic tomography system. The results obtained show that millimeter-sized phantom objects and chicken bones and/or joints can be clearly detected using our finite-element-based photoacoustic tomography method.     

Adaptive pattern correlation for two-dimensional blood flowmeasurements

One of the major drawbacks of ultrasonic Doppler instruments in measuring blood flow is their inability to measure the velocity perpendicular to the beam. Time domain RF echo or speckle tracking has been studied as an alternative to overcome this problem. By acquiring two-dimensional (2-D) echo signals, both lateral (perpendicular to the beam) and axial (parallel to the beam) velocities can be calculated with 2-D pattern correlation algorithms. One of the disadvantages of the current 2-D pattern correlation algorithms is the extensive computation time involved in computing the 2-D cross-correlation function. In this paper, we present several time-efficient bit-pattern correlation algorithms to execute 2-D speckle tracking. The proposed algorithms first estimate the noise level from the acquired signals and use it as a priori knowledge to minimize computation time. The reduction of computation time may make it more feasible for real-time measurements of flow velocities in two dimensions. Radio frequency and video data collected from two commercial scanners are used to validate the feasibility of these proposed algorithms with porcine blood as the flowing medium in in vitro experiments. The results obtained by the proposed algorithms are in good agreement with those computed from the cross-correlation function     

Local cone-beam tomography image reconstruction on chords

We develop reconstruction algorithms for local cone-beam tomography for use with generalized scanning trajectories. The algorithms are grounded theoretically in a recently developed chord-based theory for exact image reconstruction and principles of lambda tomography. Being chord based, they are distinct mathematically and conceptually from conventional local tomography reconstruction algorithms. The salient feature of our algorithms is that they permit reconstruction of discontinuities in the profiles of the object function along chords. By consideration of all possible chords, a 3D image that describes the locations of object discontinuities can be reconstructed. Results from microlocal analysis are applied for understanding the object features that can be reconstructed stably by use of the algorithms. A computer-simulation study is conducted to demonstrate the algorithms and compare their performance with an existing algorithm.     

The scattering of 3D sound sources by rigid barriers in the vicinity of tall buildings

The acoustic scattering of a three-dimensional (3D) sound source by an infinitely long rigid barrier in the vicinity of a tall building is analyzed using the boundary element method (BEM). The acoustic barrier is modeled using boundary elements, and is assumed to be non-absorbing, while the image source method is used to model the tall building as an infinite vertical barrier. A frequency domain BEM formulation is used, and time domain responses are then obtained by applying an inverse Fourier transformation.Since the geometry of the problem does not vary along one direction, the 3D solution can be calculated as the summation of a sequence of 2D problems, each solved for a different spatial wavenumber, k_z. To obtain the 3D solution, a discrete form wavenumber transform is performed by considering an infinite number of virtual point sources equally spaced along the z axis. Complex frequencies are used to minimize the influence of these neighboring fictitious sources.Numerical simulations are performed using barriers of varying sizes, evaluating the attenuation of the sound pressure level in the vicinity of the building façade. The creation of shadow zones by the barriers is analyzed and time responses are presented to better understand the sound propagation around these obstacles.     

Calculation of the radiation trapping force for laser tweezers by use of generalized Lorenz-Mie theory. I. Localized model description of an on-axis tightly focused laser beam with spherical aberration

Calculation of the radiation trapping force in laser tweezers by use of generalized Lorenz-Mie theory requires knowledge of the shape coefficients of the incident laser beam. The localized version of these coefficients has been developed and justified only for a moderately focused Gaussian beam polarized in the x direction and traveling in the positive z direction. Here the localized model is extended to a beam tightly focused and truncated by a high-numerical-aperture lens, aberrated by its transmission through the wall of the sample cell, and incident upon a spherical particle whose center is on the beam axis. We also consider polarization of the beam in the y direction and propagation in the negative z direction to be able to describe circularly polarized beams and reflected beams.     

Image reconstruction algorithm based on the extended regularised total least squares method for electrical capacitance tomography

Electrical capacitance tomography (ECT) is a non-invasive imaging technology that aims at the visualisation of the cross-sectional permittivity distribution of a dielectric object based on the measured capacitance data. Successful applications of ECT depend greatly on the precision and speed of the image reconstruction algorithms. ECT image reconstruction is a typical ill-posed problem, and its solution is unstable, that is, the solution is sensitive to noises in the input data. Methods that ensure the stability of a solution while enhancing the quality of the reconstructed images should be used to obtain a meaningful reconstruction result. An image reconstruction algorithm based on the regularised total least squares (TLS) method that considers the errors in both the sensitivity field matrix and the capacitance data for ECT is presented. The regularised TLS method is extended using a combination robust estimation technique and an extended stabilising functional according to the ill-posed characteristics of ECT, which transforms the image reconstruction problem into an optimisation problem. In addition, the Newton algorithm is employed to solve the objective functional. Numerical simulations indicate that the algorithm is feasible and overcomes the numerical instability of ECT image reconstruction; for the cases of the reconstructed objects considered here, the spatial resolution of the reconstructed images obtained using the algorithm is enhanced; as a result, an efficient method for ECT image reconstruction is introduced.