Ultrasound imaging through time-domain diffraction tomography

Time-domain diffraction tomography, a technique for imaging with acoustic (and other) fields in which a medium parameter, such as density, can be mapped from scatter data collected from one pulse, is discussed. When Born approximations hold, the technique provides an exact inversion of the acoustical scattering equations. Computer simulation of the time-domain diffraction tomography equations indicates that under ideal conditions, and when the Born approximation is valid, the method can reconstruct maps of parameter variations. However, when data are collected from an incident pulse whose bandwidth is limited, the reconstruction is no longer perfect. A simple question is derived that characterizes the performance of time-domain diffraction tomography, and the limitations are explained as the effect of a spatial filter that eliminates some of the spatial frequencies. Relations between the object parameters, pulse bandwidth, and reconstruction accuracy are investigated with numerical experiments.     

Superresolution in total internal reflection tomography

We simulate a total internal reflection tomography experiment in which an unknown object is illuminated by evanescent waves and the scattered field is detected along several directions. We propose a full-vectorial three-dimensional nonlinear inversion scheme to retrieve the map of the permittivity of the object from the scattered far-field data. We study the role of the solid angle of illumination, the incident polarization, and the position of the prism interface on the resolution of the images. We compare our algorithm with a linear inversion scheme based on the renormalized Born approximation and stress the importance of multiple scattering in this particular configuration. We analyze the sensitivity to noise and point out that using incident propagative waves together with evanescent waves improves the robustness of the reconstruction.     

A pseudoinverse filter for limited-angle diffraction tomography involving objects with planar structure

A reconstruction technique for limited-angle diffraction tomography is described in which a special pseudoinverse filter is applied to the back-propagation. Using this approach, it is possible to reconstruct a ten-layered object with only 19 projections having angles ranging from -10 degrees to +10 degrees . It is concluded that the algorithm proposed here offers an efficient and computationally easy method for reconstructing an object with planar structure. Even when the number of layers is large and the range of incident angle is limited, the method will give good images.     

Homogeneous and evanescent contributions in scalar near-field diffraction

The contributions of homogeneous and evanescent waves to two-dimensional near-field diffraction patterns of scalar optical fields are examined in detail. The total plane-integrated intensities of the two contributions are introduced as convenient measures of their relative importance. As an example, the diffraction of a plane wave by a slit is considered.     

Stiffness tensor random fields through upscaling of planar random materials

Unique effective material properties are not possible for random heterogeneous materials at intermediate length scales, which is to say at some mesoscale above the microscale yet prior to the attainment of the representative volume element (RVE). Focusing on elastic moduli in particular, a micromechanical analysis based on the Hill–Mandel condition leads to the conclusion that two fields, stiffness and compliance, are required to bound the response of the material. In particular, we analyze means and correlation coefficients of a random planar material with a two-phase microstructure of random checkerboard type. We employ micromechanics, which can be viewed as an upscaling, smoothing procedure using the concept of a mesoscale “window”, and random field theory to compute the correlation structure of 4th-rank tensor fields of stiffness and compliance for a given mesoscale. Results are presented for various correlation distances, volume fractions, and contrasts in stiffness between phases. The main contribution of this research is to provide the data for developing analytical correlation functions, which can then be used at any mesoscale to generate micromechanically based inputs into analytical and computational mechanics models.     

Uniform theory for the diffraction of evanescent plane waves

A uniform diffracted field is obtained in terms of Fresnel functions with complex argument by subtracting the unit step function from the Fresnel integral. The method is applied to the problem of diffraction of inhomogeneous plane waves by a perfectly conducting half-plane and wedge. The results are plotted numerically and compared with results reported in the literature.     

Spherical-wave intensity diffraction tomography

An extension of the recently developed method of intensity diffraction tomography is derived that assumes that the probing field is a spherical wave produced by a point source sufficiently far from the scatterer. A discussion of the method and numerical reconstructions of a simulated three-dimensional scattering object are presented.     

Polychromatic diffraction contrast tomography

This tutorial review introduces the use of polychromatic radiation for 3D grain mapping using X-ray diffraction contrast tomography. The objective is to produce a 3D map of the grain shapes and orientations within a bulk, millimeter-sized polycrystalline sample. The use of polychromatic radiation enables the standard synchrotron X-ray technique to be applied in a wider range of contexts: 1) Using laboratory X-ray sources allows a much wider application of the diffraction contrast tomography technique. 2) Neutron sources allow large samples, or samples containing high Z elements to be studied. 3) Applied to synchrotron sources, smaller samples may be treated, or faster measurements may be possible. Challenges and particularities in the data acquisition and processing, and the limitations of the different variants, are discussed.     

Stochastic geophysical diffraction tomography

We revisit geophysical diffraction tomography (GDT) and cast it into a stochastic framework, in which the geophysical formation to be imaged is modeled as a realization of a two-dimensional stationary random process. It is shown that the optimum reconstruction algorithm, in both the cases of offset vertical seismic profiling and well-to-well probing, attains a modified filtered backpropagation form.©1994 John Wiley & Sons Inc     

Relation between computed tomography and diffraction tomography

The relationship between computed tomography (CAT) and diffraction tomography (DT) is investigated. A simple condition with a clear physical meaning is derived for the applicability of CAT. Corrections due to scattering are incorporated into CAT, and it is shown that the effect of scattering may be characterized by a two-dimensional fractional Fourier transform. The implications of these results for the three-dimensional imaging of weakly scattering objects are also discussed.     

The optical cross-section theorem with incident fields containing evanescent components

Abstract

The optical cross-section theorem is extended to cases in which the incident field contains evanescent waves. Physical interpretations are discussed. Some explicit examples are given and possible applications are proposed.     

Superresolution and increased depth of focus: An inverse problem of vector diffraction

Abstract

Using vector diffraction theory, we have addressed the issue of finding the pupil function when the rate of decay of the intensity in the vicinity of the Gaussian focus along the optical axis is prescribed. The problem posed here reduces to a Fredholm integral equation, which is then solved to obtain the pupil function. We show that the diffraction integrals, as formulated by Wolf, are invariant if they are expressed in terms of the zth (the direction of the optical axis) component of the unit normal to the aberrated wave front. This makes it possible to obtain the pupil function from the solution of the Fredholm integral equation. We present results for lenses with high numerical aperture and show that the depth of focus is significantly increased without any loss of transmitted energy. Results further indicate that the FWHM of the primary lobe is significantly narrower than the clear aperture.     

Contour reconstruction in diffraction tomography

We address the problem of reconstructing the directional derivative and/or the Laplacian of an object function f characterizing a weakly inhomogeneous scatterer directly from data collected in a set of scattering experiments. We employ the Rytov approximation to model the complex phase of the scattered wavefields and show that a minimum-norm least-squares solution can be obtained from the well known filtered backpropagation algorithm of diffraction tomography with appropriate modification of the tomographic filters employed in the filtering step of the algorithm. The procedure is illustrated by a computer simulation study.     

Infrared evanescent field sensing with quantum cascade lasers and planar silver halide waveguides

We demonstrate the first midinfrared evanescent field absorption measurements with an InGaAs/AlInAs/InP distributed feedback (DFB) quantum cascade laser (QCL) light source operated at room temperature coupled to a free-standing, thin-film, planar, silver halide waveguide. Two different analytes, each matched to the emission frequency of a QCL, were investigated to verify the potential of this technique. The emission of a 1650 cm(-1) QCL overlaps with the amide absorption band of urea, which was deposited from methanol solution, forming urea crystals at the waveguide surface after solvent evaporation. Solid urea was detected down to 80.7 microg of precipitate at the waveguide surface. The emission frequency of a 974 cm(-1) QCL overlaps with the CH3-C absorption feature of acetic anhydride. Solutions of acetic anhydride in acetonitrile have been detected down to a volume of 0.01 microL (10.8 microg) of acetic anhydride solution after deposition at the planar waveguide (PWG) surface. Free-standing, thin-film, planar, silver halide waveguides were produced by press-tapering heated, cylindrical, silver halide fiber segments to create waveguides with a thickness of 300-190 microm, a width of 3 mm, and a length of 35 mm. In addition, Fourier transform infrared (FT-IR) evanescent field absorption measurements with planar silver halide waveguides and transmission absorption QCL measurements verify the obtained results.     

声衍射层析成像研究进展

在计算机层析成像中用声波或电磁波取代X射线照射目标时波长不能再看作无限小,需要将Fourier切片定理修改为Fourier衍射投影定理,基于射线的CT相应地推广为衍射CT。概述了近年来衍射CT的发展,特别是声衍射CT。在理论和算法方面讨论了非均匀Fourier变换算法及其实现、仅根据强度信息的图像重建方法、多频率入射的情况、不完整测量数据条件下的图像重建等问题。此外还扼要介绍了不同领域中衍射CT的研究和应用情况。     

Multistage parallel algorithm for diffraction tomography

A multistage parallel algorithm with iterative processing is discussed for the processing of information in diffraction tomography. The algorithm is based on matrix partitioning, which results in mostly parallel stages of processing. Each successive stage is designed to minimize the remaining error. The process is iterated until convergence. The major advantages of the multistage algorithm are the reduced computational time from faster convergence as compared with a single-stage iterative algorithm, further reduction of computation time if the stages are implemented mostly in parallel, and better performance in terms of reduced reconstruction error.     

Hybrid diffraction tomography without phase information

We introduce a hybrid tomographic method, based on recent investigations concerning the connection between computed tomography and diffraction tomography, that allows direct reconstruction of scattering objects from intensity measurements. This technique is noniterative and is intuitively easier to understand and easier to implement than some other methods described in the literature. The manner in which the new method reduces to computed tomography at short wavelengths is discussed. Numerical examples of reconstructions are presented.     

Submillimeter planar gyrotrons with transverse diffraction output of radiation

In order to increase the integral output power of short-wave gyrotrons, it is suggested to use a planar scheme with the transverse (relative to the direction of electron translation) diffraction output of radiation. An advantage of the planar design in comparison to the traditional cylindrical gyrotron geometry is the possibility to ensure the coherence of radiation at a greater oversized factor by using a diffraction mechanism of mode selection with respect to the transverse coordinate. The results of simulation of the nonlinear dynamics of a planar gyrotron with a polyhelical ribbon electron beam show that it is possible to reach an output power of several hundred kilowatt at frequencies up to 1 THz. An additional advantage of the proposed scheme is the possibility of frequency tuning by changing the distance between plates.     

Deterministic regularization of three-dimensional optical diffraction tomography

In this paper, we discuss a deterministic regularization algorithm to handle the missing cone problem of three-dimensional optical diffraction tomography (ODT). The missing cone problem arises in most practical applications of ODT and is responsible for elongation of the reconstructed shape and underestimation of the value of the refractive index. By applying positivity and piecewise-smoothness constraints in an iterative reconstruction framework, we effectively suppress the missing cone artifact and recover sharp edges rounded out by the missing cone, and we significantly improve the accuracy of the predictions of the refractive index. We also show the noise-handling capability of our algorithm in the reconstruction process.     

Partial spatial coherence and partial polarization in random evanescent fields on lossless interfaces

We consider partial spatial coherence and partial polarization of purely evanescent optical fields generated in total internal reflection at an interface of two dielectric (lossless) media. Making use of the electromagnetic degree of coherence, we show that, in such fields, the coherence length can be notably shorter than the light's vacuum wavelength, especially at a high-index-contrast interface. Physical explanation for this behavior, analogous to the generation of incoherent light in a multimode laser, is provided. We also analyze the degree of polarization by using a recent three-dimensional formulation and show that the field may be partially polarized at a subwavelength distance from the surface even though it is fully polarized farther away. The degree of polarization can assume values unattainable by beamlike fields, indicating that electromagnetic evanescent waves generally are genuine three-dimensional fields. The results can find applications in near-field optics and nanophotonics.