Computed tomography with linear shift-invariant optical systems

Optical systems capable of three-dimensional transmission imaging are considered; these systems employ a conventional tomographic setup with an added linear shift-invariant optical system between the sample and the detector. A theoretical analysis is presented of image formation and sample reconstruction in such systems, examples of which include diffraction tomography and phase-contrast tomography with the use of analyzer crystals. An example is introduced in which the image is obtained by scanning the beam along the line orthogonal to the optic axis and to the axis of rotation with a one-dimensional slit or grating parallel to the rotation axis. We show that under certain conditions the proposed system may allow quantitative local (region-of-interest) tomography.     

Cone-beam tomography with a digital camera

We show that x-ray computer tomography algorithms can be applied with minimal alteration to the three-dimensional reconstruction of visible sources. Diffraction and opacity affect visible systems more severely than x-ray systems. For camera-based tomography, diffraction can be neglected for objects within the depth of field. We show that, for convex objects, opacity has the effect of windowing the angular observation range and thus blurring the reconstruction. For concave objects, opacity leads to nonlinearity in the transformation from object to reconstruction and may cause multiple objects to map to the same reconstruction. In x-ray tomography, the contribution of an object point to a line integral is independent of the orientation of the line. In optical tomography, however, a Lambertian assumption may be more realistic. We derive an expression for the blur function (the patch response) for a Lambertian source. We present experimental results showing cone-beam reconstruction of an incoherently illuminated opaque object.     

Linearized inversion methods for three-dimensional electromagnetic imaging in the multiple scattering regime

In optical or microwave computational tomography, the sample permittivity is reconstructed numerically from the measurements of its scattered field for various illuminations. When the light sample interaction involves multiple scattering, the relationship between the scattered field and the permittivity is non-linear and a direct reconstruction is not possible. Using a simple physical approach, adapted to the three-dimensional vectorial electromagnetic framework, we derive an iterative inversion technique, based on the linearization of the scattering operator, for imaging (possibly anisotropic) targets in the multiple scattering regime. We investigate the performances of different approximations of this operator accounting for more or less multiple scattering. Our method is applied to the reconstruction of targets in the microwave domain using experimental data.     

Computationally efficient and statistically robust image reconstruction in three-dimensional diffraction tomography

Diffraction tomography (DT) is an inversion scheme used to reconstruct the spatially variant refractive-index distribution of a scattering object. We developed computationally efficient algorithms for image reconstruction in three-dimensional (3D) DT. A unique and important aspect of these algorithms is that they involve only a series of two-dimensional reconstructions and thus greatly reduce the prohibitively large computational load required by conventional 3D reconstruction algorithms. We also investigated the noise characteristics of these algorithms and developed strategies that exploit the statistically complementary information inherent in the measured data to achieve a bias-free reduction of the reconstructed image variance. We performed numerical studies that corroborate our theoretical assertions.     

A new coded-excitation ultrasound imaging system. I. Basicprinciples

A new approach to ultrasound imaging with coded-excitation is presented. The imaging is performed by reconstruction of the scatterer strength on an assumed grid covering the region of interest (ROI). Our formulation is based on an assumed discretized signal model which represents the received sampled data vector as a superposition of impulse responses of all scatterers in the ROI. The reconstruction operator is derived from the pseudo-inverse of the linear operator (system matrix) that produces the received data vector. The singular value decomposition (SVD) method with appropriate regularization techniques is used for obtaining a robust realization of the pseudo-inverse. Under simplifying (but realistic) assumptions, the pseudo-inverse operator (PIO) can be implemented using a bank of transversal filters with each filter designed to extract echoes from a specified image line. This approach allows for the simultaneous acquisition of a large number of image lines. This could be useful in increasing frame rates for two-dimensional imaging systems or allowing for real-time implementation of three-dimensional imaging systems. When compared to the matched filtering approach to similar coded-excitation systems, our approach eliminates correlation artifacts that are known to plague such systems. Furthermore, the lateral resolution of the new system can exceed the diffraction limit imposed on conventional imaging systems utilizing delay-and-sum beamformers. The range resolution is compared to that of conventional pulse-echo systems with resolution enhancement (our PIO behaves as a pseudo-inverse Wiener filter in the range direction). Both simulation and experimental verification of these statements are given     

Tomographic optical breast imaging guided by three-dimensional mammography

We introduce a modified Tikhonov regularization method to include three-dimensional x-ray mammography as a prior in the diffuse optical tomography reconstruction. With simulations we show that the optical image reconstruction resolution and contrast are improved by implementing this x-ray-guided spatial constraint. We suggest an approach to find the optimal regularization parameters. The presented preliminary clinical result indicates the utility of the method.     

Semi-three-dimensional algorithm for time-resolved diffuse optical tomography by use of the generalized pulse spectrum technique

Although a foil three-dimensional (3-D) reconstruction with both 3-D forward and inverse models provide, the optimal solution for diffuse optical tomography (DOT), because of the 3-D nature of photon diffusion in tissue, it is computationally costly for both memory requirement and execution time in a conventional computing environment. Thus in practice there is motivation to develop an image reconstruction algorithm with dimensional reduction based on some modeling approximations. Here we have implemented a semi-3-D modified generalized pulse spectrum technique for time-resolved DOT, where a two-dimensional (2-D) distribution of optical properties is approximately assumed, while we retain 3-D distribution of photon migration in tissue. We have validated the proposed algorithm by reconstructing 3-D structural test objects from both numerically simulated and experimental date. We demonstrate our algorithm by comparing it with the calibrated 2-D reconstruction that is in widespread use as a shortcut to 3-D imaging and proving that the semi-3-D algorithm outperforms the calibrated 2-D algorithm.     

Three-dimensional modeling using x-ray shape-from-silhouette

We present the application of the shape-from-silhouette technique to reconstruct the three-dimensional profile of ancient handworks from their x-ray absorption images. The acquisition technique is similar to tomography, since the images are taken all around the object while it is rotated. Some reference points are placed on a small and light structure corotating with the object, and are acquired on the images for calibration and registration. The reconstruction algorithm gives finally the three-dimensional appearance of the handwork. We present the analysis of a bronze pendant of VI-VII century B.C. (Venetic area, Italy) completely hidden by corrosion products. The three-dimensional reconstruction shows that the pendant is a very elaborated piece, with two embraced figures that were completely invisible at the excavation.     

Electron holographic tomography

The exact knowledge about intrinsic electrostatic potentials and in particular their three-dimensional distribution at the nanometer scale is a key prerequisite for understanding the solid state properties. Electron holographic tomography (EHT), the combination of off-axis holography with tomography in the transmission electron microscope, provides a unique access to this information. We review the development and application of automated EHT to reconstruct 3D potentials in nanostructures such as the mean inner potential of a material or the diffusion potential across p–n junctions in semiconductors. We also discuss future challenges of the 3D reconstruction of electric crystal potentials at atomic resolution and magnetostatic fields as well as ways to overcome present limitations of the method.     

Signal-to-noise ratio study of full-field fourier-domain optical coherence tomography

We report a new approach in optical coherence tomography (OCT) called full-field Fourier-domain OCT (3F-OCT). A three-dimensional image of a sample is obtained by digital reconstruction of a three-dimensional data cube, acquired with a Fourier holography recording system, illuminated with a swept source. We present a theoretical and experimental study of the signal-to-noise ratio of the 3F-OCT approach versus serial image acquisition (flying-spot OCT) approach.     

Three-dimensional plasma field reconstruction with multiobjective optimization emission spectral tomography

A novel emission spectral tomography algorithm based on multiobjective optimization is proposed. Its reconstruction results for asymmetrical emission coefficient fields are studied with computer simulation. The results show that this algorithm provides a significant improvement in reconstruction precision and convergence over traditional algorithms and is suitable for real-time reconstruction of an emission-coefficient field with incomplete data. In an experiment of the argon-arc plasma diagnosis, we adopted this algorithm and the spectrum relative-intensity method to obtain the three-dimensional distributions of temperature, ionization coefficient, and electron (ion) and atom densities.     

Tomographic reconstruction of three-dimensional refractive index fields by use of a regularized phase-tracking technique and a polynomial approximation method

We present a complete data-processing procedure for quantitative reconstruction of three-dimensional (3D) refractive index fields from limited multidirectional interferometric data. The proposed procedure includes two parts: (1) extraction of the projection data from limited multidirectional interferograms by a regularized phase-tracking technique and wavefront fitting and (2) reconstruction of the 3D refractive index fields by a modified polynomial approximation method. It has been shown that the procedure gives a satisfactory solution to the reconstruction issue in interferometric tomography, from the initial projection data extraction to the final image reconstruction. Computer simulation and experimental results are both presented.     

Electrical Capacitance Volume Tomography

A dynamic volume imaging based on the principle of electrical capacitance tomography (ECT), namely, electrical capacitance volume tomography (ECVT), has been developed in this study. The technique generates, from the measured capacitance, a whole volumetric image of the region enclosed by the geometrically three-dimensional capacitance sensor. This development enables a real-time, 3-D imaging of a moving object or a real-time volume imaging (4-D) to be realized. Moreover, it allows total interrogation of the whole volume within the domain (vessel or conduit) of an arbitrary shape or geometry. The development of the ECVT imaging technique primarily encloses the 3-D capacitance sensor design and the volume image reconstruction technique. The electrical field variation in three-dimensional space forms a basis for volume imaging through different shapes and configurations of ECT sensor electrodes. The image reconstruction scheme is established by implementing the neural-network multicriterion optimization image reconstruction (NN-MOIRT), developed earlier by the authors for the 2-D ECT. The image reconstruction technique is modified by introducing into the algorithm a 3-D sensitivity matrix to replace the 2-D sensitivity matrix in conventional 2-D ECT, and providing additional network constraints including 3-to-2-D image matching function. The additional constraints further enhance the accuracy of the image reconstruction algorithm. The technique has been successfully verified over actual objects in the experimental conditions     

Toward atomic-scale bright-field electron tomography for the study of fullerene-like nanostructures

We present the advancement of electron tomography for three-dimensional structure reconstruction of fullerene-like particles toward atomic-scale resolution. The three-dimensional reconstruction of nested molybdenum disulfide nanooctahedra is achieved by the combination of low voltage operation of the electron microscope with aberration-corrected phase contrast imaging. The method enables the study of defects and irregularities in the three-dimensional structure of individual fullerene-like particles on the scale of 2-3 A. Control over shape, size, and atomic architecture is a key issue in synthesis and design of functional nanoparticles. Transmission electron microscopy (TEM) is the primary technique to characterize materials down to the atomic level, albeit the images are two-dimensional projections of the studied objects. Recent advancements in aberration-corrected TEM have demonstrated single atom sensitivity for light elements at sub?ngstr?m resolution. Yet, the resolution of tomographic schemes for three-dimensional structure reconstruction has not surpassed 1 nm3, preventing it from becoming a powerful tool for characterization in the physical sciences on the atomic scale. Here we demonstrate that negative spherical aberration imaging at low acceleration voltage enables tomography down to the atomic scale at reduced radiation damage. First experimental data on the three-dimensional reconstruction of nested molybdenum disulfide nanooctahedra is presented. The method is applicable to the analysis of the atomic architecture of a wide range of nanostructures where strong electron channeling is absent, in particular to carbon fullerenes and inorganic fullerenes.     

Acoustical tomography based on the second-order Born transformperturbation approximation

Reconstruction algorithms and their numerical examples of acoustical tomography based on the second-order Born transform perturbation approximation are presented. The reconstruction algorithms in the second-order Born approximation are similar in form to those in the first-order Born approximation. Replacing the angular spectrum of the scattered wave in the first-order case by the result of applying a first-order operator to the angular spectrum of the scattered wave or applying a second-order operator to the angular spectrum of the incident wave leads to the second-order reconstruction algorithms. Also, comparisons of reconstruction algorithms of the first- and second-order Born approximations are given, and they show that the second-order Born approximation algorithms have a distinct advantage over the first-order approximations in many cases     

Source-detector calibration in three-dimensional Bayesian optical diffusion tomography

Optical diffusion tomography is a method for reconstructing three-dimensional optical properties from light that passes through a highly scattering medium. Computing reconstructions from such data requires the solution of a nonlinear inverse problem. The situation is further complicated by the fact that while reconstruction algorithms typically assume exact knowledge of the optical source and detector coupling coefficients, these coupling coefficients are generally not available in practical measurement systems. A new method for estimating these unknown coupling coefficients in the three-dimensional reconstruction process is described. The joint problem of coefficient estimation and three-dimensional reconstruction is formulated in a Bayesian framework, and the resulting estimates are computed by using a variation of iterative coordinate descent optimization that is adapted for this problem. Simulations show that this approach is an accurate and efficient method for simultaneous reconstruction of absorption and diffusion coefficients as well as the coupling coefficients. A simple experimental result validates the approach.     

Exact and efficient signal reconstruction in frequency-domain optical-coherence tomography

We address the problem of tomogram reconstruction in frequency-domain optical-coherence tomography. We propose a new technique for suppressing the autocorrelation artifacts that are commonly encountered with the conventional Fourier-transform-based approach. The technique is based on the assumptions that the scattering function is causal and that the intensity of the light reflected from the object is smaller than that of the reference. The technique is noniterative, nonlinear, and yields an exact solution in the absence of noise. Results on synthesized data and experimental measurements show that the technique offers superior quality reconstruction and is computationally more efficient than the iterative technique reported in the literature.     

A modified algebraic reconstruction technique taking refraction into account with an application in terahertz tomography

Terahertz (THz) tomography is a rather novel technique for non-destructive testing that is particularly suited for the testing of plastics and ceramics. Previous publications showed a large variety of conventional algorithms adapted from computed tomography or ultrasound tomography which were directly applied to THz tomography. Conventional algorithms neglect the specific nature of THz radiation, i.e. refraction at interfaces, reflection losses and the beam profile (Gaussian beam), which results in poor reconstructions. The aim is the efficient reconstruction of the complex refractive index, since it indicates inhomogeneities in the material. A hybrid algorithm has been developed based on the algebraic reconstruction technique (ART). ART is adapted by including refraction (Snell’s law) and reflection losses (Fresnel equations). Our method uses a priori information about the interface and layer geometry of the sample. This results in the ‘Modified ART for THz tomography’, which reconstructs simultaneously the complex refractive index from transmission coefficient and travel time measurements.     

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.     

Influence of multiple scattering on three-dimensional imaging with optical diffraction tomography

Optical diffraction tomography is an imaging technique that permits retrieval of the map of permittivity of an object from its scattered far field. Most reconstruction procedures assume that single scattering is dominant so that the scattered far field is linearly linked to the permittivity. In this work, we present a nonlinear inversion method and apply it to complex three-dimensional samples. We show that multiple scattering permits one to obtain a power of resolution beyond the classical limit imposed by the use of propagative incident and diffracted waves. Moreover, we stress that our imaging method is robust with respect to correlated and uncorrelated noise.