Efficient non-linear 3D electrical tomography reconstruction

Non-linear electrical tomography imaging can be performed efficiently if certain optimisations are applied to the computational reconstruction process. We present a 3D non-linear reconstruction algorithm based on a regularized conjugate gradient solver and discuss the optimisations which we incorporated to allow for an efficient and accurate reconstruction. In particular, the application of image smoothness constraints or other regularization techniques and auto-adaptive mesh refinement are highly relevant. We demonstrate the results of applying this algorithm to the reconstruction of a simulated material distribution in a cubic volume

Optimal finite element modelling and efficient reconstruction in non-linear 3D electrical resistance tomography

Electrical Impedance Tomography can provide images with well-defined characteristics using a fully non-linear reconstruction process when appropriate constraints are imposed on the solution to allow the ill-posed inverse problem to be solved. Using appropriate finite element discretizations for forward solution and inverse problem offers additional advantages in the image reconstruction process, such as (a) inclusion of prior knowledge, (b) generic model templating to adapt to, for example, individual head shapes, and (c) obtaining accurate results without unnecessary computational overhead. We have developed an efficient 3D non-linear reconstruction algorithm based on a regularized inverse conjugate gradient solver which incorporates (a) local image smoothness constraints, and (b) a number of optimisations which reduce the computing power required to obtain an accurate solution. We show results from applying this to various problems which arise in medical resistivity reconstruction given only surface potential measurements and demonstrate the importance of the FE discretization. Keywords: 3D non-linear electrical impedance tomography, FE template modelling, optimal finite element meshes, 3D visualization, FE discretization

Efficient non-linear 3D electrical tomography and finite element optimizations for functional source imaging

An essential factor in functional source imaging is the accurate knowledge of the conducitvity dostribution inside the body. Current models for electrophysiological forward and inverse problems use tabulated conductivity values obtained from experiments. This article shows how EIT-derived conductivities can be used in EEG reconstructions of a head slice

An optical trigger source for hydrophone-based ultrasound measurement systems: a feasibility study

Ultrasound is routinely used in many medical applications. Concern for the safety of subjects undergoing investigations has led to the development of systems to quantify the acoustic output of such devices. One system, the NPL ultrasound beam calibrator, uses a multi-element hydrophone to determine rapidly the temporal and spatial characteristics of the acoustic output. When investigating pulsed systems it is necessary to synchronise data acquisition with the launch of the acoustic pulse, a procedure that currently can be both time consuming and difficult. This article examines the feasibility of using an alternative, optical approach, generating a trigger signal in response to the changes in refractive index associated with propagation of the acoustic pulse

Non-linear electrical tomography reconstruction of simple test objects and a simulated head slice

Fully non-linear reconstruction in Electrical Tomography produces images with well-defined characteristics when explicit guides are imposed on the accessible solutions. In this paper, we revisit the formulation of the problem and apply the algorithm to some simulated test objects, and to a simple 2-dimensional model of the human head. The results demonstrate the best fidelity of reconstruction which may be achieved with existing and potentially attainable levels of signal to noise. We use a finite element model with some adaptive capability so that the images generated by the chosen constraint are not perturbed by the coarseness of the mesh. The algorithm incorporates a number of optimisations to reduce the required computing power and storage space, these include:Sparse matrix storage scheme and optimised sparse numerical handlingProblem-adapted element shape and densityUsage of high quality finite element meshesPre-evaluation of used quantities and matrices and application of numerical techniques such as the Woodbury formul

Imaging of free-space interference patterns used to manufacture fiber Bragg gratings

A technologically important use of the free-space interference patterns formed by phase gratings is in the creation of the refractive-index variation along optical fiber Bragg gratings. The patterns can be imaged directly by use of a tapered optical fiber tip, which acts as a local probe of the optical field. We present measurements of these patterns under varying conditions and compare them with theoretical predictions. In discussing the results within the context of fiber grating manufacture, we also demonstrate the effects of incident-beam misalignment and wave-front curvature

Evanescent field imaging of an optical fiber Bragg grating

We have investigated the evanescent field associated with an optical fiber Bragg grating using the sub-wavelength imaging properties of scanning near-field optical microscopy (SNOM). Imaging of either the field distribution within the grating, or the periodic refractive index changes along the grating can be performed by tuning the launched light on or off the grating resonance. These measurements reveal non-uniformity in the resonant standing-wave pattern that occur due to phase errors in the refractive index profile of the grating under study

Near-field imaging of fiber Bragg gratings

Fiber Bragg gratings are an important component of modern telecommunications systems. Characterisation of gratings is usually performed by interrogating the whole grating in either reflection or transmission along the fiber, and there is considerable interest in possible errors and defects in the gratings. In these experiments we have used near-field optical techniques to characterise Bragg gratings on a microscopic scale. Using D-fibers in order to access the evanescent fields normally within the cladding of the fiber, direct imaging of the standing wave patterns formed when the propagating laser is on resonance with the grating has been performed. Changes in patterns with laser wavelength can be observed, and compared with theories of grating reflectivity which predict superstructure on the standing wave patterns. The SNOM tip can also be used to study the free-space patterns formed by the phase masks used to write the gratings into the core of the fiber. Our images of the patterns agree well with theoretical predictions developed from earlier work, and clearly show the effect of errors in writing wavelength on the visibility of fringes