In this paper, the propagation of TEM waves along a coaxial waveguide with a step discontinuity on its outer wall is investigated rigorously by applying the direct Fourier transform and reducing the problem into the solution of a modified Wiener–Hopf equation. The solution for the field terms are determined in terms of an infinite number of unknown coefficients, which satisfy an infinite set of linear algebraic equations. These equations are solved numerically and the effect of area ratio is presented graphically at the end of the analysis. The same problem is also analyzed by applying the mode-matching technique and the results of the two approaches are compared. It is observed numerically that the Wiener–Hopf technique provides a better convergence than the mode-matching technique.
Propagation of acoustic waves in a two-dimensional duct with an impedance condition at the boundary, is studied. The duct is assumed to have two ends at infinity being asymptotically straight, but otherwise to be arbitrarily shaped.The so called Building Block Method allows us to synthesize propagation properties for ducts with complicated geometries from results for simpler ducts. Conformal mappings can be used to transform these simple ducts to straight ducts with constant cross-sections.By using recently developed techniques for numerical conformal mappings, it is possible to construct a transformation between an infinite strip and an arbitrarily shaped duct with smooth or piecewise smooth boundary, keeping both smoothness and the well controlled boundary direction towards infinity that the above mentioned method requires.To accomplish a stable formulation of the problem, we express it in terms of scattering operators. The resulting differential equation is solved using wave splitting and invariant embedding techniques. We expand the involved functions in Fourier series, and hence, it is possible to give the operators a matrix representation. Numerical results are produced using truncated matrices.
Electro-magnetic scattering is studied in a waveguide with varying shape and crosssection. Furthermore, an impedance or admittance condition is applied to two of the waveguide walls. Under the condition that variations in geometry or impedance take place in only one plane at the time, the problem can be solved as a two-dimensional wave-scattering problems. By using newly developed numerical conformal mapping techniques, the problem is transformed into a wave-scattering problem in a straight two-dimensional channel. A numerically stable formulation is reached in terms of transmission and reflection operators. Numerical results are given for a slowly varying waveguide with a bend and for one more complex geometry.
A set of semi-analytic techniques based on Fourier analysis is used to solve wave-scattering problems in variously shaped waveguides with varying normal admittance boundary conditions. Key components are the newly developed conformal mapping methods, wave splitting, Fourier series expansions in eigenfunctions to non-normal operators, the building block method or the cascade technique, Dirichlet-to-Neumann operators, and reformulation in terms of stable differential equations for reflection and transmission matrices. For an example, the results show good correspondence with a finite element method solution to the same problem in the low- and medium-frequency domains. The Fourier method complements finite element analysis as a waveguide simulation tool. For inverse engineering involving tuning of straight waveguide parts joining complicated waveguide elements, the Fourier method is an attractive alternative including time aspects. The prime motivation for the Fourier method is its added physical understanding primarily at low frequencies.
Wave analysis is efficient for investigating the interior of objects. Examples are ultra sound examination of humans and radar using elastic and electromagnetic waves. A common procedure is inverse scattering where both transmitters and receivers are located outside the object or on its boundary. A variant is when both transmitters and receivers are located on the scattering object. The canonical model is a finite inhomogeneous string driven by a harmonic point force. The inverse problem for the determination of the diffractive index of the string is studied. This study is a first step to the problem for the determination of the mechanical strength of wooden logs. An inverse scattering theory is formulated incorporating two regularizing strategies. The results of simulations using this theory show that the suggested method works quite well and that the regularization methods based on the couple of spaces (L2; H1 ) could be very useful in such problems.
A substrate integrated waveguide, SIW, is a waveguide that is integrated directly on a subtrate. These structeres has recently been developed for different applications. The simplest SIW design is a rectangular waveguide in a subtrate formed by metallization of the upper and lower surfaces of the substrate and by placing vertical metal vias periodically along two parallel lines. Different types of SIW are analyzed and simulated in this contribution. In particular wave propagation along an SIW is analyzed.
The acoustic properties of an in-duct orifice are modeled with a vortex sheet model. Building block elements are used to construct a single slit in a two dimensional model of a flow duct. The foundation of this analytical model is the scattering properties of a trailing and leading edge, semi infinite splitter plate in an infinite duct. From the achieved model of the single slit, mode complex element can be constructed, such as periodically spaced orifices.
Important transmission paths for the noise produced by fans, engines and other machinery are the connecting ducts used for transport of gases. Hence, reliable methods for calculating the acoustic attenuation in such systems are of great interest. In the presence of sharp edges strong interaction between sound and flow may occur even at low Mach numbers, which should be accounted for. The interaction has been successfully described using the vortex sheet model with an unexpanded and unstable jet. The current paper deals with the generalization to stable jets.
By using the so-called Building Block Method, rather complex silencers can be modelled from the results of two canonical problems: the scattering at the trailing and leading bifurcations, respectively. The strong flow-acoustic interaction occurs at the trailing edge only. Results are presented here for the bifurcation and the sudden area change at the trailing edge.
The flow in the large part of the duct downstream and upstream of an area change is modelled in two regions where the acoustically thin shear layer is described by a newly proposed set of coupling conditions. We use a simple model with physically realistic stability properties for acoustically thin layers allowing for a hydrodynamically thick shear layer. In fact, the dynamic properties of the shear layer are changed continuously with the shear layer Strouhal number s from the unstable at vanishing s to a stable layer at high s. The transfer Strouhal number marks the border between the unstable and stable region.
Like the vortex sheet model, two coupling conditions relate the fields on each side of the sheet, one of them being continuity of pressure. The second coupling condition means continuity of a variable ranging from displacement, similar to the vortex sheet model, at vanishing s via velocity to pressure gradient at infinite s. The used shear layer model is uniformly valid for all s and allows a straightforward generalization of a scattering theory for unstable shear layers, i.e. for small s. Analytic as well as numerical results for the acoustic scattering are presented.
This paper provides a general framework for electromagnetic (EM) modeling, sensitivity analysis, computation, and measurements regarding the wave propagation characteristics of high-voltage direct-current (HVDC) power cables. The modeling is motivated by the potential use with transient analysis, partial-discharge measurements, fault localization and monitoring, and is focused on very long (10 km or more) HVDC power cables with transients propagating in the low-frequency regime of about 0-100 kHz. An exact dispersion relation is formulated together with a discussion on practical aspects regarding the computation of the propagation constant. Experimental time-domain measurement data from an 80-km-long HVDC power cable are used to validate the electromagnetic model, and a mismatch calibration procedure is devised to account for the connection between the measurement equipment and the cable. Quantitative sensitivity analysis is devised to study the impact of parameter uncertainty on wave propagation characteristics. The sensitivity analysis can be used to study how material choices affect the propagation characteristics, and to indicate which material parameters need to be identified accurately in order to achieve accurate fault localization. The analysis shows that the sensitivity of the propagation constant due to a change in the conductivity in the three metallic layers (the inner conductor, the intermediate lead shield, and the outer steel armor) is comparable to the sensitivity with respect to the permittivity of the insulating layer. Hence, proper modeling of the EM fields inside the metallic layers is crucial in the low-frequency regime of 0-100 kHz.
This paper presents a stable and efficient fullwave cable model and a detailed study of the relatedmodel uncertainties regarding the wave propagation characteristics of very long HVDC power cables at low frequencies. The model can be used to predict the dispersion characteristics of the cable with respect to its electromagnetic parameters, or as an inverse problem to estimate some parameters of the cable (armour permeability, metal layer conductivities, temperature, length, etc.) based on measurements. The electromagnetic model is based on a magnetic frill generator that can be calibrated to the current measured at the input of the cable, and a layer recursive computation of the axial-symmetric fields. Measurements of pulse propagation on an 82 km long HVDC power cable over a bandwidth of 100 kHz have been used to validate the model. The main conclusion of the study is that the conductivity (and thus the temperature) of the conductor and the lead sheath are of utmost importance to achieve an accurate model. At the same time, some parameters are in principle insignificant regarding the dispersion characteristics in the low-frequency regime, such as the permittivity and the conductivity of the semi-conducting screens. The paper contains an investigation and a discussion on the electromagnetic properties of all layers of a typical HVDC power cable.
This paper addresses electromagnetic wave propagation in High Voltage Direct Current (HVDC) power cables. An electromagnetic model, based on long (10 km or more) cables with a frequency range of 0 to 100 kHz, is derived. Relating the frequency to the propagation constant a dispersion relation is formulated using a recursive approach. The propagation constant is found numerically with normalized residue calculation. The paper is concluded with a sensitivity analysis of the propagation constant with respect to the electrical parameters ε_{r} (the real relative permittivity) and σ (the conductivity)
The purpose of this paper is to establish a formal mathematical framework for the electromagnetic wave propagation in an arbitrary cavity. The walls of the cavity are not assumed perfectly conducting and we use the transmission boundary conditions for the tangential fields. Our main tool is the Laplace transform. The focus here is on the modeling and detailed proofs or calculations are not provided.
Quantization of Maxwell’s equations in waveguides is considered together with an analysis of the quantum correlation functions of the radiation field. Both the spatial and temporal dependence of the polarization correlation functions for entangled states are evaluated. Predictions for experiments for the study of the spatial dependence of the polarization correlation functions for entangled photons are given.
A passive approximation problem is formulated where the target function is an arbitrary complex-valued continuous function defined on an approximation domain consisting of a finite union of closed and bounded intervals on the real axis. The norm used is a weighted L-p-norm where 1 <= p <= infinity. The approximating functions are Herglotz functions generated by a measure with Holder continuous density in an arbitrary neighborhood of the approximation domain. Hence, the imaginary and the real parts of the approximating functions are Holder continuous functions given by the density of the measure and its Hilbert transform, respectively. In practice, it is useful to employ finite B-spline expansions to represent the generating measure. The corresponding approximation problem can then be posed as a finite-dimensional convex optimization problem which is amenable for numerical solution. A constructive proof is given here showing that the convex cone of approximating functions generated by finite uniform B-spline expansions of fixed arbitrary order (linear, quadratic, cubic, etc.) is dense in the convex cone of Herglotz functions which are locally Holder continuous in a neighborhood of the approximation domain, as mentioned above. As an illustration, typical physical application examples are included regarding the passive approximation and optimization of a linear system having metamaterial characteristics, as well as passive realization of optimal absorption of a dielectric small sphere over a finite bandwidth.
A passive approximation problem is formulated where the target function is an arbitrary complex valued continuous function defined on an approximation domain consisting of a closed interval of the real axis. The approximating function is any Herglotz function with a generating measure that is absolutely continuous with Hölder continuous density in an arbitrary neighborhood of the approximation domain. The norm used is induced by any of the standard L^{p}-norms where 1 ≤ p ≤ ∞. The problem of interest is to study the convergence properties of simple Herglotz functions where the generating measures are given by finite B-spline expansions, and where the real part of the approximating functions are obtained via the Hilbert transform. In practice, such approximations are readily obtained as the solution to a finite- dimensional convex optimization problem. A constructive convergence proof is given in the case with linear B-splines, which is valid for all L^{p}-norms with 1 ≤ p ≤ ∞. A number of useful analytical expressions are provided regarding general B-splines and their Hilbert transforms. A typical physical application example is given regarding the passive approximation of a linear system having metamaterial characteristics. Finally, the flexibility of the optimization approach is illustrated with an example concerning the estimation of dielectric material parameters based on given dispersion data.
We present a simple classical (random) signal model reproducing Born's rule. The crucial point of our approach is that the presence of detector's threshold and calibration procedure have to be treated not as simply experimental technicalities, but as the basic counterparts of the theoretical model. We call this approach threshold signal detection model (TSD). The experiment on coincidence detection which was done by Grangier in 1986 [22] played a crucial role in rejection of (semi-)classical field models in favour of quantum mechanics (QM): impossibility to resolve the wave-particle duality in favour of a purely wavemodel. QM predicts that the relative probability of coincidence detection, the coefficient g((2)) (0); is zero (for one photon states), but in (semi-) classicalmodels g((2)) (0) >= 1 : In TSD the coefficient g((2)) (0) decreases as 1/epsilon(2)(d); where epsilon(d) > 0 is the detection threshold. Hence, by increasing this threshold an experimenter can make the coefficient g((2)) (0) essentially less than 1. The TSD-prediction can be tested experimentally in new Grangier type experiments presenting a detailed monitoring of dependence of the coefficient g((2)) (0) on the detection threshold. Structurally our model has some similarity with the prequantum model of Grossing et al. Subquantum stochasticity is composed of the two counterparts: a stationary process in the space of internal degrees of freedom and the random walk type motion describing the temporal dynamics.
We show that quantum probabilities for photon detection can be reproduced by a model in which classical random fields interact with detectors of the threshold type. This approach is applied to the old problem of distinguishing classical and quantum light sources with the aid of the coefficient of second-order coherence g^{(2)} (0) ( the problem of "existence of photon"). In our classical random field model, we obtain an estimate of this coefficient implying that it becomes strictly less than one for sufficiently small value of parameter is an element of = (epsilon) over bar/epsilon(d), where (epsilon) over bar (pulse) is the average energy of pulses (photons) emitted by a source and epsilon(d) is the detection threshold. This prediction can in principle be tested experimentally. Thus in the presented model experimental technicalities (such as e. g. the detection thresholds) are lifted to the level of the fundamental entities of theory.
The electromagnetic fields of a single optic fibre mode are quantized based on the observationthat these fields can be derived from a scalar harmonic oscillator function depending on onlytime and the axial wavenumber. Asymptotic results for both the one-photon probabilitydensity and two-photon correlation density functions within the forward light cone arepresented, showing an algebraic decay for large times or distances. This algebraic decay,increasing the uncertainty in the arrival time of the photons, also remains in the presence ofdispersion shift, in qualitative agreement with experimental results. Also presented are explicitformulae to be used in parameter studies to optimize quantum optic fibre communications.
We obtain Born's rule from the classical theory of random waves in combination with the use of thresholdtype detectors. We consider a model of classical random waves interacting with classical detectors and reproducing Born's rule. We do not discuss complicated interpretational problems of quantum foundations. The reader can select between the "weak interpretation," the classical mathematical simulation of the quantum measurement process, and the "strong interpretation," the classical wave model of the real quantum (in fact, subquantum) phenomena.
The distance dependence of the probability of observing two photons in a waveguide is investigated and the Glauber correlation functions of the entangled photons are considered. First the case of a hollow waveguide with modal dispersion is treated in detail: the spatial and temporal dependence of the correlation functions is evaluated and the distance dependence of the probability of observing two photons upper bounds and asymptotic expressions valid for large distances are derived. Second the generalization to a real fibre with both material and modal dispersion, allowing dispersion shift, is discussed.
This paper gives a detailed derivation of the classical electromagnetic modes of a layered circularly symmetrical dielectric waveguide. The corresponding Hamilton function is derived by using suitable canonical observables and the standard analogy to the classical harmonic oscillator. The derivation is generic in the sense that it can be used as an "algorithm" to compute the electromagnetic field of the waveguide. The associated Hamilton operator can then be obtained by using the standard quantization procedure where the canonical observables are replaced by the corresponding operators i.e., the creation and the annihilation operators of the photon (or equivalently, the position and the momentum operators of the harmonic oscillator) and by taking the appropriate commutation relations into account.
The paper explores the fundamental physical principles of quantum mechanics (in fact, quantum field theory) that limit the bit rate for long distances and examines the assumption used in this exploration that losses can be ignored. Propagation of photons in optical fibers is modelled using methods of quantum electrodynamics. We define the "photon duration" as the standard deviation of the photon arrival time; we find its asymptotics for long distances and then obtain the main result of the paper: the linear dependence of photon duration on the distance when losses can be ignored. This effect puts the limit to joint increasing of the photon flux and the distance from the source and it has consequences for quantum communication. Once quantum communication develops into a real technology (including essential decrease of losses in optical fibres), it would be appealing to engineers to increase both the photon flux and the distance. And here our "photon flux/distance effect" has to be taken into account. This effect also may set an additional constraint to the performance of a loophole free test of Bell's type-to close jointly the detection and locality loopholes.
The problem of modelling sound waves in a two-dimensional wave-guide of general shape carrying a mean flow is addressed. The mean flow may be inhomogeneous but is irrotational. A convective wave equation for the velocity potential is derived. It is in a form suitable for generalizing an earlier developed theory for a stable modelling of acoustic waves in quiescent waveguides with complicated geometry to also include a mean flow. The theory is illustrated with numerical results for reflection and transmission demonstrating the effectiveness of the method for low and medium frequencies.
The acoustic properties of a duct may change radically if a mean flow is introduced. The reflection coefficient may for instance reach a peak greater than one at an abrupt open pipe termination and at sudden area expansions the reflection properties may have a strong Strouhal number dependence.
Simulations of these phenomena using a model of an issuing jet with a constant cross-section coupling to the slower or quiescent medium by a vortex layer have compared favourably with experiments.
Stability of the flow should have a central role in this flow-acoustic interaction. To investigate the importance of stability for the scattering of sound at edges this paper deals with the study of waves in a duct where the flow is not necessary unstable. An accompanying paper treats the scattering of sound at edges in the duct. The flow-acoustic coupling is modelled with a newly proposed set of coupling conditions relating the fields on both sides of an acoustically thin shear layer.
The model is uniform in the Strouhal number s based on the shear layer thickness at the exit. For vanishing s the model agrees with the unstable vortex layer model, the layer is stable for $s larger than a transfer Strouhal number and the model reduces to the quiescent case for infinite s. In addition to continuity of sound pressure we use continuity for a quantity, being displacement for vanishing s, velocity for s equals the transfer Strouhal number and pressure gradient for infinite s. The stabilizing mechanism reduces for increasing s the acoustic transverse length scale compared to the corresponding scale for the mean flow.
The current paper deals with motivating and using the new coupling conditions to study the waves in a duct. The main purpose is to investigate the properties of the acoustic and hydrodynamic waves as well as their interaction. Of interest is also to verify the required stability properties of the model.
This conference illuminates and benefits from relations between different types of waves, i.e., quantum physics methods in classical wave modeling. The proceedings are intended for researchers and graduate students in fundamental as well as applied sciences. The preface classifies and summarizes the conference giving relations between the papers.
This paper discusses criteria for establishing uniqueness of wave propagation problems. Causality, or passivity that implies causality, is adopted as the fundamental principle. It is stressed that radiation conditions are not applicable for waveguide modes that carry no active power. The Jones' criteria for causality in the frequency domain, which covers the convectively unstable case, are presented and analysed, the vanishing absorption principle, VAP, in particular. It is proposed to use L^{2} for a lossy medium but a weighted L^{2} for the lossless case.
Textbooks on quantum mechanics often give the impression that the Schrödinger equation can be solved exactly only for a few
simple potential models. However, exact solutions are available in terms of hypergeometric functions and their confluent variants for the so-called Natanzon potentials. These potentials include the Pöschl-Teller, Manning-Rosen and Rosen-Morse potentials that are also special cases of the Eckart potential. The Natanzon potentials are reviewed and connections are made to problems in classical physics like propagation of electromagnetic waves in inhomogeneous media and of acoustic waves in a variable speed profile. The availability of exact solutions is of particular interest for the explicit construction of time evolution operators
and in the solution of inverse scattering problems.
With the purpose of source localization in high voltage direct current submarine power cables general layered waveguide models are investigated. It is concludes that the non-discrete modes can usually be ignored in comparison with the least attenuated discrete mode. Only a finite number of discrete modes are of importance for a band limited signal. Accurate analytical expressions are derived in the time domain for both discrete and non-discrete electromagnetic waveguide modes for large distances together with an error analysis.
This paper presents accurate analytical expressions in the time domain for discrete electromagnetic waveguide modes for large distances together with a discussion of the errors. The main application is source localization for high voltage direct current submarine power cables. The research behind this paper is part of the project “Fundamental wave modelling for signal estimation on lossy transmission lines” funded by the Swedish Research Council and ABB High Voltage Cables AB in Sweden.
There are two optic fibre properties in particular that obstruct the transfer over long distances in quantum communications. One of them is dispersion, which reduces the maximum bit rate. In classical communication with modern highly purified fibres, dispersion is the major limiting factor. The other property is the material loss that causes fluctuations in addition to a general annihilation with distance of photons. It is believed that losses are the major limiting factor in quantum communication over long distances if the bit rate is not an issue. Of major interest in quantum communication is the photon source. It is therefore a high priority to develop methods for the determination of properties like initial temporal modes, repeatability, independence of sequentially emitted photons, etc., for a source emitting single photons in a given spatial mode. In the current paper we suggest that the source properties can be estimated using statistics of the run times of the photons. This requires that the fibre is modelled with sufficient accuracy. To simplify the analysis, it is assumed that the fibre losses can be neglected and that the photons are independent and identically generated. Energy detection in one spin state is employed, making the modelling scalar. The one photon initial temporal mode is found by maximizing a maximum-likelihood function based on running time statistics. Unfortunately, this optimization problem is, in general, not convex. However, for photon detection in the so-called asymptotic radiation zone, where the probability density can be determined to a sufficient degree with asymptotic methods, the optimization problem is convex. In the current paper, quantum tomography in fibres based on this convex optimization method is presented, and its generalization to more complicated situations like the introduction of losses in the modelling is discussed.
For the purpose of determining the twist of a homogeneous, locally reacting, uniaxial cylinder, an inverse microwave scattering theory is presented. Remote measurements of the spiral grain of trees and logs are the prime application. Based on practical considerations, it is assumed that the transmitting and receiving antennas are collocated, requiring a three-dimensional modelling. A general theory is first developed, followed by an asymptotic analysis assuming that the distance from the antennas to the cylinder is many wavelengths and many cylinder radii. In this way, a substantial reduction of the numerical complexity, to the level of the two-dimensional case, is achieved. The error of the determined twist angle as function of inherent parameters of the problem using a CramEacuter-Rao analysis is given. The results from numerical simulations show that this error is low enough for determining the grain angle. Presented parameter studies of the error can be used for minimizing the errors in a measurement set up, of particular interest for non-sophisticated instruments and non-ideal laboratory conditions, by selecting optimum parameters such as frequency and antenna gain. Finally, it is stated that the model has a great potential for developing efficient algorithms for measuring the twist angle.
An inverse microwave scattering theory is presented for the determination of twist of a homogeneous locally reacting uniaxial cylinder. The prime application is remote measurements of spiral grain of trees and logs. From practical considerations, the transmitting and receiving antennas are near each other
requiring a three-dimensional modelling. First a general theory is developed. Then asymptotic formulae are derived assuming that the distance from the antennas to the cylinder is many wavelengths and many cylinder radii granting a substantial reduction of the numerical complexity compared to the twodimensional case. Finally, the error of the determined twist angle as function of inherent parameters of the problem is given using a Cramer Rao analysis.
We study delta-shocks in one-dimensional system of zero-pressure gas dynamics. In contrast to well-known papers this system is considered in form of mass, momentum and energy conservation laws. It order to define such singular solutions special integral identities are introduced which extend the concept of classical weak solutions. Using these integral identities, the Rankine-Hugoniot conditions for ±-shocks are obtained. It is proved that the mass, momentum and energy transport processes between the area outside of the delta-shock wave front and this front are going on such that the total mass, momentum and energy are independent of time, while the mass and energy concentration processes onto the moving delta-shock wave front are going on. Therewith the total kinetic energy transfers into total internal energy.
For one-dimensional system of zero-pressure gas dynamics, we derive the balance laws describing mass, momentum and energy transport from the area outside the δ-shock wave front onto its front. It is proved that the total mass and momentum of area outside δ-shock wave front and the the δ-shock wave front are conserved, while the kinetic energy of the area outside the δ-shock wave front and total kinetic energy are decreasing quantities. It is also proved that if the kinetic energy is conserved then the Cauchy problem cannot have any nontrivial δ-shock wave type solution.
Twist in wood, being closely related to spiral grain, may cause
serious problems in building structures, furniture, and joinery. It is therefore of great interest to sort out, at an early stage in the manufacturing process, trees, logs and boards that have an access of spiral grain. The spiral grain pattern is described by a helical deviation of the fibre direction in relation to the longitudinal direction of a living tree or a log and seems to be an indicator for other defects such as compression wood. Remote microwave sensing of spiral grain has received a large interest during the latest two decades. Its development has been impeded by the large variation with moisture content of the microwave properties of wood and by the complexity in modelling the electromagnetic field in a log with spiral grain. A review is presented of a direct method with no requirement of information on moisture content for boards. This procedure has recently been generalized to cylindrical logs and trees having a constant slope of the grain. A further generalization is presented here to allow for the normal spiral grain pattern with radially changing slope of grain in wood under bark. Based on this theory, a measurement procedure is proposed for the detection of wood grain angle with radial dependence, requiring no information on moisture content in the sapwood, also applicable for completely or partially frozen wood. A suitable application would be an instrument to use in the forest for measurements on living trees or logs.
An adjoint field approach is used to formulate a general numerical framework for Fisher information based sensitivity analysis in electrical impedance tomography. General expressions are given for the gradients used in standard least squares optimization, i.e., the Jacobian related to the forward problem, and it is shown that these gradient expressions are consistent with commonly used electrode models such as the shunt model and the complete electrode model. By using the adjoint field formulations together with a variational analysis, it is also shown how the computation of the Fisher information can be integrated with the gradient calculations used for optimization. It is furthermore described how the Fisher information analysis and the related sensitivity map can be used in a preconditioning strategy to obtain a well balanced parameter sensitivity and improved performance for gradient based quasi-Newton optimization algorithms in electrical impedance tomography. Numerical simulations as well as reconstructions based on experimental data are used to illustrate the sensitivity analysis and the performance of the improved inversion algorithm in a four-electrode measurement set-up.
An adjoint field approach is used to formulate a general numerical framework for Fisher information-based sensitivity analysis in electrical impedance tomography. General expressions are given for the gradients used in standard least-squares optimization, i.e. the Jacobian related to the forward problem, and it is shown that these gradient expressions are compatible with commonly used electrode models such as the shunt model and the complete electrode model. By using the adjoint field formulations together with a variational analysis, it is also shown how the computation of the Fisher information can be integrated with the gradient calculations used for optimization. It is furthermore described how the Fisher information analysis and the related sensitivity map can be used in a preconditioning strategy to obtain a well-balanced parameter sensitivity and improved performance for gradient-based quasi-Newton optimization algorithms in electrical impedance tomography. Numerical simulations as well as reconstructions based on experimental data are used to illustrate the sensitivity analysis and the performance of the improved inversion algorithm in a four-electrode measurement set-up.