Iterative calculation of reflected and transmitted acoustic waves at a rough interface

A rigorous iterative technique is described for calculating the acoustic wave reflection and transmission at an irregular interface between two different media. The method is based upon a plane-wave expansion technique in which the acoustic field equations and the radiation condition are satisfied analytically, while the boundary conditions at the interface are satisfied numerically. The latter is accomplished by an iterative minimization of the integrated squared error in the boundary conditions by a conjugate gradient technique, leading to a converging and relatively simple scheme. The plane interface result can be used as starting value. Although in principle the method is rigorous, numerical examples show that in practice there is a lower bound on the error in the boundary conditions which can be achieve

Ultrasound wave propagation through rough interfaces: Iterative methods

Two iterative methods for the calculation of acoustic transmission through a rough interface\ud between two media are compared. The methods employ a continuous version of the conjugate\ud gradient technique. One method is based on plane-wave expansions and the other on boundary\ud integral equations and Green’s functions. A preconditioner is presented which improves the\ud convergence for spectra that include evanescent modes. The methods are compared with regard to\ud computational efficiency, rate of convergence, and residual error. The sound field differences are\ud determined for a focused ultrasound beam distorted by surfaces having a Gaussian roughness\ud spectrum. The differences are evaluated from the root-mean-square differences on the rough surface\ud and in the focal plane

Simulation of wave propagation through aberrating layers of biological media

Two iterative methods for the calculation of acoustic reflection and transmission at a rough interface between two media are compared. The methods are based on a continuous version of the conjugate gradient technique. One method is based on plane-wave expansions while the other method is based on boundary integral equations and Green's functions. The methods are compared with regard to computational efficiency, rate of convergence, and residual erro

Surface effects on nanowire transport: numerical investigation using the Boltzmann equation

A direct numerical solution of the steady-state Boltzmann equation in a cylindrical geometry is reported. Finite-size effects are investigated in large semiconducting nanowires using the relaxation-time approximation. A nanowire is modelled as a combination of an interior with local transport parameters identical to those in the bulk, and a finite surface region across whose width the carrier density decays radially to zero. The roughness of the surface is incorporated by using lower relaxation-times there than in the interior. An argument supported by our numerical results challenges a commonly used zero-width parametrization of the surface layer. In the non-degenerate limit, appropriate for moderately doped semiconductors, a finite surface width model does produce a positive longitudinal magneto-conductance, in agreement with existing theory. However, the effect is seen to be quite small (a few per cent) for realistic values of the wire parameters even at the highest practical magnetic fields. Physical insights emerging from the results are discussed.Comment: 15 pages, 7 figure

Application of iterative techniques for electromagnetic scattering from dielectric random and reentrant rough surfaces

Cataloged from PDF version of article.Stationary [e.g., forward–backward method (FBM)] and nonstationary [e.g., conjugate gradient squared, quasi-minimal residual, and biconjugate gradient stabilized (Bi-CGSTAB)] iterative techniques are applied to the solution of electromagnetic wave scattering from dielectric random rough surfaces with arbitrary complex dielectric constants. The convergence issues as well as the efficiency and accuracy of all the approaches considered in this paper are investigated by comparing obtained scattering (in the form of normalized radar cross section) and surface field values with the numerically exact solution, computed by employing the conventional method of moments. It has been observed that similar to perfectly and imperfectly conducting rough surface cases, the stationary iterative FBM converges faster when applied to geometries yielding best conditioned systems but exhibits convergence difficulties for general geometries due to its inherit limitations. However, nonstationary techniques are, in general, more robust when applied to arbitrarily general dielectric random rough surfaces, which yield more ill-conditioned systems. Therefore, they might prove to be more suitable for general scattering problems. Besides, as opposed to the perfectly and imperfectly conducting rough surface cases, the Bi-CGSTAB method and FBM show two interesting behaviors for dielectric rough surface pro- files: 1) FBM generally converges for reentrant surfaces when the vertical polarization is considered and 2) the Bi-CGSTAB method has a peculiar convergence problem for horizontal polarization. Unlike the other nonstationary iterative techniques used in this paper, where a Jacobi preconditioner is used, convergent results are obtained by using a block-diagonal preconditioner

Application of a nudging technique to thermoacoustic tomography

ThermoAcoustic Tomography (TAT) is a promising, non invasive, medical imaging technique whose inverse problem can be formulated as an initial condition reconstruction. In this paper, we introduce a new algorithm originally designed to correct the state of an evolution model, the \emph{back and forth nudging} (BFN), for the TAT inverse problem. We show that the flexibility of this algorithm enables to consider a quite general framework for TAT. The backward nudging algorithm is studied and a proof of the geometrical convergence rate of the BFN is given. A method based on Conjugate Gradient (CG) is also introduced. Finally, numerical experiments validate the theoretical results with a better BFN convergence rate for more realistic setups and a comparison is established between BFN, CG and a usual inversion method.Comment: Preprint version of the articl

Axial range of conjugate adaptive optics in two-photon microscopy

We describe an adaptive optics technique for two-photon microscopy in which the deformable mirror used for aberration compensation is positioned in a plane conjugate to the plane of the aberration. We demonstrate in a proof-of-principle experiment that this technique yields a large field of view advantage in comparison to standard pupil-conjugate adaptive optics. Further, we show that the extended field of view in conjugate AO is maintained over a relatively large axial translation of the deformable mirror with respect to the conjugate plane. We conclude with a discussion of limitations and prospects for the conjugate AO technique in two-photon biological microscopy