Computational method for acoustic wave focusing (original) (raw)

Theoretical analysis of the focusing of acoustic waves by two-dimensional sonic crystals

Physical review. E, Statistical, nonlinear, and soft matter physics, 2003

Motivated by a recent experiment on acoustic lenses, we perform numerical calculations based on a multiple scattering technique to investigate the focusing of acoustic waves with sonic crystals formed by rigid cylinders in air. The focusing effects for crystals of various shapes are examined. The dependence of the focusing length on the filling factor is also studied. It is observed that both the shape and filling factor play a crucial role in controlling the focusing. Furthermore, the robustness of the focusing against disorders is studied. The results show that the sensitivity of the focusing behavior depends on the strength of positional disorders. The theoretical results compare favorably with the experimental observations, reported by Cervera, et al. [Phys. Rev. Lett. 88, 023902 (2002)].

The inverse problem of an impenetrable sound-hard body in acoustic scattering

Journal of Physics: Conference Series, 2008

We study the inverse problem of recovering the scatterer shape from the far-field pattern(FFP) of the scattered wave in presence of noise. This problem is ill-posed and is usually addressed via regularization. Instead, a direct approach to denoise the FFP using wavelet technique is proposed by us. We are interested in methods that deal with the scatterer of the general shape which may be described by a finite number of parameters. To study the effectiveness of the technique we concentrate on simple bodies such as ellipses, where the analytic solution to the forward scattering problem is known. The shape parameters are found based on a least-square error estimator. Two cases with the FFP corrupted by Gaussian noise and/or computational error from a finite element method are considered. We also consider the case where only partial data is known in the far field.

Directional acoustic source by scattering acoustical elements

Applied Physics Letters, 2007

Highly directional sources are desirables in a variety of fields for many applications. The authors report an inverse designed scattering acoustical element device that transforms an omnidirectional ultrasonic source into one highly directional. This two-dimensional design shows an overall better modeled performance than other previously proposed, including a half-power angular width less than 5°. The experimental demonstration is performed in the ultrasonic range, using a hydrophone as omnidirectional source and an array of alumina rods as building blocks for the scattering acoustical elements. The measured half-power angular width is 6°, a value that supports the high reliability of the designing tool.

A Two-Stage Method for Inverse Acoustic Medium Scattering

We present a novel numerical method to the time-harmonic inverse medium scattering problem of recovering the refractive index from noisy near-field scattered data. The approach consists of two stages, one pruning step of detecting the scatterer support, and one resolution enhancing step with nonsmooth mixed regularization. The first step is strictly direct and of sampling type, and it faithfully detects the scatterer support. The second step is an innovative application of nonsmooth mixed regularization, and it accurately resolves the scatterer sizes as well as intensities. The nonsmooth model can be efficiently solved by a semi-smooth Newton-type method. Numerical results for two-and three-dimensional examples indicate that the new approach is accurate, computationally efficient, and robust with respect to data noise.

The factorization method for inverse acoustic scattering in a layered medium

Inverse Problems, 2013

In this paper, we consider a problem of inverse acoustic scattering by an impenetrable obstacle embedded in a layered medium. We will show that the factorization method can be applied to recover the embedded obstacle; that is, the equationFg = φ z is solvable if and only if the sampling point z is in the interior of the unknown obstacle. Here,F is a self-adjoint operator related to the far field operator and φ z is the far field pattern of the Green function with respect to the problem of scattering by the background medium for point z. The validity of the factorization method is proven with the help of a mixed reciprocity principle and an application of the scattering operator. Due to the established mixed reciprocity principle, knowledge of the Green function for the background medium is no longer required, which makes the method attractive from the computational point of view. The paper is only concerned with sound-soft obstacles, but the analysis can be easily extended for sound-hard obstacles, or obstacles with separated sound-soft and soundhard parts. Finally, we provide an explicit example for a radially symmetric case and present some numerical examples.

On the inverse scattering problem in the acoustic environment

Journal of Computational Physics, 2009

In this report, we construct numerical algorithms for the solution of inverse scattering problems in layered acoustic media. Our inverse scattering schemes are based on a collection of so-called trace formulae, and can be viewed as extension of the work started in . The speed c of propagation of sound, the density ρ, and the attenuation γ are the three parameters reconstructed by the algorithm, given that all of them (ρ(x, y, z), c(x, y, z), γ(x, y, z)) are laterally invariant, i.e., depend only on the coordinate z. For a medium whose parameters c, ρ, and γ have m ≥ 1 continuous derivatives, and data measured for all frequencies ω on the interval [−a, a], the error of our scheme decays as 1/a m−1 as a → ∞. In this respect, our algorithm is similar to the Fourier Transform. Our results are illustrated with several numerical examples.

Contribution to the numerical reconstruction in inverse elasto-acoustic scattering

2018

The characterization of hidden objects from scattered wave measurements arises in many applications such as geophysical exploration, non destructive testing, medical imaging, etc. It can be achieved numerically by solving an Inverse Problem. However, this is a nonlinear and ill-posed problem, thus a difficult task. A successful reconstruction requires careful selection of very different parameters depending on the data and the chosen optimization numerical method.The main contribution of this thesis is an investigation of the full reconstruction of immersed elastic scatterers from far-field pattern measurements. The sought-after parameters are the boundary, the Lame coefficients, the density and the location of the obstacle. First, existence and uniqueness results of a generalized Boundary Value Problem including the direct elasto-acoustic problem are established. The sensitivity of the scattered field with respect to the different parametersdescribing the solid is analyzed and we e...

Method for obtaining a nearfield inverse scattering solution to the acoustic wave equation

The Journal of the Acoustical Society of America, 1981

Since the classic paper by Gelfand and Levitan [Am. Math. Sac. Transl., Ser. 2, 1, 253-304 (1955)], much has been published on the inverse scattering problem. Assuming no bound states, there are several well-known solutions that reconstruct one-dimensional or spherically symmetric potentials from farfield scattering information. Moses [Phys. Rev. 102, 559-567 (1956)] and Newton [Phys. Rev. Lett. 4, 541 (1979)] have generalized these procedures for three-dimensional potentials. In this paper, we show how the work of Moses and Newton can be extended to provide a nearfield inverse scattering solution to the acoustic wave equation. In particular, we describe a procedure for obtaining a nearfield inverse scattering solution when the incident probes are arbitrary, unknown, and not necessarily reproducible.