This thesis deals with electronic focusing of ultrasonic probes. There is theoretically described, what is the electronic focusing. Further, there are calculations that are used to achieve focusing. These calculations are then implemented into the algorithm that was developed in Matlab. The paper also contains the simulation conducted using the proposed algorithm and the GUI. These simulations are then compared with characteristics measured on a real ultrasound probe.

Nearfield Acoustical Holography (NAH) is an acoustic field visualization technique that can be used to reconstruct three-dimensional (3-D) acoustic fields by projecting two-dimensional (2-D) data measured on a hologram surface. However, linear NAH algorithms developed and improved by many researchers can result in significant reconstruction errors when they are applied to reconstruct 3-D acoustic fields that are radiated from a high-level noise source and include significant nonlinear components. Here, planar, nonlinear acoustical holography procedures are developed that can be used to reconstruct 3-D, nonlinear acoustic fields radiated from a high-level noise source based on 2-D acoustic pressure data measured on a hologram surface. The first nonlinear acoustic holography procedure is derived for reconstructing steady-state acoustic pressure fields by applying perturbation and renormalization methods to nonlinear, dissipative, pressure-based Westervelt Wave Equation (WWE). The nonlinear acoustic pressure fields radiated from a high-level pulsating sphere and an infinite-size, vibrating panel are used to validate this procedure. Although the WWE-based algorithm is successfully validated by those two numerical simulations, it still has several limitations: (1) Only the fundamental frequency and its second harmonic nonlinear components can be reconstructed; (2) the application of this algorithm is limited to mono-frequency source cases; (3) the effects of bent wave rays caused by transverse particle velocities are not included; (4) only acoustic pressure fields can be reconstructed. In order to address the limitations of the steady-state, WWE-based procedure, a transient, planar, nonlinear acoustic holography algorithm is developed that can be used to reconstruct 3-D nonlinear acoustic pressure and particle velocity fields. This procedure is based on Kuznetsov Wave Equation (KWE) that is directly solved by using temporal and spatial Fourier Transforms. When compared to the WWE-based procedure, the KWE-based procedure can be applied to multi-frequency source cases where each frequency component can contain both linear and nonlinear components. The effects of nonlinear bent wave rays can be also considered by using this algorithm. The KWE-based procedure is validated by conducting an experiment with a compression driver and four numerical simulations. The numerical and experimental results show that holographically-projected acoustic fields match well with directly-calculated and directly-measured fields.

Orientador: Andréa Cristina Prokopczyk Arita / Abstract: This work presents some results of the theory of the (a,k)-regularized resolvent families, that are the main tool used in this thesis. Related with this families, one result proved in this work is the zero-one law, providing new insights on the structural properties of the theory of (a,k)-regularized resolvent families including strongly continuous semigroups, strongly continuous cosine families, integrated semigroups, among others. Moreover, an abstract nonlinear degenerate hyperbolic equation is considered, that includes the semilinear Blackstock-Crighton-Westervelt equation. By proposing a new approach based on strongly continuous semigroups and resolvent families of operators, it is proved an explicit representation of the strong and mild solutions for the linearized model by means of a kind of variation of parameters formula. In addition, under nonlocal initial conditions, a mild solution of the nonlinear equation is established. / Resumo: Este trabalho apresenta alguns resultados da teoria de famílias resolventes (a,k)- regularizadas, que é a principal ferramenta utilizada nesta tese. Relacionado com estas famílias, um resultado provado neste trabalho é a lei zero-um, que fornece novas percepções de propriedades estruturais da teoria de famílias resolventes (a,k)- regularizadas, incluindo os semigrupos fortemente contínuos, as famílias cosseno fortemente contínuas, os semigrupos integrados, entre outras. Além disso, uma equação hiperbólica degenerada não-linear abstrata é considerada, a qual inclui a equação semilinear de Blackstock-Crighton-Westervelt. Propondo uma nova abordagem baseada em semigrupos fortemente contínuos e famílias resolvente, é demonstrada uma representação explícita das soluções forte e branda para a linearização do modelo por uma espécie de método de variação dos parâmetros. Por fim, sob condições iniciais não-locais, uma solução branda da equação não-linear é estabelecida. / Doutor

The main topic of this diploma thesis is the modeling of nonlinear effects in ultrasonic fields. The work deals with application of finite difference method (FDTD) on the Westervelt equation and the subsequent creation of the model of ultrasonic fields in MATLAB. This thesis also includes theoretical analysis of ultra-acoustic and technical aspects of diagnostic ultrasonography. In addition, this document includes verification of theoretical assumptions by using created model.