Objective: The aim of this study was to compare aberration correction methods for transmit and receive focusing through tissue in ultrasonic imaging. Methods: Propagation of ultrasonic pulse wavefronts through cross-sectional maps of abdominal wall and breast sections was calculated using a full-wave, k-space method that accounts for spatial variations in density, sound speed, and frequency-dependent absorption and includes perfectly matched layer absorbing boundary conditions. To obtain a distorted receive wavefront, propagation from a point source through the tissue path was computed. Receive focusing used an angular spectrum method. Transmit focusing was accomplished by propagating a pressure wavefront from a virtual array through the tissue path. As well as uncompensated focusing, focusing that employed time-shift compensation and time-shift compensation after backpropagation was investigated in both transmit and receive, and time reversal was investigated for transmit focusing. Results: In receive focusing, the mean −20 dB effective radius improved, e.g., from 2.5±0.8 mm (avg±std) before compensation to 1.4±0.4 mm after time-shift compensation and to 1.2±0.4 mm after backpropagation followed by time-shift compensation for breast, while the corresponding radius for the water path (ideal) case is 0.9 mm. In transmit focusing, the size of the focus as quantified by the −20 dB effective radius was larger for transmit focusing than for receive focusing, e.g., 4.3±2.8 vs 2.5±0.8 mm uncompensated and 2.4±1.5 vs 1.4±0.4 mm using time-shift compensation for breast, while the mainlobe for time-reversal focusing was wider than for the other compensation methods because the received wavefront undergoes frequency-dependent absorption and was weighted to reduce the amplitude at the aperture edges. Conclusions: The receive focus was corrected better than the transmit focus. Time-shift compensation after backpropagation improved the focus from that obtained using time-shift compensation alone, but the improvement was less in transmit focusing than in receive focusing. Transmit focusing by time reversal resulted in lower sidelobes but a wider mainlobe than the other investigated transmit compensation methods.

A k-space method for large-scale simulation of ultrasonic pulse propagation is presented. The present method, which solves the coupled first-order differential equations for wave propagation in inhomogeneous media, is derived in a simple form analogous to previous finite-difference methods with staggered spatial and temporal grids. Like k-space methods based on second-order wave equations, the present method is exact for homogeneous media, unconditionally stable for “slow” [c(r)⩽c0] media, and highly accurate for general weakly scattering media. In addition, unlike previous k-space methods, the form of the method allows straightforward inclusion of relaxation absorption and perfectly matched layer (PML) nonreflecting boundary conditions. Numerical examples illustrate the capabilities of the present k-space method. For weakly inhomogeneous media, accurate results are obtained using coarser temporal and spatial steps than possible with comparable finite-difference and pseudospectral methods. The low dispersion of the k-space method allows accurate representation of frequency-dependent attenuation and phase velocity associated with relaxation absorption. A technique for reduction of Gibbs phenomenon artifacts, in which compressibility and exponentially scaled density functions are smoothed by half-band filtering, is introduced. When employed together with this smoothing technique, the k-space method provides high accuracy for media including discontinuities, high-contrast inhomogeneities, and scattering structures smaller than the spatial grid resolution.

Ultrasonic focusing in two dimensions has been investigated by calculating the propagation of ultrasonic pulses through cross-sectional models of human abdominal wall and breast. Propagation calculations used a full-wave k-space method that accounts for spatial variations in density, sound speed, and frequency-dependent absorption and includes perfectly matched layer absorbing boundary conditions. To obtain a distorted receive wavefront, propagation from a point source through the tissue path was computed. Receive focusing used an angular spectrum method. Transmit focusing was accomplished by propagating a pressure wavefront from a virtual array through the tissue path. As well as uncompensated focusing, focusing that employed time-shift compensation and time-shift compensation after backpropagation was investigated in both transmit and receive and time reversal was investigated for transmit focusing in addition. The results indicate, consistent with measurements, that breast causes greater focus degradation than abdominal wall. The investigated compensation methods corrected the receive focus better than the transmit focus. Time-shift compensation after backpropagation improved the focus from that obtained using time-shift compensation alone but the improvement was less in transmit focusing than in receive focusing. Transmit focusing by time reversal resulted in lower sidelobes but larger mainlobes than the other investigated transmit focus compensation methods.

The influence of nonuniform transducer velocity distribution in the near-field echo formation scattered from a cavity in steel is analyzed. In the present study, the velocity amplitude on the transducer face was modeled using an offset error function. Using this distribution, the echo waveforms scattered from a cylinder cavity in steel were estimated and compared with the echo estimated using uniform distribution and echo observed experimentally. The estimation accuracy of the near-field echo waveforms were improved quantitatively.

The conventional holographic reconstruction produces large error when it is applied to the long range propagation of the acoustic wave.1,2 This is because the propagator that is defined by the sampled frequency response causes strong artifacts by overlaying wrapped images on the true reconstruction. In this paper, a robust reconstruction technique is proposed based on the convolution of observed data and the propagator rather than the direct manipulation of data in the frequency domain. It is shown that when the observed data are backpropagated to the plane that includes the finite sound source, the sampling interval of the data can be taken to be significantly larger than the half-wavelength. On the other hand, by taking the pixel interval of the reconstructed source image as less than or equal to the half-wave length, the acoustic field at an arbitrary point can be evaluated by the successive forward propagation of the source image.

The velocity amplitude on the transducer face was estimated using the near-field transient radiation on the axis of the circular transducer obtained experimentally. The velocity amplitude can be obtained by deconvolving the pressure waveform with the electrical characteristics of the transducer and then integrating the result. Using the estimated velocity amplitude, the pressure waveforms were numerically calculated and compared with those obtained experimentally.

A simple, computationally inexpensive algorithm is developed for estimating the frequency and decay rate of a complex exponential. Two iterations of the algorithm attains the Cramer-Rao bound on the variance of the frequency and decay rate estimate for a complex exponential in white Gaussian noise. The algorithm uses an adaptive window that changes its shape with the estimate of the decay rate. Formulas are derived for the bias and variance of the estimator, and its performance is demonstrated in simulations

A method for estimating sound velocity distribution of a scattering medium is developed. The sound velocity is estimated by iterating the WKB (Wentzel, Kramers and Brillouin) approximation for the calculation of the scattered field. The iterative procedure incorporates “simulated annealing” for determining of the optimal distribution of sound velocity. Estimations for the cylinder and 2-layer cylindrical shell models are carried out numerically and experimentally. The estimated sound velocity agrees well with the original distribution.

The scattering of wideband ultrasonic pulses from simulated cavities in a metal block was estimated using a mathematical description of the echo based on the expression for echoes reflected from a strongly scattering object. The theoretically estimated echo waveforms and the corresponding Fourier power spectra of the scattered pulses are compared with those obtained experimentally with good agreement. Interpretations show that both the pulse-time record and the power spectrum can be utilized to detect roughly the shape of a cavity in a metal block.

An analytical description for the radiation field of a planar source by fast converging binomial series expansion is derived. The terms of the series correspond to the Fresnel solution and its derivatives. Consequently, if the Fresnel solution of the diffraction integral is expressed by differential functions, the radiation field can be obtained by calculating the series. As a result of the expansion, this method can be applied to any region except the points on the surface of transducer. The results are compared with the correct computations and those obtained by conventional Fresnel approximation.

Quantitative analysis of ultrasonic wavefront distortion caused by propagation through biological tissue is important for the development of both imaging and tissue characterization techniques. In this study, using a periodic phantom made of oil jelly, quantitative analysis was performed to investigate the relationship between wavefront distortion and the degradation of directivity caused by it. The effect of wavefront distortion due to biological tissue is also discussed.

An extension of Rife's discrete Fourier transform (DFT) interpolation into a complex form is presented. The method has several advantages over Rife's original formula. It can estimate the decay rate of the input sequence as well as the frequency, and does not require a square-root operation. An error analysis suggests a powerful but simple refinement step which can nearly attain the Cramer-Rao (CR) bound. An interpolation formula is derived, and its iteration into a refinement procedure is discussed. The procedure also allows the use of arbitrary windows to suppress the interference of other frequency components in the data that are typically found with real and/or damped sequences

A computerized tomography reconstruction technique with the fast Fourier transform (FFT) is discussed. A fast backprojection method through the use of interpolated FFT is presented. An approach to interpolating and backprojecting the convolved projections onto the image frame is proposed. First, the Fourier series expansion of the convolved projection is calculated. It is then projected onto a rectangular grid in the frequency domain, using the aliasing-free interpolation of FFT bins. The total amount of computation in this procedure for a 512*512 image is 1/6 of the conventional backprojection method with linear interpolation. This technique also allows arbitrary control of the frequency characteristics.<>

The determination of local reflectivity characterizing the interior of a unknown object from acoustic impulse echo data might be considered as a standard problem of acoustical imaging. In many cases this inverse problem can be formulated as a deconvolution problem. By one-dimensional axial deconvolution of a single time trace, assuming plane wave propagation, an estimate of the acoustic impulse response of the scatterer is obtained within the usable band-width of the transducer. This one dimensional scattering function enables an improved discrimination of echoes of one or more reflectors [1], For special cases like the analysis of a discrete layered medium, a priori information can be used in order to extend the usable frequency range [2], In [3] the lateral resolution is increased by deconvolution with the spatial characteristics of the transducer. In these cases only one part of the complex transducer characteristics is considered.

We recently developed a diffraction theory for solid obstacles. The waves diffracted by a thick circular plate are estimated by this theory and the results are compared with those obtained by experiments. The comparison shows the validity and a limitation of our theory.

Recently we have developed a diffraction theory for solid obstacles. The waves diffracted by a cylinder are estimated by this theory and the results are compared with those obtained by the rigorous relation and the conventional approximation. Comparison shows that our theory is effective if the radius of the cylinder is smaller than the wavelength of sound waves.

When FFT is applied to the frequency detection, the accuracy has been limited to the distance between adjacent frequency bins of the transform. Although the technique has been known to improve accuracy by stretching the data sequence with zero padding, it only improves the accuracy to the reciprocal of the extended sequence length and cannot detect the phase for the non-harmonic frequency. In this paper, we present an interpolation scheme of the FFT sequence. It does not require zero padding and gives accurate values of the frequency, amplitude and phase as well. A numerical experiment is performed to show the efficacy under actual conditions.

This paper describes a systematic procedure to calculate the echo signal from a polyhedron of arbitrary shape. The echo is defined as the integration over the surface of the object. We assume that in the case of a convex object, the echo from each facet contributes independently to the total echo signal. Numerical evaluation of the integration is performed by an exponent integral scheme and shows good agreement with the experiments.

It is well-known that there appear many artifacts such as acoustic shadowing, enhancement and so on, in B-mode echo patterns especially those of breast. These artifacts are resulted from the difference of acoustic parameters (sound velocity, attenuation, and specific acoustic impeadance) of intervening medium from those of surrounding medium. It would improve OUK ability of tissues characterization if the relation between the artifacts and the acoustic parameters of the intervening medium were understood fully. been reported some attempts to study the relation by using a phantom model of tissues but it may be rather difficult to study the cases exhaustively. In this report computer simulation of artifacts produced by refractive and/or attenuating intervening medium is carried out for the scatterer which is composed of a lot of point reflectors. The results show that appearance of posterior acoustic shadowing changes by the attenuation of the intervening medium as well as the degree of sound velocity difference between the two media. There have

We have derived simple mathematical expressions for echo signal from wave equation for inhomogeneous medium. These relations have been applied successfully for the analysis of echo signal scattered by random medium, simple regular objects, and inclined plane. In these analysis it is assumed that an ultrasonic transducer and the scatterer lie in the same medium (one medium case).The transducer is often immersed in a different medium and the wave has passed through the interface twice during the measurement. In this paper the relation for echo signal is modified to the two media case. The amplitude of echo signal scattered by a simple object placed at the focal point of the transducer is estimated for the spherical and plane interface and compared that with experimentally obtained echo amplitude. With no adjustable parameters, rather good agreement between these two echo amplitude is observed.