Makoto Tabei

Simulation of ultrasonic focus aberration and correction through human tissue

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.

A simple estimator for frequency and decay rate

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 two‐dimensional array system for studies of ultrasonic imaging with aberration correction

A two‐dimensional array system is described for pulse‐echo studies of aberration correction. The transducer array is an 80×80 array with a center frequency of 3.0 MHz and a −6‐dB bandwidth of 56%. At the center frequency, each element has a physical size of 1.04 wavelength and spacing of 1.2 wavelength. A multiplexer accesses any contiguous 128 elements for transmission and any contiguous 16 elements for simultaneous reception. Transmit electronics have independently programmable waveforms. Each receive channel includes a 20‐MHz, 12‐bit A/D converter, and a time varied gain programmable over 40 dB. Transmit and receive apertures up to the size of the array are formed synthetically. A method that iteratively predistorts transmit waveforms to produce a transmit focus compensated for aberration has been implemented. Point‐spread functions have been measured for propagation through a water path and through a tissue‐mimicking aberration path. Pulse‐echo images have been formed through a water path, through a t...

A maximum likelihood estimator for frequency and decay rate

An extension of Rifes discrete Fourier transform (DFT) interpolation into a complex form is presented. The method has several advantages over Rifes 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.<<ETX>>

On the sampling conditions for reconstruction of an acoustic field from a finite sound source.

A simple and accurate method for the estimation of ultrasonic transducer fields is developed. In the method, the angular spectrum is employed to evaluate the three-dimensional propagation from a measured plane to an arbitrary parallel plane. The implementation uses a discrete convolution that is described in detail. Relative to conventional spatial-frequency representations, the implementation of the angular spectrum method in this paper has the advantage of being free from artifacts, enabling sample spacing to be greater than one half wavelength, using memory efficiently, and interpolating the measured data. The loosened sampling requirement and natural interpolation of the method permit efficient reconstruction of the full three-dimensional acoustic field from a coarse sound pressure measurement on single plane.

Ultrasonic scattering from a simulated cavity in steel

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.

Spectrum of Echo Scattered by Inclined Plane

In this paper a spectrum of an echo scattered by an inclined flat surface is analyzed theoretically using a mathematical description of the echo signal based on a discrete expression of scatterers. The analysis shows that the spectrum can be characterized by two parameters, a normalized inclination angle and a Fresnel number, and is proportional to the frequency of ultrasonic waves hyperbolically. Theoretically estimated spectra are compared with those obtained experimentally with rather good agreement.

Near-field ultrasonic scattering from a cavity in steel considering the velocity amplitude on the transducer face using an error function model

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.

Analysis of the Near-Field Transient Radiation Considering the Velocity Amplitude on the Transducer Face

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.

FAST CONVERGING BINOMIAL SERIES FOR RADIATION FIELD CALCULATION

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.