Modeling and Optimal Design of Annular Array Based Ultrasound Pulse-Echo System
Li Wan
MS Thesis, Dept. of Electrical and Computer Engineering, Worcester Polytechnic Institute, April 3, 2001.
SUMMARY
This thesis describes the implementation of two numerical modeling methods for calculating received signal from a transducer in a pulse-echo system. One method is the simple, but computationally demanding Huygens Method, based on the Huygens’ Principle, and the other one is the computationally more efficient Diffraction Response for Extended Area Method (DREAM). The DREAM method operates by dividing the surface of the reflector into a relatively small number (say, a few hundred) of rectangular or triangular “tiles” and performing the spatial integration of the diffraction response over each tile by an equivalent low pass filtering.
COMPLETE ABSTRACT
The ability to numerically determine the received signal in an ultrasound pulse-echo system is very important for many ultrasound applications such as tissue characterization, complex object recognition, identification of surface topology, and etc. The relationship between, on one hand, the output signal from an ultrasound pulse-echo system, and, on the other hand, the specified ultrasound transducer and the geometry, orientation and location of the reflector, is very complex. Consequently, only by numerical modeling can the output signal for a given measurement configuration be predicted. Especially when it comes to optimizing the design of an ultrasound system to carry out such tasks as identifying objects of specified shapes, determining surface topology or alignment of surface, etc., numerical modeling is the only practical way. This thesis is concerned with the numerically modeling and optimal design of annular array based ultrasound pulse-echo system.
This thesis describes the implementation of two numerical modeling methods for calculating received signal from a transducer in a pulse-echo system. One method is the simple, but computationally demanding Huygens Method, based on the Huygens’ Principle, and the other one is the computationally more efficient Diffraction Response for Extended Area Method (DREAM). The DREAM method operates by dividing the surface of the reflector into a relatively small number (say, a few hundred) of rectangular or triangular “tiles” and performing the spatial integration of the diffraction response over each tile by an equivalent low pass filtering. In this thesis, the DREAM method is implemented using both rectangular and triangular tiles. To determine the optimal tile size for the DREAM method for various combinations of transducers size, reflector location, etc, the results obtained by DREAM method are compared with the corresponding results obtained from the Huygens method as an accurate reference. Both graphical and numerical results are presented. The modeling concept is further extended to include ultrasound pulse-echo system using planar annular array transducers where the calculation for the individual array elements is based on calculation of the received signals from planar circular transducers.
The optimal design of the ultrasound pulse-echo system for object recognition is based on the annular array transducer that gives us the flexibility to create a wide variety of insonifying fields and receiver characteristics. These fields and receiver characteristics can be realized by assigning different delay and amplitude gain values to each array element in transmit and receive, respectively. As the first step towards solving the optimization problem for identifying a given type of reflector among many possible ones, the problem of optimally identifying one out of two specific reflectors is investigated. To solve this problem, we propose to find the set of transmit and receive delay values which will maximize the energy of the difference signal between array output signals from the two reflectors. Two optimization methods have been investigated for the optimal delay set, the Global Search Method and the Waveform Alignment Method. The Global Search Method operates by searching through all possible combinations of delay values, applied to the individual transmitting elements and the receiving elements of the annular array transducer, then calculates the energy of the difference signal between received output signals from the two reflectors for each delay value combination. The set of delay values that produces the largest energy in difference signal is considered the optimal delay set. The Waveform Alignment Method operates by using a time shifted and amplitude scaled version of a specific waveform to represent the calculated waveform in the received signal matrix which contains the received signal for all combinations of transmitting and receiving array elements. Thus, each received signal in the received signal matrix can be represented by a delay value and amplitude scale factor. In this thesis, only the delay values are used to align these waveforms to get the optimal delay matrix. The results obtained by the Global Search Method and the Waveform Alignment Method are presented and compared to each other.
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