Non-paraxial multi-Gaussian beam model of Leaky Rayleigh waves generated by a focused immersion transducer.

A non-paraxial multi-Gaussian beam (NMGB) model is proposed for Leaky Rayleigh Waves (LRWs) generated by a focused immersion transducer at oblique incidence. Using the NMGB model, the velocity fields are calculated and compared with the corresponding results obtained by the paraxial multi-Gaussian beam (MGB) model and the more exact Rayleigh-Sommerfeld integral (RSI) model. Numerical results show that the LRW beam behavior obtained using the NMGB model agrees well with that using the RSI model, but the NMGB model is much more efficient.

K-space Prony's method for generating the basis functions of multi-Gaussian beam models.

The expansion coefficients of a multi-Gaussian ultrasonic beam model are obtained by a new approach that applies Prony s method in a K-space domain. This method allows the fitting of the Gaussian beam directly at the face of the transducer with very high computational efficiency. It is demonstrated that the K-space Prony's method can be used to accurately model the transducer field of planar and focused piston transducers, as well as probes that do not act as pistons.

Modeling the radiation of ultrasonic phased-array transducers with Gaussian beams.

A new transducer beam model, called a multi-Gaussian array beam model, is developed to simulate the wave fields radiated by ultrasonic phased-array transducers. This new model overcomes the restrictions on using ordinary multi-Gaussian beam models developed for large single-element transducers in phased-array applications. It is demonstrated that this new beam model can effectively model the steered and focused beams of a linear phased-array transducer.

Characterization of the system functions of ultrasonic linear phased array inspection systems.

This work characterizes the electrical and electromechanical aspects of an ultrasonic linear phased array inspection system, using a matrix of system functions that are obtained from the measured response of individual array elements in a simple reference experiment. It is shown that for the arrays tested all these system functions are essentially identical, allowing one to use a single system function to characterize the entire array, as done for an ordinary single element transducer. The variation of this single system function with the number of elements firing in the array or with changes of the delay law used is examined.

Determination of an ultrasonic transducer's sensitivity and impedance in a pulse-echo setup.

The role that an ultrasonic piezoelectric transducer plays in an ultrasonic measurement system can be described in terms of the transducer's input electrical impedance and its sensitivity. Here, a new model-based approach is proposed to determine both the transducer impedance and sensitivity in a pulse-echo setup. This new method is much simpler to apply than previous "self-reciprocity" calibration methods for determining sensitivity and generalizes those methods.

An ultrasonic measurement model using a multi-Gaussian beam model for a rectangular transducer.

To date, ultrasonic measurement models have primarily treated systems where circular transducers are used. Recently, however, a highly efficient ultrasonic beam model for a rectangular transducer has also become available where the transducer is represented as a superposition of a relatively few Gaussian beams. Thus, using the multi-Gaussian beams, we developed ultrasonic measurement models for systems where a rectangular transducer is employed.

Generation of the basis sets for multi-Gaussian ultrasonic beam models--an overview.

By using a small number of Gaussian basis functions, one can synthesize the wave fields radiated from planar and focused piston transducers in the form of a superposition of Gaussian beams. Since Gaussian beams can be transmitted through complex geometries and media, such multi-Gaussian beam models have become powerful simulation tools. In previous studies the basis function expansion coefficients of multi-Gaussian beam models have been obtained by both spatial domain and k-space domain methods.