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A method for ultrasonic synthetic aperture imaging using finite-sized transducers is introduced that is based on a compact, linear, discrete model of the ultrasonic measurement system developed using matrix formalism. Using this model a time-domain algorithm for deconvolution of the transducer's spatial impulse responses (SIRs) is developed that is based on a minimum mean square error (MMSE) criterion. The algorithm takes the form of a spatiotemporal filter that compensates for the SIRs associated with a finite-sized transducer at every point of the processed image. A major advantage of the proposed method is that it can be used for any transducer, provided that its associated SIRs are known. This is in contrast to the synthetic aperture focusing technique (SAFT), which treats the transducer as a point source. The performance of the method is evaluated with simulations and experiments, performed in water using a linear phased array. The results obtained using the proposed method are compared to those obtained with a classical time-domain SAFT algorithm. For a finite aperture source, it is clearly shown that the resolution obtained using the proposed method is superior to that obtained using the SAFT algorithm.

A new implementation of a synthetic aperture focusing technique (SAFT) based on concepts used in synthetic aperture radar and sonar is presented in the paper. The algorithm, based on the convolution model of the imaging system developed in frequency domain, accounts for the beam pattern of the finite-sized transducer used in the synthetic aperture. The 2D fast Fourier transform (FFT) is used for the calculation of a 2D spectrum of the ultrasonic data. The spectrum is then interpolated to convert the polar coordinate system used for the acquisition of ultrasonic signals to the rectangular coordinates used for the presentation of imaging results. After compensating the transducer lobe amplitude profile using a Wiener filter, the transformed spectrum is subjected to the 2D inverse Fourier transform to get the time-domain image again. The algorithm is computationally attractive due to the use of 2D FFT. The performance of the proposed frequency-domain algorithm and the classical time-domain SAFT are compared in the paper using simulated and real ultrasonic data.

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Uniform circular arrays (UCAs) with 360° azimuthal coverage are very useful for structural health monitoring (SHM) of large planar structures. Difficulties encountered when working with Lamb waves include their dispersive and multi-modal nature. In this article three different methods for estimating the direction-of-arrival (DOA) of incoming Lamb waves are compared and verified using simulated and experimental data. The previously proposed phase-mode excitation-based beamformer is compared with two high-resolution spectral estimation techniques, the Capon method and the multiple signal classification method. Design consideration and guidelines for UCAs are presented. To experimentally evaluate the performance of the considered DOA methods a prototype array consisting of 16 separate pinducers arranged in a ring was constructed. The array was provided with an analog multiplexer that enabled recording signals received by the individual elements using a digital oscilloscope. The array was used for the reception of ultrasonic pulses sent by broadband piezoelectric transmitters and propagating in an aluminum plate. A selection of simulation and experimental results is presented showing the superior performance of the Capon beamformer.