Extension of the distributed point source method for ultrasonic field modeling

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Research highlights

★ DPSM was extended based on least squares optimization. ★ The extension provides a solid mathematical foundation. ★ The extended method provides a new way for accurate field modeling without scaling. ★ The fields for circular and rectangular transducers were systematically studied.

The distributed point source method (DPSM) was recently proposed for ultrasonic field modeling and other applications. This method uses distributed point sources, placed slightly behind transducer surface, to model the ultrasound field. The acoustic strength of each point source is obtained through matrix inversion that requires the number of target points on the transducer surface to be equal to the number of point sources. In this work, DPSM was extended and further developed to overcome the limitations of the original method and provide a solid mathematical explanation of the physical principle behind the method. With the extension, the acoustic strength of the point sources was calculated as the solution to the least squares minimization problem instead of using direct matrix inversion. As numerical examples, the ultrasound fields of circular and rectangular transducers were calculated using the extended and original DPSMs which were then systematically compared with the results calculated using the theoretical solution and the exact spatial impulse response method. The numerical results showed the extended method can model ultrasonic fields accurately without the scaling step required by the original method. The extended method has potential applications in ultrasonic field modeling, tissue characterization, nondestructive testing, and ultrasound system optimization.

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