Testing of a spatial impulse response algorithm for double curved transducers

The spatial impulse response (SIR) method for solving the Rayleigh integralis a well known method for fast time response simulation of acoustic waves.Several analytical expressions have been found for simple transducer geometriessuch as rectangles and discs. However, no analytical solution is known fordouble curved transducers (DCT), i.e. transducers with both concave and convexradius.

To calculate the SIR from such transducers Field II uses a far-fieldapproximation by dividing the surface into smaller flat elements and thenperforms a summation of the response from all the elements using Huygen'sprinciple. This calculation method involves several summations, and it relies onexact phase calculation to avoid numerical noise in the response.

A stableanalytical expression for the SIR would thus be beneficial to the Field IIsoftware as an alternative solver. A semi-analytic algorithm (SAA) has beendeveloped, and it is the objective of this work to validate an analyticalapproximation of the algorithm as an alternative solver for Field II. Twoapproximations of a SAA that efficiently finds the SIR for DCT have beenimplemented into a MATLAB and a C-code environment.

The root mean square (RMS)error of calculating the SIR using Field II and the C-implemented approximationare calculated relative to a high resolution solution obtained with MATLAB on aDCT, a linear concave, and a flat transducer. The computation time for solving apoint 400 times is also found. Calculations are performed at samplingfrequencies ranging from 100 MHz to 15 GHz in steps of 100 MHz.

The transducerwidth is 250 μm and the height is 10 mm. The C-implementation exhibits errorsranging from 4.9.10-4 % to 0.91 % and Field II 0.0117 % to 0.94 %. Aslight trade off between accuracy and computation time is found. Field IIoutperforms the SAA in computation time if high accuracy is not needed.

However,if a higher accuracy is required, the SAA is the best model choice. © 2010IEEE.