Testing of a spatial impulse response algorithm for double curved transducers

The spatial impulse response (SIR) method for solving the Rayleigh integral is a well known method for fast time response simulation of acoustic waves. Several analytical expressions have been found for simple transducer geometries such as rectangles and discs. However, no analytical solution is known for double curved transducers (DCT), i.e. transducers with both concave and convex radius. To calculate the SIR from such transducers Field II uses a far-field approximation by dividing the surface into smaller flat elements and then performs a summation of the response from all the elements using Huygen´s principle. This calculation method involves several summations, and it relies on exact phase calculation to avoid numerical noise in the response. A stable analytical expression for the SIR would thus be beneficial to the Field II software as an alternative solver. A semi-analytic algorithm (SAA) has been developed, and it is the objective of this work to validate an analytical approximation of the algorithm as an alternative solver for Field II. Two approximations of a SAA that efficiently finds the SIR for DCT have been implemented 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 approximation are calculated relative to a high resolution solution obtained with MATLAB on a DCT, a linear concave, and a flat transducer. The computation time for solving a point 400 times is also found. Calculations are performed at sampling frequencies ranging from 100 MHz to 15 GHz in steps of 100 MHz. The transducer width is 250 μm and the height is 10 mm. The C-implementation exhibits errors ranging from 4.9-10^-1 % to 0.91 % and Field II 0.0117 % to 0.94 %. A slight trade off between accuracy and computation time is found. Field II outperforms 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.