A comparison of array element surface vibration calculated by finite element modelling and laser interferometer measurements

For several years the standard in ultrasound imaging has been second harmonic imaging. Recently, a new imaging modality dubbed super harmonic imaging (SHI) was proposed. SHI uses the higher - third to fifth - harmonics produced by either nonlinear propagation or contrast agent response. This modality requires a transducer with a high bandwidth (>130%), which was achieved by choosing different frequencies for the odd (4 MHz) and even (1 MHz) elements. For SHI it is important to minimize both crosstalk and the transmission of odd transducer harmonics. To determine the influence of geometry on these issues a 3D transducer model is necessary. In this paper we compare array element surface vibrations calculated by a finite element model (FEM) with measurements obtained using a laser interferometer system. A custom array was built (element size 13 x 0.2 mm², resonance frequency 1.6 MHz, no matching layer, backing 5.3 MRayl). Its elements were excited using continuous signals or impulses and its spatially and time dependant surface vibrations were measured in air using a laser interferometer setup. The array element (characterized by its dimensions, piezo parameters from the data sheet and measured bulk parameters of the backing) was modelled using the ANSYS 11 FEM package and subjected to the same excitation. The fundamental resonance, third harmonic, fifth harmonic and lateral resonance of the array elements were measured at 1.6, 6.2, 9.9 and 7.9 MHz and predicted by the FEM simulation at 1.7, 6.1, 9.9, and 8.0 MHz. The excursion during continuous wave excitation was measured at 27.6 nm and predicted by FEM at 26.4 nm. The ripple in the y-displacement over the long axis of the element had a 1.2 - 1.3 mm wavelength both in the measurements and in the FEM simulation. Good agreement was achieved between the FEM predicted surface vibrations and the laser interferometer results.