A New Method of Ultrasonic Hydrophone Calibration using Wave Propagation Modeling Hendrik J. Bleeker* and Peter A. Lewin$ *ATL Ultrasound, 22100 Bothell Everett Highway, P.O. Box 3003, Bothell, WA 98041 and $ The School zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA of Biomedical Engineering, Science and Health Systems and Department of Electrical and Computer Engineering, Drexel University, Philadelphia, PA 19104 Abstract: A new method is presented for hydrophone calibration using the Khokhlov - Zabolotskaya - Kuznetsov (KZK) equation. Simulated and experimental on-axis finite amplitude distortion time waveforms and frequency spectra are compared. The hydrophone calibration up to 100 MHz is estimated for two different hydrophones. INTRODUCTION Most commercially available ultrasonic transducers exhibit finite amplitude distortion in water during hydrophone measurements. The frequencies observed due to finite amplitude distortion can easily exceed 10 times the source nominal center frequency. Newly proposed hydrophone calibration specifications suggest sensitivity variations less than f3 dB from l/20 to 8 times the source center frequency during finite amplitude distortion measurements (1). Therefore, hydrophone calibration should be available to at least 80 MHz for high frequency diagnostic ultrasound transducers (typically, highest excitation frequency of 10 MHz). If this specification is not met, the misrepresentation of harmonic energy will distort the measured acoustic waveforms and increase the uncertainty in intensity and pressure measurements. Hydrophone calibrations are typically available from 1 to 15 or 20 MHz, only. The proposed technique will use the existing calibration information and extend it up to 100 MHz. METHOD AND EXPERIMENT The hydrophone calibration was determined for two hydrophones in the frequency range up to 100 MHz. First, a measured finite amplitude distorted waveform was compared with the corresponding simulated waveform. It was initially assumed that any difference in the frequency content was solely due to the hydrophone spectral characteristics. To facilitate the comparison, the source center frequency was selected to be within the known hydrophone calibration frequency range and the simulated and measured spectral energy were normalized with respect to the source center frequency. The difference between the simulated and measured spectral responses contains desirable information on the hydrophone frequency response from the source center frequency to 100 MHz. The time-domain algorithm that solves the KZK nonlinear parabolic wave equation was selected for the simulating model. The ability of the model to predict the nonlinearity, diffraction and absorption of focused circular transducers has already been demonstrated in several papers (2-4). The measurement equipment consisted of a test tank with positioning apparatus, Lecroy 334AL digital oscilloscope, HP 81 l6A pulser/function generator, Amplifier Research 25AlOOM2 power amplifier, two 50pm bilaminar membrane hydrophones (from two different vendors) with preamplifiers and with 0.5 and 0.6 mm active element diameters, and a 5 MHz ECHO Ultrasound single element focused circular transducer. The source radius and geometrical focus were determined to be 5.5 mm and 40.0 mm, respectively. Based on these measurements, three dimensionless parameters needed as inputs for the finite difference algorithm that solves the KZK non-linear parabolic wave equation were determined as G = 8.0, A = 2.5E-2 and N = 0.47 (4). The transducer was excited with a 15 cycle sine wave burst at 5 MHz and with 3 volts peak to peak for the transducer characterization. The geometrical transducer axis was aligned with the gantry axis (and hydrophone) to within 0.2 degrees. The actual axial peak distance, which was expected to be shallower than the geometric focus, was found to be located at 35 mm and the measured waveforms were found to have harmonic energy less than -30 dB from the fundamental. The excitation voltage was then increased to 65 volts to introduce finite amplitude zyxwvutsrqponm 1849