Hydrophone Reciprocity Calibration in Spherically Focused Ultrasonic Field From 1 MHz to 15 MHz

A method of hydrophone calibration using spherically focusing transducers based on the self-reciprocity technique is studied in this article. The reciprocity theorem for weakly focusing transducers is derived and the diffraction effects in the self-reciprocity calibration are determined. The diffraction correction coefficient is obtained by using O'Neil integral and compared with Chen's approximate formulas. The calibration could be influenced by the spatial averaging effect of the hydrophone, particularly when a focusing transducer is used. The evaluation method of spatial averaging and effective diameter of hydrophone are analyzed in detail. The reflection coefficient of focusing beams on water-steel interface is averaged. Besides, the advantage of measuring first echo current and open-circuit voltage is to avoid the drawback of possibly damaging the electrical unit by measuring the short-circuit current. Additionally, the correction of water attenuation is not needed in this experimental arrangement, which is advantageous especially for high frequency hydrophone calibrations. The alternative absolute hydrophone calibration method was experimentally validated using focusing transducers with the frequency range of 1-15 MHz. The expanded uncertainties of hydrophone sensitivity at 95% confidence level are 7% from 1 MHz to 3.5 MHz, 10% from 5 MHz to 10 MHz and 15% at 15 MHz. The comparison of the calibration data obtained with those supplied by national laboratory corroborates the validity of the technique - the largest discrepancy is 3.17%.