Hydrophone spatial averaging corrections from 1 to 40 MHz

The purpose of this study was to develop and experimentally verify a practical spatial averaging model for frequencies up to 40 MHz. The model is applicable to focused sources of circular geometry, accounts for the effects of hydrophone probe finite aperture, and allows calibration by substitution to be performed when the active elements of reference and tested hydrophone probes differ significantly. Several broadband sources with focal numbers between 3 and 20 were used to produce ultrasound fields with frequencies up to 40 MHz. The effective diameters of the ultrasonic hydrophone probes calibrated in the focal plane of the sources ranged from 150 to 500 μm. Prior to application of the spatial averaging corrections, the hydrophones with diameters smaller than that of the reference hydrophone exhibited experimentally determined absolute sensitivities higher than the true ones. This discrepancy increased with decreasing focal numbers and increasing frequency. It was determined that the error was governed by the cross-section of the beam in the focal plane and the ratio of the effective diameters of the reference and tested hydrophone probes. In addition, the error was found to be reliant on the frequency-dependent effective hydrophone radius. After applying the spatial averaging correction, the overall uncertainty in the hydrophone calibration was on the order of ±1 dB. The model developed is being extended to be applicable to frequencies beyond 40 MHz, which are becoming increasingly important in diagnostic ultrasound imaging applications.