Correction for Hydrophone Spatial Averaging Artifacts for Circular Sources

This article reports an investigation of an inverse-filter method to correct for experimental underestimation of pressure due to spatial averaging across a hydrophone sensitive element. The spatial averaging filter (SAF) depends on hydrophone type (membrane, needle, or fiber-optic), hydrophone geometrical sensitive element diameter, transducer driving frequency, and transducer F number (ratio of focal length to diameter). The absolute difference between theoretical and experimental SAFs for 25 transducer/hydrophonepairs was 7% ± 3% (mean ± standard deviation). Empirical formulas based on SAFs are provided to enable researchers to easily correct for hydrophone spatial averaging errors in peak compressional pressure (ρ
_c
), peak rarefactional pressure (ρ
_r
), and pulse intensity integral. The empirical formulas show, for example, that if a 3-MHz, F/2 transducer is driven to moderate nonlinear distortion and measured at the focal point with a 500-μm membrane hydrophone, then spatial averaging errors are approximately 16% (ρ
_c
), 12% (ρ
_r
), and 24% (pulse intensity integral). The formulas are based on circulartransducersbut also provide plausible upper bounds for spatial averaging errors for transducers with rectangular-transmit apertures, such as linear and phased arrays.