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/hydrophone pairs 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 (${p}_{c}$), peak rarefactional pressure (${p}_{r}$ ), 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-$\mu \text{m}$ membrane hydrophone, then spatial averaging errors are approximately 16 (${p}_{c}$), 12 (${p}_{r}$), and 24 (pulse intensity integral). The formulas are based on circular transducers but also provide plausible upper bounds for spatial averaging errors for transducers with rectangular-transmit apertures, such as linear and phased arrays.