Directivity and Frequency-Dependent Effective Sensitive Element Size of Needle Hydrophones: Predictions From Four Theoretical Forms Compared With Measurements

Directivity is a hydrophone specification that describes response as a function of angle of incidence. The goal of this study was to compare, in the context of needle hydrophones, the commonly used rigid baffle model for hydrophone directivity to three alternative models: soft baffle, unbaffled (UB), and rigid piston (RP). Directivity measurements were performed at 1, 2, 3, 4, 6, 8, and 10 MHz from ±7° in two orthogonal planes for two ceramic and two polymer needle hydrophones with nominal geometrical sensitive element diameters of 200, 400, 600, and 1000 $\mu \text{m}$ . Effective hydrophone sensitive element radius was estimated by least-squares fitting the four models to directivity measurement data using the sensitive element radius (a) as an adjustable parameter. For $ka$ > 4 (where $k=2\pi /\lambda$ and $\lambda$ = wavelength), the RP model outperformed the other three models. For $ka=1$ , the average error in estimated sensitive element radius was 7% [95% confidence interval (CI): 3%–12%] for the RP model while the lowest average error by the other three models was 46% (95% CI: 38%–54%) for the UB model.